KEN AKIBA

QUINE AND THE LINGUISTIC DOCTRINE OF LOGICAL TRUTH

(Receivedin revised form 9 February 1994)

The linguistic doctrine of logical truth, which was advocated by the logical positivists such as Camap, is the thesis that logical truths are true by linguistic convention. By now philosophers seem to have reached a consensus that Quine has given a decisive refutation to the linguistic doctrine. I think this opinion is unfounded, however, and in this paper I will examine and criticize Quine's arguments against the linguistic doctrine and argue that a certain form of conventionalism is still defensible and indeed fairly plausible. I don't mean to defend all, most, or even much of what has been said under the name of the linguistic doctrine; indeed, I myself will point out a couple of significant mistakes its advocates have made. But I will argue that Quine's main arguments against the doctrine are deficient, and I will try to uncover what I think the advocates of the doctrine should have said, and came very close to saying, but didn't. I assume the reader's moderate familiarity with the linguistic doctrine and Quine's arguments against it, although I will sketch Quine's arguments immediately below. Quine has given several different arguments against the doctrine mainly in his four writings, viz., "Truth by Convention" (Quine, 1936), "Two Dogmas of Empiricism" (Quine, 1951), "Carnap and Logical Truth" (Quine, 1960), and Philosophy o f Logic (Quine, 1970). In all they span more than three decades, and it would not be easy to make a complete summary of his arguments, but I think we could distinguish and summarize the arguments as follows (in order of their first appearance):

Philosophical Studies 78: 237-256, 1995. © 1995KluwerAcademicPublishers. Printed in the Netherlands.

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(i)

"'If in describing logic and mathematics as true by convention what is meant is that the primitives can be conventionally circumscribed in such fashion as to generate all and only the accepted truths of logic and mathematics, the characterization is empty; ... the same might be said of any other body of doctrine as well" (Quine, 1936, pp. 118-9; 1976, p. 102. See also Quine, 1960, sec. 7.)

(ii)

If 'convention' is to be understood as explicit general statements of rules, then "derivation of the truth of any specific statement from the general convention ... requires a logical inference, and this involves us in an infinite regress" (Quine, 1936, p. 120; t976, p. 103. See also Quine, 1960, sec. 4.)

(iii)

The linguistic doctrine "seems to imply nothing that is not already implied by the fact that elementary logic is obvious or can be resolved into obvious steps" (Quine, 1960, p. 355; 1976, p. 112). The linguistic doctrine is empty, of no explanatory value. (See also Quine, 1936, pp. t23-4; 1976, p. 106; 1970, ch. 7.)

(iv)

There is no clear and plausible distinction between the analytic and the synthetic. (See, Quine, 1951, secs. 1-4, and 1960, sec. 9.)

(v)

Logic and mathematics are tested, if only remotely, by observations and thus are not immune to revision. In this regard there is no essential difference between them and empirical science; there is only a difference in degree. (See Quine, 1951, sec. 6; 1960, sec. 6; 1970, ch. 7.)

Before starting our discussion, let me make clear what I will not deal with in the present examination. First, I will not deal with analytic truths in the broad sense, such as 'all bachelors are unmarried': I will focus on logical truths in the narrow (proper) sense of the word ('all unmarried men are unmarried', etc.). Although there are prominent objections to Quine's view about the analytic/synthetic distinction (e.g., Grice and

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Strawson, 1956; Putnam, 1962, 1975a), I regard as indisputable at least one of his points that the extension of analytic truths is not as clear as the extension of logical truths of "elementary" logic (i.e., classical first-order logic). Thus, in what follows I won't discuss the argument (iv) at all. Secondly, I will also set aside m a t h e m a t i c a l truths in the present examination (though apparently things somewhat analogous to what will be said about logical truths can be said about mathematical truths too.) Our focus will be strictly on the so-called truths o f logic. (Also, I won't deal with the argument (i), simply because I think the argument is far less significant than the others.) This is what I am going to do: First, in the next section I will examine the argument (ii), the most celebrated 'regress' argument, point out its flaw (yes, there definitely is one), and contend that the argument does not fill the bill. The examination will naturally lead us to distinguish two kinds of conventionalism which both Quine and the conventionalists have failed to distinguish. Then in Section III I will point out that Quine has overlooked the distinction in some other arguments, namely (iii) and (v). Finally, in Section IV I will consider the argument (v), the revisability argument, more closely, and conclude that at least one of the two kinds of conventionalism is still defensible.

