### Quine: Normativity and logic, part II

Some time ago I wrote about the then upcoming Quine seminar led by Arché Professors Graham Priest and Stewart Shapiro. The semester now coming to an end, it's appropriate to talk a little bit about the subject that I briefly touched upon back then: Quine and normativity. Now, the seminar hasn't only been about Quine's view on logic - the discussion has ranged over most of Quine's philosophy (naturalism, meaning & analyticity, holism, revisability, physicalism, intensionality vs extentionality - we've even gone so far as to discuss Quine on ethics and the mind) but with an emphasis on the places where his philosophy overlaps with Arché projects, e.g., modality, vagueness, neo-Fregean philosophy of maths, second-order logic. However, the seminar being headed by two philosophers with a keen interest in the philosophy of logic, the sessions have been dominated by Quine's musings over logic. I'm not complaining.

Obviously, giving a summary of the discussion is out of the question, so I'll just start a bit in medias res, at the point where I thought the discussion was at its most interesting. This - needless to say - has to do with Quine and normativity. In particular, I want to put down in writing some distinctions proposed by Graham Priest on the difficult issue of logic and revisability in Quine. Anyone familiar with Quine's texts on the philosophy of logic will recognize that it's not easy to find a stabel position on the revisability of logic that accomodates all the relevant passages. There is textual evidence both for the position that logic is revisable (it's just normally not practicle to do it - that is, logic is in the centre of our webs of belief) but also for the position that logic, in some sense or other, is (at least partially) exempt from revision. Priest and Shapiro dubbed the former "Radical Quine", so I'll simply call the latter "non-radical Quine".

To provide some context it is perhaps wise to check out some of the interesting papers. In 'Two Dogmas', the tension between Radical Quine and Non-radical Quine surfaces: early on in the paper he distinguishes between two types of analytic statements, namely (1) those that are logically true and the other (2), statements that "can be turned into a logical truth by putting synonyms for synonyms". In the subsequent attack on the notion of analyticity, Quine's focus is on (2), a focus which stays the same throughout the the first part of the paper. Only in §6. Empiricism without the Dogmas, do we see the contours of Radical Quine. Here he says:

It is not altogether easy to square this translatory picture with revision of logic. Shapiro gave the following problem (attributing it to one of his students): Suppose that you are a classicist but become convinced by relevantist arguments, thus revising your logic. Since radical translation 'starts at home', upon changing the logic it would appear as if you had always been reasoning according to relevant logic. Consequently, you could not revise your logic and know about it, although the logic could perhaps change without you noticing. To settle whether such a situation would count as revision of logic, it's time to introduce the distinctions promised above.

Graham Priest laid out the following three versions:

(i) Revision of logical beliefs;

(ii) Revision of logical practice;

(iii) Revision of logic (per se, whatever that means)

So what is the difference? