University of Southern California Dissertations and Theses

Prescriptive Deontic Logic: A Study Of Inferences From Linguistic Forms Expressing Choice And Conditional Permission And Obligation

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Prescriptive Deontic Logic: A Study Of Inferences From Linguistic Forms Expressing Choice And Conditional Permission And Obligation

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Content PRESCRIPTIVE DEONTIC LOGICi A STUDY OF INFERENCES FROM LINGUISTIC FORMS EXPRESSING CHOICE AND CONDITIONAL PERMISSION AND OBLIGATION by Jack Ray A Dissertation Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY Speech Communication June 1971 72-576 RAY, Jack Leroy, 1924- PRESCRIPTIVE DEONTIC LOGIC: A STUDY OF INFERENCES FROM LINGUISTIC FORMS EXPRESSING CHOICE AND CONDITIONAL PERMISSION AND OBLIGATION. University of Southern California, Ph.D., 1971 Speech University Microfilms, A XERO X C om pany, Ann Arbor, M ichigan THIS DISSERTATION HAS BEEN MICROFLIMED EXACTLY AS RECEIVED UNIVERSITY OF SOUTHERN CALIFORNIA THE GRADUATE SCHOOL UNIVERSITY PARK LOS ANGELES, CALIFORNIA 9 0 0 0 7 This dissertation, written by under the direction of h.XS.... Dissertation C o m mittee, and approved by all its members, has been presented to and accepted by The G radu ate School, in partial fulfillment of require ments of the degree of D O C T O R O F P H I L O S O P H Y Dean D ate.. DISSERTATION COMMITTEE To Greta, Karl and Ian ii ACKNOWLEDGMENTS I wish to extend my thanks to Dr. James A. McBath for encouraging me to complete my work at the University of Southern California, and for serving as a member of my committee, I am indebted to Dr. Dallas Willard for his original suggestions about the course this study should take, his confidence in my work, and his suggestions and criticisms of the dissertation as a member of my committee Most especially, I wish to express my deepest thanks to Dr. Walter R. Fisher, chairman of my committee, for his faith in me, his encouragement, his helpful comments on the manuscript, and most of all his insistence that I not delay in finishing the work that I had started. Finally, I wish to thank my wife for her excellent help in editing the manuscript. TABLE OF CONTENTS CHAPTER I INTRODUCTION THE PROBLEM ORGANIZATION OF THE STUDY THE METHOD OF ANALYSIS JUSTIFICATION OF THE STUDY NOTES ; CHAPTER II I THE DEONTIC LOGIC OF VON WRIGHT THE DEONTIC CALCULUS OF VON WRIGHT j VON WRIGHT'S DECISION PROCEDURE Analysis of Some of the Deontlc Tautologies Using von Wright's Decision Method THE RELATION OF SENTENTIAL LOGIC AND DEONTIC LOGIC The Operation of Sentential Logic upon Separately Qualified Deontlc Forms The Operation of Sentential Logic Totally within the Scope of a Deontlc Form | The Operation of Sentential Logic I Involving the Breaking of a Scope THE LATER WORK OF VON WRIGHT i I The Paradoxes of Deontlc Logic I The Alf Ross Paradox i I iv l 3 6 7 8 10 11 11 lk 18 23 2k 27 28 33 36 37 Contrary-to-Duty Paradox CONCLUSION NOTES CHAPTER III THE NATURE OF DEONTIC CONCEPTS DEONTIC CONCEPTS Hypothetical and Categorical Permission and Obligation THE INTERDEFINABILITY OF PERMISSION AND OBLIGATION The Relation of 0, P, and F PERMISSION, OBLIGATION, AND TRUTH-FUNC TIONALITY THE PRINCIPLE OF PERMISSION AND THE INFERENCE FROM 0 TO P CONCLUSION NOTES CHAPTER IV PERMITTED AND OBLIGATORY CHOICES THE SYSTEM OF ANALYSIS The Interdefinability of Permission, Obligation, and Forbiddenness PERMITTED AND OBLIGATORY CONJUNCTION Permitted Conjunction Obligation Conjunction Forbidden Conjunction 85 Summary of the Analysis of Permitted, Obligatory, and Forbidden Conjunction 86 PERMITTED AND OBLIGATORY CHOICES 86 The Meaning of Inclusive Obligatory Choice 87 The Meaning of Inclusive Permitted Choice 89 The Meaning of Exclusive Obligatory Choice 91 The Meaning of Exclusive Permitted Choice 93 Summary of Permitted and Obligatory Inclusive and Exclusive Choices 9^ TWO ADDITIONAL MEANINGS OF "OR" 95 The Ma£ "Or" 96 The Free "Or" 99 Obligatory May "Or" Choices 100 Obligatory Free "Or" Choices 102 Permitted May "Or" Choices 102 Permitted Free "Or" Choices 105 Summary of Permitted and Obligatory May and. Free Choices 106 NEGATED PERMITTED AND OBLIGATORY CHOICES 107 Non-Permitted Choices 107 Non-Obligatory Choices 109 Summary of Non-Permitted and Non-Obligatory Choices 111 CONCLUSION 112 NOTES 115 ____________ vi_____________________________ CHAPTER V THE LOGIC OF PRESCRIPTIVE PERMITTED AND OBLIGATORY CHOICE PRELIMINARY ASSUMPTIONS SUMMARY OF THE DEFINITIONS AND EQUIVALENCIES OF PERMITTED AND OBLIGATORY CHOICE UTTERANCES THE RELATION OF PERMITTED AND OBLIGATORY CHOICE AND PERMITTED AND OBLIGATORY CONJUNCTION De Morgan Type Two Principles PRESCRIPTIVE DEONTIC DETACHMENT AND COMBINATION PRINCIPLES Simplification, Conjunction, and. Deontlc Dissolution The Principle of Addition and the Alf Ross Paradox PRESCRIPTIVE DEONTIC LOGIC DISJUNCTIVE SYLLOGISM Disjunctive Syllogism and Mixed Modes Principles of Obligation Compliance CONCLUSION NOTES CHAPTER VI CONDITIONAL PERMISSION AND OBLIGATION MEANING AND INTERPRETATION OF CONDITIONAL DEONTIC UTTERANCES Conditional Obligation Conditional Permission Biconditional Permission Utterances Negative Permitted and Obligatory Conditional Utterances Conflicts of Norms and Rules CONCLUSIONi SUMMARY OP THE DEFINITIONS OF OBLIGATORY AND CONDITIONAL UTTERANCES NOTES ! CHAPTER VII I THE LOGIC OF PRESCRIPTIVE DEONTIC CONDITIONALS | RELATIONSHIPS BETWEEN PRESCRIPTIVE DEONTIC ' CONDITIONALS, CONJUNCTIONS, AND DISJUNCTIONS Relationships between Prescriptive Deontlc Conditionals and Conjunctions Relationships between Permitted and Obligatory Conditionals Relationships between Choice and Conditional Utterancess Prescriptive Deontlc Material Implication Interpretation of Prescriptive Deontlc Material Implication in Ordinary Language Transposition of Deontlc Conditionals i Transposition and Ordinary Language | Utterances ! I viii Prescriptive Deontic Material Equivalencies PRESCRIPTIVE DEONTIC ARGUMENT PATTERNS Prescriptive Deontlc Detachment Principles Detachment Principles Involving Mixed Modes Problems in Interpreting Some Detachment Forms in Ordinary Language ADEQUACY OF THE SYMBOLS FOR CONDITIONAL j PERMISSION CONCLUSION I [ NOTES : CHAPTER VIII I CONCLUSION THE METHOD OF THE STUDY IMPORTANCE OF THE STUDY SUMMARY OF PRESCRIPTIVE DEONTIC INFERENCE PRINCIPLES ! BIBLIOGRAPHY FIGURES Figure I Deontic Truth Table 16 Figure II Deontlc Truth Table 19 CHAPTER I INTRODUCTION The word "argument" is most commonly used in one of two senses. The two senses are related in that the first is a necessary component of the second sense. Argument in ! the first sense names situations where someone makes a j claim and offers a reason or set of reasons which support, I back, warrant, prove, etc., that claim. The model of this sense of argument is R —^-C, The process is thus "reasoning11! that is, the giving of reasons or the pro- j cess of arriving at conclusions from reasons. The arrow j in the model indicates a relationship between R and C, a relationship that can be thought of as an inference, in | the most general use of that word. A number of English words are associated with the arrow of the model. For example, the following words and phrases are used to introduce reasons* "because," "for," "since," "it is a fact that," "the facts are," "the evi- I dence is," "the data is," "it is true that," "the reason j is," "granted that," "this is indicated by," "in support," M'this is warranted by," "on the hypothesis that," and so !forth. The following words and expressions often are used j |to Introduce a claim or conclusion* "so," "then," "thus," "hence," "ergo," "therefore," "consequently," "apparently," i "surely," "obviously," "of course," "for this reason," "it must be that," "It surely is the case that," "it fol lows that," "it is evident that," "probably," and so on. The word "argument" is also used to name a verbal controversy. But all verbal controversy is not to be in cluded in this meaning. The childlike "tis, taint" dispute ; often engaged in where one person says that something is so and the other says that it is not, is not to be counted j as a case of argument in the second sense. To be an argu- j I ment in this sense, there must be verbal disagreement in- j volving reasoning. That is, argument in the second sense j i names cases where claims are made and disputed by means j of giving and disputing reasons for the claims. Both senses of "argument" involve reasoning, and thus, some form of inference. i Argument can be studied from many points of view. j The psychologist, the communication scientist, the soci- j i ologist, the rhetorician, and the logician all have their special interest in the Inferential process whereby con clusions are related to reasons. Logicians construct highly specialized artificial logical languages. These ■calculi have rules governing the formation of proposi- i Itional forms, ‘ the transposition of one form into another, and the inference possibilities from these forms. Though the logician seems to have his eyes only upon |symbols, which he has invented and which are but marks on jpaper, and upon the relationships between these marks, 3; surely his study Is about human argumentation. Over thirty years ago, Rudolph Carnap wrote that "The chief task of logic . . . Is supposed to be that of formulating rules according to which judgements may be Inferred from other judgements; in other words, according to which con- ! elusions may be drawn from premises."1 More recently, i another logician, Gary Iseminger, said that It is "infer- ! j ability in virtue of which we can argue to one assertion j O | from another which is the logician’s concern." Thus the j subject of logic most generally is that of the study of j human argumentation, and more specifically the study of j human inference making. j i i THE PROBLEM j The study undertaken here is concerned with infer- | i ences Involving linguistic utterances containing such i ] modal words as "may" and "ought." Such words are used to express permissions and obligations. The logic of permission and obligation has been widely studied in recent years by Georg Henrik von Wright3 and others. The area of study is known as "deontic logic." The root of the word "deontic" is "deon," meaning "that which is binding." The word "deontology" is used in ethics i :to refer to the study of duty or moral obligation or com- imltment. Deontic logic is not restricted to the logic of i !moral reasoning and discourse. It is more generally the logic of permission and obligation or, more precisely, the logic of permitted and obligatory acts. The concepts of permission and obligation are general categories, in cluding not only utterances expressing permissions and obligations by the use of such words as "permitted,1 1 "obligated," "may," "should," "must," and "ought," but also linguistic events such as normative utterances, rules, commands, and advice. These are prescriptive utterances which direct human behavior. This study will be concerned with two main kinds of deontic utterances: permitted and obligatory choice ut terances, where a certain choice of alternative action is allowed or demanded, and conditional utterances, where a certain course of action is permitted or obligated upon the meeting of some condition. The focus of the study is upon the definition of various kinds of permission and ob ligation choice and conditional utterances and the infer ences that may follow from such utterances. Four specific tasks will be undertaken. The first task is to identify and define various kinds of permitted and obligatory choice utterances. The definitions will ; be constructed so that the interaction of such deontic I words as "may" and "ought" and the logical words "not," | "and," "or," and "if . . . then" will be taken into ac- : count. In deontic logic, as developed by von Wright and jothers, the logical connectives have been taken to operate as ordinarily defined in standard logical theory, and the interaction of the logical connectives and the deontic words has not been adequately treated. The con tention here is that deontlc words, such as "ought" and "may," and logical connectives, such as "or" and "if," cannot be defined independently but must be defined in relation to each other. It will also be argued that the standard interpreta tions of the logical relationship corresponding to the English word "or" are Inadequate in translating many de ontic utterances. It will be contended that in addition to the two standard logical Interpretations of the word "or," at least one and perhaps two additional meanings are often used in utterances expressing permitted and obligatory choices. The second task is to develop inference principles associated with permitted and obligatory choice utter ances. The third task is to define various kinds of per mitted and obligatory conditional utterances. And the final task is to consider the effects of permission and |obligation words upon hypothetical reasoning patterns and !to develop inference principles associated with condi- i itional deontic utterances. ORGANIZATION OF THE STUDY Chapters II and III contain background material for the main analysis, which follows In Chapters IV, V, VI and VII, Chapter VIII is the summary and conclusion of the findings of the study. Chapter II summarizes and ana- ; lyzes the original calculus of von Wright and some of the problems and later developments in deontic logic. Chapter ! I III is devoted to a discussion of the nature of deontic j concepts, such as permission and obligation, and the rela- I i i tion of these to other concepts, such as norms and rules, j The interdefinability of permission and obligation and i the concept that "ought” implies "may” are also discussed. ! i These two chapters are preliminary material developed for j i a better understanding of the analysis of choice and con- j dltlonal deontic utterances which follows in Chapters IV, ! V, VI and VII. I In Chapter IV, various kinds of permitted and obliga tory choice utterances are defined; and in Chapter V the ; consequences of these definitions are followed in develop ing some Inference principles involving choice utterances. In Chapter VI, various kinds of conditional permission and ! obligation utterances are defined; and in Chapter VII the | consequences of these definitions are followed In develop- | ing some inference patterns involving conditional utter- i i ances. i THE METHOD OP ANALYSIS The method of this study is analytical. The subject matter is logical reasoning, and the method of study is logical reasoning; the subject is also formal logic, and the study will employ the methods of formal logic. Though the method used here is not, strictly speaking, that of the ordinary language philosopher, some of his methods will be used; for example, the method of attempting to find examples called paradigm cases that can be analyzed and accounted for. The first step in the analysis is the establishing of definitions for various kinds of choice and conditional permission and obligation utterances. A tabular method of displaying possible relations between two acts, similar to a truth table in sentential logic, will be employed. Various symbols will be used to represent deontic modes, acts, and logical relationships. These symbols will be used to formalize the different kinds of deontic choice and conditional utterances and to display the tabular def initions of these forms. Throughout the development of the definitions, examples felt to be paradigm instances of : the kind of permission and obligation utterances spoken in ; ' actual discourse will be appealed to in Justifying the ! :definitions. j i i The second phase of the analysis will be the devel- ■opment of Inference patterns involving forms of utterances j 8 previously defined. At the outset, three assumptions will he madei that permission and obligation are inter- definable, that "ought" implies "may," and that the order of the elements of conjunctions and disjunctions may be reversed without affecting the meaning of the utterance. The analysis of other Inference forms will be developed by an inspection of the tabular definitions. Still other principles will be developed by deducing them from the principles that were either accepted as assumptions or developed from the definitional schema. Throughout the development of the inference principles, attention will be given to some of the problems of interpretation of the in ference pattern by the use of ordinary language examples. JUSTIFICATION OF THE STUDY Much of the discourse and argumentation of everyday life and affairs involves the use of norms, rules, com mands, and advice. Standard sentential and quantification logic cannot deal with permission and obligation utter ances. Surely inferences involving deontic expressions are: i important in and of themselves, but also they are important] in any attempt to study human argumentation. Much has been| : I :written on deontic logic, but this study differs in two iimportant ways. First, it differs in that the modal de- i i i iontic concepts of permission and obligation are defined | I ! ispecifically in relation to the concepts of choice alter nation and conditional relationships. Second, previous_____ 9 studies of deontic logic have been concerned primarily with the logic of statements about norms, rules, and other de ontic utterances (see Chapters II and III). This study will be concerned not with statements about permissions and obligations, but with the meanings of and Inferences ;involving actual prescriptive deontic utterances. It is hoped that the results of this study will shed some light on modal logic in general, and deontic logic in particular. It Is also hoped that it will be a basic step In producing a useful tool for the understanding and criti cism of actual discourse, and that it will in some measure add to the general theory of human argumentation. 10 NOTES - t - The Logical Syntax of Language (Londons Rout ledge and Kegan Paul, I937), p. 1-2; quoted by Yehoshua Bar- Hillel, "Logical Syntax and Semantics," Language. XXX (195*0. 230. ^An Introduction to Deductive Logic (New York: Appleton-Century-Crofts, 196$), 2, 3ceorg Henrik von Wright first presented his article "Deontic Logic" in Mind. 60 (1951)» 1-15* The article has been reprinted several times; for example, in von Wright's own work, Logical Studies (New Yorks The Human ities Press, 1957)» and recently in Contemporary Readings in Logical Theory, ed. Irving M. Copi and James A. Gould (New York: The Macmillan Company, 1967). PP. 303-315* CHAPTER II THE DEONTIC LOGIC OF VON WRIGHT Deontic logic was first developed by Georg Henrik von Wright and presented in his article "Deontic Logic" in Mind. January, 1951.1 The purpose of this chapter is to review the beginnings of deontic logic and some of the later developments as a basis for understanding the devel opment of some principles of prescriptive deontic logic in later chapters. THE DEONTIC CALCULUS OF VON WRIGHT The deontic modes of von Wright's logic are obli gation, permission, forbiddenness, and indifference. The deontic modes apply to acts; thus acts may be obligatory, permitted, forbidden, or deontically indifferent. Von Wright uses the symbols "0" and "P" to refer to the con cepts of obligatoriness and permittedness. These are called "deontic operators." He uses the symbols "A", "B", "C", and so on, to represent the names of acts. "OA" means act A is obligatory, and "PA" means act A is per mitted. The deontic operators can apply to the name of a single act or to a molecular complex of the names of acts. Thus "P(A or B)" means that it is permitted to do act A or |do act B. "A or B" is said to be "within the scope"2 of |"P" in this example, and thus under its influence. i ii The deontic calculus of von Wright operates in con junction with and presupposes standard sentential logic. Von Wright uses the symbols "v", " -V', and 11O" as logical connectives. These are roughly equivalent to the English words "not," "and," "or," "if, then," and "if and only if." In the present discussion of von Wright's calculus, the symbols " . ", "v»'( "d", and "=" will be used. In von Wright's article, and in many later ver sions and discussions of deontic logic by other writers, the logical connectives are treated as though they were truth-functional connectives. This point will be dis cussed in the next chapter. Von Wright defines all of the deontic modes in terms of permission, which is the only undefined deontlc cate gory. An act is obligatory if not doing the act is not permitted. An act is deontically indifferent If doing the act and not doing it are permitted, and an act is for bidden if the act is not permitted. Using the symbols "OA" to mean act A is obligatory, "PA" to mean act A is permitted, "IA" to mean act A is Indifferent, and "FA" to mean act A is forbidden, and the symbol for negation, the definitions of the deontlc i imodes are as follows* j I OA =df. ~P~A PA undefined ' IA =df. PA . P~A 13 The definitions with "0” undefined would be as follows: OA undefined PA =df• ~0~A IA =df < ~0A • ~0~A FA =df . 0~A The interdefinability of P and 0 is fundamental in the calculus. It is expressed in rule ia in the following list of deontic tautologies.3 (i) Two laws on the relation of permission to obli gation and vice versa: a. PA is identical with ~0~A, i.e., PA = ~0~A expresses a deontic tautology. b. OA entails PA, i.e., OA :o PA expresses a deontlc tautology. (ii) Four laws of the "dissolution" of deontlc opera tors: a. 0(A • B) is identical with OA * BA. b. P(A v B) is identical with PA v PB. c. OA v OB entails 0(A V B) . d. P(A • B) entails PA • PB. (iii) Six laws on "commitment": a. OA • 0(A d B) entails OB. If doing what we ought to do commits us to do something else, then this new act is also something which we ought to do. b. PA • 0(A Z) B) entails PB. If doing what we are free to do commits us to do something else, then this new act is also something which we are free to do. In other words, doing the per-: mitted can never commit us to do the forbidden. c. ~PB • 0{A r> B) entails ~PA. This is but a new : version of the previous law. If doing some- j thing commits us to do the forbidden, then we are forbidden to do the first thing. For in stance: If it is obligatory to keep one's promises and if we promise to do something | which is forbidden, then the act of promising this thing is Itself forbidden. j d. OA d (B V C) • ~PB • ~PC entails ~PA. This is I a further version of the two previous laws. An| act which commits us to a choice between for- j _____________bidden alternatives is forbidden. . . j 14 e. ~[0(A v B) . ~PA . ~PB]. It Is logically Im possible to be obliged to choose between for bidden alternatives. f. OA . 0[](A . B) r> C] entails 0(B r> C) . If doing two things, the first of which we ought to do, commits us to do a third thing, then doing the second thing alone commits us to do the third thing. "Our commitments are now affected by our (other) obligations." g. 0(~A z> A) entails OA. If failure to perform an act commits us to perform it, then this act is obligatory. VON WRIGHT1S DECISION PROCEDURE Von Wright's decision procedure for determining which forms are deontic truths depends upon the idea of "dis junctive normal form." A disjunctive normal form is a form in which only the signs "~'*f ".", and "v" are em ployed, in which the negation sign applies to atoms and not to molecules, and in which no conjunction sign extends h, over a disjunction sign. The simplest way to arrive at a disjunctive normal form is to construct the following tabulation, which is similar to a truth tablet P v.-.q. 1. p . q 2. ~p . q 3. p . ~q 4. ~p . ~q : Lines 1 through 4 tabulate all of the combinations of p, ; ^p, q, and / ' - q. The disjunctive normal form of "p V q" is "(p . q) v |(~P . q) v (p . ~q)", which is derived from lines 1, 2, jand 3 of the table. The definition of "v" requires that line 4 would render the form "p v q" false* thus a truth 15 table analysis will show that "p V q" Is equivalent to »~(~p . ~q)", and that "p v q" is also equivalent to Its disjunctive normal form* n[(p • q) v (~p . q) v (p • Von Wright uses the expression "perfect disjunc tive normal form." The perfect disjunctive normal form of the permission of "A" in relation to "B" is "P(A • B) v P(~A • B) v P(A . ~B) V P(~A . ~B)". As can be seen, these forms are simply the disjunction of all of the pos sibilities of the conjunction of "A" and "B" and their negations. Von Wright uses these forms to construct a truth table,5 which appears on the two following pages (Figure I). Von Wright's method assumes the principle of permis sion, which states that "Any given act is either itself permitted or its negation is permitted."6 Thus "PA" and "P~A" cannot both be false. Von Wright argues that all the deontic units cannot be false, for then an act and its negation would both be forbidden* "~PA • ~P~A", This would mean that the act itself is both obligatory and for bidden* for "~P~A = OA" (by la); thus "(~PA . ~P~A s (~PA • OA)". Or, in other words, act A is forbidden and act A is obligatory. The truth table on the following pages includes the 16th row, which von Wright omits be cause of his principle of permission. The derivations of columns 5i 6, 8, 9, 10, and 11 are indicated at the bottom of the columns. 16 Figure I 1 2 3 4 p(A . b! P(A . ~B) P<~A . BT P(~A . ~B] 1. T T T T 2. T T T F 3. T T F T 4. T T F F 5. T F T T 6. T F T F 7. T F F T 8. T F F F 9. F T T T 10. F T T F 11. F T F T 12. F T F F 13. F F T T 14. F F T F 15. F F F T 16. F F F F 17 5 6 7 ngure x 8 \ continued. / 9 10 11 PA P~A P(A . B) P (A V B) P(A z> B) P(A a B) P (A V ~A) T T T T T T T T T T T T T T T T T T T T T T F T T T T T T T T T T T T T T T T T T T T T T T T T T T P T T T T T T T F T T T T T T F T T F T T T F T T T T T F F T F F T P T F T T T T P T F T T F T P T F F T T T F F F F F F F 1V2 3v4 1V2V3 lv3v^ lvA 5v6 18 Analysis of Some of the Deontlc Tautologies Using Von Wright's Decision Method A truth table sufficient to test all of von Wright’s deontlc truths (with the exception of Hid and iiif, which contain the names of three acts) is provided on the fol lowing pages (Figure II). Again the derivation of each column is indicated at the bottom of the column, and the 16th row is included. Von Wright says that the forms MP(A . B)" and "0(A v ~A)" are contingent, and these are clearly so by his system. He refers to the form "0(A . ~A)M as contra dictory, and the form MP(A v ~A)" as a deontlc tautology.? These are contradictory and tautologous if and only if the 16th row of the truth table is disallowedi P(A . «A) is contingent PA . P~A is contingent 0(A v -A) is contingent OA v 0~A is contingent P(A V ~A) is tautologous PA v P«A is tautologous (till 16th row) (till 16th row) 0(A . ~A) is contradictory OA . 0~A is contradictory (till 16th row) (till 16th row) The reason that the form "P(A v ~A)" is tautologous is that the principle of permission says that either an act or its negation is permitted. The reason that "0(A . ~A)M is contradictory is that M0(A . -A)1 1 is equivalent to "~P~(A . ~A)M by law ia, and is equivalent to H~P(A v '*-A)" by De Morgan's Theorem, Commutation, and Double Negative* 19 Figure II 1 2 3 P (A . B) P(A . ~B) P( . ~B) P("A . ~B) 1. T T T T 2. T T T F 3. T T F T T T F F 5. T F T T 6. T F T F 7. T F F T 8. T F F F 9. F T T T 10. F T T F 11. F T F T 12. F T F F 13. F F T T l*f. F F T F 15. F F F T 16. F F F F I Figure II (continued) 5 6 7 8 P(A V B) P(~A V ~B) p (a v ~b) > 1 cu T T T T T T T T T T T T T T T T T T T T T T T T T T T T T F T T T T T T T T T T T T T T T T T F T T T T T T F T F T T T F F F F 1V2V3 2v3V^ 1V2V^ Iv3v4 Figure II (continued) 21 9 10 11 12 13 I** 15 16 PA P~A OA 0~A PB P~B OB 0~B T T F F T T F F T T F F T T F F T T F F T T F F T F T F T T F F T T F F T T F F T T F F T F T F T T F F T T F F T F T F T F T F T T F F T T F F T T F F T T F F T T F F F T F T T F T F F T F T F T F T T T F F F T F T T F T F F T F T F T F T F F T T F F T T lv2 3vi* ~(3vi*) -10 ~(1V2) _ ~9 lv3 2vl* ~(2vl*) ~ll* ~(lv3) -13 i i t 22 and if "P(A v ~A)" is a tautology, then "~P(A v ~A)" is a contradiction. Using von Wright's method, all of the laws given above were checked, except ia, iiid, and llif. ia was not tested because it is assumed in making the truth table; iiid and illf were not checked because they contain three variables. Since there are a total of twelve possible combinations of the conjunction of A, B, and C and their negations, testing these formulae would require, instead of the sixteen lines used to test two variables, a truth table 212, or ^,096 lines long. This is an impractical size for a truth table. The forms could be tested by a computer, but it was thought that testing these formulae would not contribute any new Information about von Wright’s decision procedure. Law ib, "OA ia PA", is a tautology if and only if the l6th row is not taken into account. Also, law iiie, "~[0(A V B) • ~PA . ~PB]", is a tautology if and only if row 16 is not counted. This form is tested by converting the law into "~[~P~(A v B) • ~PA • ~PBj]" by la, and then to "~[~P('vA • ~B) • ~PA • ~PB]" by De Morgan’s Theorem. These two laws seem intuitively correct. They are the only two {of those tested) that are affected by the 16th row, and they are the only ones that seem to be directly dependent upon the principle of permission. Von Wright's four laws of the dissolution of deontlc operators (11 a, bt c, and d) are inadequate. These laws do not function with negated permission and obligation operators. Thus the following list needs to be added, all of which are valid by von Wright’s decision procedurei lie ~P (A V B) id ~PA V ~PB iif ~0{A V B) ~0A V ~0B llg ~PA . ~PB id «^P (A . B) iih ~0A . ~0B id ~G(A . B) THE RELATION OF SENTENTIAL LOGIC AND DEONTIC LOGIC Von Wright claims that “deontlc functions are similar to performance-functions (and truth-functions) in regard to disjunction, but not similar in regard to negation and g conjunction." Although he speaks only of permission and forbiddenness, the discussion here will also concern obli gation. Von Wright says that "from the fact that at least one of the two acts A and B is performed, it follows that A v B is performed, and from the fact that none of the two acts A and B is performed, it follows that A v B is not performed. Similarly, from the fact that at least one of the acts Is permitted, It follows that their disjunction is permitted, and from the fact that both acts are for bidden, it follows that their disjunction is forbidden."^ With regard to negation, von Wright contends that "from the fact that A is performed, we can conclude to the 24 fact that -A Is not performed. But from the fact that A is permitted, we can conclude nothing as to the permitted or forbidden character of "-*A"One may be permitted to enter the library and also permitted not to enter the library. Indeed, if one were not permitted to do and not to do a certain act, then either doing the act or not doing the act would be obligatory. On the other hand, if an act is obligatory then not doing the act is not oblig atory. The inference from "OA" to "~0~A" is justified in von Wright's system by rules la and ib. Buie ib allows the Inference from "OA" to "PA", and rule ia allows the transformation of "PA" to "~o~A". With regard to the conjunction of two acts, von Wright says that "from the fact that A and B are both performed, it follows that A & B is performed. But from the fact that A and B are both permitted, it does not fol low that A & B is permitted.One of the acts, either by rule or by the nature of the act, may preclude the doing of the other. This restriction is reflected in rule iid. On the other hand, it does follow that if two acts are separately obligatory, their conjunction Is obliga tory. This is reflected in rule iia. The Operation of Sentential Logic upon Seijarately Qualified Deontlc Forms Other than the brief discussion of the relation of deontlc logic and truth functions summarized above, von 25 Wright does not detail the ways in which sentential logic operates in relation to the deontlc modal operators. Cer tain statements, however, can he made concerning the functioning of deontlc logic in relation to sentential logic. The inference rules of the sentential calculus can he used with deontically qualified atoms or molecules just as they are in quantified logic, as long as the scope of an operator is not affected. Rules of inference must operate only upon independent forms, that is, on complete lines in a formal proof, whereas the rules of replacement may he used upon partial lines. The following are examples of correct formulae involving P and O t Simplification (Simp.) (PA . PB) 3 PA (OA . OB) 3 OB Disjunctive Syllogism (D.S.) [(PA v PB) . ~PA] 3 PB [(OA V OB) . ~0A] 3 OB Modus Ponens (M.P.) [ (PA 3 PB) . PA] 3 PB [ (OA 3 OB) . OA] 3 OB Modus Tollens (M.T.) [(PA 3 PB) . ~PB] 3 ~PA [(OA 3 OB) . ~0B] 3 ~0A 26 Addition (Add.) PA a (PA V PB) OA = (OA V OB) The rules of of Simplification, Disjunctive Syllogism, Modus Ponens, Modus Tollens, and Addition were tested by means of the truth table provided in Figure II. Hypo thetical Syllogism and the forms of the Dilemma were not tested, because they contain three variables. The rule of Conjunction was not tested because, as in sentential logic, it is not testable by the truth table method. How ever, presumably "PA, PB PA . PB1 ' is a valid formula. The rules of replacement (Double Negative, Tautology, Commutation, Transposition, De Morgan's Theorems, Material Implication, and Material Equivalence) were tested both for P and 0 and found to be valid. Thus the following are correct formulae in von Wright's deontic logici D.N. PA a ~~PA Taut. PA s (PA v PA) Com. (PA v PB) — (PB v PA) Trans. (PA =5 PB) a (~PB 3 ~PA) De M. ~(PA V PB) a (~PA • ~PB) ~(PA • PB) a (~PA V ~PB) Impl. (PA v PB) a (~PA 3 PB) (PA 3 PB) a (~PA V PB) Equiv. (PA a PB) a [ (PA 3 PB) • (PB 3 PA)] (PA a PB) a [(PA • PB) V (~PA . ~PB)] The corresponding 0 forms are also valid. 27 The Operation of Sentential Logic Totally within the Scope of a Deontlc Form In addition to the operation of sentential logic upon deontlcally qualified atoms and molecules where the scope is not affected, the rules of replacement, though not the rules of inference, may operate freely within the scope of P or 0. The following are examples of correct formulae for P and 0* D.N. PA s P— A Taut. PA s P(A v A) PA h P(A • A) Com. P(A V B) s P(B V A) P(A • B) s P(B • A) Trans. P(A 3 B) = P(~B 3 ~A) De M. P~(A • B) s P(~A v ~B) P~(A V B) s P(~A • ~B) Impl. P(A v B) s P(^A 3 B) P(A 3 B) h P(~A V B) Equlv. P(A 3 B) =P[(A 3 B) • (B 3 A) ] P(A 3 B) 3 P[(A . B) V (~A . ~B)] If these formulae are correct, then presumably the cor responding formulae for Association, Distribution, and Exportation would also be correct. Also, the forms given above would apply as well to atoms and molecules deon- tically qualified by "O", The problem is that most of 28 these forms are not directly testable by using the truth tables provided. Only Tautology is testable. "PA 2 P(A v A)" is tested by using rule iib to convert "P(A v A)" to "PA v PA"1 "PA 2 (PA v PA)" is obviously valid. The form "OA 2 0(A • A)" can be similarly tested by the use of rule j iia. But the forms "PA 2 p(A • A)" and "OA 2 0(A v A)" are not testable, for the rules do not allow the conversion of ”P(A • A)" to "PA • PA", or the conversion of "0(A V A)" to "OA v OA". The Operation of Sentential Logic Involving the Breaking of a Scope So far the discussion has concerned the use of rules of inference and replacement where the logical inference has applied to entire deontically qualified units, or has been entirely within the scope, or influence, of a deontic operator. Next to be considered are cases where the scope of a deontic operator is affected. The first part of the discussion Involves certain uses of the rules of Material Equivalence, Implication, and De Morgan where the scope is affected, and the second part involves inference patterns j similar to Modus Ponens, Modus Tollens, and Disjunctive j Syllogism where the scope is affected. ; The truth value of "P(A 2 B)" is given by von Wright j and is derivable from the disjunctive normal form, "P(A • B) v P(~A • ~B)". In testing the forms "0(A = B) 2 o(A | i 1 ....... __..J 29 3 B) • 0(B 3 A)" and "0(A = B) = 0(A • B) v 0(^A • ~B)", the form "0(A • B) V 0(~A • ~B)" was used to establish a truth value for "0(A = B)n. The following forms corresponding to -the rule of Material Equivalence (Equiv.) are Invalid. P(A s B) s P(A 3 B) • P(B = 3 A) 0(A a B) a 0(A =5 B) • 0(B 3 A) 0(A a B) = 0(A • B) V 0 ( ~ & • ~B) On the other hand, the following forms are validi P(A a B) => P(A =3 B) . P(B =3 A) P(A 5 B) a P(A . B) V P(~A . ~B) F(A • B) V P(~A • ~B) = P(A 3 B) . P(B 3 A) The rule of Material Implication works freely within the scope of a deontlc operator, but there is another form similar to Material Implication where the deontlc operator is negated. The following forms are validi ~P(A 3 B) 3 P(A v B) till 16th row ~P(A v B) 3 P(A 3 B) till 16th row The following forms are invalidi P(A V B) 3 ~P(A 3 B) P(A 3 B) 3 ~P(A V B) 0(A V B) 3 ~0(A 3 B) ~0(A 3 B) 3 0(A V BJ 0(A 3 B) 3 ~0(A V B) ~0(A V B) 3 0(A 3 B) Although De Morgan*s Theorems operate as usual within a scope, they operate in a special way upon the operator and its scope. The following are tautologous implications involving variants of De Morgan’s Theoremsi ~P(~A • ~B) id P(A v B) ~?(*mA v ~B) ^ P(A . B) till 16th row ~P(A . B) id P(~A V ~B) till 16th row ~P(A v B) o P(-mA . ~B) till 16th row The following would he the corresponding rules for 0« 0(A V B) "o ~0(/mA • ~B) 0(A • B) z> (~A v ~B) 0 (<~A v ~B) id ~0 (A • B) 0 {''■A • ~B) 3 /s/0 (A V B ) The rules permit the movement from obligation to permis sion, but never from permission to obligation. This is In keeping with the principle of permission. The following analysis is concerned with such forms as "[P(A id B) • PA] id PB" and similar forms involving what appear to be forms of Modus Ponens, Modus Tollens, and Disjunctive Syllogism. One hundred and twenty-eight forms were tested for P and 0, These forms include some that seem obviously valid and many that appear obviously in- j valid. The conclusions are interesting in that not all of j the forms which, on surface appearance, seem to be valid j | are valid, and some which, on cursory examination, do not j i seem to be valid are in fact valid. The testing of 31 disjunctive syllogism type inferences is accomplished in the same analysis, because in testing a formula Involving such forms as "P(A 3 B)", the form is converted to "P(~A v B)" by the rule of Implication. The form "[P(A 3 B) • PA] 3 PB" and similar forms such as "[P(~A 3 B) • P~A] 3 PB" might appear to be inferences like those following the rule of Modus Ponens, but such forms are invalid. The operation of permission and obligation utterances differ markedly in this kind of pattern. While "[P(A =3 B) . PA] 3 PB" is invalid, the form M[0(A 3 B) • OA] 3 OB" is valid. This latter form is listed by von Wright as the first of his six laws of "commitment" (liia). The following patterns involving hypothetical permis sion statements are validi [P(A =3 B) . ~P~A] 3 PB [P(~A 3 B) • ~PA] =3 PB £P (A 3 ~B) • ~P'vA] id P~B [P(~A = ~B) • ~PA] =3 P~B [P (A D3 B) • ~PB] 3 P~A [P(~A 3 B) • ~PB] z> PA [P(A 3 ~B) . ~P~B] 3 P~A [P(~A 3 ~ B) . ~P~B] 3 PA The following patterns Involving alternative permission statements are validi 32 [P(~A V B) . ~P~A] 3 PB [P(A V B) • ~PA] 3 PB [P(~A V ~B) . ~P~A] 3 P~B [P(A V ~B) • ~PA] 3 P~J [P(~A V B) • ~PB] 3 P~A [P(A V B) . ~PB] 3 PA [P(~A V ~B) . ~P~B] 3 P~A [P (A V ~B) . ~P~B] 3 PA When obligation statements are involved, there are more correct patterns available. The following are valid pat terns involving obligationi [0(A 3 B) • OA] 3 OB [0(~A 3 B) • 0~A] 3 OB [0(A 3 ~B) * OA] 3 0~B [0(~A 3 ~B) • 0~A] 3 Q~B [0(A 3 B) • OA] 3 ~0~B till 16th row [0(~A 3B) . 0~A] 3 ~0~B " ' • " [0(A 3 ~B) * OA] 3 ~0B 1 1 " " [0(~A 3 ~B) . 0~A] 3 ~0B " » " [0(A 3 B) • ~0~A] 3 ~0~B [0(~A 3B) • ~QA] 3 ~0~B [0(A 3 ~B) • ~0~A] 3 ~0B [0 (~A 3 ~B) . ~0A] 3 ~QB 33 [0(A 3 B) * 0~B] 3 O-kA [0(~<A 3 B) • 0~B] 3 OA [(A 3 ~B) ‘ OB] 3 0~A [(~A 3 ~B) • OB] 3 OA £0(A 3 B) • 0~B] 3 ~OA till 16th row [0(~A 3 B) • 0~B] 3 ~0~A » » " [0(A 3 ~B) • OB] 3 ~0A " " " [0(~A 3 ~B) . OB] 3 ~0~A " 1 1 « £0(A 3 B) • ~0B] 3 ~QA H 0 ('■vA 3 B) • ~0B ] 3 ~0~A £0(A 3 ~B) • ~0~B] 3 ~0A [0(~A 3 ~B) • ~0~B] 3 ~0—A As with the above formulae involving permission, the valid formulae corresponding to Disjunctive Syllogism can be interpreted from this list by converting forms such as "0(A 3 B)" to "0(~A V B)". THE LATER WORK OF VON WRIGHT In 1956 von Wright suggested the symbolic form »P(p/c)», which is to be read "p is permitted under con ditions c." Thus he briefly introduced the idea of con ditional permission and obligation in a short article, "A Note on Deontic Logic and Derived Obligation."12 The concept of conditional permission and obligation has since become very Important in the writings of von Wright 3^ and many others. In an article published In Philosophloal Studies in 1958, Nicholas Rescher examines the idea of conditional permission and obligation. In Rescher*s sys tem obligation and permission are interdefinable thusx "0(p/c) =df. ~P(~P/c),,.13 In Norm and Action, published in 1963» von Wright develops a new deontic logic which has an under structure of three logical systems. The first layer is the logic of propositions or, in other words, standard sentential logic. The second layer Is the logic of change. The logic of change employs the symbols "p", "q", etc., for propositions representing states-of-affairs before and after change. The symbol "T” is used to indicate trans formation or transition from some initial state-of-affairs to some end state-of-affairs. "pTq” means that state "p” changes or is transformed to state "q1 *. "pTp” and "~pT~pM mean that some state-of-affairs is unchanged, "pT~p" and M~pTp" indicate situations where a state is transformed to its opposite condition.3 - ^ The third layer is the logic of action, which uses the symbol , f d" to mean the doing of a certain act, and the symbol "f” for the forbearing or not doing of a certain act, "d(~pTp)" means the act of changing from a state of ’ ’^p" to a state of "pM. "f(~pTp)M means that one forbears to change through action the state of **~p" to the state of "p".3-^ The logic of permission and obligation is then constructed upon these 35 three layers. As In the original calculus, the symbols "P" and 110” are used as the deontlc operators. One major dif ference, in addition to the subs trueture, is that in the new calculus the deontic modes of "P" and "0" are inde pendent and not defined in terms of one another. If "p" is used to represent the state of a certain window being closed, then the expression "Pd(~pTp)" can be used to represent such an utterance as "You may close the window," the expression "Of(~pTp)" can be used to represent such an utterance as "You ought to let the window remain open," or, in other words, "You ought to forbear the closing of the window."16 one additional symbol is used to complete the calculus. This is the symbol "/", called the "stroke. The symbols used after (to the right of) the stroke repre sent the condition or conditions under which one is per mitted or obligated to perform or forbear a certain act of change. For example, the formula "0 d(pTp) / qTq" would mean that one is obligated to cause state "p" to remain, under the condition that "q" remain unchanged. Suppose, for example, that a certain door would not remain open unless it were kept open. One might issue the command or state the norm that one ought to keep the door open in the | case that another person is following you through the door. The formula above could be used to express this command or ! norm. 36 The advantage of the new symbolism is that one can express such ideas as the forbearance of an act and the act of maintaining a certain state-of-affairs more easily than one could in the older symbolism. The new symbolism is richer and perhaps more accurate, but it is more complex and more difficult to read without considerable concen tration and study. The Paradoxes of Deontic Logic From 1951 until the present many philosophers, fol lowing the lead of von Wright, have given their attention to deontic logic, including A, N. Prior, R. M. Chisholm, Alan Ross Anderson, Lennart Aqvist, Nicholas Rescher, Mark Fisher, Ruth Barcan Marcus, Manfred Moritz, and many others. The articles range from the invention of new cal culi, questions concerning the interdefinability of permis sion and obligation, the relation of deontic logic to other modalities (including the problem of quantifying deontic utterances), the basic nature of deontic modalities, to a host of discussions of conditional permission and obli gation and to the many problems of interpreting deontic formulae in ordinary language, often referred to as "the ; paradoxes of deontic logic." A systematic analysis and evaluation of the many recent articles on deontic logic andj ; 1 deontic concepts has not been attempted, for such an [analysis would be lengthy and, for the most part, far from j | the analysis which follows, J 37 Two paradoxes are of particular Interest, These are the Alf Ross paradox, which Involves the form "OA z> 0(A V B)11, and the R, M. Chisholm paradox, often called the "contrary-to-duty" paradox, which involves the form "0~A 0(A 3 B)". It should be noted that these forms are paral lel to the forms "p => (p v q)" and "~p z> (p z> q)11, the first of which Is an instance of the rule of Inference called Addition, and the second of which is an instance of -l Q the counterfactual paradox of material implication. It should also be noted that although the rule of Addition is not usually considered to lead to any paradoxes, while the form "~p z (p z q)" is considered paradoxical when rend ered in ordinary language, the form "~p Z) (p n q)n is equivalent to "~p " = > (~p V q)" by the rule of Implication, and thus it is an Instance of the rule of Addition. The Alf Ross Paradox^9 Consider the situation in which one is obligated to help a certain person, Mr. A. Letting "H" stand for "helping Mr. A," we have the obligation "OH". Now from "OH" we can deduce "0(H v K)" by a rule analogous to the rule of Addition. Indeed, this Is a correct move in von Wright's original calculus. If "K" is used to stand for "killing Mr. A," then it would seem that if one is obli gated to help Mr, A ("OA"), then one is, by implication, obligated to help Mr. A or kill him ("0(A v B)"). This seems strange, for If someone obligated someone else to help a third person, then surely he would not intend that that person be obligated to help a third person or kill him. Von Wright suggests that the form "OA 3 0(A V B)" is certainly no more paradoxical than the form "p 3 (p v q)" in sentential logic.20 "p 3 (p v q)" is not paradoxical, because if some state-of-affairs "p" exists, then it fol lows that "p v q", for since "p" is true then the propo sition "p v q" will be true. One might claim to have met his obligation to help Mr. A by killing him on the grounds that the obligation to help Mr. A implied the obligation to help Mr. A or kill him. If "OA1 1 and "0(A v B)" were mutually inferable, which they are not, then one might argue that the ful filling of the obligation "0(A v B)" fulfilled the origi nal obligation. But this is not the case. Even if kill ing Mr, A satisfies the obligation "0(A v B)", the obli gation ‘ 'OA" from which "0(A V B)f l is derived still re mains unfulfilled. Thus one does not fulfill his obli gation to help Mr. A by killing him. And thus there is no paradox, But it remains that one might assent to the utterance "You ought to help Mr. A" and yet reject the utterance "You ought to help Mr. A or kill Mr. A," which logically follows from it. The problem of this paradox can be clarified by making the distinction between prescriptive 39 deontic utterances and descriptive deontlc statements. This distinction will be presented in the following chapter in connection with a discussion of the truth-functionality of deontic utterances. The question of the application of the rule of Addition and the Alf Ross paradox to prescrip tive utterances will also be discussed in Chapter VII. Contrary-to-Duty Paradox The contrary-to-duty paradox involves the forms "OA r> 0(~A Z3 B)" and "0~A d 0{A d B)". If there is an obli gation to perform some act, then not doing the act obli gates the doing of any act whatever. Or, If there is an obligation to refrain from doing some act, then the doing of the forbidden act obligates the doing of any act what ever. If one were obligated to refrain from trespassing, then he would be obligated such that if he disregarded the prohibition, he would be obligated to kill the owner of the property or to eat a peanutbutter sandwich, or to do any other act we could name. This paradox shares all the dif ficulties encountered in the counterfactual paradox of material implication. The question raised by Roderick Chisholm in connec tion with the puzzle he presents in his article of 1963 is whether deontic logic can formulate contrary-to-duty O '! obligations. "Exhortations often take the form 'you ought to do a, but if you do not do a, then you must, by all means, do b1." Chisholm contends that the form ^0 "0(A => B)" is inadequate to translate such obligatory 22 utterances. Consider the following sentences* ^ 1. It ought to be that Smith refrains from robbing Jones. 2. Smith robs Jones. 3. If Smith robs Jones, he ought to be punished for robbery. 4-. It ought to be that if Smith refrains from rob bing Jones he is not punished for robbery. The sentences can be formulated in the following way, with "R" standing for "Smith robs Jones," and "J" standing for "Smith be jailed (punished) for robbing Jones"* 1. 0~R 2. R 3. R 3 0J . 0 (~R ~ J) The problem is that from lines 2 and 3 one may deduce 0J, and from lines 1 and 4 one can deduce 0~J. Thus we may conclude both that "Smith ought to be punished for robbing Jones" and "Smith ought not be punished for robbing Jones." If the form "B/c" is Interpreted as a conditional | statement of the form "if c then A", then the problem is not solved by this formulation, for "0(J/R)" would be equivalent to "0(R => J)" and "0(~J/~R)n would be equiva- I i lent to "0(~R z) ~J)», and thus there is no improvement by ; kl using the stroke symbol. If the stroke is not to be in terpreted as a conditional, then the question remains, in what way is it to be Interpreted? Von Wright has produced a new solution to this and other paradoxes based upon distinguishing various levels of permission and obligation. The solution is highly technical and complicated and, In the opinion of this writer, neither clear nor well worked out. It is based upon an Idea worked out by Nicholas Rischer and presented in his article "Semantic Foundations for Conditional Per- 2k mission." Von Wright's new Ideas are to be found In his book length article, "An Essay in Deontic Logic," pub lished In 1968. CONCLUSION In this chapter the original calculus of von Wright has been presented and the decision procedure examined. Even though von Wright's decision procedure can be ques tioned on the grounds that it uses a truth table method with entities which might well be considered to be non truth-functional, the original calculus is of great impor tance, because It forms the basis of his later work and the basis of the work of many followers in recent years. The analysis of the relation between sentential logic and Von Wright's calculus has been long and difficult. The analysis was provided because it is lacking in the b z literature on deontic logic, and because von Wright, in his original work and in his later work, and the followers of von Wright, have assumed the functioning of sentential logic without examining the implications of that assump tion* In the final part of this chapter, the later work of von Wright and some of the problems that later writers have concerned themselves with have been presented. The material in this chapter and the discussion of the basic nature of deontic concepts in the next chapter are included because they form a base for the better understanding of the analysis in the following chapters. 43 NOTES 1Mlnd, 60, 1-15. All subsequent references will be to the article as reprinted in Contemporary Readings in Logical Theory, ed. Irving M. Copi and James A. Gould, pp. 303-315• because of the ready availability of this source to the reader. 2It should be noted that the punctuation In von Wright's article as reprinted In Copi and Gould does not make the scope of a deontic operator clearj thus, the punctuation of the original Mind article will be followed. 3yon Wright, "Deontic Logic," pp. 314-315* ^Robert Neidorf, Deductive Forms (New York: Harper and Row, 1967), PP. 198-201. 5"Deontic Logic," p. 311. 6Ibid., p. 309. 7Ibid.. p. 312. 8Ibid., p. 308. 9lbld., p. 307. 10Ibid.. p. 307. 10Ibid., p. 307. 12Mlnd, 65 (1956), 507-509? reprinted in Copi and Gould, pp. 316-318. ■*-3"An Axiom System for Deontic Logic," Philosophical Studies. 9 (1958), 24-30. l^CLondoni Routledge and Kegan Paul, Ltd.), pp. 27 f ^Norm and Action, pp. 42 f. l^Norm and Action; see Chapter V for a full discus sion of the translation of these kinds of utterances. 17lbld.. see p. 171. l8por a discussion of the counterfactual paradox, see Nelson Goodman, "The Problem of Counterfactual Condition als," Journal of Philosophy. 44 (February 1947), 113-128; David Mitchell, An Introduction to Logic. Anchor Books (Garden Cityi Doubleday, 1970), pp. 71-72; and W. V, 0. Quine, Methods of Logic (New York; Holt, 1959), P. 14. 44 ^Alf Ross, "Imperatives and Logic," Theorla, 7 (1941), 53-71. The paradox is discussed by^Bengt Hansson in "An Analysis of Some Deontic Logics," Nous 3 (1969) 383-384. 20"Deontic Logics," American Philosophical Quarterly. 4 (1967), 137. 2l"Contrary-to-Duty Imperatives and Deontic Logic," Analysis. 23 (1963)* 33-36. 22Ibld.. pp. 33-34. 2^See Lennart Aqvist, "Good Samaritans, Contrary-to- Duty Imperatives, and Epistemlc Obligation," Nous, 1 (1967), 364j and Bengt Hansson, "An Analysis of Some Deontic Logics," p. 385 (see n. 19 above). ^Philosophical Studies. 18 (June 1967), 56-61. 25»'An Essay in Deontic Logic and the General Theory of Action," Acta Philosophlca Fenriloa. 21 (1968), (Am- sterdami North-Holland Publishing Company), 3-110. CHAPTER III THE NATURE OF DEONTIC CONCEPTS Deontic utterances employ such words as "permitted," "permission," "may," "can" (used in the sense of "may"), "right," "obligation," "obligatory," "should," "ought," "must," "duty," "command," "imperative," and so on. The generic categories are permission and obligation. Thus such words as "permitted," "permission," "may," and some uses of "can" are classified as words expressing the mode of permission, and words such as "obligation," "ob ligatory," "should," "ought," "must," "duty," and so on, are classified as in the mode of obligation. Utterances expressing permission or obligation may be prescriptive or descriptive. An utterance, for example, may be used to perform the act of giving or granting permission to per form some act, or it may be used to state that a certain permission has been granted. An utterance may be used to perform the act of commanding, or the act of advising, or of stating that a certain obligation, moral duty, command, and so forth, exists. There is an obvious difference be tween commanding or advising, on the one hand, and, on the other, telling someone that he has been advised or commanded. After discussing the general nature of obligation and permission and the problems involved in the attempt 45 A6 to define the various deontic modes in terms of one an other, the question as to whether deontic utterances should be viewed as being prescriptive utterances or de scriptive statements about norms will be considered, in relation to the question of whether deontic utterances can be taken to express propositions which are capable of being counted as true or false. The final part of the present discussion will concern the idea that "ought" im plies both "can" and "may." DEONTIC CONCEPTS Deontic utterances such as "You are obligated to do such-and-such," or "You ought to do such-and-such," or "You may do such-and-such" do not occur in a zero context. They occur in some deontic realm. As Mark Fischer sug gests in his article, "A Three-Valued Calculus for Deontic Logic," "It is clearly understood that a deontic sentence is always used in the context of a set of rules."1 The idea of "rules" is not easy to clarify. In one sense rules can be thought of as linguistic expressions stipulating actions. Games such as chess are obviously governed by what we call "rules." Language is sometimes said to be "rule-governed behavior." These rules are written down in books on language and grammar. But it might also be said that rules governing language behavior, or any other kind of behavior, may be in operation even though the rules as discreet language events have not been formulated and recorded. The word "rule1 * is being used here in the very general sense, meaning some kind of prin ciple governing human behavior. Such rules may be expli citly formulated or not. Rules differ from scientific law in that rules are not "discovered," but are made up by men either explicitly or in the process of social evolution. Rules are thus arbitrary, man-made principles governing his own behavior. Deontic utterances will relate to some system of rules governing human interaction, some value structure or norm system or moral system, or to some taboo system, custom, convention, set of laws, or even rules of a game. The idea of a set of rules suggests other conceptsj for instance, "sanction," "authority," "power system," and "penalty." Deontic utterances are not about states-of- affairs, such as are the propositions "Tom is tall," "Richard M. Nixon is President of the United States in 1970," or "There are two fish in my fish bowl." They are about conduct. They are about the permittedness, forbid denness, and obligatoriness of certain behaviors. Permis- i sion and obligation utterances usually do not contain any j information about the source of the permission or obliga- j I tion, but some force or authority rests behind permissions j and obligations. A person is permitted by someone or j something, and a person is obligated by someone or . . ___________ . J 48 something# The authority, of course, may be a person such as a parent, an organization such as a church, school, or business, an abstract entity such as God, a code or a set of laws, or even merely a set of conventions such as custom. A penalty may be explicitly a part of the rule or norm, as in the case of the laws of the state. It may be implicitly understood in the context, such as when dis obeying the order of an employer or boss. Or the penalty, if it can be called a penalty, could simply be breaking the rules. Most people have broken a rule, a norm, a custom, and even disobeyed an order without "getting in trouble." It is doubtful that the idea of a penalty can be counted as a necessary feature of a rule structure. On the other hand, the idea of violation seems to be neces sarily connected with the concept of rule-bound behaviors. Alan Ross Anderson states that "it is analytic of the notion of obligation that if an obligation is not ful filled, then something has gone wrong." Using the symbol "V" to stand for the concept of violation, Anderson sug gests that utterances such as "It is obligatory that p" can always be expressed in the form "if not-p, then V".2 Thus when a rule authority of whatever kind invokes a rule, if the rule is disobeyed there is a violation and 1 sometimes, though not necessarily always, a penalty. ^9 Von Wright chooses to restrict the area of deontic utterances to the class of norms rather than the class of rules. ^ In his analysis rules are a kind of norm. He points out that there are three "basic kinds of normsi first, rules, such as the rules of a game and the rules of grammar* second, prescriptions, such as commands, per missions, and laws of the state; third, directives or technical norms. Directive norms are concerned with the relation between acts and ends and will often take the form, "if you want x, then you ought to y," Von Wright then identifies three additional related kinds of normsi first, there are customs, which are related to both rules and prescriptions; second, there are moral principles, which are related to both prescriptions and technical norms; and finally, there are ideal rules, which are re lated to rules and technical norms. Ideal rules are such norms as standards; for example, a standard for judging a good painting, or a superior teacher, or a correct logical system. But whether the concept of norm or rule Is taken as the generic category of deontic utterances, the idea remains that deontic utterances operate in some kind of i area of restriction. | | On the other hand, normative or rule restrictions are j | such that they operate in an area of freedom of a kind. j Natural law (that is, scientific law) differs from moral i law, custom, convention, and rules in that the natural law j 50 cannot be 'broken,' but if it be 'broken' the law is ques tioned and revised. But moral law, custom, convention, rules of a game, or laws of a state can be and are broken. A deontic utterance expressing permission to perform some action presupposes the possibility to ignore or at least attempt to ignore the permission. Similarly, if an act is forbidden, it is presupposed that one could at least at tempt to do it anyway, though the doing or the attempted doing may involve a penalty of some kind. Also, if a deontic utterance expresses an obligation, it must be possible to violate that obligation. If the word "ought" is taken as a deontic "ought," then it would make no sense to say "If you Jump out of the airplane, you are obli gated to fall." The words "freedom" and "restriction" can be defined in terms of each other. Neither word is mean ingful in the absence of the other concept. Thus a de ontic realm is an area of restriction within an area of freedom to act. Norms and rules are such kinds of re strictions. Hypothetical and Categorical Permission and Obligation H. A. Prichard insists that there is a useful dis tinction to be made between moral and non-moral impera- tlves. In making the distinction, Prichard calls atten tion to Kant's distinction between hypothetical and categorical imperatives. A hypothetical imperative 51 declares that one ought to do some act because of some pur pose or goal of the agent. A categorical imperative, on the other hand, asserts that one ought to do some act for Its own sake. Prichard insists that the two imperatives have a distinct meaning. There is quite a difference be tween saying "You ought not discriminate against minorities because they might burn down your house," and saying "You ought not discriminate against minorities, because it is wrong." Prichard refers to the two kinds of imperatives as non-moral and moral imperatives. He insists that not only are the grounds for uttering a moral "ought" and a non-moral "ought" different, but also that there is a basic difference in the meaning of the word "ought." Moral imperatives are categorical imperatives. They might be thought of as self warranting or self authorizing, or as being authorized by reference to another moral prin ciple. Non-moral imperatives are authorized by some prac tical necessity or some non-ethical goal of the person involved. Von Wright's distinction between categorical and hypothetical norms differs slightly from Prichard's. Von ■ i Wright distinguishes between categorical and hypothetical J | norms such that the utterances "Close the window" or "You i i ought to close the window" or "You may close the window" are categorical norms, while utterances such as "You ought to close the window if it rains" or "You may close the 52 window If you are cold" are hypothetical norms.