Reprinted from the Philosophy of Science Vol. 33 Nos. 1 2 March June 1966 DISCUSSION: THE TRUTH AND FALSITY OF DEFINITIONS* REM B. EDWARDS Unioersity of Tennessee Why don't Philosophers agree on this simple question: Are lexical definitions capable of truth and falsity ? This essay hopefully will be a contribution toward such agreement. That logicians do not agree on the answer to the question whether ordinary dictionary definitions are capable of truth or falsity can be estabiished easily by reviewing some of the relevant recent discussions. In the camp of those offering a negative answer are Salmon,l and Parker and Veatch.2 In the works rvhich I surveyed, the affirmative opinion seems to be the majority opinion. An affirmative answer is offered by Stebbing,s Cohen and Nagel,a Copi,5 and Black.6 In an earlier rvork,T Beardsley took an affirmative stand; but in a more recent discussion,s he seems to have reversed his opinion without fully explaining why. Whether a negative or positive answer is given to our question seems to depend upon diverse presuppositions as to the nature of lexical definitions themselves. Those giving an affirrnative answer all hold what I shall call the "proposition theory," and those giving the negative answer all adhere either to the "phrase theory" or to the "proposal theory." If definitions are propositions or declarative statements, they are thereby capable of being either true or false; and if they are either fragmentary phrases or proposals, they are thereby incapable of either truth or falsity. Thus to decide our original question we need to decide whether definitions are propositions, phrases or proposals. Whether they are capable of truth or falsity s'ill follorv from this. The majority view is that lexical definitions are propositions to the effect that u'ithin the context of some established language certain \r'ords have certain conventional uses or meanings. "Bitch" means "femaie canine" is taken as a proposition asserting that within the context of ordinary English the definiens is the established meaning for the definiendum. Lexical definitions thus report facts about some established language which can be verified or falsified as easily as most other facts of man's complex social life and by the same scientific methods. If the facts are such that "bitch" ordinarily means "female canine" rather than "female feline" then the former definition would be true and the latter false. Such is the "proposition theory." The "phrase theory" asserts that definitions lack the basic grammatical components * Received September, 1965. l Wesley C. Salmon, Logic, Englewood Cliffs: Prentice Hall, 1963, p. 93. 2 Francis H. Parker and Henry B. Veatch, Logic as a Human instrument, New York: Harper and Brothers, 1959, p. 81. 3 L. S. Stebbing, A Modern Introduction to Logic, London: Methuen & Co., 1933, p. 426. a Morris R. Cohen, and Ernest Nagel, An Introduction to Logic and Scientific Method, New York: Harcourt, Brace & Co., 1934, p. 230. 5I. M. Copi, Introduction to Logic, New York: Macmillan, 1961, p. 102. 6 Max Black, Critical Thinking, New York: Prentice Hall, 1946, p. 190. 7 Monroe C. Beardsley, Practical Logic, Englewood Cliffs: Prentice-Hall, 1950, p. 166. 8 Monroe C. Beardsley, and Elizabeth Lane Beardsley, Philosophical Thinhing, New York: Harcourt, Brace & World, 1965, p. 25. 76 77 THE TRUT}I AND FALSITY OF DEFINITIONS of complete seutences and fail to be propositions capable of truth or falsity as a matter of pure svntax. The "proposal theory" asserts that definitions have the linguistic status of proposals or rules to govern future linguistic habits and as such make no declarative assertions about the u,orld capable of truth or falsity. l,et us examine the adequacy of these two alternatives to the "proposition theory." The adherents of both of the alternative theories all agree that definitions are not propositions. As Beardsley puts it, "a definition itself-an ascription of meaning-is not an assertion or statement and cannot be true or false."e Parker and Veatch maintain that although definitions may be asserted in propositions, they are themselves only "ccncepts or phrases rather than propositions or sentences."1o And Salmon informs us that "A definition itself has the force of a proposal to use a certain rvord with a certain meaning; as such it is neither true nor false."l1 The basic difficulty is that there is no agreement on the standard or proper form tor stating definitions. Consider these alternatives: 1) "Bachelor" means "an unmarried adult male." (The definiendum means the definiens). 2) "Bachelel"-rrsp unmarried adult male." (Definiendum-definien s). 3) Let "bachelor" mean "an unmarried adult male." (Let the definiendum mean the definiens). Example l) gives the proper form for stating definitions according to the adherents of the proposition theory, example 2) the proper form for the phrase theory, and example 3) the proper form for the proposal theory. I shall argue that the proposition theory is basically correct but that the two alternative theories are correct in rvhat they assert and mistaken only in denying that definitions are capable of truth and faisity. In other word:i, they are mistaken only in claiming to be exclusiz.:ely correct. Initially, the phrase theory seems to be the strongest of the trvo alternatives to the proposition theory because all dictionaries seem to follorv its suggested standard form and not forms 1) or 3). Dictionary definitions do not explicitllt contain a "means" or a "let." They offer a definiendum and a definiens but do not explicitly state how they are ccnnected or even that thev are connected. \\'ithout "means" as a connecting verb, they are not sentences containing all the necessarv parts of speech; and consequently thev are incapable of truth or falsin'. Hou'ever, I do not think one can infer from this that they are not propositions. It is safe to assume that the users of the dictionary understand that the definiendum means the Cefiniens without having to say this each time a definition is presented. The "means" is always there implicitly if not explicitly. If it were not, users of the dictionarv likely would have either an incorrect conception of the connection betu'een the definiendum and the definiens or no conception at all. But dictionaries are rvritten and used primarily to give and receive information about this connection. Part of the plausibility of the phrase theorv as defended by Parker and Veatch rests on a confusion and confounding of the tu'o theories that (a) the definition is incapable of truth or falsity and that (b) the definiens is incapable of truth and falsity. Certainly (a) does not follow from (b) unless "definition" and "definiens" are always synonyms. Parker and Veatch seem to argue only for (b) when they write: e Beardsley and Beardsley, p. 25. 