II

Let us take a close look at the 'regress' argument (Quine, 1936). First of all I repeat relevant statements in somewhat abbreviated forms: (3)

A --+ (--,A --+ A);

(5)

[A --+ (-~A --+ A)] --+ {[(-~A ---+A) --+ A] -+ (A --+ A)}; [(~A ---+A) ---+A] ---+(.4 -+ A);

(6)

where A is short for 'Time is money'. And: (II)

VxVyVz[(x = 'p' & y = ' q' & z = 'p --+ q' & x and z are true)

--+ y is true],

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where "z -- 'p ~ q'," for instance, is an abbreviation of "z is of the form °p -+ q'." Quine's goal is to show that (II) (and the like) cannot be regarded as a convention. To open the argument, Quine says: in deriving (6) from (3) and (5) on the authority of (II) we infer, from the general announcement (II) and the specific premise that (3) and (5) are true statements, the conclusion that (7)

(6) is to be true.

An examination of this inference will reveal the regress. (Quine, 1936, p. 120; 1976, p. 103) The regress is basically as follows: From the structure of (3), (5), and (6), we will have: (8)

(3) -- 'p' & (6) = 'q' & (5) -- 'p --+ q' & (3) and (5) are true.

Also as an instantiation of (II) we will have: (9)

[(3) -- 'p' & (6) -- 'q' & (5) -- 'p --+ q' & (3) and (5) are true] --+ (6) is true.

But to derive (7) from (8) and (9), we again have to appeal to (II), and the same pattern will go on indefinitely. The moral Quine draws from this argument is that (II) cannot be introduced as a convention as if it were just another premise comparable to (3) and the like; rather, it should be implicitly observed from the beginning; but then the meaning of '(II) is a convention' becomes unclear. Now, the notion of such an implicit convention may be defensible (see Lewis, 1969). But for the sake of argument I may grant here that a convention must be explicit (or could have been made so from the beginning). I claim that still the above argument doesn't hold up. First of all, I would like to draw the reader's attention to Quine's use of 'truth' in the argument. As we saw in the quotation, the task Quine set on himself was to derive (6) from (3) and (5). But to do so why did he need to semantically ascend from (3) and (5) to '(3) is true' and '(5) is true' first, make inferences at that level, and in the end semantically descend back from '(6) is true' to (6)? Why the detour?

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In this connection, there are a couple of curious things about the logical system Quine employed for the attempted derivation. One is that nowhere in Quine's logical system can we actually find rules which make the ascent and the descent possible. Quine either did not notice that there are the further steps we need rules for, or if he did notice it, did not think much of it. Another, related point is that the logical system Quine employed is based on Lukasiewicz's (1929) axiomatic system, but it is not Lukasiewicz's system itself but the semantic version of it ('truth' being counted as semantic). Lukasiewicz's original system is a deductive system for first-order logic, so the notion of truth does not appear in it. All of these points seem to suggest a certain confusion, or at least lack of attentiveness, on Quine's part. Indeed, they seem to point to a strategy for the derivation of (6) which is far more natural than Quine's: that is, why don't we just derive (6) directly from (3) and (5), without any appeal to the notion of truth? Like this:

(3)

A--+(~A--+A)

(5)

[A---+(~A--+A)]~

{[(~A--+A)~A]--+(A~A)}

[(-~A -+ A) ---+A] --+ (A ---+A).