^ He dis tinguishes between technical norms (also called "direc tives") and hypothetical norms such that "If such-and-such condition arises you ought to do such-and-such" Is hypo thetical, and "If you want such-and-such, then you ought to do such-and-such" Is technical or directive.® The dif ference Is that Prichard's hypothetical imperative states a goal or end which directs an obligation. Prichard's "hypothetical imperatives" are like von Wright's "technical norms." Von Wright's "hypothetical norms" state the con dition under which one may or ought to do such-and-such an act, THE INTERDEFINABILITY OF PERMISSION AND OBLIGATION Von Wright, in his original calculus, and most of the recent writers, for example, Alan Ross Anderson,? have accepted the interdefinability of "P" and "0". "0A" is equivalent to "~P~A", and "PA" is equivalent to "~0~A". In his book Norm and Action, von Wright suggests that "the independent status of permissive norms is open to debate." : Because of certain doubts, von Wright chooses to leave the question unanswered and to construct his system with "P" j and "0" independent concepts.® In his later essays, how- ] ! ever, the interdefinability of "P" and "0" are again ! ! accepted.^ ; I i j i Obligation words such as "obligation," "obligatory," j : I and "ought" are often associated with imperatives or J commands. Bengt Hansson argues that utterances lilce "It is obligatory that p" are not all imperatives, "because one can point out to a person that he ought to do so-and-so without actually telling him to do it,"10 Words such as "ought" have two distinguishable, though closely related, uses. An "ought" statement may be used to advise or to command. One might say "You ought to do A" and mean you are advised to do A or you are obligated or even commanded to do A, If one is commanded to do a certain act, then it follows that the commander (the authority, law, norm, etc.) does not permit the not doing of A, But when one is ad vised to do a certain act,_does it follow that he is not permitted not to do it? In a sense it does. Certainly the not doing of the act is contrary to the advice. If one follows the advice, he is not permitted by that advice to not do the act. Thus whether an "ought" statement is commanding or advisory, the corresponding permission statement will be commanding or advisory. Whatever it is that binds us or compels us or advises us to do a certain act, whether au thority, penalty, or some desire within us, it is the same thing which binds us or compels us or advises us that we ;may not not do the act. Similarly, whatever permits us to :do a certain act, whether an authority or ourselves, also does not obligate us not to perform the act. 5^ The Relation of 0, P. and F Manfred Moritz claims that permission is simply the absence of a prohibition against some act.11 If this is the case, then "PA" is equivalent to "—FA". Obligation seems clearly definable in terms of forbiddenness. If one is obligated to do an act, then he is forbidden not to do that act. Even in Norm and Action, where he had tempo rarily set aside the interdefinability of permission and obligation, von Wright accepted the interdefinability of obligation and forbiddenness. "Ought" utterances can be rendered as "must not" utterances. Thus if one ought to do such-and-such, then he must not not do it. In other words, "OA" Is equivalent to "F—A ".12 If "OA" is equiva lent to "F—A", and "PA" is equivalent to "—FA", then "OA" is equivalent to "—P—A". Stated as a rule, the lnter- : definability of "P" and "F" involves changing and negating the operator. Thus the following are equivalenciesi PA a -FA OA e F—A -PA s FA -OA 9 -F-A P—A s —F—A 0—A = FA —P—A a F—A —0—A = —FA Thus it follows that if "PA 3 -FA", and "—FA = -0-A", then I | "PA 3 —0—A". The question of the interdefinability of "P" j | and "0" then hinges upon the question of whether permission I can be defined in terms of non-forblddenness, "PA = —FA". In chess one is permitted to move the rook in a cer tain pattern in proper turn sequence, and one is (except in some chess tournaments) permitted to chuckle while doing it. There are no restrictions against chuckling in chess rules. And given that it is in proper turn se quence, and in some instances within a certain time peri od, there is no restriction against moving the rook in a certain pattern. Thus, if permission is defined merely as the absence of forbiddenness, then one is permitted to move the rook in a certain pattern and one is permitted to chuckle. But while one does not necessarily have the right to chuckle, one has the right to make a certain proper move in chess. Bengt Hansson points out that it is important to dis tinguish between rights and permission. A right entails not only permission, but also obligations of people not to forbid certain actions. A right is a kind of guarantee that an action may be performed* a simple act of permis sion is merely the state of not being forbidden. Hansson maintains that it is this weak meaning of permission as opposed to rights which is employed in deontic logic.^ j Thus, in this weak sense, being permitted to do A ("PA") ; | is equivalent to not being forbidden to A("~FA"). And not being forbidden to A ("~FA") is equivalent to not being obligated to not A ("~0~A"). In other words, if I am permitted to have a peanutbutter sandwich, then I am not forbidden to have or prohibited from having a peanutbutter sandwich, and I am under no obligation to refrain from having one. Thus, given the weak sense of permission, the concepts of obligation and forbiddenness are interdefin- able . But is the weak sense of permission satisfactory for the analysis of permission statements? In Norm and Action, von Wright distinguishes two senses of permis sion* the first and weakest sense, in which permission is simply the absence of prohibition or restriction, and the stronger sense, in which permission is itself a kind of prohibition or restriction. For von Wright, an act is permitted in the weak sense if the act is not forbidden. The same is true of the stronger sense of permission ex cept that in the stronger sense the act in question is subject to some set of norms. In other words, It operates within some deontic realm. Further, the strong sense of permission logically implies the weak sense, but the weak sense does not imply the strong sense. For von Wright, only the strong sense of permission involves norms, and thus only the strong sense is applicable to deontic logic, i Further, von Wright differentiates degrees of j "strongness1 1 by distinguishing between permissions, rights, and claims.1^ A permission in the strong sense Involves an authority (a person, a code, a set of conven tions, and so forth) that will tolerate a certain act. 57 "In granting a right to some subject, the authority de clares his toleration of a certain act (or forbearance) and his intolerance of certain other acts"^ on the part of other people. The strongest level of permission is when a person has a "claim' 1 to perform a certain act. Claims involve tolerance, plus prohibitions to others against Interference, plus the authority enabling the person to perform the act. Von Wright chooses the simple strong meaning of permission, where permitting an act Implies not forbidding the act, but where the act is sub ject to a norm system. If permission were taken in the weak sense, then all acts would be permitted unless expressly forbidden. One may chuckle while playing chess. If there are rules against chuckling, or any other such behavior, in a cer tain chess tournament, these rules are not rules of chess but of the tournament. The rules of chess themselves are indifferent with regard to chuckling. But within the realm of the rules of chess, certain moves are permitted and others forbidden, and the rules may be stated either in terms of permission or forbiddenness. Thus permission and forbiddenness are lnterdefinable, such that "PA" is equivalent to "~FA", and "P-^A" is equivalent to "~F~A", only within a certain sphere or realm of norms or rules. And consequently, "P" and "0" are lnterdefinable only within a deontic realm. If permission, obligation, and forbiddenness are to be counted as lnterdefinable, it must be clear that they are lnterdefinable not only in terms of operators, but also in connection with negation. The question remains of what it means to negate a deontic operatori "—O", "~PM, and "~FH. There is a difference between there being a rule or norm or command that some act is not forbidden, and the absence of a rule or norm or command that that act is forbidden. M~0A" could be interpreted to mean that there is a rule, or norm, that one is not obligated to do such-and-such. Or "~0A" could be Interpreted to mean that there is no rule, or norm, obligating such-and-such an action. The two interpretations of "~GA", "~PA", and • ‘ —FA1 1 are as follows* Interpretation 1 Interpretation 2 ~0A rule (~0A) no rule (OA) ~PA rule (~PA) no rule (PA) ~FA rule (~FA) no rule (FA) Interpretation two must be ruled out. One could not con clude that because there were no rule forbidding an act, it followed that there were a rule permitting the act. There clearly might be no such rule or norm. It also does not seem reasonable to conclude that because there is no rule forbidding an act, there is, by implication, a rule ; permitting the act. Similarly, the absence of a permis- ; sion does not imply the existence of a prohibition. But 59 under interpretation one, if there is a rule in some de ontic realm expressly not forbidding an act, then it fol lows that the act is permitted. And if there is a rule expressly not permitting an act, then it follows that the act is forbidden, PERMISSION, OBLIGATION, AND TRUTH-FUNCTIONALITY The question of whether deontic utterances can be interpreted as propositions that are capable of being counted as either true or false is a difficult one. Some writers, for example Mark Fisher, contend that deontic 17 utterances do not express propositions, ' Bengt Hansson argues that deontic utterances are not ordinarily con sidered to be propositions that are true or false, and that since deontic logic employs standard sentential logic, the only courses open are to reinterpret standard senten tial logic or to consider obligation and permission as properties of the description of acts. Hansson chooses the latter course.-1 '® In his original article in 1951. von j Wright chose a similar course. He used the variable letters A, B, etc., for the names of acts which may be :modified by the concepts of obligation and permission.^ It is difficult in dealing with any modal utterance j ; I !to know exactly what it is that is being asserted, but it I !is clear that when asking if deontic utterances are true or false, one is not asking whether the acts referred to, described, or named by a deontic utterance are true or false. It may be reasonable to ask about some assertion such as "John is permitted to leave now," "Is it true that John is permitted to leave now?" But it is unreasonable to ask, for example, "Is the command ‘John, you ought to leave now1 true?" But it could be asked whether the ut terance "John, you ought to leave now" is warranted by some social or moral code, or law or rule, or some prac tical necessity. It may be true that some authority has given John permission to leave or that some code or set of rules require John’s leaving. It is highly questionable, even if deontic utterances such as "PA" can be counted as true or false, that such forms as "P(A v B)" are truth-functional, because even if "A" and "B" are capable of being counted as true or false names or descriptions of acts, their truth or falsity has no bearing upon whether they are permitted or not. On the other hand, if we can speak of the truth or falsity of such forms as "P(A v B)", their truth or falsity would not be determined by the truth of "A" or "B" but by the truth of "PA" and "PB». Notwithstanding the doubts which can be raised, von Wright has steadfastly maintained the interpretation of deontic utterances as expressing propositions. In one of his publications he asserts that the interpretation of the form "Op" is that one is obligated to see to it that state-of-affairs p be the case.2® In a later article he says that 1 1 'Pp' may be read 'it is permitted that (it is the case that) p.'"21 In his major work on deontic logic, Norm and Action, he maintains that compound forms such as "Od(pTq)'' are truth-functional. The symbols "p" and "q" are prepositional variables representing states-of-affairs. One problem with this analysis is that the form "pTq", which means that state p is changed or transformed to state q, can be interpreted as "pTq" or as 11' p1 T 'q'". In other words, the interpretations can be state-of-affairs p changes to state-of-affairs q, or proposition 1 1 p" changes to proposition "q". The former is obviously von Wright's interpretation, A certain top hat is empty and then con tains a rabbit. An apple is whole and then is sliced. These changes can be observed, and propositions asserted about them can be verified and thus counted as true or false. "d(pTq)n similarly can be counted as true or false» either the magician did or did not perform the trick, and either the cook did or did not slice the apple, j The question now is, in what way can forms such as "Od(pTq)" be thought of as true or false? The key to von ] Wright's contention that deontic utterances express prop ositions is the distinction between prescriptions and de- j l I scriptions. A prescriptive norm, for example "OA", can be j interpreted in ordinary English as "You ought to do A." A | descriptive norm, on the other hand, must be interpreted j 62 as "There is a norm, rule, convention, etc., such that you ought to do A."22 Deontic utterances, in von Wright's view, do not permit or obligate or command, but advise that there is a permission, obligation, or command. Thus the truth of "P(A v B)", for example, depends not upon "A" and "B" as acts, but upon the existence of the norms "PA" and "PB". If forms such as "OA" and "PA" are true or false de pending upon the existence of such a rule or norm in some deontic realm, then they are subject to truth-functional analysis. "OA" must be interpreted as a shortened form of something like "There is a rule QA." "~0A" can be given two interpretations, either "There is a rule ~0A," or "There is no rule QA." If such forms as "OA" are truth- functional, then "OA" Is true if "~0A" is false, but what does this mean? Interpretation one yieldsi "There is a rule OA" is true if "There Is a rule ~0A" is false. This Interpretation will not do, for it is possible for there to be contradictory rules, and Just because it is false that there is a rule which states that one is not obli gated to do a certain act, it does not follow that there is a rule that one ought to do that act. Consider inter pretation twot "There is a rule OA" is true if "it is not the case that there is a rule OA" is false. In other words, "If it is not the case that there is no rule OA," then it follows that "there is a rule OA." Thus only 63 under interpretation two of such forms as "~QA" f "~PA", and "~FA" can deontic forms be counted as truth-functional. But, as we have seen, only under interpretation one can the deontic operators be counted as lnterdefinable. Thus, if this analysis is correct, one cannot maintain both the truth-functionality and the interdefinability of deontic utterances. Still, even if expressions of the form "P(A v B)" were interpreted as prescriptive in meaning rather than descriptive, the acceptability or meaningfulness of "P(A v B)" would depend in some way upon the acceptability or meaning of "PA" and "PB". R. M. Hare argues that the definition of the logical connectives may be made not in terms of truth or falsity, but in terms of assenting and dissenting.^ Quine has recommended what he calls "seman- 2k tic criteria" for the meaning of the logical connectives. Thus one would assent to "P(A v B)" if he would assent to "PA" or to "PB" or to both. The criteria for the truth of ; a state-of-affairs alternation is that the compound is true if one or the other or both alternatives is the case. The criteria for the acceptability of a permitted choice j alternation is not dependent on whether the choice is actually made or not. Its acceptability depends only upon j I the manner of availability of the alternatives. The j statement "You may choose A or B" or "You may do A or B" would mean (if "or" is used in an inclusive sense) that 6k one could do or choose either of the alternatives or both. The statement "You may choose A or B" would be meaningless or unacceptable or Incorrect if it were the case that nei ther choice were, in fact, available. THE PRINCIPLE OP PERMISSION AND THE INFERENCE FROM 0 TO P That "ought" Implies both "can" and "may" is gen erally accepted by philosophers who deal with these con cepts. Von Wright's second law of the relation of P and 0 is exemplified by the formula "OA z> PA". This law Is based on the principle of permission, which von Wright states in three different ways* "Any given act is either Itself permitted or its negation is permitted," and "If the nega tion of an act is forbidden, then the act itself is per mitted," and "If an act is obligatory, then it Is per mitted."2^ One of the reasons for the interest in the idea that "ought" implies "can" and "may" is that Kant formulated the idea that "ought" implies "can", and David Hume in sisted that what ought to be and what is are not logically 1 related. Von Wright's view that "ought" implies "can" ; does not conflict with the Humean idea of the independence ; of what ought to be and what is, because, as von Wright i puts it, "The principle that Ought entails Can . . . does i not affirm a relation of entailment between a norm and a j ! proposition. The entailment is between (true or false) norm-propositions, on the one hand, and propositions about human ability, on the other hand." He further argues that the proper interpretation of the Kantian principle is "That there is a ore script Ion which enjoins or permits a certain thing, presupposes that the subject(s) of the prescription can do the enjoined or -permitted thing. Thus von Wright handles the possible conflict between the Kantian and Humean principles by saying that "ought" im plies "can" is not a logical move from what ought to be to what is, but from statements about "what ought to be" to statements about "what is." Von Wright goes on to contend that the relation of "ought" to "can" may not, after all, be a relation of entailment, but one of presupposition. Obligation presupposes ability, "ought" presupposes "can." In any event, "can" is not a deontic modality. But "may" is, and von Wright accepts the inference from "ought" to 27 "may" as part of his calculus. It seems reasonable that "ought" should imply or at least presuppose both "can" and "may," Surely if a person j is obligated to do act A within some deontic realm, then it would make little sense for him to be obligated if he could not or if he may not perform act A, This is not to say that it is logically impossible for one to be com manded, ordered, or in some other way obligated, or ad vised to do what he can or may not do. Such commands, orders, and advice are in fact Issued, but they are, or 66 seem to be, in some sense, irrational commands, B. M, Hare maintains that "ought" implies "can" when "ought" is used with its full force, that is, in its prescriptive /)0 sense. One might say "You ought to do A, but alas, you cannot" without jarring our sense of logicality; but if someone says, "You ought to do A, so do A, even though you cannot do A," then the one to whom the remark was directed might be Inclined to say "Are you crazy?" But what is the source of the objection? Is it logical, or something else? Manfred Moritz, in his article "On Second Order Norms,argues that "’ought1 implies ’can1" and "'ought' implies 'may'" are not logical truths, but are second order norms, or what he calls "supernorms"; they "regulate regulating,He holds that "'Ought' implies 'can' is another way of formulating the supernormj 'When an action H cannot be performed by the person P; do not oblige P to perform the action HI'" And he suggests that "'If an action is commanded it is also permitted1 is only another formulation of the supernorm; 'When you have commanded a person P to perform the action H; do not (simultaneously) : prohibit that person P from the action HI "'31 His argu- i ment, briefly summarized, is as follows; Such utterances I as "x ought to perform action A" implies "x can perform I action A" or "If a person is commanded to do A then he may do A" may be interpreted as empirical statements. But if they are empirical statements, surely they are sometimes 67 false. On the other hand, the interpretation might be that "'ought* implies 'can'" and 11'ought1 implies 'may'" are the consequent of the meanings of the words involved. Under this interpretation, "If someone obligates x to do H and forbids x to do H he has committed a verbal error • . . This is the linguistic hypothesis. But since we can say a person has been 'wrongly' or 'unjustifiably' obliged to perform an action which he cannot perform, and since it is possible to say that a person is obligated to do some thing but cannot do it, the linguistic hypothesis must be false," Thus, since the hypothesis that "'ought' Implies 'can* and 'may'" is empirical fact, and the hypothesis that such statements are the implication of the words in volved must be rejected, Moritz adopts the hypothesis that such statements are themselves norms, that is, super- 32 norms. J It is difficult to decide whether the objection to one's being obligated to do a certain act and at the same time forbidden to do that act ("OA • FA") is a matter of violating a behavioral norm or convention, as Moritz sug gests, or a matter of logical Inconsistency. "OA • FA" is ! i equivalent to "OA • 0~A". Although "OA • ~0A" is a con- j I tradiction, "OA • 0~A" would seem to be and is, in von i | Wright's system, a contingent statement. Yet the utter- i i ance "You ought to vote for your party candidates and you I ought not to vote for your party candidate s'? is surely contradictory advice or a contradictory command. "QA • FA” Is not, In Itself, contradictory, ttut leads readily to a contradiction. If it is assumed that in a certain deontic realm one is to obey all rules or commands, and if "OA • FA" is commanded, then the obeying of "OA" by doing A would require the violation of the command "FA". But then It would be the case that though one must obey all com mands in a given deontic realm, one must not obey all com mands in that deontic realm, and this is a contradiction. If "'ought' implies 'may'" is a supernorm, as Moritz suggests, then "'ought' implies 'may'" is a supernorm that must, of logical necessity, be a norm of any norm system, to avoid the logical absurdity of compelling one to obey the norms of a certain system and at the same time com pelling him not to obey all the norms of that system. The fact that one can issue a command that will lead to a contradiction does not make the case that "'ought' i implies 'may'" is merely a supernorm which, like the lower ‘ order norms, is conventional and arbitrary. It is both . . empirically and logically impossible to do act A and not j to do act A, but it is logically as well as empirically possible to issue commands to do and not to do some act. Deontic utterances do not occur freely in discourse, but are associated with some norm system or system of rules or other deontic realm. If "'ought' Implies 'may'" is not a logical truth, then at least it is required to make the 69 particular deontic realm within which such utterances occur consistent and coherent. Bengt Hansson argues that "The deontic axioms . . . do not have the status of logical truths, but they express properties of the norm-system used. Those who are at tracted to the axioms may then, if they so want, regard them as criteria of rationality or of inner coherence of norm-systems or moral or legal theories."^3 One problem with counting all deontic axioms as themselves norms, or even supernorms, is that then deontic logic would be a logic with non-logical content. That is, it would be a logic that contains only non-logical truths. Whether ’ "ought* implies •may'" is a logical truth of a kind like or similar to the logical truths of the sentential calculus, or whether it is a logical truth of deontic logic such that its truth is dependent upon the meaning of the words "ought1 1 and "may," or whether it is a supernorm, or whether, like von Wright’s interpretation of '"ought* implies 'can*,1 1 "ought" should be considered to presuppose "may," cannot be answered here. But it remains the case that an inferential move from "ought" to "may" is assumed in all versions of deontic logic encoun tered. The inference from "may" to "ought" is ruled out by von Wright^ and others, and rightly so. Nonetheless, it will be argued in the next chapter that an inference from a permitted choice to an obligatory choice is 70 possible, and is accountable strictly on the basis of the meanings of the words "ought" and "or," CONCLUSION The concept of a deontic realm is important in under standing deontic concepts, for permission and obligation statements are made within some area of restriction and control over human behavior. Only within some deontic realm are the deontic concepts of permission, obligation, and forblddenness interdefinable. The Interdefinability of deontic operators and the interpretation that deontic utterances are truth-functional require different inter pretations of the meaning of a negated deontic operator. The question as to whether deontic utterances can be counted as descriptive and thus truth-functional Is a difficult one. Most deontic logicians have assumed the propositional character of permitted and obligatory utter ances, Whether this interpretation can be rigorously maintained Is in doubt. However, the distinction that von ; Wright has insisted upon between descriptive and prescrip- j tlve norms will become important in the analysis of the relation of deontic words and connective words, and the inferences related to permitted and obligatory choice and conditional utterances in the chapters that follow. The final consideration has been the attention that has been given to the implication from "ought" to "may." 71 This, too, will be of importance in the later chapters, for it will be argued that in some cases not only can one infer permission from obligation, but also obligation from per mission. 72 NOTES iTheorla. 2? (1961), 108, ^"Some Nasty Problems in the Formal Logic of Ethics," Nods, 1 (1967), 3 **-6-3*1-7. 3Norm and Actiont see Chapter I, particularly pp. 1-16. ^Moral Obligation (Oxford: Clarendon Press, 19*1-9), PP. 90-91. 5von Wright, Norm and Action, pp. 7*1—75, 168-169. 6Ibld., p. 169. 7"Some Nasty Problems in the Formal Logic of Ethics," P. 35*K ^Norm and Action, pp. 85, 92. ^"Deontic Logics," American Philosophical Quarterly. *+ (1967), 136-137; "An Essay in Deontic Logic and the General Theory of Action," Acta Phllosophlca Fennloa. 21 (1968), 1*1-15. 10"An Analysis of Some Deontic Logics," Nous, 3 (1969), 375. 1 1 On Second Order Norms," Ratio. 10 (1968), 112. l^Norm and Action, p. 85. 13"An Analysis of Some Deontic Logics," p. 382. l^Norm and Action, pp. 86-88, 15l~bia., pp. 88-90. l6Ibld., p. 89. | 17"A Three Valued Calculus for Deontic Logic," p. 107. | l®"An Analysis of Some Deontic Logics," pp. 37*1—375. 19»Deontlc Logic," pp. 303—30*+ • 20»Deontic Logics," American Phllsophlcal Quarterly, P. 137. 73 21»»An Essay in Deontic Logic and the General Theory of Action," p. 16. 22see von Wright*s discussion in Norm and Action, pp. 132-13^. ^ The Language of Morals (New Yorki Oxford Univer sity Press, 1908), p. 25. V. 0, Quine, Word and Ob.lect (Cambridge* The M.I.T. Press, i960), pp. 57-58* 25»Deontic Logic," pp. 309-310} see also Norm and Action, p. 167. ^Norm and Action, pp. 110-111 (Italics in the orig inal) . 2?See Norm and Action, pp. 14^-1^7» 158, 16^. ^Freedom an(j Reason (Oxfordi Clarendon Press, 19&3) PP. 51-53. ^^Moritz, pp. 101-115. 3°Ibld., p. 101. 31lhld., p. 106. 32ibld., pp. 107-110. 33»An Analysis of Some Deontic Logics," p. 375* 3^Norm and Action, p. 158. CHAPTER IV PERMITTED AND OBLIGATORY CHOICES Linguistic utterances permitting or obligating cer tain behaviors employ such words as "may," "must," "ought," "permitted," "obligatory," and so forth. The logic of von Wright and others has assumed the functioning of sentential logic as the base logic of deontic logic, and thus has assumed the functioning of the logical connectives "and," "or," and others. Surely deontic words and other modal words such as "probably," "necessarily," "verified," and "falsified," interact with and affect the functioning of connective words such as "and" and "or," yet this inter action has not been adequately taken into account in the literature of deontic logic. In his discussion of the language of morals, R. M. Hare suggests that there may be different meanings for "if, then," "or," and other connectives in "imperative con texts" than in "indicative contexts."