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1 632 Notre Dame Journal of Formal Logic Volume 35, Number 4, Fall 1994 Reply to Robert Koons ANIL GUPTA and NUEL BELNAP We are grateful to Professor Robert Koons for his excellent, and generous, review (henceforth KR)ofour book The Revision Theory of Truth (henceforth RTT). Koons provides in KR a welcome guide to our RTT, and he puts forward objections that deserve serious consideration. In this note we shall respond only to his principal objection. 1 This objection, which is developed on pp of KR,calls into question our main thesis. As we argue below, however, the objection is not successful. We should forewarn the reader that this note is not self-contained. It presupposes familiarity with RTT (primarily, Chapter 4) and with KR. The main thesis of RTT is that truth is a circular concept. We argued that the Tarski biconditionals, read as partial definitions, constitute an intensionally adequate definition of truth. In other words, if T is a predicate defined by the Tarski-style infinitistic definition (1), (1) x is T = Df (x = p and p) or (x = q and q) or..., then truth and T have the same signification in all possible worlds. 2 Since T is obviously circular, we concluded that truth is circular also. Koons finds fault with this last step. He writes: We can use the Tarski biconditionals to define a new notion, Tarski-wahrheit, which is certainly a circular concept, since the Tarski biconditionals are circular. Gupta and Belnap argue that truth and Tarski-wahrheit are intensionally equivalent. However, is that enough to enable us to conclude that truth itself is a circular concept? [KR, pp ] Koons goes on to argue that it is not enough. He puts forward a condition, stated in (2) below, that he thinks ought to be satisfied before we can legitimately claim that truth is circular. He believes that this condition cannot be satisfied and concludes that our argument is flawed and our main thesis false. Putting in a little more detail, Koons s objection is as follows. Koons observes that the intensional equivalence of a definiendum (e.g., x is a bachelor ) to a circular definiens (e.g., x is either a bachelor or an unmarried male adult ) is insufficient to establish any circularity in the definiendum. Furthermore, Koons thinks, this kind Received May 10, 1995

3 634 ANIL GUPTA and NUEL BELNAP Third, with circular definitions certain distinctions that are hardly in view elsewhere become vitally important. One such is the distinction between intensional equivalence and intensional adequacy of a definiens to a definiendum. With noncircular definitions, the intensional equivalence between a definiendum, x is G, and a definiens, A(x), proves that the definition, x is G = Df A(x), is adequate from the intensional point of view. Not so with circular definitions. For example, the definiendum x is a bachelor is intensionally equivalent to itself. But this does not show that the circular definition, (3) x is a bachelor = Df x is a bachelor, is intensionally adequate to x is a bachelor. For, according to the definition, the statement Benazir Bhutto is a bachelor is Truth-Teller-like, whereas actually it is categorically false. Thus, the circular definiens x is a bachelor is intensionally equivalent to the definiendum but is not intensionally adequate to it. Another way of putting the point is this. The signification of the circular concept defined by (3) is not the same as that of bachelor. Hence, the concept defined by (3) is not intensionally equivalent to the concept of bachelor. Two claims about circular definitions should be clearly distinguished. Let G be an ordinary concept and let (4) be proposed as a definition for it. (4) x is G = Df A(x, G). The two claims are: (5) If the definiens A(x, G) contains G essentially and is intensionally equivalent to the definiendum x is G then G is a circular concept. (6) If the definiens A(x, G) contains G essentially and is intensionally adequate to the definiendum x is G then G is a circular concept. 5 It is correctly observed in KR that (5) is false; the bachelor example above establishes this. But this shows nothing about (6), for (5) and (6) do not say the same thing. (5) is false but (6), we think, is true. And it is (6) that we need for our argument. Observe that (6) is equivalent to (7). (7) If a concept G is intensionally equivalent to a concept H, where H is given an essentially circular stipulative definition, then G is a circular concept. Since truth and T are agreed to be intensionally equivalent, and since (1) is an essentially circular stipulative definition of T, the desired conclusion follows: truth is a circular concept. Fourth, RTT argues that circular concepts have a unique kind of signification. Circular concepts behave in a distinctive way. They exhibit a distinctive pattern of pathological and nonpathological behavior. This pattern ought to be reflected in, and explained by, their signification. The source of the pattern, according to RTT, is the hypothetical character that circular concepts impart to their signification. Since the hypothetical character is associated only with the signification of circular concepts, we think that (7) is plausible. The following analogy might be helpful here. Intensional equivalence with an (essentially) vague concept proves vagueness; intensional