(6)

After all, this is what we usually do, isn't it? But then what is the principle that entitles us to make this one-step derivation? Presumably it would be something like the following: (II*)

VxVyVz[(x = 'p' & y = 'q' & z = 'p -+ q') --+ y is derivable

from {x, z}]. This can be called the principle of modus ponens. Compare this carefully with (II). Now Quine's regress argument can be reformulated as follows: if (II*) is added to the derivation system as just another premise, then a Quinean regress will arise, for in order to derive (6) from premises (3), (5) and (II*), we have to apply to the premises modus ponens, the principle (II*) itself. (In addition, were we to escape from the regress,

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still the consequence we would arrive at would be only that '(6) is derivable from (3) and (5)', not (6) itself.) In this respect Quine was absolutely correct: (II*) must be implicitly observed from the beginning, not as a premise but as a policy. What I mean by this is that (II*) is a description of a pattem we should obey in derivations. (A further abbreviated form of the description is 'p, p -+ q ~- q'.) When we derive (6) from (3) and (5), it is direct: there are no intermediate steps. (Ii*) is a description of this derivation and derivations of the same pattern. 1 Quine was quite right about this. My point is, however, that in this reformulation of Quine's regress argument, the notion of truth does not appear; that is, truth has nothing to do with the core of the argument. What Quine has really shown is that (II*) and similar principles along Lukasiewicz's original line (e.g., universal instantiation in terms of derivability) must be observed from the beginning, not as premises but as what I call policies; otherwise (6) will not be derived from (3) and (5). But if they are thus observed, then (II) need not be: (II) can be introduced as a premise, as an explicit convention. Still (6) will be derived from (3) and (5) successfully. What is the moral of this? I think it is this: There are indeed two distinct issues involved in Quine's original argument: one is the issue of what derivation rules (or the rules of logical inference) 2 are, 3 and the issue of whether that is determined by convention; the other is the issue of whether those derivation rules are truth-preserving, and the issue of whether that is determined by convention. Note that (II) asserts in effect that the derivation rule modus ponens expressed by (II*) is truthpreserving. Quine conflated these two distinct issues, but the above examination reveals that there still remains a possibility that while what derivation rules are is not determined by convention (at least not by an explicit one), whether they are truth-preserving or not is determined by convention; and consequently, while what the so-called "logical truths" are (i.e., their extension) is not determined by convention, 4 whether the "logical truths" are true or not is determined by convention. So 'logical truths are true by convention" ("Truth by Convention") may still hold true. Note, moreover, that in the present picture, no circularity is involved in language learning. To be sure, we must learn (II*) and the other

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derivation rules in action, not by words; that consists roughly of our being encouraged to derive statements of the form 'q' from statements of the forms 'p' and 'p -+ q' and becoming able to do so (and similarly for the other rules). That way we come to understand the meaning of the logical operators involved. 5 Once this is done, however, there is no problem for us to understand (II) by words (as it is stated above). 6 Or even more radically, we can simply be told that all the derivation rules are truth-preserving: that if a sentence B is derivable from a set F of sentences, then if all the members of F are true, so is B. We can take either this or (II) and the other piecemeal conventions as partial definitions of truth (so no prior comprehensive understanding of the notion of truth is necessary). Not all of this needs to be a part of the actual human history; Quine wouldn't ask for that much for a defense of conventionalism. A possibility is enough. (Recall that Quine has tried to show that it is impossible for us to have (II) as an explicit convention.) Of particular significance in this connection is the fact that in reality, we may have (and may have had) a logic of the truth predicate. Roughly, 7 the logic could have Tarski's (1933) Convention T (viz., 'p' is true +-+p) as its sole axiom, or equivalently it could have the ascension and descension rules (the introduction and elimination rules for the truth predicate) as its derivation rules. (This logic is the one Quine assumed but did not make explicit.) Now, this adds a certain complication to the formulation of our problem: from the standpoint that those derivation rules are already involved in our logic, what I said two paragraphs back is not quite right. If we have the logic of the truth predicate, then it is simply a matter of logic that (II) holds if (II*) does. Or in general, it is not correct to say as I did that there are two distinct issues: one is whether the derivation rules, including those for the truth predicate, are determined by convention, and the other is whether the fact that the derivation rules are truth-preserving is determined by convention; for the derivation rules for the truth predicate themselves determine that all the derivation rules are truth-preserving, so if the former issue is solved negatively, there is no room for the latter issue to be solved positively. So was my contention incorrect after all? Not really. In the present standpoint, what I should have said is that there are two distinct issues: one is whether some derivation rules