^ In this and in the following chapters, the relationship and interaction of the deontic modes and conjunctive, disjunctive, and conditional logical connectives will be explored. In analyzing and defining the logical connectives in relation to deontic modal operators, the distinction be- ween prescriptive and descriptive deontic utterances will be strictly maintained. Deontic logic has been developed 75 by von Wright and others exclusively as a logical system involving descriptive statements about the permittedness and obligatoriness of acts. The analysis undertaken here concerns not the meanings and properties of statements about norms, but the meanings and properties of prescrip tive deontic utterances. Furthermore, the analysis pre sented in this chapter concerns utterances involving per mitted and obligatory choice. Because the system of analy sis to be presented and employed depends in part upon the interdefinability of the concepts of permission, obliga tion, and forbiddenness, the interdefinability of these deontic modes as prescriptive deontic modes will be con sidered. The system of analysis will be used to define various possible meanings of permitted and obligatory alternative choice utterances. The definitional schema to be pre sented assumes the concepts of conjunction and negation; thus, a preliminary discussion of permitted, obligatory, and forbidden conjunction will precede the analysis of deontic choice utterances. It will be argued that the analysis shows that in some instances an inference from a permission to an ob ligation utterance can be made, and further, that in some j ! uses of deontic modal words the distinction between per- i i ; mission and obligation dissolves. Further, it will be j ! claimed that the standard interpretations of the word 76 "or" will prove to be insufficient for the analysis of many permitted and obligatory choice utterances. Chapter V will consider the question of whether cer tain standard inferential patterns, such as the principles of De Morgan's Theorems, Addition, and Disjunctive Syl logism, function in prescriptive deontic logic as they do in sentential logic. Chapter VI will concern the meanings of and Chapter VII the inference possibilities from per mitted and obligatory conditional utterances. THE SYSTEM OF ANALYSIS Forms such as "P(A • B)" and "0(A • B)" can be thought of as formalizing either prescriptive or descrip tive deontic utterances. Prescriptive deontic utterances may be interpreted in English variously as "You may do A," "One ought to do A," and so on. Such utterances are im peratives, commands, permissions, advice, and so forth. On the other hand, descriptive utterances are statements about the existence of a norm, rule, command, permission, obligation, advice, and so forth. Such utterances, strictly speaking, must be rendered in English as "There is a norm, rule, command, permission, piece of advice such that . . . ." The analysis that follows is applicable to prescriptive utterances only, and not to descriptive utterances. In the analysis of prescriptive utterances the symbol will be retained for negation, but the symbol "n", 77 which can be called the "upside-down cup," will be used for conjunction} the symbol "u", called the "cup", will be used for alternation (disjunction)} the symbol "=»", called the "conditional" sign, will be used for conditional or hypothetical utterances} and the symbol called the "biconditional," will be used for biconditional or equiv alent relationships. The system employed for providing a definition for alternation and other relationships in relation to obli gation and permission will be a tabular method similar to a truth table. The basic tabulation will be the symbols for acts and their negations. This tabulation is parallel to a truth table tabulation; The truth table exhausts all of the possible truth value combinations of the relation of two propositions. The tabulation of acts and their negation exhausts all of the possible combinations of the performance and non performance of two acts in relation to one another. This tabulation is qualified by a set of deontic operators such as P,P,P,P, or P,I,I,I, thus displaying the meaning of a form. For example, "P(A u B)" involves the following qualified tabulation; a n b a n b a n ~b -A n ~b T F T F T T F F 78 P(A U B) p( a n b7 p (~a n b ) p( a n ~b ) ~p ( ~a n ~b ) The analysis cannot be used in defining conjunction or negation because these are used as part of the mechan ism. Thus a preliminary discussion of conjunction is necessary before defining the forms of alternative choice. Also, before considering the meaning of permitted and ob ligatory choice utterances, it is important to discuss the interdefinability of the deontic modes within a purely prescriptive deontic logic. The Interdefinability of Permission. Obligation, and Forbiddenness of Prescriptive Utterances The discussion in the previous chapter of the inter- definability of the deontic concepts applied strictly to descriptive utterances. The question now raised is whether prescriptive uses of "P", "0", and MF" are simi larly interdefinable. The rules governing the relation of "P", "0", and "F" are as follows« 1) In changing a ttpn expression to an "F" expression, change the deontic operator and change the negation qualification of the oper ator from negation to affirmation or from affirmation to negation. 2) In changing an "F" expression to an "0" expression, change the deontic operator and change the negation of the act. 3) In changing a "PM expression to 79 an "0" expression, change the deontic operator, change the negation of the operator, and change the negation of the act. The following displays indicate the kind of trans formations involved* PA ~FA ~0~A ~PA ~P~A FA ^ ^ 0~A F~A ^ ^ OA P~A / \ ~F~A ^ ~ 0 A First, considering the relation between "0" and "F", it seems correct to assume that obligating an act commands or requires the act and has the effect of ruling out the not doing of the act. Ruling out the not doing of some act is the same as forbidding the act. Similarly, for bidding an act is, in effect, to rule out the act, and thus the same as compelling or obligating the not doing of the act. If a person said "You are commanded to go to the party" or "you are ordered to go," then if the person to whom the command or order were addressed said, "Then I must not skip it" or "Then I am forbidden to skip going," the first person must respond, "Yes." If the first person asserted, "You are forbidden to go to the party," and the 80 second person said, "Do you mean that I am obliged not to go?", the answer would have to be, "Yes." The only problem is that "forbidden" and "must not" seem to be stronger words than "obligated" or "obliged." Also, the words "commanded" and "ordered" are stronger words than "obligated" in some everyday uses. But it remains that in considering obligation and permission interdefinable, all that is being claimed is that the strength or force of the obligatoriness and forbiddenness intended by such words as "ought" and "must not" and others remains the same in interdefining obligation and forbiddenness. If an act Is permitted, then not doing the act is indifferent. But permitting an act is surely not ruling the act out, and ruling an act out is the same as not per mitting the act. Forbidding an act is ruling the act out and ruling it out is not allowing that act, and this is the same as not permitting it. Although saying "You may : go to the party" (meaning "You are permitted to go to the party") may not always carry the same message as "You are not forbidden to go to the party," being permitted to go to the party means, among other things, that one will not ■ be forbidden to enter. If a sign reads "You may not enter ! this building," it would be the same as if it read "You I I ■ | are forbidden to enter this building." I | The only problem in holding to the interdefinability ! | : of the deontic permission, obligation, and forbiddenness j 81 words is that such words often carry additional meanings and differ in various contexts. If the meanings are held constant in some context and in some deontic realm, and if the extra-deontic meanings are set aside, then the words can be interdefined. PERMITTED AND OBLIGATORY CONJUNCTION Permitted Conjunction If an authority, or set of rules, or norm, permits the conjunction of two acts only if they are both per formed, then that permission rules out other possibil ities. The schematic analysis is as follows* A and B are permitted If and only if conjoined p( A and Bj —P(~A and B) ~P( A and ~B) I(~A and ~B) According to this analysis the doing of neither of the acts is indifferent. One is free to do both acts but not free to do one without the other. If, in the above tabu lation, all of the lines but the first were forbidden (not permitted), then the effect would be to make "A and B" obligatory* A and B are permitted and obligatory P( A and B} F(~A and B) F( A and ~B) F(~A and ~B) ; Although one might use the words “may" and "and" to indi- ; cate this kind of a permission, it would be more i i i 82 appropriate to employ the words "ought" and "and" for that purpose. If a permission utterance were made in a context of some particular deontic realm where only those acts that are expressly permitted are permitted, and all other acts, including an act of not acting, are forbidden, then in that deontic realm all permitted acts are obligatory. But this condition is not consistent with the usual nature of most norm systems or conventions or sets of rules or authority systems. We can conceive of a tabulation such that all pos sibilities are permitted* A and B are permitted but not obligatory p( A and B) P(~A and B) P( A and ~B) P(~A and ~B) If permitting two acts involved the permitting of all other possibilities, then permitting two acts would rule out obligating the two acts, for obligating an act has the effect of ruling out or forbidding the not doing of the act. The sense of permitted conjunction utterances ordi narily used when employing the words "may" and "and," and the sense used in basic permission conjunction utterances in deontic logic would seem to be as follows* A and B are permitted when conjoined P( A and B) I(-mA and B) I( A and ~B) I(~A and ~B) This is the analysis that is adopted for the form "P(A n B)". When one says, for example, "You are permitted to do acts A and B" in the weak sense employed here, he is granting permission to do the two acts together and nothing more. The use of "I" (indifference) in this schema needs some interpretation. In von Wright's original calculus, "I" was defined as "PA . P~A", If this definition is interpreted as a descriptive statement form, then it would correspond to an utterance such as "There is a norm such that one may or may not do A," Though perhaps a strange way to express the idea, this is the same as saying that (with respect to some deontic realm) there is no norm or convention or rule, and so on, governing the doing or not doing of action A, As a prescriptive utterance "PA and P~A" corresponds to an utterance such as "You are free to do A and you are free not to do A," If this were to be our interpretation of "I", then placing "I" before the scope of the second, third, and fourth row of the tabulation in the analysis of "A and ; j B are permitted" above would have the effect of making all possible combinations permitted, and thus exclude the j ! i possibility of the acts being also obligatory. The inter pretation of "I" which is used in this study does not count indifference as a deontic mode, but rather as a deontic disclaimer. "I" means that the acts within its Bio scope are simply not deontically qualified. In a certain deontic realm the not doing of two acts, A and B, may be permitted, forbidden, or even obligatory, but with respect to the simple utterance "You may do.A and B," or "A and B are permitted," nothing is said or implied about the not doing of both acts, nor is anything said or implied about the doing of one and not the otherj thus these are indif ferent, or not accounted for within the utterance "A and B are permitted." With respect to "~A and B", "A and ~B", and "~A and ~B", "A and B are permitted" is silent. Obligation Conjunction If two acts are not themselves obligatory, but it is obligatory that if either is done, both be done, then the following tabulation would be appropriatei It is obligatory that A if and only if B I — P( A and B) ~P(~A and B) ~P ( A and ) - P(~A and ~B) This tabulation perhaps corresponds to the form "0(A « B)"f but not to the form "0(A n B)", for in the above tabu lation the conjunction of acts A and B is not obligatory. The conjunction of obligated acts could only be rendered by the following tabulation* A and B are obligatory 0( A and B) ~P(~A and B) ~P( A and ~B) ~P(—A and ~B) 85 Forbidden Conjunction The conjunction of two acts may be forbidden because both are separately forbidden, as, for example, it being forbidden to murder and rape. The tabulation for this kind of forbidden conjunction would be as follows* A and B are forbidden F( A and B ) F(~A and B) F( A and ~B) 0(~A and ~B) j If only one act is forbidden, the tabulations would be different. ; The simplest and weakest sense of forbidden conjunction and the one taken to be the tabulation of the form "F(A D : B)1 1 is as follows* A and B are forbidden when together F( A and B) E l (~A and B) I ( A and ~B) I(~A and ~B) ! Forbidding A and B in this weak sense makes one or more j of the other alternatives obligatory. What is obligatory ; is the disjunction of the other possibilities. It might | be forbidden to smoke in the room in which explosives are i i kept, yet it may neither be forbidden to smoke nor to be in the explosives room. Using "E" for "being in the ex plosives room" and "S" for "smoking," this rule might be A is forbidden F( A and IT“ I (~A and B) F( A and ~B) I(~A and ~B) B is forbidden F( A and B) F(~A and B) I( A and ~B) I(~A and ~B) formalized as "F(E n S)", Another way of formalizing the rule might be "~P(E n S)"f "It Is not permitted to smoke in the explosives room." Summary of the Analysis of Permitted. Obligatory, and Forbidden Conjunction As a result of the analysis, the following tabula tions are adopted for the forms "P(A n B)", "0(A n B)", "F(A n B)", and their negations: P(A P I B) ~P(A n B) p( A n b) A_r i bT i(~a n b ) ,-i (~a n b) i( a n ~b) o \- K a n ~b) i(~a n ~b) I — i(~a n ~b) o(a n b ) ~o(a n B) o( A n B) ~o( a n bT f (~a n b) i(~a n b) F( a n ~B) K a n ~B) F(~A n ~B) I(~A n ~B) F(A n B) ~F(A n B) F{ A n B) ~F( A n B) i-1(~a n B) i(~a n B) o\-i( a n ~b) K a n ~b) i - 1 (~a n ~b) i(~a n ~b) PERMITTED AND OBLIGATORY CHOICES We are dealing with utterances which prescribe al ternative behaviors. Thus we are dealing with permitted and obligatory choices. State-of-affairs alternations are such that if one says that "p is the case or q is the case," he should mean that he believes that at least one of the two states-of-affairs is the case. State-of- af fairs alternations and choice alternations are similar, 87 but in some respects quite different. One might say of some state-of-affairs that "p or q is the casej I do not know which." One might say, "You may choose A or B, I don’t know which," but if a choice were actually being given, then the appropriate comment would be "You may choose A or B, it's your choice." If a descriptive state- • i ment were being made, one might say, "You are obligated to j do A or B, I don’t remember which," or "You are permitted i ! to do A or B, I don't remember which"} but if a prescrip tive utterance were being issued, such as "You are permit ted to do A or B," or "You are obligated to do A or B," then the addition of "I don't remember which" would be nonsensical. Thus choice and state-of-affairs utterances I are logically different* I ! The Meaning of Inclusive Obligatory Choices j The "or" used in permission and obligation choice utterances has the same kind of ambiguity as "or" in ; state-of-affairs alternative propositions. The meaning of the symbol "U", which stands for an alternative relation between acts, is taken to be analogous to "v", and thus is ; an alternative connective of the inclusive type. Obli gations of this kind are common. Consider the example, ! "You ought to work for the election of your party's can- i > dldates or give money to the campaign fund." Such obli- i I gations often may contain a preferred alternative, but 88 state the minimum for discharging an obligation. If there be a preferred alternative, often the words "at least" will appear before the least desired alternative. In such cases we are obligated to make a choice to do at least one of the two alternatives. The obligation does not preclude the doing of both, but it rules out, forbids, or does not , permit the skipping of both alternatives, if the obliga- ; tion is to be met. Similarly, if one were to advise that "You ought to go to college or get a job," the advice | might not preclude doing both, but doing neither would be ; | contrary to the advice of an inclusive "ought-or" utter- I ; j ance. The principle of inclusive obligatory choice is 1 that an obligatory inclusive choice excludes or rules out , ; the not doing of both (or all) of the acts inclusively disjoined, and compels the disjunction of any other con- : joined combination of the acts and their negations. ; The definition of the form "0(A U B)" is given by the * following tabulation* i 0(A U B) I p ( A n bT O h P(~A n B) ■ — p( a n ~b ) I ~p(~a n ~b) In an obligatory choice of this kind, one must choose be- j j tween alternatives and is not permitted to choose any ; ! combination. Though none of the possibilities is in it- I ! self obligatory and one Is forbidden, what is obligatory j Is the choice of "(A n B)" or " (~A n B)" or "(A ( 1 —B) ; j . _ _ __ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ . . . . J and H(~A n ~B)" is forbidden. This meaning of "ought-or" in the Inclusive sense parallels the meaning of the weak or inclusive sense of "or" in sentential logic. In sen tential logic, the form "p v q" is equivalent to the form "(p • q) v (~p • q) v (p . ~q)", and equivalent to "~(~p • ~q)". Analogously, "0(A U B)M is equivalent to "0£(A D i B) U (~A n B) U (A n ~ B ) , and equivalent to "0~(~A n i ~B)". Thus, when one is obliged to do A or B in this sense he is also obliged to not do ~A and ~B. j ! The Meaning of Inclusive Permitted Choices A person might make an offer to a subordinate in bus iness to choose between working late to finish a partio- I ular job or coming in on Sunday to finish. The option of i I skipping both alternatives is not open. If a third al- j ternative were proposed by the employee, then it would j remain to be seen if the employer would include this as an | : i option. Again, if a child were permitted to choose to be j : punished by either not going to the movies or not watching television the choice would be inclusive, although no ! child would normally be expected to exercise his option to jbe punished in both ways. The principle of inclusive per- Imitted choice is that a permitted inclusive choice ex- | I eludes or rules out the not doing of both (or all) of the i j jinclusively joined acts, and includes or rules in the doing of any of the other combinations of acts and their 90 negations. The definition of a permitted inclusive choice; utterance is as followsi P(A U B) p( A n bT p (~a n b ) p( a n ~b ) ~p ( " > < a n ~b ) ' Thus, if "or" is used in a sense analogous to the i weak, inclusive sense in sentential logic, then what is ! permitted is the choice between "A and B" or "not A and B" j j or "A and not B". And the alternative "not A and not B" is not permitted. Thus "P(A u B)" is equivalent to "P£(A n B) u («-A ( 1 B) u ~B)]", and equivalent to "~P(~A n ~B)". If a choice is offered in such a way that one may choose one of the alternatives or both alternatives, but may not | reject both alternatives, then it would follow that one is j i I obligated to refrain from choosing neither alternative. ! I Thus, from a permission utterance, an obligation follows, j This kind of permitted choice may seem not to suffice for a great many actual permitted choices. Indeed, this is j correct, and a discussion of additional kinds of permitted : and obligatory choices will follow. Given this kind of choice, a person would not only | be permitted to make the choice, but obligated to make it, ! If the tabulation exhausts all of the possibilities of 1 ; doing and not doing two actions and one is forbade the choosing to take neither option, then he is obligated to choose one of the other options, namely "(A n B) U (~A n B) 91 u (A n ~B)". Thus the distinction between obligatory and permitted choices of the inclusive type dissolves. And thus the definition of "P(A u B)'1 can be considered iden tical with the definition of "0(A u B)"» P(A U B) i-P( A n Bl 0 hP(~A n B) L P( A f l ~B) ~p (~a n ~b ) The Meaning of Exclusive Obligatory Choices An exclusive obligatory choice requires a choice such that only one alternative may be chosen, and further, it excludes the skipping of both alternatives. An obligatory choice might be considered exclusive, either because it is i impossible to do both acts, or because the obligator rules out the doing of both acts. A couple might feel obligated I to spend some holiday with either the parents of the husband or the parents of the wife, and be unable to do . both because one set of parents lives in Chicago and the j other is in Los Angeles. An employer may allow his em ployees to handle only one client at a time and thus say, "You ought to choose to handle the account of Mr. Jones or j ! Mr. Setherton." The employee would be obliged to make an I : exclusive choice. Only the second example Is clearly an j ; i i obligation choice of the exclusive variety, for the idea | : of an exclusive obligatory choice is that the authority or | j : obligator rules out the choice of both alternatives, not j I i i that both alternatives are incompatible. j 92 To distinguish exclusive from inclusive alternation, ; the symbols "ve" and f , ueir will be used for exclusive al ternation. In sentential logic, an exclusive alternation of two propositions has the following truth tablei v ve q T F T [ F T T T T F | F F F j A proposition "p ve q" is true if either p or q are true, and false if both are true or both are false. Similarly, a deontic utterance such as "You ought to choose (exclu sively) act A or act B" means that one is obligated to ■ choose, but forbidden to choose both or neither alterna tive. The principle of exclusive obligatory choice is that j i i an obligatory exclusive choice excludes or rules out both the doing of both (or all) of the exclusively disjoined acts and the doing of neither (or none) of the exclusively ; disjoined acts, and compels the disjunction of the other ; possible combinations of acts and their negations. The I definition of "0(A (Je B)M is as follows* 0(A Ue B) ~P( A n bT ' fir P(~A n B) p( a n ~B) ; ~p (~a n ~b ) i "p ve q" is true if "(~p • q) v (p • ~q)" is the case, and I if "~(p • q) • ~(~p . ~q)" are the case. As the truth I I table will show, "p ve q" Is equivalent to "(~p • q) v 93 (p • ~q)", and is equivalent to "~(p • q) • ~(~p • ~q)". Analogous to these relationships, obligating an exclusive choice is equivalent to permitting "~A n B" or "A n ~B", and not permitting (or forbidding) "A f l B" and "~A n ~B". i The Meaning of Exclusive Permitted Choices i If a teacher were to say to his students, "You may take the final examination or you may write a paper," he ! would be giving an exclusive or inclusive choice. The choice would be inclusive if it were allowed that the stu- : dents do both for extra credit. The choice would be ex clusive if only one option were allowed. Presumably the ; teacher would not permit the skipping of both options. Words such as "may," "choose," and "or" do not give clues | i i I as to whether the choice is inclusive or exclusive. Just j i as with the propositional connective "or", the context : must be examined to determine if an obligatory or permitted. : choice is exclusive or inclusive. The principle of ex- | elusive permitted choice is that a permitted exclusive i choice excludes or rules out both the doing of both (or | all) of the exclusively disjoined acts and the doing of i neither (or none) of the exclusively disjoined act’ s, and includes or rules in the doing of either of the other possible combinations of the acts and their negations, A j j permitted exclusive choice is defined as follows: 9 k P(A Ue B) ~p( A n bT p (~a n b ) p( a n ~b ) ~p(~a n ~b) As with Inclusive permission and obligation, the dis tinction between exclusive permission and obligation fades,' If one is exclusively permitted to choose, then he is ob ligated to refrain from choosing certain alternatives, and further, if he is obligated to refrain from certain alter natives, then the disjunction of the other permitted al ternatives is obligatory. Thus the definition of "P(A Ue B)n can be considered Identical with that of M0(A Ue B)"i P(A Ue B) ~P( A n b7 | r n b ) I ° L p ( a n ~b ) ! ~p(~a n ~b) i I i i Summary of Permitted and Obligatory Inclusive and Exclusive Choices Thus far, certain definitions have been laid down for inclusive and exclusive permitted and obligatory choices. They are as followsi Inclusive permitted choice P(A u B) P( A D B) P(~A n B) P( A n ~B) ~p(~a n ~b ) 95 Inclusive obligatory choice 0(A U B) 0 P{ A n B) — P(~A n B) L- p( a n ~b ) ~p(~a n ~b ) Exclusive permitted choice P(A ue 3) ~p( a n b) p (~a n b) p ( a n ~b) ~p(~a n ~b ) Exclusive obligatory choice 0(A ue B) 0 i — P(~A n B) ; L- P( A f l ~B) ! ~P(~A n ~B) These definitions correspond to two common kinds of ; permitted and obligatory choice utterances. The analysis indicates that certain meanings of "ought-or" and "may-or" j utterances carry restrictions, and that the "may-or" usage carries the same restrictions as the "ought-or" usage. ; Thus one can infer obligations from inclusive and exclu- ! j slve choice permission utterances. Inclusive and exclu- j sive choices are not the only kinds of choices; thus, in ■ | j ! the next section two additional possible meanings of the j i I word "or" will be considered. i j i | TWO ADDITIONAL MEANINGS OF "OR" j i I The two senses of "or" already discussed are insuf- flolent to account for many uses of "or" in permission_____ 96! 1 and obligation utterances. The senses of "or" yet to be presented are, It will be argued, common in permission and obligation utterances, but rather uncommon in state-of- affairs alternations. Nonetheless, they are sometimes used in state-of-affairs alternative propositions? thus, i the discussion will first concern the two new senses as ! used in propositional molecular compounds. The first of these senses will be called the "may or" because of its common use in permitted choices. The sym bol "vm" will be used for the sentential connective, and the symbol "um" will be used for the prescriptive deontic connective. The second sense of "or" will be called the "free or," for it permits all possible choices. The sym bol "vf" will be used for the sentential connective, and "(jf" will be used for the prescriptive deontic connective. i The May "or" A state-of-affairs alternative employing the may "or", i.e., "p vm q", is true if either p or q is true or neither p nor q are true, but false if p and q are true. The truth-functional definition of "p vm q" is as followst P q. P v m q T T F F T T T F T F F T ; This definition is in contrast with the definitions of the ! inclusive and exclusive "or" given below» L __________________________ ____________________________________________ __________________________________________________________________________________ 97 P V q p q P Ve g T T T T T F F T t F T T T F T T F T F F F F F F If a person knew that two states-of-affairs might be the case and that both could not be the case, then he might say, for example, "I think the car was blue, or it was gray," or "I don't remember, but It was probably Tuesday or it was probably Thursday." These examples involve more than an alternation of propositions, for one is compelled in giving examples to insert such words as "I think" and "I don't remember" and "probably." The English word "or" is probably used rarely, if ever, to express such state- of-affairs alternations as defined in the truth table above, but an analogous kind of disjunction is common in I certain permitted choices, as will be argued later. | I First, however, the analysis of the form "p vm q" will be continued, however rare such propositions are, in order to have a firm basis for the discussion of may permitted choices. »vm" can easily be constructed upon the wedge and negation or upon the dot and negation. "(p vm q)" =df, "~(p • q)" and "(p vm q)" =df. "(~p v ~q)", for the truth table lines are the same: p q (p Vm q) = ~ ( p « a ) =(~P V ~ q ) T T F F T F F T T T F T T F T T F T p F T T F T 98 The relationship between the exclusive, the inclu sive, and the may "or" can be seen by the fact that the formula for the exclusive "or11, "(p v q) • ~(p • q)", con tains both the inclusive and may "or"; the first part of the formula being the inclusive "or" and the second part the may "or." This relationship can be schematized as follows s p ve q P V q P Vm q The inclusive and the may "or" are co-equal in level, in the sense that both can be deduced from the exclusive "or" by Simplification. The truth table values of "(p V q)" and "(p v1 1 1 q)" show a reverse relationship, such that the truth table of "(p ve q)" can be derived by combining those of "v" and "vm": p q P V q o Vm q P Ve q T T T F F F T T T T i p p i p ( j i ij\ F F F T F Just as the exclusive "or" can be derived from the inclusive "or" and the Inclusive "or" from the exclusive "or," so the inclusive and exclusive "or" can be derived from the may "or" and negations b q (p V q )=df (p Vm q) vm (~p » ) T t F T F p rp T T F T F T T T F F F F T F T 99 ; p q (p ve q)=df (p Vm q ) « ~(~P * ~q) T T F F F T F i F T T T T T F T F T T T T F F F F T F F T This analysis does not suggest that the may "or" should be taken as the basic "or" from which the others ! are constructed, but only that the choice of the basic j "or," whether "v", Mve", or "v1 1 1 ", must be made on other grounds than that all others can be constructed from it, for, as we have seen, any one of the three "or's" can be, j with other connectives, the base for the other two. j i The reader may have already noted the relation of the may "or" and the stroke ("1").^ The may "or" and the stroke are identical in truth values P vm q pJ.q T T F F F T T T T F T T F F T T Thus, as with the stroke, so from the may "or" all other functions can be definedi ~p=df (p vm p) (p • q )=df [(p Vm q) vm (p vm q)] (p V q)=df [(p vm p) vm (q vm q)] (p z) q)=df [p Vm (q Vm q)] The Free "or" The second additional sense of "or" is called the free "or" and symbolized as "vf". This sense of "or" is 100 perhaps even more uncommon as a state-of-affairs alterna tion, but it is relatively common in choice alternations. The truth value of "p vf q" is always true. Defined in terms of inclusive alternation, conjunction, and negation, the free "or" would be as followsi P q (p vf q) =df [(pvq) V~(p » q)~l T T T T T F T i F T T T T T F ! T F T T T T F j p p j F T T F All possibilities are open, The alternative proposition "(p vf q)" is true if p is true, if q is true, if both are true, and if neither is true. The maker of a statement expressing a proposition of this form would not be making much of a statement. In effect, he would be saying maybe j I either, maybe neither, maybe both. j j Obligatory May "or" Choices j . . . . — . . . . j An obligatory choice of the may "or" type would obli gate one to select one alternative or the other and forbid him to take both alternatives, and yet permit the skipping of both alternatives. In effect, it allows the exclusive choice between two acts, but allows skipping the choice altogether. This kind of choice is equivalent to obli gating or advising one not to do both, and it is also equivalent to obligating that if one act is chosen then the other must be forborne. Obligatory choices of this kind are difficult to think of and seem rare in ordinary 101 I speech. The fact that two choices are mutually exclusive is not sufficient for this kind of obligation. Thus the following example would not qualify as an example of this kind of choice obligation* "If you go on vacation you j I ought to go to Hawaii or to New York." Even if it were j j not possible in a particular time period and on a particu lar budget to go both places, these alternatives would not qualify the example as a may "or" choice, for the idea is that one be obligated to refrain from choosing both of two alternatives, not that the alternatives are mutually ex clusive. Thus, if someone said, "You must choose either to buy the sweater or the slacks," and what was meant was that "If you choose, you must choose either the sweater or the slacks," then he would have issued an obligatory may choice. Perhaps this could be said more economically, "You ' may not have both." j The principle of obligatory may choice is that an obligatory may choice excludes or rules out the doing of both (or all) of the disjoined acts and compels the dis junction of the other possible combinations of the acts and their negations. The definition of the obligatory may "or" choice is as follows* 0(A Um B) -pfAn by E p(~a n b) p( a n ~b) p( ~a n ~b) 102 I It Is obligatory to choose either A or B or neither and i forbidden to choose both. Obligatory Free "or" Choices The principle of an obligatory free choice is that an obligatory free choice compels the doing of some combina tion of the disjoined acts and their negations. The defi nition of "0(A Uf B)" would be as followsi 0(A Uf B) rP( A n bT ~p(~a n b) -p( a n b) p ( ' ■ mA . n ~b ) 0 This kind of obligation could only be a case where one is obligated to make a choice, as opposed to letting others do it or to waiting for whatever will be, and where the choice is completely open. Permitted May "or" Choices ; A permitted may "or" choice is a common kind of ; choice situation presented by parents to children. Sup pose a mother says to her child, "You may have candy or I you may have ice cream." If this disjunction were meant ! in either the exclusive or Inclusive sense of "or," then i ; the mother would be saying, "You must have at least one of \ | the two treats." If the child chose to reject the treat j ! altogether and take neither, would this violate the per mission? Clearly such choices offered by mothers do not rule out the possibility of both alternatives being 103 ; rejected. A may choice is a permissive choice— the child may choose— it is not a forced choice where the child must choose one or the other. If the mother presented the child with the choice situation between going to the circus or going to the j movies, she would not necessarily be demanding a forced choice between the two such that the child could not re ject both alternatives. If the mother offered a choice between going to the circus or staying home, then the choice might be of the may, or exclusive, type. If the child chose to reject both alternatives and choose an other, say, going to visit his grandmother, then the moth er might say no, indicating that the choice was exclu sively between going to the circus or staying home, A j I I choice between taking his medicine or getting a spanking | would not be a may choice but a must choice, presumably of the exclusive type, Irving Copi gives the example of a mother giving her i child a choice between "a cookie or a piece of cake” as an I : exclusive "or." Surely this example has to be a mistake, for Copi describes the situation by saying: "When a ■ mother succumbs to her child's teasing and gives permls- I j sion to take ’a cookie or a piece of cake,1 it would be a | backward or disobedient child who helped himself to both. i i t I j But surely the choice does not preclude the possibility of { not choosing either a cookie or cake. The mother, of 104 : course, may become angry at the child and insist that since the child had begged and teased for a treat, he must now eat the cake or the cookie, but the mother would have changed the alternative to the exclusive sense. Quine makes the same error as Copi in giving the fol- I j lowing as an example of exclusive alternation* "In an = example given by Tarski it is supposed that a child asks j his father to take him to the beach and afterwards to the movie. The father replies, in a tone of refusal, 'We will i i | go either to the beach or the movie'.Quine and Tarski, I i ; of course, may be correct if the father intends definitely to go with his son to the beach or to the movie, but re- : fuses only to go both places. But if the father is offer ing a permitted choice, then surely he would not forbid the not going to either place. Milton Fisk, in giving an example of exclusive alternation, says, "When a-waitress says you can have either pie or sherbert with your meal, she is spelling out a policy of refusing to honor a demand for both."