4 REPLY TO BOOK REVIEW 635 equivalence with an (essentially) partial concept proves partiality; similarly, we think, intensional equivalence with an (essentially) circular concept proves circularity. Let s note a methodological consequence of (7): one does not need a finegrained, or substantive, analysis of a concept to establish its circularity. All one needs is an analysis that fixes the intension; nothing more. Consequently, an analysis that suffices to prove circularity may well not and typically will not explain many important features of the concept. This is precisely what we think happens with the Tarski biconditionals (understood definitionally). The biconditionals fix the intension of truth, but they do not explain many important features of the concept. (See the discussion of the Intension and Implication Theses in RTT; see also [1].) Towards the end of KR, it is objected that definitions such as (1) do not explain a certain asymmetry of truth and falsehood. We willingly grant this point, but it leaves undisturbed the argument and the main thesis of RTT. Certain philosophical purposes require a more substantive account of truth than that found in (1). But to establish the circularity of truth, (1) suffices. We have discussed in this note only some of the objections in KR. There are other important objections in KR objections that deserve serious consideration in any assessment of the revision theory of truth. NOTES 1. Our responses to some other objections are in RTT itself and in a letter we wrote to Koons. Koons has, very generously, included extracts from this letter in his review. 2. See RTT, Section IV of Chapter 4 and Sections 6A 6C of Chapter 6. For an explanation of our use of signification, see pp of RTT. 3. At an earlier point in his review, Koons formulates a different demand. He requires that we show that the concept of truth could be introduced for the first time to a cognitive agent by means of the deployment of [a circular] definition [p. 626]. Our view of this demand is stated in the second of our four points. 4. Furthermore, (2) implies, contrary to the message of KR, that every intensionally adequate definition is philosophically adequate. Note that the righthand side in (2) is of the form, Were someone to do ϕ then p. That is, it is a generalized counterfactual conditional. The consequent of this conditional is bound to hold for an intensionally adequate definition. Hence, by the standard stated in (2), such a definition is going to be philosophically adequate. Condition (2) rules, therefore, that (1) is a philosophically adequate definition of truth. The arguments of KR show at most that, with truth, the generalized conditional contained in (2) will have a necessarily false antecedent. But this does not show that the conditional itself is false. 5. Note that the qualification essentially is needed in these claims to rule out trivial counterexamples such as the following: (i) x is H = Df x is an even number & x is prime &(x is either H or non-h). (ii) x is J = Df either [x = a & (a or b is J)] or[x = b & neither a nor b is J]. H and J are defined circularly in (i) and (ii), but this does not establish that H and J express circular concepts. The reason is that circularity, though present, is eliminable and inessential in (i) and (ii). (See RTT, 5A.11, for a discussion of Example (ii).)

5 636 ANIL GUPTA and NUEL BELNAP REFERENCES [1] Gupta, A., A critique of deflationism, Philosophical Topics, vol. 21 (1993), pp [2] Gupta, A., and N. Belnap, The Revision Theory of Truth, MIT Press, Cambridge, [3] Koons, R., Book Review, Notre Dame Journal of Formal Logic, vol. 35 (1994), pp Anil Gupta Department of Philosophy Indiana University Bloomington, IN Nuel Belnap Department of Philosophy University of Pittsburgh Pittsburgh, PA

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