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other than thosefor the truth predicate (say, the derivation rules of firstorder logic) 8 are determined by convention, and the other is whether the derivation rules for the truth predicate are determined by convention. Then my claim would be that the answer to the latter question may still be affirmative even if the answer to the former is not. Tarski's so-called Convention T can really be a convention. So whichever way you put it, there is a genuine distinction which Quine has failed to make. (In what follows, for the sake of clarity I will continue to draw the distinction as one between rules and truth rather than one between rules not about truth and rules about truth.) Incidentally, the view that Convention T is really a convention offers a certain viewpoint from which to see the philosophical significance of Tarski's theory of truth, a viewpoint which is altemative to the realistic or physicalistic viewpoint Field (1972) portrayed most lucidly. The resulting view will be indeed quite congenial to the so-called disquotationat (or deflationary) theories of truth proposed by such authors as Grover, Camp and Belnap (1975), Leeds (1978), the later Field (1986), and Horwich (1990). This seems to me to be all in the right direction, but this may make one wonder what more there is in the claim that Convention T is just a convention than in the claim that it is just a logical (disquotational) device-. Admittedly not as much as if Convention T is taken non-disquotationally (somewhat along the line of, say, a correspondence theory of truth). But the claim of conventionality still seems to have a further significance if you consider the following: The initial problem both Quine and the conventionalists were concerned with is the problem of the justification of logic, viz., how the logic we employ, say first-order logic, is justified. If we could claim that the employment of it is just a matter of convention, then that would solve the problem, but Quine showed that at least in one sense of convention (i.e., an explicit convention that could have been stated at the beginning), we can't so claim. Another answer we are now given is that the logic in question is truthful just as a consequence of the logic of truth, but by itself it is unclear why this could be the answer, because it seems that it only replaces the justification problem of first-order logic with the justification problem of the logic of truth; to say that the truth predicate is just a logical device no more solves the problem than to say that conjunction,

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disjunction, negation, etc., are just logical devices. But if we can claim that the employment of the logic of truth is a matter of convention, then it finally solves the entire problem of justification. At least to this extent the claim that the logic of truth is conventional is of fiarther significance. (Indeed, Quine (1970, ch. 1) himself acknowledged that the truth predicate is a useful logical device, but I don't think he would have said that we employ the logic of the truth predicate as a convention.) Now that we untangled the complication caused by the possibility that rules of the truth predicate could be a part of our inferential rules, let us go back to the main issue about the distinction between rules and truth. In response to my claim about the distinction above, one may say in Quine's defense that the distinction I made was not acknowledged even by the conventionalists. With this I agree. They generally failed to notice the important distinction between conventions about rules and conventions about truth. Indeed, how could, say, Carnap have acknowledged this distinction in Carnap (1937) when (at least officially) he eschewed the concept of truth? I think the early conventionalists ought to be faulted for conflating the two issues. If the determination of the derivation rules is taken to be a matter of convention, we must abandon the aforementioned requirement that a convention be explicit. We may be able to do so, but it will require extra work. Whether the early conventionalists actually accepted such a requirement is not my present concern. But as I see it, the conflation of the two distinct issues on the part of the conventionalists has made the linguistic doctrine more vulnerable than it should have been. The main concern of the linguistic doctrine was as its slogan indicates the issue of truth, so if it remains possible that the truthfulness of logical truths is determined by convention, that would be of utmost significance. Now, according to the above view, there can be two kinds of conventionalism: one is conventionalism about what inferential rules are, or rule conventionalism for short; and the other is conventionalism about whether inferential rules are truth-preserving or not, or truth conventionalism. (As regards the choice of the terms, recall the parenthetical remark at the end of the third paragraph back.) In these terms, Quine might have shown, given the explicitness condition, that rule conventionalism is untenable, but he has failed to show that truth

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conventionalism is. In what follows I would like to suggest that truth conventionalism is indeed a defensible view.