-* But there is no policy of denying the right i to have neither; thus "You may have pie or sherbert with ; your dinner" is a may alternation. The principle of permitted may choice is that a per- i | mitted may choice excludes or rules out the doing of both I | (or all) of the disjoined acts, and includes or rules in j | any of the other possible combinations of the acts and i ! their negations. The definition of a permitted may "or" i choice is as followst P(A Um B) ~P( A n b7 p(~a n b) p( a n ~b) p(~a n ~b ) Since three of the alternatives indicated by the tabula tion are permitted, but one is forbidden, it would make i the disjunctive choice between the three permitted alter- j natives obligatory. Thus, as with exclusive and inclusive choices, the distinction between permission and obligation j fades. The definition of "P(A Um B)" can be considered identical with that of "0(A um B)"i P(A Um B) ~P{ A H B) | r — P (~A n B) ; o h p( A n ~B) | i — p(~a n ~b ) ! Permitted Free “or1 1 Choices | Some choices are free and some are restricted. Only j the free "or" permits a free choice and carries no obli- ! gation. Consider the example of the hostess who says to her guest, "You may have a roast beef sandwich or you may have a turkey sandwich." If the quantity of food is re stricted, then she might be offering a may choice. The I choice could not be exclusive, for surely she does not , intend to force the food upon her guest— although in some ; cultures and sub-cultures it amounts to this. If there is i plenty of food and the hostess Is not the Aunt Verda type 106 who insists that everybody eat, then she may mean merely that she has roast beef and turkey, and she Is offering a choice. It is a choice such that one may have one, the other, or both, or neither. In a sense, it is an empty choice, and perhaps better expressed by such utterances as "You may have A and B if you want," The principle of per mitted free choice is that a free choice includes or rules in all possible combinations of the disjoined acts and their negations. The definition of the form "P(A B)" is as follows* P(A Uf B) p( A n bT p(~a n b) p( a n ~b) p ( ~a n ~b ) In some deontic realm, if all acts which are not expressly permitted are forbidden, then the free choice permission would be a significant statement of freedom of choice. It is the only free choice. It is the only kind of permitted choice utterance that is without restriction. And thus it is the only permitted choice utterance that does not imply obligation and forbiddenness. Summary of Permitted and Obligatory May and Free Choices May permitted choice P(A Um B) ~p( a n bT p(-*a n b) p( a n ~b) p ( ~a n ~b ) 107 May obligatory choice 0(A Um B) ~P( A n bT r p (~a n b ) 0 r- P ( A f l ~B) u p(~a n ~b) Free permitted choice P(A Uf B) P( A h bT p (~a n b ) p( a n ~b ) p ( ~a n ~b ) Free obligatory choice 0(A Ur B) rP( A O Bj -p(~a n b) -p( a n ~b) — p (~a n ~b) NEGATED PERMITTED AND OBLIGATORY CHOICES Negated choices are choices that are either not per mitted or not obligatory. A "~P" choice is a choice that is ruled out, forbidden, not allowed, or not permitted. A "~0" choice is a choice that one Is not obligated to make. Non-Permltted Choices A permitted inclusive choice permits the doing of both of two acts or one of the acts, and forbids the doing of neither of the acts. If one is not permitted to make such an inclusive choice, then he would be permitted only to refrain from doing both acts, and also obligated to re frain from doing both actsi ~p(a n b) ~p( a n b7 ~p ( ~a n b ) ~p(An ~b ) o(~a n ~b ) Not permitting an exclusive choice between two acts would not allow the choosing of one alternative or the other, but permit the doing of both or neither: ~P(A ue b ) P( A n bT ~p ( >mA n b ) ~p( a n ~b) p(~a n ~b) Not allowing or not permitting a choice of the may type would be to disallow the choosing of one of the al ternatives and the skipping of both alternatives, while permitting and obligating the doing of both alternatives: ~P(A Um B) 0( A n b7 ~p (~a n b ) ~p (An ~b) •~p ( ^ mA n ~b ) Not permitting a free choice would be defined as follows: ~P(A ljf B) ~P( A n bT ~p(~a n b) ~p( a n ~b) ~p(~a n ~b ) The form "~P(A B)" seems, in a sense, to be contradic tory, for if the tabulation exhausts all of the possibil ities of doing two acts in relation to one another, then if one were not permitted to do any combination of doing 109 and not doing, he would be forbidden to act and not to act. If there were a choice between buying a motorcycle and buying a sports car, then not permitting, or forbid ding, an inclusive choice between the two, "~P(M U S)", would, in effect, require the not buying of either vehicle. If an exclusive choice were forbidden, "~P(M ue S)", then one must either buy both or neither. If a may choice be tween the motorcycle and the sports car were forbidden, "~P(M um S)", then one would be forbidden to choose one or the other or neither and thus must buy both. Expressions such as "You may not do such-and-such or so-and-so" com monly employ the inclusive sense of "or." But the may "or" is also often used, as when someone says, "You are not allowed a choice," meaning "You must do both." Using the example above, if a free choice were not permitted, "~P(M S)", then the effect would be to say, "You may not buy a motorcycle and a sports car," and "You may not buy just a sports car," and "You may not buy just a motorcycle," and "You may not buy neither a motorcycle nor a sports car." If one were forbidden all these alter natives, then one must, of necessity, disobey the author- j ; lty who asserts an utterance of the form "~P(A B)". j \ ' ■ j Non-Obligatory Choices | The deontic qualifications of non-permltted choices j ; j ■ of the various kinds has been the reverse of permitted 110 choices. This kind of reversal will not be the case for non-obligatory choices. An utterance that a certain kind of alternative choice Is not obligatory Is a declaration that one does not have to choose between a certain set of alternatives. If one is not obligated to make an inclusive choice, then he is not obligated to do act A and B, and not obli gated to do just one of the acts. The form "~0(A u B)" would seem to be silent as to the skipping of both alter natives! thus n ~BM is indifferent. The definition of non-obligatory inclusive choice is as followsi ~0<A u B) ~0( A n B) ~0(~A n B) ~0 (An ~B) i(~a n ~b ) An utterance that one is not obliged to make a cer tain exclusive choice would give information about the non-obligatoriness of n~A and B" and "A and ~B", but would give no information about the doing of both alternatives or the skipping of both alternatives! ~0(A ue B) i( A n §7 ~o(~A n b) ~o(An ~b) I(—A n ~b ) Similarly, the definition of a non-obligatory may choice would be as follows! Ill ~0(A Um B) i( A n bT ~o (~ a n b) ~o( a n ~b) ~0 ('■vA n ~b ) The form f , ~0(A B)" is simply a disclaimer as to any obligation to make a choice between two actst ~Q(A B) ~0( A D B7 ~0 (~A n B) ~0( A n ~B) ~0(~A n ~B) Summary of Non-Permitted and Non-Obllgatory Choices Non-permitted Inclusive choice ~P(A U B) ~P( AnBl ~p ( n b ) ~p( a n ~b ) o(~A n ~b) Non-permitted exclusive choice ~P(A ue B) P( A n B) < ■ —p (~a n b ) ~p( a n ~b) p(~a n ~b) Non-permitted may choice ~P(A Um B) o( A n bT ~p ( n b ) ~p(An ~b ) ~p ( ~a n ~b ) Non-permitted free choice ~P(A Uf B) ~P( A n Bj ~p (~a n B) ~p(An ~b) ~p ( ' > a n ~b ) 112 Non-obligatory inclusive choice ~0(A u B) ~0( A n B) ~0(~A n B) ~0 ( A f l ~B) X (' ' A . n ~B) Non-obligatory exclusive choice ~0(A Ue B) i( A n b7 ~o (' mA n b ) ~o ( A n ~b ) i(~a n ~b ) Non-obligatory may choice ~Q(A Um B) I( A n Bj ~0(~A n B) ~0 (An ~B) ~0 ( ~A n ~B ) Non-obligatory free choice ~0(A uf B) ~o( A n bT ~o (~a n b ) ~o( a n ~b ) ~o ( n ~b ) I CONCLUSION A system of analysis has been adopted that displays all of the posslbilities-of doing and not doing two acts in ; relation to each other. This system of analysis was used i to stipulate definitions for various kinds of permitted andl i i | obligatory choice utterances. It must be remembered that i ; : the system is only one of systematically laying down def- : i initions, and not a decision procedure for determining the j ; j ' validity of inferences. The system is a guide to our j ; j 113 Intuitions of the possible meanings of various kinds of permitted and obligatory choice utterances. The analysis proceeded by first laying out the basic schemes for permitted and obligatory conjoined acts. Then the meanings of inclusive and exclusive permission and obligation were given. Two additional meanings of the English word "or" were suggested. These two meanings are uncommon in making statements about alternative states-of- affairs, but common in making permission and obligation utterances. Four kinds of permitted and obligatory choices were identified! permitted and obligatory inclusive choices* permitted and obligatory exclusive choices* permitted and obligatory free choices* and permitted and obligatory may choices. Only free permitted choices are without restric tions and carry no obligations. Inclusive, exclusive, and may permitted choices carry the same restrictions as ob ligatory inclusive, exclusive, and may choices. Thus permissions of these three types imply obligations. Only an exclusive permitted choice is a forced choice between two (or more) alternatives. If a person is given a choice ! i : | of the inclusive type, he may avoid the choice between two j j (or more) alternatives by choosing both (or all) of the j i j ; alternatives. If a person is given a choice of the may i j i ! type, he may avoid the choice between two (or more) alter- j natives by rejecting both (or all) of the alternatives. 114 An exclusive choice is the most restrictive, allowing only two possible combinations of two acts. An inclusive choice is less restrictive, because it allows the choice of either of two alternatives or both of the alternatives. A may choice is freer, for although it offers no more possible combinations than an inclusive choice, it allows the skip ping of the choice between two acts altogether by rejecting both alternatives. A free choice is, of course, the least restrictive of all, for it allows all possible combina tions of two acts and their negations. A summary of the definitions and the corresponding equivalencies which may be concluded from the definitions will be given in the following chapter. The present chap ter will form the base for the analysis of some of the logical operations involved in the making of permitted and obligatory choice utterances. 115 NOTES iThe Language of Morals, p. 27. ^For a discussion of the stroke, see Irving Copi, Symbolic Logic (New York* Macmillan, 1967), pp. 266-267. and P. F. Strawson, Introduction to Logical Theory (New York* John Wiley, 1952), pp. 96-97. ^Introduction to Logic (New York* Macmillan, 1961), p. 2 ^ 0 . ^Methods of Logic, p. k . Modern Formal Logic (Englewood Cliffs, N. J.» Prentice Hall, 196^), p. 14-. CHAPTER V THE LOGIC OF PRESCRIPTIVE PERMITTED AND OBLIGATORY CHOICE In the previous chapter, the basic meanings of cer tain kinds of permitted and obligatory choice utterances were examined and definitions were given. The task now is to develop certain principles and patterns of inferences that operate upon the various kinds of choice utterances that have been defined. The development of acceptable principles of inference and corresponding formal patterns will depend, first, upon some preliminary assumptions concerning the interdefinability of the deontic modes, the inference from "ought" to "may," and the commutation of acts. Second, the analysis depends upon certain prin ciples and patterns that can be derived by an inspection of definitions of the kind developed in the previous chap ters, The balance of the principles are deduceable from the basic assumptions and those derived from the defini tions . PRELIMINARY ASSUMPTIONS At the outset, certain inference principles will be accepted as correct principles of prescriptive deontic logic. These are the principles of the interdefinability of "P", "0", and "F", the inference from "ought" to "may", and Commutation. The principles will be given as formulae and sometimes also as rules. Examples of the formulae 117 will be labeled by the letters "PDIP," which stand for "prescriptive deontic inference principle," and will be numbered and also named. Within the formulae the symbols and " si" will be used to Indicate inferential moves. The "ergo" symbol, stands for an implication relationship and may be read as "implies" or "yields" or "therefore." The symbol " tt" stands for a biconditional relationship and may be read as "is equivalent to" or "mutually Implies." The reason for using the symbols and " i : " instead of the conditional and biconditional symbols "=>" and is that these symbols will be defined (in the following chapter) as conditional and biconditional relationships between the acts and conditions for action, whereas the symbols and " »" are used for logical relationships between ut terances permitting or obligating certain acts. The rules of interdefinability were given in the pre vious chapter as follows! In changing a "P" expression to an "F" expression, and vice versa, change the deontic oper-j ator and change the negation qualification of the operator. In changing an "F" expression to an "0" expression, and j vice versa, change the deontic operator and change the negation of the act. In changing a "P" expression to an "0" expression, and vice versa, change the deontic oper ator, change the negation of the operator, and change the 118 negation sign of the act. Formulae corresponding to the above principles are as followsi PDIP 1. Principles of interdefinability a. Interdefinability of "P" and "F" PA 1i ~FA P'mA i t ~F~A ~PA n FA —P~A tt F—A b. Interdefinability of "F" and "0" FA it 0~A F~A i t OA ~FA 11 ~0—A ~F—A i t ~0A c. Interdefinability of "P" and "0" PA 1 1 ~0~A P~A 11 ~0A ~PA 1 1 0—A ~P 'mA i i 0 A The principle that "ought" implies "may" is that if anj j act is obligatory, it is also permitted. From an expres- j sion, either molecular or atomic, that is qualified by the j deontic operator "0", one may infer the same expression qualified by "P". One may infer "P" from "O" by this principle, but not "O" from "P". It must also be noted that the negation sign does not operate freely in the use of this principle. Though the act may be negative or affirmative, the operator may not be negative. Thus the following are not correct instances of this principlei "~0A —PA" and 0—A —P—A". The following are formulae exemplifying this principlei 119 PDIP 2. "Ought" Implies "may" OA /. PA 0 ~ k P~A The order of the acts in a conjunction expression or an alternation expression does not affect the meaning of the expression. The following definitions, for example, differ only in the order of the acts: P(A U B) P(B U A) p( A n B) p{ B n a! p (~a n b ) p (~b n a ) p( a n ~b ) p( b n ~P(~A. f l ~B) ~P(~B D >^A) Thus, the principle of Commutation is accepted as a prin ciple applicable to prescriptive deontic logic. The fol lowing forms exemplify this principle: PDIP 3. Commutation P(A U B) : : P(B U A) 0(A U B) : : 0(B U A) P(A n B) : i P(B n A) 0(A n B) : : 0(B 0 A) "OA" and "~PA" are stronger utterances than "~0A" and "PA" because they command or forbid. The expressions "ought," "must," and "may not" are stronger than "do not have to" and "may," Certain strong deontic utterances may be said to contain or imply certain weaker ones. If some- i one said, "You may not take the day off," then it would i follow, perhaps trivially, that the person to whom the ; utterance Is directed may refrain from taking the day off. j Similarly, if a general were ordered to bomb a certain j ; sector of the enemy territory, then it would follow that 120 : he, the general, is not obligated to not bomb that sector of enemy territory. These inferences seem trivial and scarcely worth mentioning, but it will be shown later that ; they will prove valuable in establishing other more impor tant deontic inference principles. i The principles allowing inferences from certain ; j stronger to weaker deontic expressions may be given as follows* An expression not permitting an act may be changed to an expression permitting the not doing of that I act by changing the symbol "~P" to "P" and by changing the j negation sign of the act; an expression obligating an act may be changed into an expression not obligating the not doing of that act by changing the symbol "0" to "^0" and by changing the negation sign of the act. The following are j correct prescriptive deontic inference patterns* PDIP Inference from strong to weaker deontic utter ances a • ~PA P~A ~P~A PA b. OA .. ~0~A 0~A ~0A I The deontic principles exemplified by these formulae do ; not have to be assumed, as were the principles exemplified I by PDIP 1 and PDIP 2, for these can be derived from the I previous assumptions, as follows* | PDIP 4 a, 1. ~PA | 2. 0~A from 1, by 1 c ! 3. P~A from 2, by 2 121 PDIP 4 b. 1. OA 2. PA from 1, by 2 3, ~0~A from 2, by 1 c SUMMARY OP THE DEFINITIONS AND EQUIVALENCIES OF PERMITTED AND OBLIGATORY CHOICE UTTERANCES Inclusive permitted and obligatory choice P(A U B) 0(A u B) p( A n b7 r p ( A n b ) p (~a n b ) oh p (~a n b) p ( a n ~b ) l_ p ( a n ~b) ~p(~a n ~b) ~p(~a n ~b) Exclusive permitted and obligatory choice P(A ye B) 0(A Ue B) ~p( a d bT ~p( A n bJ p (~a n b ) p (~a n b) p( a n ~b) 0 u p( a n ~b ) ~p(~a n ~b ) ~p(~a n ~b ) May permitted and obligatory choice P(A Um B) OfA Um B) ~p( a n bT ~p ( a n b7 p (~a n b ) r f (~a n b ) p( a n ~b) o h p( a n ~b ) p (~a n ~b ) p (~a n ~b ) Free permitted and obligatory choice P(A yf B) 0(A Uf B) pi a n bT — p ( A n b7 p(~a n b) p( a n ~b) p( ~a n ~b) p(~a n b) p( a n -b) p ( n ~b ) Inclusive non-permitted and non-obligatory choice ~P(A U B) ~0(A U B) ~P( A n B) ~0( A n B) ~p(«xA n b) ~o (~a n b ) ~p( a n ~b) ~o( a n ~b) o(~a n ~b) i(~a n ~b ) 122 Exclusive non-permitted and non-obllgatory choice ~P(A Ue B) ~0(A ue B) p( a n bT I T T n b7 ~p (~a n b ) i —o (<~ a n b ) ~p ( a n ~b ) ~ o ( a n ~b ) p ( ~a n ~b ) i ( ~a n ~b ) May non-permitted and non-obligatory choice ~P(A um B) ~0(A um B) o( A n bT i ( A n b7 ~p (' • ■ A n b ) ~o ( ~a n b ) ~p ( A n r-'B) ~o ( A n ~b ) ~p (~a n ~b) ~o(~a n ~b) Free non-permitted and non-obligatory choice ~P(A L)f B) ~0(A uf B) ~p( A n §7 ~o ( A n bT ~p(~a n b) ~o(~a n b) ~p(An ~b) —• o(An ~b) ~p(~a n ~b ) ~o(~a n ~b ) Certain equivalencies may be read off these defini tions. The definitions indicate the equivalencies just as a truth table analysis can show the equivalencies that follow from a certain truth table definition of a propo- sitional compound. "p v q" is equivalent to "(p • q) V (~p • q) v (p • ^q)1 1 and is equivalent to "~(~p • ~q)". Similarly, "P(A U B)" is equivalent to "P[(A n B) u (~A n B) u (A n ~B)3" and equivalent to "~P(~A n ~B)". The following are the formulae derivable from the definitions summarized abovei Inclusive permitted choice P(A U B) ti P[(A n B) U (~A n B) U (A f) ~B)] P(A U B) tt ~P(»A. n ~B) 123 Inclusive obligatory choice 0(A u B) i t 0[ (A n B) U (-A n B) U (A n ~B) 0(A U B) u ~P(~A n ~B) Exclusive permitted choice P{A ue B) i t P[(~A n B) U (A n ~B)] p (a ue b ) t t [~p(a n b ) n ~p (~a n ~b )] Exclusive obligatory choice 0(A Ue B) n 0[(~A f l B) U (A D ~B)] o (a ue b ) > i [~p (a n b) n ~p {~a n -b)] May permitted choice P(A Um B) t i P[(~A n B) u (A n ~B) u (~a n ~B)] P(A Um B) i t ~P(A n B) May obligatory choice 0(A Um B) II 0[{~A n B) u (A n ~B) u (~a n ~B)] 0(A um B) I t ~P(A n B) Free permitted choice P(A Uf B) i t P[(A n B) U (~A n B) U (A n ~B) U ( ~a n ~b ) ^ Free obligatory choice 0 (A Uf B) i t Of (A n B) U (~A n B) U (A f l ~B) U (-A n ~b )2 Inclusive non-permitted choice ~p (a u b) it [~p (a n b) n ~p (-a n b) n ~p (a n ~b )] ~P(A ( J B) i t 0 (~<A f l ~B) Inclusive non-obllgatory choice ~o( a y b) i t [ ^ ' ■ * > o (a n b) n ~o(~a n b ) n ~o(a n ~b )^| 12^ Exclusive non-permitted choice ~P(A Ue B) t i P[(A n B) u (~A D ~B)] ~P(A Ue B) i: [~P(~A fl B) D ~P(A n ~B)] Exclusive non-obllgatory choice ~o (a ue b ) ti [~o(~a n b ) n ~o{a n ~b )] May non-permitted choice ~p ( a um b) i t [~p (~a n b ) n ~p (a n ~b ) n ~p (~a n ~b )] ~P (A um B) II 0(A n B) May non-obligatory choice ~0(A Um B) i: [~0(~A f l B) f l «-0(A f l ~B n ~0(~A f l ~B)] Free non-permitted choice ~p (a uf b) ti [~p (a n b ) n ~p (~a n b ) n ~p (a n ~b ) n ~p (~a n ~b) ] Free non-obligatory choice ~o(A uf b) n [~o(a n b ) n ~o(~a n b) n ~o(a n ~b) n ~o(~a n ~B)] THE RELATION OF PERMITTED AND OBLIGATORY CHOICE AND PER MITTED AND OBLIGATORY CONJUNCTION The prime consideration of the previous chapter and this has been with various kinds of permitted and oblig atory choice utterances. The full understanding of a deontic choice utterance depends upon the understanding of what possible conjunctions of acts and their negations are permitted and/or obligatory. In sentential logic the principle exemplified by De Morgan’s Theorems allows the transformation of a 125 disjunctively compounded proposition into a conjunctively compounded proposition, and the converse. The formulae are often given as follows: ~(p • Q) = (~p v ~q) ~(p v q) 3 (~p • ~q) The summary of the equivalencies that may be read off the ] definitional schema indicate similar forms. Definitions j i were provided for forms such as HP(A u B)n and "0(A u B)", | i i but similar definitions could be given for forms such as "P(~A u ~B)" and H0(~A u B)"; thus the De Morgan type forms given below are not exhaustive: PDIP 5. The transformation of prescriptive deontic disjunction and conjunction— De Morgan Type 1 Inference Principles a. P(A u B) :: ~P(~A f] ~B) j b. 0(A U B) :: ~P(~A f l ~B) c■ ~P(A u B) k 0(~A 0 ~B) | d. P(A Um B) : : ~P(A n B) e. 0(A B) :: ~P(A n B) f. ~P(A Um B) :: a(A / i B) The principles corresponding to the above forms may ; be given as rules, as follows: a. To change a permitted inclusive choice expression I ! into a non-permitted conjunction, change the operator "P" | to "~P", change the symbol "u" to "fl", and change the ! negation signs of the acts? and to change a non-permitted | conjunction expression to an inclusive choice expression, 126 : change the operator "~P" to "P", change the symbol 1 1 fl" to "U", and change the negation signs of the acts. b. To change an obligatory Inclusive choice expres sion to a non-permitted conjunction expression, change the operator "O' 1 to "~P", change the symbol "u" to "fl", and I change the negation sign of the acts; and to change a non- j permitted conjunction to an inclusive obligatory choice expression, change the operator "~P" to "0", change the symbol "fl" to "U", and change the negation sign of the operators. c. To change a non-permitted inclusive choice ex- ■ pression to an obligatory conjunction expression, change the operator "~P" to "0", change the symbol "J" to "fl", I ■ I I and change the negation sign of the acts; and to change an ! i : I obligatory conjunction expression into a non-permitted j ; i : inclusive choice expression, change the operator "0" to j , , ~P, ‘, change the symbol "fl" to "Li", and change the nega tion sign of the acts. d. To change a permitted may choice expression to a ; ; non-permitted conjunction expression, change the operator : »p" to "~P", and change the symbol »um" to "fl"; and to j change a non-permitted conjunction expression to a per- j mitted may expression, change the operator "~P" to "P", ! and change the symbol "n" to "um". I | e. To change an obligatory may choice expression to non-permitted conjunction, change the operator "0" to 127 "^P", and change the symbol "u1 1 1 " to "n"t and to change a non-permitted conjunction expression to an obligatory may choice expression, change the operator "~P" to "0", and change the symbol "fl" to "um". f. To change a non-permitted may choice expression | to an obligatory conjunction expression, change the oper- j ator l , ~P" to "0", and change the symbol "u1 1 1 " to "fl"} and i to change an obligatory conjunction expression into a non-j permitted ma.v choice expression, change the operator "0" ! to n~P", and change the symbol "fl" to , 1Umi'. Some possible De Morgan type inferences must be ruled out. The forms "~0(A U B) P(~A f l ~B)" and "~0 (~A ( 1 ~B) P(A u B)" would have to be ruled out, for the schematic representation of "~0(A u B)" and , , ~0(~A f l ~B)” are as | follows* I The form "~0(A u B) is silent as to the permittednass of ”(~A u ~B)H, and the form "~0(~A 0 ~B)" is silent as to ! the status of any other combination of the acts. Although ; inferences of this kind may not be made from non- I obligatory disjunctions or conjunctions, inferences may be : made from permitted or obligatory disjunctions and con- ! junctions to non-obligatory disjunctions or conjunctions. j The following are additional De Morgan type inferences. 0(A U B) 0( A f l B) 0(~A n B) 0 ( A f l —B1 ) i(~a n ~b ) ~Q(~A f l ~B) i( A l l B) i (~a n b) I( A f l ~B) ~0 (~A f l ~B) 128 They differ from the original set in that they are impli cations rather than biconditionals» PDIP 5 continued! g. P (A 0 b ) ~o(~a n ~B) h. 0 (A u B) /. ~0 (~A f l ~B) 1. P(~A n ~B) .. ~0 (A c J B) J. 0 1 n ~B) ~0(A u B) k. P(A u m b) . ~0(A I I b ) 1. 0 (A 0 m b ) . ~o(a n b ) m. P(~A n ~B) ~o (~a um n. 1 o n ~B) ~0(~A um The above forms are easily shown to be correct by deducing them from forms in the earlier list of De Morgan type inferences plus the principles previously estab- : lished. For example, PDIP 5 h, "0(A U B) ~0(~A n ~B)"f can be derived in the following wayi 1. 0(A u B) 2, ~P(~A n ~B) from 1 by 5 b 3* P~(~A 1 1 ~B) from 2 by if a k . ~0(~A f l ~B) from 3 By 1 c The others can be derived by similar arguments. The prin ciples corresponding to these formulae will not be given, 1 as rules for them follow the same pattern as the rules ' given earlier, i ! De Morgan Type Two Principles ! The next question is whether a De Morgan type infer- | | ence may be made within the scope of a prescriptive deontic operator, such as the inference from "P(A U B)" to "P~(~A n ~B)", and from "0(A u B)" to "P~(~A n ~B)". Inference forms such as these can be deduced from the De Morgan type forms already listed, plus other forms that have been accepted. The following are correct De Morgan i type principles: i i PDIP 6. De Morgan Type 2 Principles ■ a. P (A u B) : : 0~ (~A f l ~B) b. 0(A u B) t i 0~(~A f l ~B) c . 0~(A u B) i: 0(~A f l ~B) d. P(A Um B) it o~(a n b ) e. 0(A um B) :: 0~(A n B) f . 0~(A um B) ti 0 (A n B) g. P(A U B) P~(~A ( 1 ~B) h. 0(A U B) p~(~A r i ~b ) i. 0~(A 0 B) . p (~a n ~b ) j • P (~A fl ~B) p~(a u b ) k. 0 (~A fl ~B) p~(a u b ) 1. P(A om B) , p~(a i i b ) m. 0(A Um B) , p~(a n b ) n. 0~(A Um B) p ( a t i b ) o . p (a n b ) P~(A um B) P. o(a n b ) P~(A Um B) These forms can easily be demonstrated to be correct i within this system. Simple proofs will be given for 130 PDIP 6, a, c, g, and i. The proofs for the forms In volving may choices are similar to the following: PDIP 6 Q* * 1. P(A u B) 2. ~P (~A f l ~B) from 1 by 5 a 3. 0~(~A n ~B) from 2 by 1 c ~P(~A 11 ~B) from 3 by l c 5. P(A o B) from 4 by 5 a PDIP 6 c . 1. 0~(A u B) 2. ~P(A u B) from 1 by 1 c 3. 0 (~A ( 1 —B) from -2 by 5 c ~P(A U B) from 3 by 5 c 5. 0~(A j B) from by 1 c PDIP 6 S» 1. P(A U B) 2. —p ( ~a n ~b ) from 1 by 5 a 3. P~ (~A f l ~B) from 2 by a PDIP 6 i . 1. 0~(A u B) 2. —P(A u B) from 1 by l c 3. 0 (~A f 1 ~B) from 2 by 5 c P (~A f ) ~B) from 3 by 2 The analysis of the relation of prescriptive deontic ; conjunction and disjunction (the De Morgan type princi ples) depends upon the preliminary assumptions about the interdefinability of "P" and "0", and upon the assumption that "ought implies may," and upon the adequacy of the I definitions formulated in the previous chapter. If the : analysis is correct, then it has been shown that pre- ! scriptive deontic logic allows for inferences similar to I De Morgan's Theorems in sentential logic. The principles i I developed here are similar, but far more varied and com- ! plex than the principles of sentential logic. The impor- 1 tance of De Morgan’s Theorems in sentential logic cannot i j be doubted. Similarly, the importance of De Morgan type 131 ; principles in prescriptive deontic logic is taken for granted. De Morgan type inferences are of great impor tance in constructing more complicated arguments involving normative utterances, commands, advice, and so on. i PRESCRIPTIVE DEONTIC DETACHMENT AND COMBINATION PRINCIPLES I j A combination principle is a principle of logic where-! by a more complex form may be produced by combining simpleij i forms. The combination rules in sentential logic are Addi tion and Conjunction. A detachment principle is a princi ple by which a simpler form may be released or detached i from a more complex form. Examples of detachment princi ples in sentential logic are Modus Ponens. Modus Tollens. j Simplification, and Disjunctive Syllogism. Modus Ponens j and Modus Tollens type inferences will be considered in a j i later chapter. In this section the primary concern will be! with detachment rules similar to Simplification and Dis junctive Syllogism, and combination principles similar to Conjunction and Addition, The first consideration will be with principles of Simplification and Conjunction, and with principles like those that von Wright called "laws of Deontic Dissolution." Next, the principle of deontic Addition and the Alf Ross Paradox will be examined, and following this discussion, deontic Inferences like the Disjunctive Syllogism will be examined. 