10 Parker and Veatch, p. 81. 1r Salmon, p. 93. REM B. EDWARDS Thus " "Iriangle' means 'three-sidcd piane ligure'" is eithcr true or false, but "three-sided plane figure" is not. Definitions are not true or faise but the1, are, as u'e shall shortly see, good or bad, adequate or inadequate, accorciirig as they more or less accurately present the meanings of their definiends.12 The authors here iderrtify the "definition" with the "de,finiens." Ii1 a sense, they are correct in doing so because "definition" is itseif an ambiguous word u,hich sometimes has tl,e meaning u,hich they assign to it. However, one legitinlate sense of the term is the inclusive sense in which a definition is or contains both a definiendurn and a definiens and at least implicitlv the verb "means" connr:cting them. '.[ire defenders of the proposition theory are talking about detrnitions iir this first sense rvl-ren they assert that they can be true or false. On the other hand, Parker and Veatcir clearly are not talking about definitions in this sense since they refuse to call " "I'riangle' means 'three-sided plane figure'" a "definition." A second comnlon meaning of "definition" is that'i,vhich treats "clefinition" and "definiens" as synon\ims, as rvhen \ /e say that "three-sided plane figure" is the "definition" of "triangle." In this second sense, definitions are clearly not capable of truth or falsity since a definiens is a rvord or phrase and not a ccrnpiete sentence. But it does not follor,v that definitiorrs in the first sertse are incapable of truih or faisitl' since clefinitions in the seconli sense are. Indeed, the proposition theory has never been concerned at all lr.ith the second sense. Let us turn notv to the proposal theory. Is "Let the definiendum rnean the definiens" the proper or standard form for stating definitions ? If so, definitions are no more capable of truth or falsity than any other imperative or rule, such as "Study your homeu'ork!" We have seen already that the mere fact that dictionaries do not explicitly formulate their definitions as propositions is not a sufficient reason for dismissing the proposition theory, and n'e might extend this to cover the proposal theory. \\'e cannot dismiss it merely because definitions are not explicitly formulated as imperatives. What then is \^irorg rvith it ? The proposal theory can be viervecl as an attempt to treat ail definitions in the way in which stipulative definitions are usualh-treated. Is tiris assimilation legitimate ? I{eus terrns when first introduced have no established meaning to be reported, so the introducer must propose that his definiendum rnean his definiens. Proposals can be neither true nor false. However, all dcfiniticns cannot be assirnilateci to this pattern. In lexical ciefinitions, the terms are not nerv; thev already have meanings which can be reported. Whereas part of the purpose of the dictionary may be to recommend that established definitions be carried over into the future, the main purpose of the dictionary is simply to state the established meaning or meanings of a term. The proposal theory is not entirely mistaken in its affirmations, holever. It is wrong in inferring that definitions are not propositions because they (sometimes) have an imperative force, but it is correct in pointing out that they do sometimes have an imperative force. The speaker and the writer consult the dictionary not simply to get information but perhaps primarily to get guidance for their present and future linguistic practice. But the reader who has run across a word which he does not understand consults a dictionary simply to get the facts about what is being said. Does it follow from the admission that definitions sometimes have an imperative force that "Let the definiendum mean the definiens" is the proper form for stating definitions ? It might seem at first that one cannot make this admission and still hold 12 l'arker and Veatch, pp. 8l-82. 18 79 THE TRUTH AND FALSITY OF DEFINITIONS that "The definiendum means the definiens" is the proper form, but actually this is not the case. The imperative force of lexical definitions rests partly upon the existence of past linguistic habits. If we wish to be understood, we ought to conform; and we generally do rvish to be understood. Furthermore, it is now generally acknowledged that declarative assertions can have an imperative force even when they are not formulated as imperatives, as when I say "That radiator is hot" to my little son who is about to touch it. One final argument for the proposal theory remains to be discussed. It is that the proposition theory confuses a definition proper with a meta-definitional theory. As Salmon expresses it: For purposes of logical clarity, it is essential to distinguish carefully between definitions and statements about definitions. A definition itself has the force of a proposal to use a certain word with a certain meaning; as such, it is neither true nor false. The statement that a particular definition is the accepted one is a statement about the definition, not the definition itself. This statement is either true or false.l3 In fairness to his opponent, Salmon should call attention to the fact that his own thesis that a definition "has the force of a proposal to use a certain word with a certain meaning" is also a statement about definitions, just as much as the statement that "a particular definition is the accepted one." The basic difficulty with Salmon's position is that there is really no way to infer that object-language statements are incapable of truth or falsity merely because meta-language statements do have that capability. In particular cases, the two meta-definitional statements just mentioned may be true or false; and any definition of the form "The definiendum means the definiens" may also be true or false as it correctly or incorrectly reports the accepted meaning of a term in an established language. Both object-language and meta-language staternents are propositions calable of truth or falsity. 13 Salmon, pp. 93-94. PRINTED IN BRUGES, BELGIUM, BY THE ST CATHERINE PRESS, LTD.