III

Quine's failure to distinguish the two separate issues is indeed quite widespread in his work, and because of this some of his other arguments against the linguistic doctrine prove to be equally unsuccessful. Here we will consider the arguments (iii) and (v). First, (iii): the obviousness of elementary logic. Quine maintains that whatever can be explained by the linguistic doctrine can be explained by the mere fact that elementary logic is obvious. But what is obviousness? According to Quine, A sentence is obvious if (a) it is true and (b) any speaker of the language is prepared, for any reason or none, to assent to it without hesitation, unless put off by being asked so obvious a question. (Quine, 1986, p. 206)

The obviousness of logical inference ("obvious steps") can be understood analogously: a logical inference is obvious if (a) it preserves truth from the premises to the conclusion, and (b) any speaker is prepared to make the inference without hesitation. I may grant Quine the obviousness of logical inferences in the sense of (b): logical inferences are inferences we make naturally, without hesitation. But how do we know that (a) is also the case: how do we know that the inferences we make are truth-preserving? Quine emphasizes the lack of boundary between logical truths and empirical truths, and he in fact goes so far as to suggest (Quine, 1970, pp. 96-7) that the obviousness of logical truths is no different in nature from the obviousness of the assertion, e.g., 'It is mining', made in the rain. (This must have stunned Carnap, for he presumed earlier (Carnap, 1963, p. 916) that the sense of obviousness Quine attaches to the obviousness of logical truths must be quite different from the sense he attaches to the obviousness of empirical statements.) Quine's claim suggests the view that we can simply perceive that the inferences we make are truth-preserving. But how do we do that? We make an inference naturally, without hesitation; but in addition to that,

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how do we perceive that the inference is truth-preserving? I must say I have no idea. It is thus quite inadequate to assimilate the obviousness of logical inferences to that of empirical claims. Quine's answer to the question why it is certain that the inferences are truth-preserving, is hence quite unsatisfying. In comparison, the truth conventionalist has a good answer: because we stipulate so. Whether this answer is correct or not, Quine's claim that obviousness explains everything the linguistic doctrine explains, is totally unjustified. Next, (v): the revisability of logic. We will consider later the question whether the logic we employ is revisable as a response to empirical data. But for now, we may grant Quine that it indeed is. Still, what does it mean? It may mean that rule conventionalism is untenable, for it suggests that we are not totally free to choose logic. But the revisability thesis in itself does not have any apparent effect on truth conventionalism, for the thesis itself does not say anything about the truthfulness of the inferential rules involved; it only says that they can be changed. However, it could be incompatible with truth conventionalism if, but only if, it is combined with the claim that the inferential rules may be changed because they may turn out to be not truth-preserving. This account is in fact quite in harmony with the actual attitude of the old conventionalists such as Carnap, for they did not deny that logic is revisable (see, e.g., Carnap, 1937, p. 318; 1963, p. 921); what they did deny was that a change of logic involves a correction of incorrect (viz., non-truth-preserving) inferential rules. For instance, suppose that in response to some recalcitrant facts in, say, quantum mechanics, we change logic from classical to intuitionistic by dropping the law of excluded middle p V-~p. Now, the anti-conventionalist's (or realist's) account of this change is that p V-~p has turned out to be incorrect (i.e., it has turned out that there are instances of the schema which are actually false). In contrast, the truth conventionalist's account is that when we change logic, we change the meaning of the logical connectives V and -1 (and probably all the rest if one subscribes to holism of a sort). This is the well-known 'change of meaning' thesis. The law of excluded middle was correct before the change of logic (though not so now, because it has a different meaning now); no correction of an incorrect rule is involved in the change of logic. Thus, to refute truth conventionalism, one must

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show not only that logic is open to revision, but also that a revision of logic involves a correction of an incorrect rule, not just a change of meaning. However, Quine, at least in his later work, indeed subscribes to the 'change of meaning' thesis. That is most apparent in his Philosophy of Logic, the last of the aforementioned series of writings, in which he says, for instance, "Here, evidently, is the deviant logician's predicament: when he tries to deny the doctrine [that p & -~p is logically false] he only changes the subject" (Quine, 1970, p. 81), and "In repudiating 'p or -~p' he is indeed giving up classical negation, or perhaps alternation [=disjunction], or both" (Quine, 1970, p. 83). 9 Whether or not this has been his view all along, 1° and whether or not there is any problem in the 'change of meaning' thesis, 11 it is obvious that Quine at least has failed to see that the revisability argument itself is no argument against truth conventionalism.