132! i Simplification. Conjunction. and Deontic Dissolution There Is no reason to reject the operation of prin ciples like those of Conjunction and Simplification upon utterances that are deontically qualified. If one were separately permitted or obligated to do certain acts, then! it would follow that he were permitted or obligated to I perform the one act and the other act. Thus "PA, PB PA ! f l PB" would be a correct inference. Also, if one were permitted or obligated to perform an act and also per mitted or obligated to perform another act, then it would follow that he were permitted to perform one of the acts. Thus, patterns corresponding to Conjunction and Simplifica-j tion of the kinds given below are correct: j PDIP 7. Conjunction PA, PB (PA n PB) OA, OB /. (OA n OB) i PDIP 8. Simplification (PA n PB) PA (oa n o b) oa Next, the question is whether similar principles operate when the scope of a deontic operator is affected. In his original calculus, von Wright gave the following forms as laws of the dissolution of deontic operators (see Chapter II)i 0(A . B) = OA . OB P(A V B) a PA V PB OA V OB J 0(A V B) P(A • B) ^ PA . PB In his later work, Norm and Action, von Wright came to question some of these forms.^ His discussion will not be summarized here, for the question being raised Is whether i similar forms are correct forms of Inference In prescrip- j tive deontic logic. The following forms will be considered: p(a n b) (pa n pb) (pa n pb) p(a n b) o(a n b ) (oa n ob) (oa n ob) o(a n b) P(A u B) (PA u p b) (PA u PB) P(A U B) 0{A u B) (OA U OB) (OA U OB) /. 0(A u B) The form "P(A n B) (PA n PB)" is not justifiable, for an expression of the form "P(A f l B)" was taken as the f j form of an utterance that says that two acts are permitted j when both acts are performed, and nothing more. The anal ysis was as follows: P(A i l B) P( A f l B)~ I(~A n B) i( a n ~b) i(~A n ~b ) ! "P(A n B)" conveys the idea that two acts are permitted to- i gether, and is silent as to the permittedness of other | possibilities. The form "PA f i PB" says more than this. | If the principle of simplification operates, then the form I "PA f l PB" would indicate that act A is permitted whether 13^ act B Is performed or not. This reasoning would rule out simplification of the form exemplified by the following formula: "P(A n B) /. PA". On the other hand, the form "PA n PB) P(A f t B)" would seem to be correct, for if one is permitted to per form one act and permitted to perform another act, then it would be the case that he is permitted to perform them to gether. This assumes that the form "PA" means that one is unconditionally permitted to perform that act. If one were permitted to perform some act only upon the condition that some circumstance prevails, or upon the condition of performing some other act, then the symbolism "PA" would not be appropriate. One difficulty In interpreting a form such as "(PA f ) PB) P(A n B)" Is that one may be permitted to perform one act by some permitting authority and per mitted to perform another act by some other permitting authority, yet neither authority may permit both acts. For [ the form "(PA n PB) P(A n B)" to be coherent, a constant authority must be assumed. In sentential logic, the source of an utterance expressing a proposition about some J j state-of-affairs and the one to whom the utterance Is di- | rected is of little importance in examining the logical i i relation between propositions; but in both the logic of j l statements about norms and the use of norms themselves, | both the source and receiver of deontic utterances must be ] i kept In mind. 135 The forms "0(A n B) (OA D OB)" and "(OA l i OB) 0(A i i B)" would seem to be correct. But the analysis of the form "0(A f i B)" was as followst 0(A n B) 0 ( A H B) F(~A l i B) F ( A ( | ~B) F(~A 0 ~B) The obligation to do two acts represented by the form "0(A ji B)" is an obligation to do two things, not two separate obligations. It can be argued that if one were obligated separately, "OA n OB", then the doing of A would satisfy the obligation to do A, though it would not sat isfy the obligation to do B. On the other hand, if one were obligated to do two things, as represented by the form n0(A n B)", for example, obligated to understand the issues and vote in the election, then doing only one would not meet the obligation. Thus the doing of act A would not meet half of the obligation "0(A l) B)"; It would not satisfy the obligation at all. Thus the forms "0(A n B)" and "OA f l QB" are not equivalent. It would follow, then, that "0(A f l B) (OA n OB)" is correct, but that the form "(OA i i OB) 0(A i i B)" is incorrect, for two separate obligations does not seem to lead to the single obligation to do both. Next, the relation of the forms "P(A u B)" and "0(A u B)" to the forms "PA u PB" and "OA u OB" will be consid ered. The symbol for conjunction, "fl", has been used ambiguously to represent a relation either between acts or between prescriptive utterances expressing the permitted- ness or obligatoriness of acts. This ambiguity seems not to pose any problem, but the ambiguity cannot be allowed in the case of the symbol used for choice utterances. Thus, the following are considered to be incorrect infer ence patterns in prescriptive deontic logici P(A u B) PA u PB PA u PB P(A U B) 0(A u B) /. OA U OB OA U OB 0(A U B) These forms are ruled out for the following reasonsi The forms "F(A u B)" and "Q(A u B)n were defined as choice utterances which either permit or obligate an inclusive choice between two or more alternative actions. The form "P(A u B)" corresponds to utterances such as "You are per mitted to choose (inclusively) between acts A and B, it's your choice." Similarly, the form "0(A u B)" corresponds to such utterances as "You must choose (inclusively) be tween acts A and B, it's your choice." The forms "PA U i PB" and "OA u OB" seem best suited to expressions offering j alternative permissions and obligations. Offering a per- I mitted or obligatory choice is not the same as asserting that there are alternative permissions or obligations. The forms "PA u PB" and "OA u OB" should not be counted I i i as well formed formulae in prescriptive deontic logic. j Therefore, the principles of Dissolution which are accepted are the followingi _____________ ________ 137 PDIP 9. Principles of Deontic Dissolution a. PA 1 1 PB P(A ( i B) b. 0(A f l B) OA l i OB) The Principle of Addition and the Alf Ross Paradox One of the paradoxes of deontic logic, known as the "Alf Ross Paradox,involves an implausible inference from such an utterance as "You ought to help Mr. A." to "You ought to help Mr. A. or kill him." This paradox presum ably arises in the context of statements about norms, or rules, or commands, and so forth. As a statement about the existence of a certain norm, "OA" is short for "There is a norm 'OA'." In this interpretation, there is no paradox when one asserts, "It is true that there is a norm 'OA', therefore it is true that there is a norm 'OA' or there is a norm ’OB'." That is, "OA v OB" is true if "OA" is true; this Is simply an application of the prin ciple of Addition. Nonetheless, it seems strange to reason that because there is an obligation to help Mr. A., * therefore there is that obligation or any other obligation,; including the one to kill him. In any case, the Alf j Ross Paradox arises only when dealing with utterances i about alternative norms, and not in connection with ut- i I terances permitting or obligating choices. One might say, [ "There is a command, or order, or obligation that you are to help Mr. A. or to kill him, I don't remember which," 138 the Idea being that the speaker is certain only of one thing, and that is that one of the two commands, at least, was Issued. But if one were issuing the command "I com mand, order, obligate (and so on) you to help Mr. A., or kill him, I donft remember which," then no command would have been issued, A person could, of course, be ordered to make the choice between helping and killing, but if one were merely ordered to help Mr. A. it would not follow that the order implied the choice of helping or killing him. Surely there is no sense in which an utterance like "You ought to do A" can be thought of as implying the utterance "You ought to choose doing A or doing B." If this interpretation is correct, then the effect is to rule out the functioning of the principle of inference known as Addition in relating prescriptive utterances Involving permission and obligation and other modalities, PRESCRIPTIVE DEONTIC LOGIC DISJUNCTIVE SYLLOGISM The principle of Disjunctive Syllogism Is an impor tant principle of inference in sentential logic. The form of disjunctive syllogism is commonly given as "[(p v q) • ~p] id q", It is also given as followsi i (p v q) ! Z E_____ <1 | The logic of the disjunctive syllogism is simple. A proposition of the form "p v q" is true If either or both | 139 of the disjoined propositions is true, otherwise it is false. Thus if "p v q" is true, yet either p or q is false, then the other member of the disjunction must be true • In reasoning about norms, the pattern seems to func tion as it does in sentential logic, "There is a norm •0(A v B)1" could be counted true if there is a norm "OA" or "OB", "p v q" can be the case even though "~p" is the case, as long as "q" is the case. Similarly, "There is a norm 'P(A v B),n can be thought of as being correct, even if it turns out that it is not the case that there is a norm "PA", Further, if it were known that a certain norm system contained at least one of two norms (and possibly both) but not neither, then it would follow that if one were not the case then the other would be. The question raised here is whether a similar form of inference applies to prescriptive deontic utterances. It |is proposed that the following argument form is correct* P(A u B) ~PA OB The form may be expressed as a formula as follows* P(A U B) n ~PA OB jThe conclusion may also be given as "~P~B". The definition i of "P(A U B)" is as follows* 1^0 F(A U B) p{ a n 17 p (~ a n b) p( a n ~b) ~ p (~a n ~ b ) In this definition, lines one, two, and three are quali fied by "P", and line four is qualified by "~P", indica ting that what is not permitted, or disallowed, is the conjunction of the not doing of the two acts. With the additional information that "~PA", the qualification of the area of the conjunction of the two acts must change. Act A is ruled outj thus the conjunction of acts A and B and the conjunction of acts A and ~B are now also ex cluded. Thus, in addition to the fourth line being qual ified by "~P", now lines one and three are also to be so qualified. The new area of the conjunction of the two acts is now qualified as followsi ~P< A U bT 0(~A u B) ~P ( A U ~B) ~P(~A U ~B) This tabulation would be appropriate for the form "~P(A u ~B)". Thus from the premises "P(A U B)" and "~PA" we may conclude "~P(A u ~B)". This form Is equivalent to the form "0(~A 0 B)" by PDIP 5 From this form we can con clude the form "0~A D OB" by PDIP 9* And from this, "OB" may be derived by Simplification, PDIP 8. Thus the fol lowing form Is introduced as an additional form of pre scriptive deontic inference! m-1 PDIP 10. Prescriptive Deontic Disjunctive Syllogism a. P(A U B) n ~PA OB An Inference Involving an obligatory inclusive choice of the form "0(A u B) n ~0A OB" must be rejected for the following reasons* The form "0(A u B)" neither obligates one to do A nor to do B. If a student were told "You are obligated to take the test or write a paper," the student might ask, "Then am I obligated to take a test?" and the answer would have to be, "No." Then the student might ask, "Am I obligated to write a paper?" and the answer again would have to be "No." The teacher might respond, "I am not obligating you to take the test and I am not obligating you to write the paper, but I am obligating you to do at least one of the two." The form "0{A u B)" is silent as to a particular obligation or non-obligation concerning the individual tasks, it says only that a choice of a certain kind must be made. Thus if one re ceived an order of the form "0{A u B)", the additional information that "~0A" would not allow one to conclude that he was obligated to B, for one would be no more ob ligated to B than A. The following inference form is counted as correct ; and may be Justified by the same reasoning as the dis- i I Junctive syllogism pattern involving a prescriptive | inclusive choice utterance* i PDIP 10 b. 0(A u B) n ~PA /. OB I 142 A serious problem in the interpretation of the forms involved in PDIP 10 a and b remains. An instance of the form "P(A u B)" would be an utterance such as "You may choose (inclusively) between working on the program com mittee and working on the finance committee." In a case such as this, a choice has presumably been offered. If it were added, for some reason, that "You are not permitted to work on the program committee," then the conclusion may be drawn that the person is then obligated to work on the finance committee. But it also seems to be the case that the original permitted choice has been withdrawn or modi fied. With the addition of "You are not permitted to work on the program committee," the person no longer has an inclusive choice to choose one of the two committees. We can say that the second premise modifies the first in such a way that the conclusion follows. But the question is, how can any conclusion follow from two premises when the second changes the character of the first? In sentential logic, when the premises "p v q" and "~p" are conjoined the second premise does not alter the truth value of the first premise, but in a sense it would alter its appllca- | tion in actual discourse. If one said something of the i i form "p v q" and then added "~p", a listener might say ) i ! "Then you do not mean 'p v q' but 'q'," Similarly, the ! | addition of "~PA" to the form "P(A u B)M does not change ! the meaning of the form, but it does change its 143 application. "P(A U B)" still means what it does, but it no longer applies to the person to whom the permission was uttered in the same way it would if unqualified. Disjunctive Syllogism and Mixed Modes The forms to be considered next involve mixed formu lae, where the minor premise is not a deontic utterance, but some kind of utterance about action and/or choice. Von Wright and many of his followers have ruled out mixed formulae, but he does not insist that this restriction must be maintained.^ We shall consider arguments such as the following* "You must choose (inclusively) between mowing the lawn or trimming the hedge; thus, if you choose to not mow the lawn you must trim the hedge." The symbols "A", "B", and so forth, have been used to stand for actions, or behaviors, but permitted and obliga tory choices involve two distinct kinds of human actions. First, if one were obligated to do one of two things, then he would be obligated to choose and to do. Similarly, if one were permitted to choose between two things, he would be permitted to choose and to act. Some choices do not involve overt action. Someone might say, "You must choose between a law suit or a settlement out of court"; if the one to whom the remark were addressed chose to be sued, then no action would be required. There is a difference between acting and being acted upon. If a parent demanded i W ' of a child that he choose his punishment, then the choice is all that is required--the action being provided by the parent, Thus when we speak of permitted and obligatory choice utterances, we are speaking about choices prima rily and actions secondarily. The ambiguity will be left to stand, and thus the symbols "A" and "B" will be used to stand for the choice and/or the action. This ambiguity should cause no problems in the present analysis, as long as it is kept in mind in Interpreting particular choice utterances. Sentences describing overt actions, such as going to church, or writing a paper, or taking medicine, might be considered as propositions describing states-of- affairs. But utterances about a choice having been made are not clearly propositions. For one reason, no one but the chooser can say when it is true that he has in fact made a certain choice. But a more important reason is that utterances about choices are probably modal utter ances of a kind. Utterances about what has been chosen suffer from what has been called "referential opacity."** Words such as "know" are different from words such as "is. One could argue that "John is a man, and a man is mortal, therefore John is mortal." But one could not argue that "John knows that a house cat is a small domesticated ani mal, and a house cat is a fellnus domesticus. therefore ]>5 John knows that a cat is a fellnus domestlcus." Quite clearly, John might not know this. Similarly, someone may have made a particular choice, and this choice might be in some sense equivalent to some other choice, but it would not follow that the second choice had been made. The definitions for "P(A u B)" and "0(A u B)" indi cate that if one is either permitted or obligated to make an inclusive choice, then he Is not permitted to skip both alternatives. This choice restriction is expressed in the form "~P(~A n ~B)". If a person is obligated in such a way, then if he chooses to skip one alternative, he is not permitted to choose to skip the other. Or if he acts such as to forbear doing one of the alternatives, then he is not permitted to forbear the other. Thus the following forms would also be correct inference patterns similar to Disjunctive Syllogism: PDIP 10. Prescriptive Deontic Disjunctive Syllogism (cont'd.) c. P(A u B) n ~A OB d. 0(A u B) I ) ~A OB Principles of Obligation Compliance The next question to be asked is "What conclusions j can be drawn about particular choices and/or actions from ! ] I deontic utterances expressing permitted or obligatory 1 I ! f ! choices and statements about particular choices and/or I i actions?" The answer is, in a sense, nothing, for one can I never with certainty conclude what humans will do, no mat ter how much one knows about their duty. It Is within the very nature of rules and norms and commands and advice and the like that the rules or norms can be broken, the com mands disobeyed, and the advice Ignored. One might have enough knowledge about human behavior in general, or enough knowledge about a particular person's behavior in certain circumstances, to predict well, but particular choices or actions or even general statements about human conduct cannot be deduced from deontic premises. The kind of deductions that are often made about the making of choices and the doings of acts from deontic premises are conditional upon one doing his duty, or obeying the com mand, or following the advice, or following the norm or rule. The symbol "R" will be used to mean variously "the rule or rules have been followed, the advice has been taken, the norm followed," and so forth. If one is ob ligated to perform a certain act, then if he obeys the ob ligation the act is performed. The following inference patterns may be added to our list: PDIP 11, Principles of Deontic Compliance a. OA /. (R ; . A) 0~A .. (R .. ~A) b. ~PA (R ;. ~A) j ~P~A /. (R A) ] These patterns suggest a host of problems in inter- |preting both what it means to "A" and "~A" and what it 147 means to follow the rule or command, and so forth. A question can be raised as to whether Intending to do some thing, or deciding or planning to do something, or even attempting to do it, can be counted as fulfilling an ob ligation. Is a norm followed only when an action is per formed, or is it followed by attempting, although perhaps failing, to perform or not perform a certain act? When is an act performed? When it is started, when it is underway, and when it is completed? How does an act differ from a thought, a verbal utterance, an intention, a plan, or a desire? Such questions as these will not be considered} they are simply recognized as problems of interpreting the forms that have been suggested as inference patterns in prescriptive deontic logic. CONCLUSION In the development of the principles of prescriptive deontic logic, certain principles were assumed. These were the interdefinability of the deontic modes, the prin- ; clple that "ought" implies "may," and the principle of Commutation. An additional inference pattern involving certain Inferences from stronger to weaker deontic utter- ; ! ances was derived from some of the assumptions, j The analysis then concerned inference patterns simi- J j lar to De Morgan's Theorems in sentential logic. Two pat- | terns were developed. The first was developed by i ]> 8 inspecting the definitions developed in the previous chap ter, and the second was deduced from the first type and some of the Inference patterns previously developed. The De Morgan type patterns relate choice utterances to con junction utterances. These are important because choice utterances are best understood in terms of what conjunc tions of the choice alternatives are permitted or not per mitted. Following this discussion, patterns similar to the principles of Simplification and Conjunction and certain principles of Deontic Dissolution were considered. It was also concluded that a pattern similar to the form known as Addition in sentential logic does not operate in prescrip tive deontic logic. The final part of the analysis concerned patterns of Inference similar to Disjunctive Syllogism in sentential logic. It was concluded that patterns of inference in volving a deontically qualified major premise and a deon- tlcally qualified minor premise corresponding to the form ; of Disjunctive Syllogism function in prescriptive deontic : | logic. It was also concluded that inference patterns ‘ i ! involving mixed modes, where the major premise is a deon- j i ; j tically qualified choice utterance and the minor premise j | ; j Is an assertion about the choosing and/or doing or not ! doing of a certain act, will yield utterances about the j i ! ! non-permlttedness of other acts in a pattern analogous to j the Disjunctive Syllogism. It was further concluded that the only conclusions that can be drawn from deontic ut terances about the actual choosing or doing of acts must be conditional upon utterances about the doing of one's duty or the following of rules or norms. A summary of the inference forms developed can be found in the concluding chapter. 150 NOTES - 1 -Norm and Action, see pp. 181 f. ^See Chapter II, pp. 37-39. 3"Deontic Logics," American Philosophical Quarterly, p. 136. ^See W. V. 0. Quine, Word and Ob.lect, pp. 1 ^ f,, 195-200; and Benson Mates, "Synonymity," Semantics and the Philosophy of Language, ed. L. Linsky (University of Illinois Press, 1952), pp. 120-125. CHAPTER VI CONDITIONAL PERMISSION AND OBLIGATION Previous chapters dealt with permitted and obligatory choice. Equally important are utterances that permit or obligate behaviors upon some condition or conditions. Hypothetical or conditional utterances often employ such words as "if . . . then," "when . . . then," "in the event that," "only if," "if an only if," and so forth. In sen tential logic conditional relationships between proposi tions are symbolized by the horseshoe ("3") for the condi tional relationship and the triple bar ("=") for the bi conditional or equivalency relationship. In the analysis of the meaning and logic of conditional permission and obligation, the symbols "=»" and "«" will be used for con ditional and biconditional relationships. The first problem in developing patterns of hypo thetical reasoning is to define permitted and obligatory conditional forms, such as "P(A =» B)" and "0(A =* B)", and to determine if these definitions correspond to ordinary uses involving modal words such as "ought," "should," "may," and "if . . . then." The second problem is to determine if inference patterns similar to the principles I j of Material Implication, Transposition, Exportation, and | i Material Equivalence operate upon prescriptive conditional | i forms as they are defined. The final problem is to 151 152 consider the extent to which patterns of reasoning similar to the detachment rules, Modus Ponens and Modus Tollens. operate upon prescriptive conditional deontic utterances. This chapter will be concerned with basic definitions, and the next chapter with inferences involving the defined forms. MEANING AND INTERPRETATION OF CONDITIONAL DEONTIC UTTERANCES Conditional permission and obligation utterances per mit or obligate certain behaviors, choices, or even at titudes, dependent upon certain conditions existing or being fulfilled. These conditions may be actions, atti tudes, beliefs, states-of-affairs, or circumstances. It will be argued that the relationship between the condition for action and the action will be different for obligatory and permission utterances. It will also be argued that two definitions of permitted conditionals will be required, while one will suffice for obligation utterances. In order to distinguish between the two types of permitted condi tional utterances, the symbols "=*" and "=>3" will be used. The capital letters "A" and "B" have been used to represent actions. Often it is difficult to determine if some particular event is an action or not. For example, I do the phrases "becoming an officer," "getting spanked," i | "being punished," describe actions? Also, the conditions for action or other human events are sometimes themselves actions and sometimes states-of-affairs. For the sake of simplicity, the symbols "A" and "B" will be used both for the antecedent conditions and the dependent permitted or obligatory action. This designation should cause no problem, as long as It Is remembered that the symbols are simply place holders standing for various linguistic forms referring to actions and events involving human behaviors. Conditional Obligation Utterances The following examples are common kinds of utterances expressing obligation, advice, commands, and norms or principles of conduct: (1) If it is cold, you ought to wear your overcoat. (2) If you are sleepy, then you should sleep. (3) If there is a fire, you ought to leave the building immediately. (*0 If you offend someone, you should apologize. (5) If someone gives you a gift, then you ought to say "thank you." (6) If the stop light Is red, you must stop. (7) If you are a good American, then you ought to support your president. (8) If anything will promote the general Happiness, you ought to do it.-*- (9) If the evidence is convincing, then you should convict the defendant. 15^ These examples are varied and difficult to charac terize. They range from simple advice to commands, eti quette norms, and general principles. In each of the examples given above, some condition requires some action. In all of the examples, modal words such as "ought," "should," and "must" appear. These words attach to a clause expressing what should follow upon the realization of the condition. Such utterances could be symbolized by the form "A =* OB". This form corresponds to utterance formalizations such as "if A, then ought B," "You are obligated to do B in the event that A," or "You are ob ligated that if A, then do B." Such conditional obliga tion utterances can also be symbolized by the form "0(A =* B)", as long as it is understood that the obligation qualifier is directed toward the consequent of the condi tional and is dependent upon the antecedent. In a format similar to the tabular definitions em ployed throughout this study, an analysis of the above examples follows* (1) If it is cold, you ought to wear your overcoat. You ought to wear your overcoat in the event that it is cold. 0(if it is cold, wear your overcoat) P( cold and wear overcoat; — P(not cold and wear overcoat) ~P( cold and not wear overcoat) L — P(not cold and not wear overcoat) 155 If someone were to advise or command the wearing of an overcoat in the event that it is cold, then surely the advice, if followed, would not permit the not wearing of the overcoat when it is cold. When such advice is given it does not necessarily include the advice that one should not wear an overcoat when it is not cold, nor that when one wears his overcoat it ought to be cold. Further, it must be remembered that the intent of such an utterance is probably to specify the condition and the action in such a way that what is meant is that if it is cold out side and if one goes outside, then he should wear his overcoat, (2) If you are sleepy, then you should sleep. You ought to sleep in the event that you are sleepy, 0(lf you are sleepy, then sleep) -■"p( sleepy and sleep) 0 — P(not sleepy and sleep) ~P( sleepy and not sleep) P(not sleepy and not sleep) Such advice as this would preclude being sleepy and not sleeping, but it would not necessarily preclude being not sleepy and sleeping (for some other reason), (3) If there is a fire, you ought to leave the building immediately. You ought to leave the building in the event of a fire. 156 Of If a fire, then leave the building) r- P( fire and leave the building) — Pfnot fire and leave the building) ~P( fire and not leave the building) Pfnot fire and not leave the building) The advice or command represented by the above utterances would preclude or rule out there being a fire and not leaving the building, but it would certainly not rule out there being no fire and also leaving the building. (4) If you offend someone, you should apologize. You must apologize in the event that you offend. 0 Ofif you offend someone, then apologize) - Pf offend and apologize) - Pfnot offend and apologize) «P( offend and not apologize) u Pfnot offend and not apologize) (5) If someone gives you a gift, then you ought to say “thank you.” You ought to say “thank you" in the event that someone gives you a gift. Of if someone gives you a gift, then say "thank ^------------------------------------ p P( gift and say thank you) — Pfnot gift and say thank you) ~P( gift and not say thank you) -Pfnot gift and not say thank you) It must be remembered that utterances such as these are often elliptical. That is, they are incomplete and depend upon the context and previous experience to specify the missing parts of the context. Also, most of the ut terances are ambiguous, in the sense that they may be utterances directed to particular individuals or may be 157 general utterances of an advising or commanding nature. As general advice or commands, all would be faulty in that their application in certain particular cases could be questioned. For example, it would be inappropriate to advise or command firemen to run from burning buildings or to command police cars or ambulances with sirens blar ing to stop at red lights. The point of view taken here is that although the advice or commands can be and are often uttered as general obligations, they must be inter preted as advice or commands given to someone or some segment of humanity by someone of authority, competence, or respect, at some time and for some purpose. The ques tion being posed here is what does the utterance mean to say, not does it apply to all situations or would it, in some contexts, be bad advice or advice conflicting with other advice. (6) If the stop light is red, you must stop. You must stop in the event that the light is red. 0(lf the light is red you must stop) P( red light and stop) — P(not red light and stop) ~P( red light and not stop) ^ P(not red light and not stop) 0 This example is difficult to interpret. It might seem that the command to stop at a red stop light should pre clude the stopping when the light is not red. It may be obligatory that if the light is not red that you must not stop. In this case the obligation must be considered as 158 ' some kind of a biconditional, and thus the tabulation given would be Insufficient. (7) If you are a good American, then you ought to support your president. You are obligated to support your president in the event that you are a good American. Of if good American, then support your president) — P( good American and support your pres. — Pfnot good American and support your pres. ~P( good American and not support your pres. Pfnot good American and not support your pres. The last line of the tabulation appears to be faulty. Surely one who makes such an assertion would not intend to permit the not supporting of the president, in any event. The condition of being a good American is a pseudo condition. Also, the entire expression is some kind of analytic utterance such that by definition a good American supports his president, and all who do not are not good Americans. (8) If anything will promote the general happiness, you ought to do it. You should do an act in the event that it will promote the general happiness. Ofif will promote the general happiness then do x) — P( promote the general happiness and do x) q — Pfnot promote the general happiness and do x) ~P( promote the general happiness and not do x) Pfnot promote the general happiness and not do x) The utterance above represents a highly general and ab stract moral principle. This utterance is Judged not to 159 be a biconditional, for it seems that the principle sug gests doing whatever will promote the general happiness, but not that only acts which promote the general happiness are to be done. The principle does not suggest that one refrain from an act, say, "scratching one's nose," merely because that act cannot be connected to the general good. (9) If the evidence is convincing, then you should convict the defendant. You should convict if the evidence is convincing. 