IV

I think I have shown sufficiently well that Quine's arguments against the linguistic doctrine were indeed directed mostly to rule conventionalism and have failed to refute truth conventionalism. But Quine's failure does not mean that truth conventionalism was thereby shown to be plausible. In this final section, I will try to give it some such plausibility. In particular, I will consider and give a negative answer to the issue of whether choosing or revising a logic involves the truthfulness of logical rules. In the actual proceeding below, we will focus on a revision rather than a choice of logic. I will take the anti-conventionalist's assumption that what truth-value a complex statement has, and whether a logical rule is truth-preserving or not, are determined in reality, quite independently of us (our convention or stipulation). I will argue that our abandoning a logical rule does not mean that the rule was shown to be incorrect (not truth-preserving), nor does our keeping a logical rule as it is mean that the rule was shown to be correct (truth-preserving). My argument may not be conclusive, but still I think it should provide sufficient support for truth conventionalism.

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To be specific, let us suppose that the logic we employ at present is classical first-order, or Quine's "elementary," logic. (Generalization of the argument will be discussed in note 13.) And let us consider how this logic could be revised as a response to empirical data. (We haven't actually determined that logic is revisable, but it will be suggested eventually that there is a very weak sense that it is.) First of all, suppose the relevant data are only of atomic facts, i.e., facts which are to be expressed in atomic statements. Or more accurately, suppose what we do or do not observe (in a broad sense of the word) are atomic facts; that is, only 'I observe that p' and 'I do not observe thatp',12 where p is an atomic statement, are the adequate forms of expressions of our observations and the lack thereof. Then I claim that there won't be any reason to revise our present logic. That is because elementary logic is conservative (cf. Gentzen, 1935): that is, in elementary logic we don't derive any atomic statement from any set of atomic statements unless the former is itself a member of the latter. If elementary logic were not conservative, there would be a derivation from a set F of atomic premises to an atomic conclusion B which is not in F; then if it turned out that we observe all the members of I' to hold but do not observe B to hold when and where we expected them to, the logic would be proved to be inadequate and in need of revision. (In the most extreme case, if the logic were inconsistent, it would certainly be in need of revision.) But since elementary logic is indeed conservative, this won't happen. The situation will change, however, if we take complex statements into account. To give a simple example, suppose we come to believe that Vx(Fx --+ Gx) and that Fa, but also that -~Ga (where 'F' and 'G' are certain specific predicates and 'a' is a name). Evidently there is a conflict here which we must resolve, for Ga is derivable from Vx(Fx --+ Gx) and Fa. But how? Theoretically, there are basically two ways. One way by far the easiest way - is to just drop one of the beliefs, most likely Vx(Fx ~ Gx), from our belief system or replace it with something else, without touching the inferential rules of elementary logic. But what if we don't want to throw away any of the beliefs Vx(Fx --+ Gx), Fa, or -~Ga because the first is so central in our conceptual scheme and the latter two are basic data (or for whatever reasons)? Then the only way

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out left to us - the second way - is to make changes in the inferential rules of elementary logic so that Ga will not be derivable from Vx(Fx --+ Gx) and Fa anymore. Then at least in the sense that this second option is theoretically possible, elementary logic is revisable. Admittedly, this example is somewhat simplistic. But even in more complicated cases, the pattern is the same (see, e.g., Putnam, 1969); the only difference is that in those cases we have a large stock of complex statements in our belief system, and those statements are also much more complex (and consequently the relevant derivations are much longer and more complicated). It also can be admitted that the above sense of revisability is very weak. A change of logic is a radical, comprehensive change, so extreme caution is necessary to resort to that option. And in reality it is rather dubious that there ever is a statement so important that we want to keep it even at the exceedingly high cost of a change of logic. But the unlikeliness of a revision in reality is compatible with the revisability in principle. For instance, Popper was a staunch critic of a change of logic and expressed strong caution against such a change in Popper (1970), but even he admitted in the ensuing discussion that logic is "criticizable," i.e., that "in some cases at least we can critically discuss a proposed change in logical theory" (Yourgrau and Breck, 1970, p. 35). Then at least in this sense, logic is revisable. Simplistic as it may be, the above example presents to us the way a general statement is tested. If we believe the general statement Vx(Fx --+ Gx) and observe that Fa, we predict that Ga. If we observe that Ga, the prediction was correct and the general statement will be retained in our belief system. The more we repeat the same pattern with success, the more credible the statement becomes. If it fails the test once, then we have to make changes somewhere, most likely replacing the general statement with some other general statement, but also conceivably changing the logic. Whichever happens, the same pattern of testing procedures again follows it. (But, in fact, so long as this general pattern is acknowledged, even if the possibility of the second alternative, a change of logic, is precluded in a sense other than the minimal one discussed above, it doesn't affect my following argument.)

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What I would like to claim is, however, that none of the above shows either that the general statements and the logical rules we keep as they are truthful (true or truth-preserving), or conversely that those we abandon are not truthful. Truth has nothing to do with them, I claim. My argument (if it can be called so) is extremely simple: Just look at the above stories again; there was in them absolutely no reference to truth-values. Everything was understood at the deductive-syntactic level (a derivation of one statement from others, a contradiction of one belief content with another, etc.). Whatever truth-values we assign to the statements involved, nothing needs to be changed. For instance, suppose that in reality both Vx(Fx --+ Gx) and Fa are true and Ga is false, but one of the inferential rules which allow us to derive the latter from the former, namely universal instantiation or modus ponens, is not truth-preserving. Still, if we observed that Fa but not Ga, we may (more likely) abandon Vx(Fx --+ Gx) instead of the incorrect rule. Or in rare cases the opposite may happen; that is, we may abandon a correct rule instead of a false complex statement. If we assume that the truth-values of statements are determined in reality, quite independently of us, then we certainly have no way of knowing what those truth-values are, and they have absolutely no influence on our decision of.what changes to make or not to make to resolve deductive-syntactic conflicts in our belief system. One may say that at least most beliefs acquired by observations ought to be true. I may grant that. But what are the forms of the contents of those beliefs? Atomic statements? Atomic statements and their negations at most? As I suggested in the last section, we cannot resort to the idea that complex facts are directly perceivable. And even if those privileged statements are considered true and will never be discarded, there remain the vast majority of statements, complex statements in particular, whose truth-values are still completely undetermined. Note that it begs the question to use truth-tables or other semantic devices to determine the truth-values of those complex statements. For what justifies those truth-tables? They are constructed from the inferential rules under consideration on the assumption that those inferential rules are truth-preserving. But whether this assumption is correct or not is now in question.

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Thus we may conclude that nothing in reality determines the truthvalues of complex statements and whether our inferential rules are truth-preserving or not. But if so, we may arbitrarily decide them; specifically, we may stipulate that our socially sanctioned, "correct" inferential rules be indeed truth-preserving. That is, we may say that the inferential rules are truth-preserving and the logical truths are true both by convention. Because the above stories are as I said somewhat simplistic, I wouldn't claim that truth conventionalism was decisively shown to be correct. What is manifestly missing in particular is probabilistic elements in belief revision. 13 But my point about the irrelevance of truth-values seems to hold quite generally, and combined with Quine's failure in refutation, this conventionalism seems to be at least much more plausible than Quine's kind of realism) 4