0(lf the evidence is convincing, then convict 1 P( evidence is convincing and convict) ~P(not evidence is convincing and convict) ~P( evidence is convincing and not convict) P(not evidence is convincing and not convict) This utterance is a biconditional, and thus not only is it ruled out that you not convict if the evidence is con vincing, but that one convict if the evidence Is not con- vinc ing. Though the examples are quite different in many re spects, they indicate that ordinary uses of utterances employing words such as "must," "should," and "ought" to perform the act of expressing conditional obligation cor respond to the following definitions of conditional and biconditional obligation utterances* 0(A =» B) 0(A => B) r-pc a n b) p p( a n b) 0 P (~A O B ) q ~P (—>A n B) ~p( a n ~b) ~p( a n ~b) L p(~a n ~b) L p(~a n ~b) 160 Conditional Permission Two kinds of conditional permission will be consid ered. They will be identified as weak and strong condi tional permission. For the weaker type, the symbol "=*" will be used, and for the stronger type, the symbol "=*s". A weak conditional permission utterance simply specifies that one is permitted to do some act under some condition or circumstance. It says, in other words, that it is all right for one to do something in the event that some cir cumstance prevails or some act is performed, and nothing more. It does not specify that the condition must be present. The definition is as follows: P(A => B) P( A n Bj I(~A 1 1 B) I( A n ~B) i(~a n ~b ) A parent might say, "If it rains you may go out," simply meaning that the child is not forbidden to go out in the event that it rains. The condition of rain is not re quired for permission to go out. The stronger type of conditional permission utter ance makes some condition, circumstance, or action a necessary condition for performing some act. The defini tion of this kind of permitted conditional is as follows: P(A =>s B) p( a n b7 ~p (~a n b ) p ( a n ~b) p ( < —a n ~b ) Seven examples of utterances which can be interpreted as expressing conditional permission of this kind will be examined by laying them out in a tabular form. These examples are as followst (1) If the museum is open, then you may go in. (2) If you pay the admission fee, you may go in. (3) If you are twenty-one years old, you may vote. (4) If you are a citizen, you may vote. (5) If you are registered to vote, then you may vote. (6) If you do your work, you may go to the movies. (7) If you pass the test, then you may become an officer Utterances such as these are often elliptical. In the first example, the museum being open means open to the public, and "go in" means go into the part of the museum open to the public, and not necessarily into the curator's private office. Also, the rule is applicable to the general public; it does not apply to the curator and others. Thus- utterances may be instances of an utterance being asserted to some particular person at a particular time by some authority, or as general utterances. But as general utterances, they need not, and should not, be viewed as utterances of such a general nature that they apply to all human beings. Instead, they must be thought of as being addressed to someone or some group under some circumstance. 162 Though utterances of this kind are often in the form "If A, then you may B," the meaning being considered is more suited to the forms "Only if A may you B," or "You may B only in the event that A." The first two examples may be displayed as follows! (1) If the museum is open, then you may go In. Only if the museum Is open may you go in. You may go in only in the event that the museum is open. P(lf museum Is open, then go In) P( museum open and go in) ~P(not museum open and go In) P( museum open and not go in) P(not museum open and not go in) (2) If you pay the admission fee, you may go in. Only if you pay the admission fee may you go in. You may go in only In the event that you pay the fee. P(lf you pay, then go in) pay and go in) ~P(not pay and go in) P( pay and not go in) P(not pay and not go in) In the first example, the museum being open is a necessary condition for going in, but not a sufficient condition. The idea might be expressed more completely by "If the museum Is open, then, all other conditions being met, you may go in." The other conditions might be such things as wearing clothing, not carrying cameras, and so forth. Similarly in the second example, paying is a necessary but not sufficient condition for going in. Prom both of these utterances, it would follow that one is not permitted to perform the act if the condition is not met. (3) If you are twenty-one years old, then you may vote. Only if you are twenty-one years old may you vote. You may vote only in the event that you are twenty- one years old. P(lf twenty-one, then vote) P( twenty-one and vote) ~P(not twenty-one and vote) P( twenty-one and not vote) P(not twenty-one and not- vote) (4) If you are a citizen, then you may vote. Only if you are a citizen may you vote. You may vote only In the event that you are a citizen. P(lf a citizen, then vote) pt citizen and vote) ~P(not citizen and vote) P( citizen and not vote) P{not citizen and not vote) (5) If you are registered to vote, you may vote. Only if you are registered may you vote. You may vote only in the event that you are regis tered. P(lf registered, then vote)_____ PI registered and vote) ~P(not registered and vote) P( registered and not vote) P(not registered and not vote) Being twenty-one and being a citizen are both necessary conditions for voting. There are other conditions, such as being registered, voting at the right place and at the 164- right time, wearing clothing, and so forth. Being thus permitted to vote does not require one to votej one might, by another norm, also be obligated to vote, but the utter ance under discussion does not express this idea. Being registered may satisfy the requirements of being twenty- one and being a citizen, but it does not satisfy all other possible conditions. What these utterances do not allow ■ is not being twenty-one and voting, not being a citizen | and voting, and not being registered and voting, | (6) If you do your work, you may go to the movies. Only if you do your work may you go to the movies. You may go to the movies only in the event that you j do your work. P(lf you do your work, then go to the movies) P( do your work and go to the movies) ~P(not do your work and go to the movies) P( do your work and not go to the movies) P(not do your work and not go to the movies) i If the parent did not intend to allow the skipping of the work in any case, then we would not have an instance of conditional permission of this type, but an obligation to do the work and a weak permission to go to the movies and ; worki "OA n P{A =* B)H, The theater may impose other con- | i ditions upon going to the movies such as paying, wearing : i i shoes, and not talking loud, but the parent may be placing j I i i only the one condition upon going. The utterance in ques- | ; tion simply disallows the possibility of going to the | ; l ! movies and not doing the work. (7) If you pass the test, then you may become an officer. Only if you pass the test may you become an officer. You may become an officer only In the event that you pass the test. P(lf pass the test, become an officer)______ P( pass test and become an officer) ~P(not pass test and become an officer) P(not pass test and not become an officer) : Again, the utterance might be more complete if it were expressed as "If you pass the test, then in the event that all other conditions are met, you may become an officer," The other conditions might Include passing a health exam- ; ination, and so forth. If, for the individual addressed, ; there were other ways of becoming an officer, say by political influence or bribery, then for him the permis- ! sion would not hold as described above. It might rather be a weaker form of permission, such that the person may pass the test and become an officer. Biconditional Permission Utterances The definitions of weak and strong biconditional utterance forms are as follows« j together with the discussion of an inference pattern like P( pass test and not become an officer) P(A o B) P(A < = > s B) P( A n B) P( A i l b7 i(~a n b) ~p(~a n b) I ( A 0 ~B) ' s 'P (Afl ~B) i (^a n ~b) p ('vA n ~b) These definitions will be discussed in the next chapter, 1 that of Material Implication In sentential logic 166! Negative Permitted and Obligatory Conditional Utterances Three forms will be considered* "~P(A = > B)", "~P(A =*s B)", and "~0(A =» B)". An utterance not permitting a weak conditional simply does not permit the conjunction of the condition and the act. For example, If It Is said that "It Is not permitted that if you fail the test you may graduate," or "It is not permitted that if It rains you may go out," then the following tabulations would be i appropriate* It is not permitted that If you fall, you may gradu- j ate. I It Is not permitted that in the event you fail you I graduate. ; ~P(lf you fall, then you graduate) ~P( fail and graduate) I (not fail and graduate) I( fall and not graduate) I(not fail and not graduate) j 1 It is not permitted that if it rains, you may go out. It is not permitted that in the event that it rains you may go out, j i ~P(lf it rains, then go out)_____ ~P*i( it rains and go out) I(not it rains and go out) I( it rains and not go out) I(not it rains and not go out) | | In ordinary language, such utterances will often be ex- i | i pressed in the form "If you fail you may not graduate," j and "If it rains you may not go out," rather than in the ; i more cumbersome and less conventional forms examined ! 16? \ above* Negated utterances of the kind suggested here cor respond to the weak meaning of permitted conditional ut terances, The form "~P(A =* B)" is defined by the following tabulation! ~P(A => B) ~P( A f l B) i(~a n b) K a n ~b) I(~A ( I ~B) Negated permission of the form "~P(A =>s B)" is dif ficult to interpret. The form "P(A =*s B)'1 was interpreted as corresponding to such linguistic expressions as "Only I if you do A may you do B," "Only if A is the case may you do B," "You may do B only in the event that A" and "You are permitted such that only if A then B." Negating a permission that one may do something only in the event that something else be done or some circumstance prevails has the effect of ruling out such a permission. Thus the following definition is suggested for the form "~P(A =>s B)"« ~P(A =>s B) i( A n bT ; i(~a n b) K a n ~b) X(~A 1 1 ~B) English speakers do not commonly (or ever) speak any actual utterances corresponding to this form; they would be rather vacuous utterances expressing only the idea that one is not required to B only in the event that A. 168 If one Is not obligated to do something under a cer tain condition, then he Is "off the hook"; that is, not obligated with regard to that condition. Consider the following example* You are not obligated such that if a relative is arrested you must post bail. You are not obligated that you post bail in the event that a relative is arrested. ~0(lf a relative is arrested, then post ball) ~ 0 l relative arrested and post bail) ~0(not relative arrested and post ball) I( relative arrested and not post bail) ~0(not relative arrested and not post bail) The definition of the form "~0(A =» B)" is as follows* ~0 (A => B) ~0( A ( l BT ~0(~A 1 1 B) I( A | ) ~B) ~0 (~A f | ~B) Conflicts of Norms and Rules Norms of various kinds often come into conflict. As all motorists are expected to know, the rule is that one must stop when a traffic light turns red. If one does not stop, he is subject to a penalty. Also, one ordinarily may go if the light is green, but the law also requires that one not proceed in his automobile if the conditions are not safe, or a policeman Is signaling the cars to stop, or if a police vehicle, ambulance, or fire truck Is approaching with siren sounding. If the light is red and a policeman Is signaling the traffic to go, then one is in the position of being required by one rule to stop, and by another to go. To be coherent any norm system or other system of rules must have an ordering of the rules, such that when one rule permits or obligates a certain act under a certain condition, and another permits or obli gates a conflicting act, then a master rule of the hier archy of rule application will tell us which rule to fol low. If any norm system or other set of rules were to be systematically described, these rules would be of prime importance. Systems of rules, such as, for example, the informal parental rules used in the home, often take into account the hierarchical ordering of the rules in an ad hoc and often inconsistent manner. A norm system or other system of rules will often be found to contain internal inconsistencies if there is no rule to settle the conflict of subordinate rules, ' CONCLUSIONj SUMMARY OF THE DEFINITIONS OF OBLIGATORY AND ' PERMITTED CONDITIONAL UTTERANCES The forms discussed in this chapter are forms of ut terances that may be used to express permissions, com- imands, advice, norms, and other rule-llke utterances gov- :erning human behavior. . The concern has been with the |meaning of these forms, and not with their application or j I their possible relation to other deontic utterances in i J some deontlc realm or rule system.__________________________ 170 Three distinct kinds of definitions have been des cribed? these are for the forms "P(A =* B)", "P(A = > s B)", and "0{A => B)"t and for the corresponding biconditionals and negative permission and obligation utterances. The definitions are summarized below* Conditional permission B) P I( I( I( £ A A A -A BT B) ~B) ~B) Conditional obligation 0(A = r pT a - P(~A ~P( A L P(~A *_B) T T bT ( i n n B) -B) -B) Biconditional permission P(A c» B) P( A I(~A I( A I(~A n n n n B) -B) -B) Biconditional obligation 0 0 (A < — PC A ~P(~A ~P( A u P(~A B) n \ i n n BT B) -B) -B) Negative permission ' P ( A B) -PC A n Bj I(~A n B) K a n ~b) i(~a n ~b) P (A =>s n PC A -p( ~A n P( A I I P(~A I I P (A PC -P(' -p( PC' a n -A I I A I I ■A n B) BT B) ~B) ~B) -SL. b7 B) ~B) ~B) -P(A =>s b) i ( a i i bT i(~a n b ) i ( a n ~b ) x(~a n ~b) Negative obligation ~Q(A => B) ~0( A n B)' ~0(~A n B) I ( A O ~B) ~0(~A n ~B) In the next chapter the relation between these forms and others will be explored by examining the logical con sequences of the definitions. 1?2 NOTES ^This example was used by Arthur N, Prior, Logic and the Basis of Ethics (Londoni Oxford University Press, 19^5)i PP. ^0-41. CHAPTER VII THE LOGIC OF PRESCRIPTIVE DEONTIC CONDITIONALS Based upon the definitions provided in the previous chapter, a number of relationships between various, deontic utterance forms may be developed. The first part of the chapter will deal with the relationships between prescrip tive deontic utterance conditional, conjunction, and dis junction forms. The final part of the chapter will con cern inference patterns similar to Modus Ponens and Modus Tollens, involving prescriptive deontic conditional ut terance forms, RELATIONSHIPS BETWEEN PRESCRIPTIVE DEONTIC CONDITIONALS, CONJUNCTIONS, AND DISJUNCTIONS A number of relationships between prescriptive deon tic utterances of the forms defined in the previous chap ters may be shown to be a consequence of the definitions that have been described. The first relationship to be explored will be the relation between permitted and ob ligatory conditionals and permitted and obligatory con junction. Next, the relationships between the various deontic conditional forms will be examined. Following this examination, the relation of conditionals and dis junctions similar to the principle of Material Implication in sentential logic will be considered. Finally, other 17^ relations similar to those involved in the principles of Transposition and Material Equivalence will be examined. Relationships Between Prescriptive Deontic Conditionals and Conjunctions The following inferential patterns may be read off the definitions summarized in the conclusion of the pre vious chapter* PDIP 12. Principles of the relation of prescriptive deontic conditionals and conjunctions a. P(A =» B) tt P(A n B) b. ~P(A => B) it ~P(A n B) c. P(A =»s B) it ~P(~A n B) d. 0(A =* B) it ~P(A i ' l ~B) The principle represented by 12 a and b may be stated as a rulei To change a weak permission utterance to a permitted conjunction, or to change a negated weak permission utterance to a negated permission conjunction and conversely, exchange the symbols , l=*, t and "fl". The principle of 12 c can be stated as a rulei To change a strong permission conditional to a non-permitted conjunc tion, change the negation sign of the antecedent of the conditional, change the symbol H= > s " to the symbol "fl", and negate the operator "P"j to change a negated permis sion conjunction to a strong permission conditional, drop the negation of the operator “P", change the symbol "fl" 1?5 to f , ^sH, and change the negation sign of the antecedent of the newly formed conditional. The principle of 12 d can be stated as a rule* To change an obligation conditional to a negated permission conjunction, change the negation sign of the consequent of the conditional, change the symbol ; "=»" to "n”, and change the operator from "0" to , , ~Pn j and ! to change a non-permitted conjunction to an obligation con- i ditlonal, change the operator M~P" to ,,0,t, change the sym- ; i bol 1 1 fl" to , , =*", and change the negation sign of the con- i i I sequent of the newly formed conditional. The balance of | the principles which will be developed will not be stated ! as rules, for the patterns of stating the rules would be ■ similar to those already given. Relationships between Permitted and Obligatory Condi tionals Certain forms of inference involving the relation between weak and strong permitted conditionals and obliga- I tory conditionals can be deduced from the list of forms indicated as PDIP 12* PDIP 13. Relationships between permitted and obligatory | conditionals j 1 a. ~P(A => B) * i P(~A =>s B) ; This formula can be justified by the following proof* | 1. ~P(A => B) I ! | 2. ~P(A 0 B) from 1 by 12 b. j _ ____3« P(~A =*s B) from 2 by 12 o. ____________________i 176 PDIP 13 b. ~P(A => B) n 0(A =» ~B) This form can be justified by the following prooft 1. ~P(A =» B) 2. ~P(A f l B) from 1 by 12 b. 3. 0(A =» ~B) from 2 by 12 d. PDIP 13 c. P(A =>s B) ii 0(~A = » ~B) This may be shown to be correct by the following argumenti . 1. P(A =>s B) 2. ~P(~A ( i B) from 1 by 12 c. 3. 0(~A =* ~B) from 2 by 12 d. The last principle (13 c) Is of particular importance In understanding the meaning of certain permission utter ances. A child who is permitted to go to the movies only if he finishes his work is obligated in such a way that if ; he does not do his work he may not go to the movies. Relationships between Choice and Conditional Utterances. 1 Prescriptive Deontic Material Implication In sentential logic the relation between disjunctions I I and conditionals is governed by the principle of Material Implication, which is exemplified by the formula 1 1 (p ^ q) I 3 (~p v q)". Deontic permission and obligation utterances j i may be similarly related. i | The following pairs of definitions correspondi j P( A n B) P(~A n B) P( A n ~B) ’ P (~A D ~B) P(A U B) P(A =»s -B) PT'T'Ti ■ "B) p (-a n B) p( a n ~b ) 'p (~A r i ~b) 177 p ! - A L BK P(~A B ~ p { A n b ) ~P( A n B) p ( -A n B) P(~A n B) p ( A n ~B) P( A n ~B) p ( —A n ~B) P(' -A n ~B) °( A U B) 0 ( ~A =» b ) - p ( A n B) - P( A ( i B) - p ( ~A n B) 0 - P(~A n B) - p ( A n ~B) -P( A n ~B) ~ p ( -A f i ~B) ~P (~A n ~B) °( A v . B) 0 ( j\ => ~B) ~ p ( A n B) ~P( A n B) - p ( ~A n B) r p(~a n B) - p ( A n ~B) 0 -P( A n ~B) - p ( ~A n —B) l_p (~a n ~B) The parallelism of such definitions as these lead to the establishing of the following forms of Deontic Material Implication! PDIP lA. Prescriptive Deontic Material Implication a. b. c . d. P(A 0 B) P(A um B) 0(A 0 B) 0(A um B) i t P(A = > s ~B) P(~A =»s b ) 0(~A =» B) 0(A => ~B) In addition to arriving at these forms by an inspec tion of the definitions, they can be derived by proofs such as the following! !! t: i ! b. 1. P(A u B) 2. ~P(~A n ~B) from 1 by 5 a. 3. P(A ~B) from 2 by 12 c. 1. P(A Um B) 2. ~P(A n B) from 1 by 5 d. 3* P(~A =*s b ) from 2 by 12 c ( 178 1. 0(A u B) 2. ~p(~A n ~b ) from 1 by 5 b. 3. 0(~A => B) from 2 by 12 d. 1. 0(A Jm B) 2. ~p ( a n b ) from 1 by 5 e. 3. 0(A = > ~B) from 2 by 12 d. Interpretation of Prescriptive Deontic Material Implica tion In Ordinary Language Conditionals and disjunctions are logically related, and thus conditional deontic utterances must be logically related to deontic choice utterances. But the concepts of conditional permitted and obligatory action and permitted and obligatory choice are different. When transforming a conditional to a disjunction or a disjunction to a condi tional, often the sense of what was intended by the choice utterance or conditional utterance will seem to be lost. This is probably because we commonly do not make such linguistic transformations in the actual use of English and also because often, when a conditional is transformed into a choice utterance, one would seem to be permitted or obligated to make a choice where one of the members of the alternation is not under our control. The difficul ties in making such transformations in ordinary language will be discussed in reference to some of the examples used in this and previous chapters. 179 The Inclusive choice in which a child is permitted to choose his punishment by refraining from watching tele vision or skipping the movies would, by the principles discussed above, be transformable into a conditional such that only if the child skipped watching television could he go to the movies. If a teacher gives an inclusive choice of writing a paper or taking a test, it is the same as expressing the idea that only if the student chooses ; the paper may he skip the test, or only if he chooses to i take the test may he skip the paper. Again, the utterance : "You ought to work for the election of your party's candi- dates or give money to the campaign fund," can be trans formed, in accordance with the principle exemplified by , 1^ c, as "If you do not work for the election of your party's candidate, then you ought to give money to the campaign fund." Or, it could be transformed into an ; utterance such as "It is obligatory that if you do not work for the election of the party candidate, then you give money to the campaign fund." Next consider an example of transforming a permitted ■ may choice into a permitted conditional. For example, ! "You may have candy or you may have Ice cream," could be j changed into a conditional so that an equivalent utterance would be, "If you do not choose candy then you may have | ice cream." An Inclusive obligatory choice requires one | not to skip both of two alternatives and thus obligates 180 one so that if one alternative is rejected, then the other must be accepted, A may obligatory choice, on the other hand, requires one not to take both options and thus places upon the person the obligation that if one alterna tive is accepted the other must be rejected. No problems develop from the application of Deontic Material Implica tion to choice utterances. One of the examples used in developing the defini tions of the stronger sense of conditional permission was "If you pay the admission fee, then you may go in," When transformed into an inclusive choice, the utterance could become "You may choose between paying and not going in," This utterance expresses an inclusive choice because one could both pay and not go in, but one could not skip both, that is, not paying and going in. Transposing this ex ample to a may choice utterance would produce something like, "You may choose between not paying and going." This utterance expresses a may choice because one could not do both, that is not pay and go, but he could skip both, by paying and not going. Transformations of the kind which have been consid ered do not cause any problem; however, if either a per- ! mitted or obligatory conditional utterance contains a con- : dition which is either an action or a circumstance over I which one normally does not have control, then the cor- i j responding choice utterance seems strange. The example 181 "If the stop light is red you must stop” was used in de veloping the definition of obligatory conditionals. Sym bolizing the condition of a traffic light being red by "R" and the action of stopping by "S", the rule can be given symbolically as "0(R » S)". The corresponding Inclusive and may choice utterances would by symbolized as "0(~R 0 S)" and "0 (R um ~S)", Thus one would be obliged to make an inclusive choice between there being no red light or stopping, or a may choice between there being a red light or not stopping. These may be logically correct, but they do not correspond to ordinary ways of speaking. Again, the example "If you are a citizen you may vote" was used in developing the definition of the strong sense of per mitted conditionals. The corresponding inclusive choice could be given as "You are permitted to choose (inclu sively) between being a citizen and not voting." And the corresponding permitted may choice would be "You are per mitted to choose between not being a citizen or voting." One would not in everyday speech make such transforma tions. This fact makes the application of the principles of Material Implication questionable in some kinds of con ditional usages, if what is wanted is ordinary language usage, but it does not cast doubt upon the logical ade quacy of such transformations. 182 Transposition of Deontic Conditionals In sentential logic the antecedent and consequent of a conditional may be exchanged if the negation sign of both are changed. The same logical move may be performed upon the conditionals under discussion, with the exception of the weak permitted conditional. Often, however, the resultant transposed form will not conform to ordinary ways of speaking. The form "P(A => B)", as it has been defined, may not be transposed, because the definitions of "P(A =* B)" and "P(~B =* ~A) " are quite different: P(A => B) P(~B =* ~A) P( A n B) I( B H AT i (~A n b ) i(~b n a ) I( A i l ~B) I( B ( 1 ~A) I ( ~a n ~b ) p ( ~b n ~a ) On the other hand, the definitions of "P(A =*s B) " and "P(~B =»s ~A)n correspond: P (A =>s B) P (~B =>s «vA) p( a n bT p( b n a) ~p(~a n b) p(~b n a) p( a n -b) ~p( b h ~a) P(~A n ~B) P(~B f l ~A) The principle behind the construction of these definitions is that a strong permitted conditional rules out the con junction of a denied antecedent and an affirmed consequent Thus, if "it is permitted that if you pay, then you may go in,” then it also follows that "it is permitted that if you do not go in, then you may not pay." 183: The definitions of the forms "0(A =» B)" and "0(~B =» ~A) similarly correspond. The following forms of Prescrip tive Deontic Transposition are suggested: PDIP 15. Prescriptive Deontic Transposition a. P(A =*s B) 1: P{~B =>s ~A) b. 0(A => B) : : 0(~B =» ~A) These forms may also be established by arguments such as the following: 1. P(A =*s B) 2. P(A U ~B) from 1 b y 14 a. 3. P(~B U A) from 2 b y 3. 4. P(~B =*s ~A) from 3 b y 14 a. 5. P(~B U A) from 4 b y 14 St * 6. P(A U ~B) from 5 b y 3. 7. P(A =>s B) from 6 b y 14 a. Transposition and Ordinary Language Utterances Particularly when the condition for action is one which is not ordinarily under human control, a trans position may result in a non-conventional expression. Consider the example discussed in connection with the principle of Material Implication: "Only if you are a citizen may you vote." This can be transposed as "Only if you do not vote may you not be a citizen." This is, at best, a clumsy and unusual English construction. Per haps a clearer way of expressing this unusual idea is "Only if you are a non-voter may you be a non-citizen." 18U- Perhaps an even better example is "Only if you pay may you go in," This may be transposed as "Only if you do not go in may you not pay," or "Only if you are a non-goer may you be a non-payer." In ordinary language constructions modal words such as "permitted" and "may" attach to the clause that ex presses the action which is dependent upon the condition. | It should be noted that in transposing the antecedent and | consequent of such expressions, the modal word does not ! stay with the clause to which it was attached and is not i negated along with its new clause. Thus it would be in- ' correct to transpose the expression "If you pay then you I | | may go in," to the expression "If you do not go in then it is not the case that you may pay." The way that these kinds of utterances are transposed in ordinary speech may be obscured by placing the deontic operator outside the scope of the conditional utterance in the notation. The same phenomenon of a shifting modal term may be observed in other contexts. It occurs with the word ! "probably." Consider the following conditional probabil- ; i ; ity assertioni "If you get bitten by an Anopheles mos- j i t ! quito, then you will probably get malaria." If this ut- j j i ; terance were counted as a conditionally compounded prop- j i J I ! ! osition and the rule of transposition of sentential logic | i were applied, we would get the following! Letting "A" j | stand for "you get bitten by an Anopheles mosquito" and i 185 "M" stand for "You will probably get malaria," the orig inal proposition can be symbolized as "A 3 M". By the principle of transposition we get "~M 3 ~A". In sentence form we have "If it is not the case that you will probably get malaria, then it is not the case that you got bitten by an Anopheles mosquito." This statement cannot be cor rect} rather, the word "probably" shifts from its clause and is not negated along with its new clause. Thus the correct transposition should be, "If you do not get ma laria, then you were probably not bitten by an Anopheles mosquito." The same phenomenon of a shifting modal word can be observed in the following argument similar to a Disjunc tive Syllogisms "If you do not study your Greek lesson, you will probably fail the test; and if you fail the test, you will fail the course; therefore, if you do not study you will probably fall the course," The word "probably," originally attached to one phrase in the first premise, is attached to another phrase in the conclusion.