NOTES 1 Whether the description is a description of a fact or a description of a norm is not our present concern. z I will also call them logical rules or inferential rules. 3 This includes the issue of what logical constants are. 4 Here one might complain that logical truths are usually defined semantically rather than deductively. But in the case of first-order logic, which was Quine's and the conventionalists' main concern, because of completeness the logical troths can be determined deductively too. (This is of course also tree of all the other complete logics.) Thus if the derivation rules are determined non-conventionally, so are the logical troths. 5 The locus classicus of the view that the meaning of logical operators is determined by derivation rules is Gentzen (1935). 6 When Geoffrey Hellman says, in the mouth of his fictitious Carnap*, that the 'regress' argument seems to conflate two distinct issues, the issue of language learning and the issue of language-based truth (Hellman, 1986, p. 199), he may have something similar in mind, though his contentions otherwise seem to be quite different from mine. 7 Of course, to avoid the Liar Paradox we need certain restrictions on the following rules for a rich language. But here I set aside complications unnecessm3, for our present discussion. For more precise roles, see Kripke (1975) and Kremer (1988). 8 We don't need to assume here that all the derivation rules except those for the truth predicate must be in the same status in this regard. There can be other derivation rules

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which, like those for the math predicate, could have been presented as explicit conventions without circularity or regress. We will come back to this point in note 13. 9 Or even his claim in (iii) suggests the same standpoint: the laws of elementary logic, before a revision, are obvious, according to Quine; but as we saw, obviousness is supposed to imply truth; so the laws must be, before the revision, in fact true (or math-preserving). l0 Some such as Putnam (1983) and Dummett (1976) think that Quine in the later work backslid from his earlier and presumably better position against the 'change of meaning' thesis. But Quine's sympathy with the thesis can be traced back even to his earliest work, "Truth by Convention" (the last two paragraphs of sec. 2). n In fact, I think its advocates' argument that just because certain logical operators have changed their meaning, apparently the same sentences which contain the operators changed their math-values, is not quite correct. In my view, the meaning of the operators is determined by their inferential rules, so if their inferential rules change, so does their meaning. But the change of the meaning itself does not automatically change the truthvalues of the relevant sentences; on their own, they are unrelated. It is not the meaning, but our (tacit) decision to make the new inferential rules to be math-preserving, that is what changes the truth-values of the sentences. (Should we decide not to make them so, then even when the meaning changes, the math-values might not.) By the same token, in my opinion the supposedly improved slogan (cf. Camap, 1963, p. 916) of the linguistic doctrine, 'logical truths are true solely in virtue of the meaning of the logical operators', is in fact not as good as the original, 'true by convention' version. This is another indication that there was a conflation between the issue of rules and the issue of truth in the conventionalists' thinking. 12 Note that this is different from 'I observe that --,p' in the present context. 13 Another is a generalized account for the cases in which the logic in question is not classical first-order. Three things can be said in this connection. First, note that most of the other logics we may be interested in, e.g., intuitionistic first-order logic, simple type theories for both classical and intuitionistic second- and higher-order logics, are conservative, too (cf. Gentzen, 1935; Tait, 1966; Takahashi, t967;Prawitz, 1967, t968). So without considerations about complex statements those logics won't be proved to be inadequate, either. Second, in the case of an incomplete logic, such as second- and higher-order logics, if one considers a sound but incomplete deductive system for the logic, such as simple type theory, then one can still make the same argument as above to show that nothing in reality determines that the deductive rules of the system are math-preserving; that is, theorems of the system are tree only by convention. This is slightly weaker than the thesis that logical truths (in the semantic sense) of the logic are tree by convention, but at least it shows that a large number of the "logical truths" need not be true. Third and lastly, let us not forget the possibility alluded to in note 8, that a certain portion of logic may be regarded as a convention in the same sense in which the logic of the truth predicate is, namely in the sense that its deductive rules or even its semantic rules could have been introduced explicitly without circularity or regress. This

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possibility seems to be quite realistic when a strong, incomplete logic is in question. If that portion of logic is considered to be a convention which is understandable on the basis of the understanding of a certain "core" logic (elementary logic?) together with e.g. set theory, then the point that the inferential rules of the core logic need not be genuinely truth-preserving will carry over to that portion of logic. 14 I wotfld like to thank Hartry Field, Brian Loar, and an anonymous referee for their helpful comments on the paper, and Margaret Sweetman for her kind assistance.

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