-*- Prescriptive Deontic Material Equivalencies In sentential logic the form "p = q" is equivalent to the form "(p o q) • (q 3 p)". The question being asked is whether there are meaningful biconditionals corresponding to the forms "P(A * B)», "P(A =>s B)", and "0(A => B)" in prescriptive deontic logic, and if an Inference pattern 186 similar to Material Equivalence applies in prescriptive deontic logic. The definitions of "P(A => B)1 ' and MP(B => A)" corres pond! '(A => B) P(B =» A) '( A H B) P( B D A) PJ PI i(~a n B) i(~b n a ) I ( A f l ~B) I( B f l ~A) i(~a n ~b) i(~b n ~a) Therefore, not only are the forms MP(A =» B)" and ! , P(B =» A )’ 1 equivalent to the form "P(A » B)'1, but the form "P(A => B), f is itself equivalent to MP(A » B)”, for the defini tions would be the same. The forms "P(A =*s B)H and "0(A =» B)M are quite dif ferent, A biconditional strong permission would have the following definition: (A <^s ( A n BI p( a n b T ~p ( ~a n b ) ~p(An ~b) p( ~a n ~b) Such a conditional would allow the antecedent only in the event of the consequent, and the consequent only in the event of the antecedent. It would permit two things only in the event that both were done. An adoption agency having twin children for adoption may permit a family to adopt the one child if and only in the event that they adopt the other. Thus the adopting of each child would be a condition for adopting the other. This could be 18? expressed in the form "P(A =>s B) f l P(B =>s A)", and this would be equivalent to the form "P(A os B)". A biconditional obligation would be defined as fol lows* 0 0(A o B) r- P( A 1 1 B) ~p (~A n b ) ~p(An ~b) — p(~a n ~b) It would be obligatory that if either of two actions be performed, either both be performed or neither. The def initions of "P(A »s B)n and "0(A » B)" are identical, ex cept that the tabulation of the obligatory conditional is further qualified In that the disjunction of the other alternatives is obligatory. The following forms may be added to our principles of inference* PDIP 16. Principles relating conditionals and blcondi- tionals— Prescriptive Deontic Material Equiva lence a. P(A => B) i* P(A « B) b. P(A =>s B) A P(B » A) c. P(A B) tt P[(A =»s B) H (B =*s A)] d. 0(A «■ B) tt 0[(A =» B) f l (B =* A)] PRESCRIPTIVE DEONTIC ARGUMENT PATTERNS Forms discussed in this chapter have been what may be called "transformation forms." Some of the forms have 188 been equivalencies and some implications, but all have been patterns where one form is transformed or changed to another. The following patterns will involve more than one utterance form, which are related in order to detach or infer another utterance form. The utterances from which the inference is made may be called premises, and the utterance detached or inferred, the conclusionj thus the patterns are referred to as argument patterns. The patterns to be considered are similar to the argument patterns of sentential logic known as Modus Ponens and Modus Tollens. Prescriptive Deontic Detachment Principles Some conditions upon which permission to act are dependent are themselves actions, and some are circum stances over which one does not normally have any control. The argument form being considered here would apply mainly to cases where it would be appropriate to say "You are permitted to do A," The forms to be considered first are theset P(A =*s B) PA P(A =»s B) PB PA PB These forms may be rendered as formulaei (1) P(A =*s b ) f l PA PB (2) P(A =*s B) f l PB PA ............189 The first of these two forms must be ruled out on the grounds that, as defined, a permission utterance of this form provides only that to qualify for doing the act B, the condition A or the act A must be present. Consider the example, "Only if you have a membership card may you enter the club lounge," Having a membership card is re quired, it is a necessary condition for entering, but it may or may not be the only condition. Additional condi tions may be proper dress and behavior, and entering only during certain hours. Thus, permitting a person to have j a membership card permits him to enter only upon com- j i pliance with all of the other conditions that may be re- ; l quired. The second form must also be ruled out. If we exam ine the argument form in light of the tabular definition of the form "P(A =*s B)", the argument form seems plau- | sible, though highly trivial. Consider the followingi P(A =*s B) PB /. PA P( A l l Bj ~p (~a n b) p( a n ~b ) | p (~ a n ~ b ) j I The second premise indicates permission to perform act Bj j : i act B only appears in the tabulation in lines one and two, | but B is not permitted in conjunction with not doing act A. I Thus it would appear that act A is permitted. But this j inference is Incorrect. If one were granted permission by an utterance such as "Only if you have a membership card may you enter the club lounge," and one were also granted a permission such as "You may enter the membership lounge," then we might ask on what grounds is the second permission granted. If the grounds be that the person has a membership card, then "PA" would have been presupposed . in the granting of the permission "PB". If permission to enter the club lounge were granted on some other grounds, ; then the original permission utterance has not been fol- ; lowed. In any event one might, for some highly special | reason, be permitted on some occasion to enter the club i lounge, and yet not be permitted to be a member of the | club. Such a circumstance might cast doubt upon the rule I ! i that "Only if you have a membership card may you enter the ; club lounge." Such rules as this one often have unspoken | exceptions, such as ", . . unless you are a trial member, ! a medical doctor attending to the ill, the janitor, or a < ; workman working on the plumbing." Next, three additional forms involving permission qualification will be considered* | i (1) p (a =»s b) n ~pa o~b I (2) P(A =>s B) n ~P~B OA I \ \ (3) P(A =>s B) n ~PB 0~A I I I j The first two of these forms are considered to be correct, j i i i The third is considered not to be correct. The first two j I i forms can be justified by converting the first premise j | j into an inclusive permitted alternation, revealing that | 191 the form Is an instance of Prescriptive Deontic Disjunc tive Syllogism (PDIP 10 a). These forms may also be Jus tified by arguments such as the following: 1. The definition of P(A =>s b ) is as follows: P( A =>s B) P[ A n B) ~p(~a n b ) p( a n ~b ) p(~a n ~b) 2. The addition of ~PA rules out lines one and three. 3. Thus the new tabulation is as follows: ~P( A n bT ~p(~a n b ) ~p(An ~b) o(~a n ~b ) This is the tabulation of ~P(A U B) 5* 0(~A n ~B) from ^ by 5 °• 6. 0~A 0 0~B. from 5 ^ 9 b, 7. 0~B from 6 by 8. The following formulae are thus accepted as correct prin ciples: PDIP 17. Principles of Deontic Detachment a. P(A =»s B) f i ~PA 0~B : b. P(A b ) n ~P~B OA Examples of the above argument forms are the follow- i ing: ' ’Only if you have a passport may you travel abroad, i and you may not have a passport, therefore you may not travel abroad," and "Only if you have a passport may yor 192 travel abroad, and you must travel abroad, thus you must have a passport.’ 1 The second form perhaps seems odd. The oddity comes from the fact that the permission to travel is given by one authority and most likely the obligation to travel would be placed upon a person by himself or some other authority. One major problem in deontic logic centers around the ! question of who the utterance is spoken by and to whom it | is spoken, and around the problem of who or what the ob- ! ligator and permission giver is. Consider the following j | example of the second argument form given abovej "Only if ! you pass the test may you become an officer, and you must : (ought to) become an officer, therefore you must pass the ; test," The army may place the requirement of passing the test upon anyone who seeks to become an officer, but it surely does not obligate anyone either to become an of ficer or pass the test. The obligation to become an of ficer might be placed upon a young man by his family, thereby obligating him to pass the test. The third form, "P(A =>s B) D ~PB 0~A" , is Incorrect, but it is worth examining, for it seems a plausible argu- ! ment form. It is rejected because an examination of the , definition of the first premise, together with the second j premise, shows that the conclusion does not follow. The I argument, with the first premise defined, is as follows* 193 PfA =»s B) f | ~PB 0~A or ~PA P( A n bT ~P(~A n B) p( a n ~b) p (~a n ~b) The addition of ”~PB” to the first premise rules out line one, but lines three and four remain permitted* thus the non-permission of A does not follow. Still, the argument •'Only if you have a passport may you travel abroad, but you may not travel abroad, thus you may not have a pass port” may seem plausible. The question to be asked is on what grounds might someone say "You are not permitted to travel.” If the grounds are that the person has no pass port, then the argument might be thought of as circular. If the grounds are other than not possessing a passport, then what would seem to be denied is not permission to perform the act named in the antecedent, but the entire conditional permission utterance. Next, two forms of arguments involving obligation, both of which are considered to be correct, will be exam ined. These forms arei (1) 0 (A => B) n OA OB (2) 0(A => B) n 0~B /. 0~A The first argument form may be justified by the following argumenti 1. The definition of the form of the first premise isi 19^ 0(A => B) - p ( A n bJ n - P(~A n b) u ~p( a n ~b) p { ~a n ~b ) 2.- The addition of OA rules out lines two and four, 3, Therefore the new tabulation is as follows* o'( ATn bT '-P ( ~a n b ) ~P ( A f l ~B) ~p ( ~a n ~b ) This is the definition of the form "~P(~A U ~B)", 5. 0(A n B) from ^ by 5 c. 6. OA n OB from 5 by 9 b. 7. OB from 6 by 8, The second form may be justified by a similar argument! 1, The definition of the major premise given above, 2, The addition of 0~B rules out lines one and two, 3, Therefore the new tabulation is as follows* ~p( A n IT ~P (~A f i B) ■~p ( A n ~b ) 0 (~A n ~B) This is the definition of the form M~P(A U B)tt. 5. 0(~A n ~B) from ^ by 5 c, 6. 0~A 0 0~B from 5 t>y 9 b, 7. 0—A from 6 by 8, The following are accepted as correct principles of pre scriptive deontic logic. 195 PDIP 17. (continued) c. 0(A => B) D OA OB d. 0(A => B) 0 0~B 0~A The argument forms accepted so far involve only minor premises that are forms of utterances expressing either obligations or non-permittedness (forbiddenness). Argu ment forms with permitted or non-obligatory minor premises have not been accepted. "~PA" and "OA" represent stronger utterances than "PA" and "~0A". Obligation and forbid denness are stronger than permission and non-obligation. They are stronger in the sense that forbiddenness and ob ligation utterances are more restrictive, whereas permis sion and non-obligation utterances are open. One can say without qualification that one must do something or that one is not permitted to do somethings but one cannot with the same degree of force say that one is absolutely per mitted or unquestionably not obligated to do something. Detachment Principles Involving Mixed Modes The following arguments, involving a minor premise not qualified by a deontic operator, are judged to be correctt PDIP 17 (continued). e. P(A =>s B) n ~A 0~B f. P(A =*s B) ft B /. OA g. 0(A =* B) n A OB 196 h. 0(A =» B) n ~B 0~A These forms are accepted by the following analysis. The definition of the form HP(A =>s B)" is as followsi P(A = > s B) p( a n bT ~p(~a n b) p( a n ~b) p(~a n ~b) With the addition of the information that act ~A is chosen or performed, that is, act A is not performed, the field of consideration is restricted to lines two and four of the tabulation. ~A is done, but ~A is not permitted to gether with act Bj thus it is obligatory that ~B. Similarly, the addition of the premise that act B is chosen or done restricts the field of consideration to the first two lines of the definition. B is done, but it is not permitted that B be done together with the not doing of A. Thus, it follows that since B is done it is obliga tory to do act A, The addition of the information that act A was performed or that act B was not performed would not restrict the field of consideration such as to draw any conclusion about the permittedness or obligatoriness of the other variable. The definition of the form "0(A => B)n is as followst 0 -Q(A => B) - p( a n b) - p(~a n b) ~p (An ~b ) - p(~a n ~b ) 19? The addition of the information that act A is chosen or performed restricts the consideration to lines one and three. Act A is done, but it is not permitted that act A be done together with thus it is obligatory that act B be done. Similarly, the addition of the information that act B is not chosen and done restricts the field of consideration to lines three and four. B is not done, and this is not permitted if act A be done? thus it is obliga tory to refrain from doing act A. The symbols "~A" and M~Bn cannot be considered as meaning simply not choosing or not acting, but as meaning a specific act of choosing not to do a certain act. Problems in Interpreting Some Detachment Forms in Ordinary Language It must be kept in mind that with the exception of two forms, all of the detachment forms similar to the forms called Modus Ponens and Modus Tollens in sentential logic developed above apply most clearly to utterances where the condition upon which a permission or obligation is dependent is under human control and choice. Two of the forms, PDIP 17 e and g, can apply where the permission or obligation condition is not necessarily under human control, for the second premise is simply an utterance recognizing that the condition is either present or not present. 198 To discuss the difficulties of interpreting some of these forms in natural language, four utterance examples will be examined. These instances involve typical uses of modal words such as ''ought,” "should,” and so forth. The major premises are as followsi (1) If you come to someone's house as a guest, you are obligated to honor his customs, 0(if enter as a guest, then honor his customs) (2) If you accept a guest into your home, you must honor him. 0(if accept a guest, then honor him) (3) If you make a promise, you should keep it. 0(if make a promise, then keep it) (4) If you are a Democrat, you should vote for the Demo cratic candidate. 0(if a Democrat, vote Democratic) (5) If you are a good American, then you ought to sup port the president. 0(if good American, then support president) These examples will be used as major premises in argu ments of the following formsi PDIP 17 d. 0(A =* B) f | 0~B 0~A h. 0 (A =* B) f t ~B 0~A The first example cast as the major premise of the above argument forms is as follows: 199 (1) If you come to a person’s house as a guest you are obligated to honor his customsj and you ought not honor his customs; therefore, you ought not enter his house as a guest. If you come to a person’s house as a guest you are obligated to honor his customs; and you do not honor those customs; therefore, you ought not enter that house, The second example Is as followsi (2) If you accept a guest Into your home you must honor him; and you ought not honor him (a particular per son); therefore, you ought not invite him as a guest. If you accept a guest into your home you must honor him; and you do not honor him; therefore, you should not invite him. This example could also be given as follows, but it would require a tense change in the conclusioni If you accept a guest into your home you must honor him; but you did not honor him; therefore you should not have invited him. Arguments corresponding to the third example might be as f ollows: (3) If you make a promise you should keep it; you should not keep this promise; therefore, you should not have made It. 200 If you make a promise you should keep it; you did not; keep your promisej therefore, you should not have made the promise. Arguments corresponding to the fourth example might be given as follows: (^) If you are a Democrat you ought to vote for the Demo cratic candidate? but you ought not vote for this Democratic candidate; therefore, you ought not be a I Democrat• If you are a Democrat, then you ought to vote for the Democratic candidate; but you did not vote for the Democrat, therefore you ought not be a Democrat. And arguments corresponding to the fifth example are as follows: (5) If you are a good American you ought to support your president; you ought not support your president; therefore, you ought not be a good American. If you are a good American you ought to support your president; you did not support your president; thus you ought not be a good American. The arguments with example three as the major premise i do not cause any problems. But the arguments using exam- j ; pies four and five as major premises seem less than ade- I ; I quate. The first form of argument using example four may j be correct, but many times when an utterance such as "You i i ought not vote for this Democratic candidate'* is made, j 201 what is meant is that even though you are a Democrat you should not vote for that party's candidate. This minor premise would not yield the conclusion indicated by the form under discussion. Similarly, the utterance that "you ought not support your president" cannot be taken at face value. Rarely would the two utterances, "If you are a good American, you ought to support your president" and "You ought not support the president" be made by the same person on the same occasion. In all likelihood, the second utterance would involve a denunciation of the first utterance. Thus, in Interpreting arguments of the forms under consideration, one must examine the context to see if what is meant is something of the form "0~B" or rather, something like "it is not the case that f0(A =» B)*". ADEQUACY OP THE SYMBOLS FOR CONDITIONAL PERMISSION It might be questioned why two separate symbols are used for weak and strong permitted conditionals, A weak conditional permission merely says that there is no pro hibition against doing act B in the event that act A is done or occurs, and the form "P(A n B)" adequately sym bolizes this idea. It is true that the form "P(A =» B)" is equivalent to "P(A n B)" by PDIP 12 a. But If a sep arate symbol for weak and strong conditional permission were not employed, some unwanted conclusions would result from employing the principle that "ought" implies "may." 202 ’ Consider the example of a strong conditional permission* "Only if you have a ticket may you enter." Using "T" to represent "have a ticket" and "G" to represent "go in," the example may be symbolized "P(T =*s G)". From this "0(~T => ~G)" can be derived by 13 c. This form could be read as "You are obligated that if you have no ticket you do not go in." Employing the principle that "ought" im- plies "may" (PDIP 2), the form "P(~T =» ~G)" may be de- ; rived. If the same arrow symbol were used for strong permis- j sion and obligation conditionals, then the form derived above would be equivalent to "~P(T f i ~G) " by 12 c, and could be expressed as "You are not permitted, to have a ticket and not go in." But this is not in keeping with the original permission that "Only if you have a ticket may you go in," Surely such permissions do not compel one to go in if he has a ticket, or deny one the possibll- ity of having a ticket and still not going in. The difficulty could be solved in two ways. It could be avoided by modifying the principle that "ought" implies "may" such that a conditional obligation utterance j could be changed to a permitted conjunction. Thus the j I formula "0(A => B) P(A n B)" would have to be added to j I i PDIP 2. The other solution is to differentiate between j : strong and weak permission conditionals. The problem is j t j avoided by using the symbols "=»" and "=»s»f for what is 203 obtained from the form "0(~T =» ~G)" is "P(~T = » ~G)M, which is equivalent to "P(~T n ~G)n, and simply means MYou are permitted to not have a ticket and not go in.” CONCLUSION In this chapter the consequences of the definitions developed in the previous chapter have been followed out. First, certain transformation principles were developed. These are principles involving the various relationships ! between prescriptive deontic conditionals, conjunctions, i and disjunctions. Secondly, principles of prescriptive deontic detachment were developed. The method of analysis was that of examining the definitional schema and determining certain consequents, then deducing from these and other principles already accepted other similar relationships. The patterns de veloped are, in some respects, similar to those of senten tial logic. It was concluded that the only patterns of prescrip tive deontic detachment involving a deontically qualified minor premise that can be justified are those in which the i i j minor premise Is an utterance expressing the forbiddenness or obligatoriness of an action, and in which the conclu- l f sion is an utterance expressing obligation. The patterns j developed are similar to Modus Ponens and Modus Tollens in j sentential logic, but they are far more varied and | complex. The principles of prescriptive deontic inference will be summarized in the concluding chapter of this study. 205 NOTES lAn argument similar to this example is discussed by Jack Ray and Harry Zavos, "Reasoning and Argumenti Some Special Problems and Types," in Perspectives on Argumen tation, eds. Gerald R. Miller and Thomas R. Nilsen (Chicago> Scott, Foresman, 1966), pp. 82-83. CHAPTER VIII CONCLUSION Many utterances In ordinary discourse and argument involve the modal concepts of permission and obligation and employ modal words such as "may," "ought," "should," ; and many others. The logic of permission and obligation is known as deontic logic and has been widely studied since the appearance of Georg Henrik von Wright's original | article, "Deontic Logic," In 1951* The logic of von i ! | Wright and some of the later developers of deontic logic ! has been summarized and examined in Chapter II of this ■ ; study. In Chapter III the basic nature of deontic con- i i cepts was discussed. Particular problems, such as the Interdefinability of permission and obligation, the rela tion of permission, obligation, and truth-functionality, ; and the principle that obligation implies permission, were , reviewed. It was concluded that the literature on deontic logic has been devoted almost exclusively to the logic of state ments about the existence of norms, rules, commands, per- ; missions, obligations, and the like. But there is a j j difference between saying, for example, "There is a norm ; permitting you to do act A," and saying, "You are per- | mitted to do act A." The first utterance Is a descriptive statement about the existence of a norm; the second is 206 a prescriptive utterance offering a certain permission to act. In this study an analysis was made of the meanings of prescriptive deontic utterance types, and patterns of in ference Involving prescriptive deontic utterance forms were developed. The study has two primary areas of focus. The first is upon prescriptive permitted and obligatory choice utterance's and inference patterns involving deontic choice, and the second focus is upon conditional permis sion and obligation utterances and inference patterns in volving these forms. The remaining four chapters were devoted to these problems. THE METHOD OF THE STUDY The first step in the analysis was to symbolize the components of a prescriptive deontic utterance. Following the original analysis of von Wright, the symbols "P" and "0" were used for the deontic operators of permission and obligation. These symbols stand for the linguistic func tion performed by such modal words as "may," "permitted," "ought," and "obligated." The deontic operators were used to qualify an act or a complex of acts related in some way. The symbols "A" and "B" were used to stand for human acts, and the symbols "n", "U", and "«>" were used to represent logical relations such as those associ ated with the English words "and," "or," "if, then," and "if and only if." A choice utterance of a certain kind, for example, was symbolized "P(A U B)". The next step was to define various prescriptive deontic forms. Instead of defining the symbols for deon tic operators, acts, and logical connectives separately, the course taken was to define entire deontic forms, thus defining, for example, "permission" in relation to dis junction or, in other words, modal concepts such as "may" in relation to "or." In preparing the definitions, two concepts were taken as primitive and thus undefined. These were the concepts of negation, symbolized by the conventional tilde, "~", | and conjunction, symbolized by the upside down cup, "fl". These correspond to such English words as "not" and "and." Definitions for the deontic forms were given by a tabula tion of the symbols for acts and their negations, similar to a truth table which exhausts all of the possible rela tionships between two acts and their negations. In Chap ter IV definitions were provided for various kinds of per- j : j mitted and obligatory choice utterances. In Chapter VI definitions were provided for various conditional permis- j : i i i I ; slon and obligation utterance forms. The definitions were | i | ; stipulated and must be accepted as correct for the remain- i der of the analysis to be accepted. In presenting the ! ' definitions, care was taken to argue that these defini tions correspond to everyday uses of language expressing 209 ’ permitted and obligatory choices and conditional permis sions and obligations. Thus a number of examples were generated and discussed in relation to the definitions. It was argued that the conventional interpretations of the logical connectives in sentential logic corres ponding to words such as "orH and "if, then" are not suf- ; ficient to account for a great many uses of permitted and ; obligatory choice utterances and many uses of conditional | permission and obligation utterances in ordinary language. i | At the outset of the analysis of the logic of per- 1 ' ; ! mitted and obligatory choice utterances, it was necessary to make certain preliminary assumptions in addition to the ■ ! definitions. Three assumptions were made: that permis- i sion and obligation are interdefinable, that "ought" im- ; plies "may," and that the order of the elements of con- ; junctions and disjunctions may be reversed without affect- j ing the meaning of the utterance, In Chapters V and VII, seventeen principles of pre scriptive deontic logic were developed from the defini- ; tlons and assumptions. These are summarized at the end | of this chapter. The forms are called "principles," but, j j ! | strictly speaking, they are formulae exemplifying the j j principles involved. I j 1 [ IMPORTANCE OF THE STUDY j ! The results of the study should shed some light on j modallogic in general, and deontic logic in particular.__ j 210 ; The study was predicated on the lack of a sufficiently complete calculus of prescriptive deontic logic. It offers a step in the development of such a calculus. The analysis and conclusions presented here are put forward with some confidence, but they are also held tentatively and given as a first step in the analysis of prescriptive deontic logic. The analysis of the meanings of and inferences which | may be made from expressions which permit, obligate, com- ; i ' ! mand, and advise human conduct, will be of value in the | understanding and analysis of actual discourse involving ; the concepts of permission and obligation, and it should i contribute to the general theory of human argumentation, ! SUMMARY OF PRESCRIPTIVE DEONTIC INFERENCE PRINCIPLES I PDIP 1, Principles of interdefinability a. Interdefinability of "P" and ”F" PA it ~FA P~A ti ~F~A —PA ti FA —P-A ii F—A j b. Interdefinability of HFM and "0" FA it 0~A | F—A t i OA | ~FA ti ~0~A —F—A it —OA ! c. Interdefinability of "P" and "O” i PA 1 1 — 0 — A j P—A ti ~0A | —PA ti 0—A —P—A ti OA 211 PDIP 2. "Ought" Implies "may" OA PA 0<—A P~A PDIP 3. Commutation P(A U B) tt P(B U A) 0(A U B) *s 0(B U A) P (A D B) tt P(B 0 A) 0 (A 0 B) : i 0(B n A) PDIP Inference from strong to weaker deontic utterances a • ~PA P~A ~P ~A ,. PA b • OA . ■ ' —0~A 0~A ■ —OA PDIP 5. The transformation of prescriptive deontic disjunction and conjunction--De Morgan Type 1 Inferences Principles a. P (A U B) tt ~P (~ A n ~b ) b. 0(A U B) t! ~ P ( ~A n ~b ) c. ~P(A U B) t t 0(~A ( 1 -B) d. P (A Um B) t t ~P (A n b ) e. 0 (A Um B) t t ~P(A n b ) f. ~P (A Um B) t t 0 (A n b ) S. P (A U B) —o (~a n ~B) h. 0 (A U B) ~o ( < —a n ~B) I. P(~A n ~ b ) ~0 (A U B) j. 0(~A 0 ~B) ~o (a U B) k. P (A Um B) . \ ~o(a n B) 1. 0(A Um B) . a —* 0 1 B) m. P (—A n ~b ) ~0 (~A Um —B) n. 0 (—A n ~b ) ~0 ( ~A Um ~B) 212 PDIP 6 PDIP 7 PDIP 8 PDIP 9 De Morgan Type 2 Principles a. P(A U B) tt 0~(~A 0 ~B) b« 0(A U B) t t 0~('vA f l ~B) c. 0~(A U B) t t 0(~A f l ~B) d. P(A Um B) t t (MA n B) e. 0(A Um B) t t 0~(A f l B) f. 0~(A Um B) tt 0(A D B) g. P(A U B) P~(~A f l ~B) h. 0(A U B) P~(~A n ~B) 1. 0~(A U B) P(~A n ~B) j. p (~a n ~b) p~(a u b ) k. o(~a n ~b) p~(a u b) 1. P(A Um B) P~(A n B) m. 0(A um B) P~(A n B) n. 0~(A Um B) P(A n B) o. P(A n B) P~(A um B) p. 0(A n B) P~(A um B) Conjunction PA, PB / , (PA n PB) OA, OB (OA f l OB) Simplification (PA n PB) PA (oa n ob) oa Principles of Deontic Dissolution a. PA n PB /. P(A D B) b. o(a n b) oa n ob 213 PDIP 10. Prescriptive Deontic Disjunctive Syllogism a. P(A U B) f l ~PA /. OB b. 0(A U B) n ~PA OB c. P(A U B) f l ~A OB d. 0(A u b) n ~A OB PDIP 11. Principles of Deontic Compliance a. OA (R A) o~a (r ~a ) b. ~PA (R ~A) ~P~A (R A ) PDIP 12. Principles of the relation of prescriptive deontic conditionals and conjunctions a. P(A =* B) t i P(A n B) b. ~P(A =» B) t > ~P{A n B) c. P(A =>s B) t i ~P(~A n B) d. 0(A =» B) i i ~P(A f l ~B) PDIP 13, Relationships between permitted and obligatory conditionals a. ~P(A => B) P(~A =>s B) b. ~P(A => B) / . 0(A =* ~B) c. P(A =*s B) 0(~A =» ~B) PDIP 14. Prescriptive Deontic Material Implication a. P(A u B) t t P(A =*s —B) b. P(A Um B) i t P(~A =>s b) c. 0(A U B) t t 0(~A =» B) d. 0(A Um B) tt 0(A => ~B) PDIP 15 PDIP 16 PDIP 17 » Prescriptive Deontic Transposition a. P(A =*s B) it P(~B _a ) b. 0(A =» B) 1 1 0(~B => ~A) Principles relating conditionals and bicondi tionals— Prescriptive Deontic Material Equiva lence a. P(A => B) i t P(A » B) b. P(A =>s B) P(B A) c. P(A »s B) it P[(A =>s B) n (B =>s A)] d. 0(A * B) i t 0[ (A =» B) n (B =» A)] . Principles of Deontic Detachment a. P (A =>s B) n ~PA , . 0—B b. 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Creator Ray, Jack Leroy (author)

Core Title Prescriptive Deontic Logic: A Study Of Inferences From Linguistic Forms Expressing Choice And Conditional Permission And Obligation

Degree Doctor of Philosophy

Degree Program Speech Communication

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag OAI-PMH Harvest,Speech Communication

Language English

Contributor Digitized by ProQuest (provenance)

Advisor Fisher, Walter R. (committee chair), McBath, James H. (committee member), Willard, Dallas (committee member)

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c18-534332

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Identifier 7200576.pdf (filename),usctheses-c18-534332 (legacy record id)

Legacy Identifier 7200576

Dmrecord 534332

Document Type Dissertation

Rights Ray, Jack Leroy

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the au...

Repository Name University of Southern California Digital Library

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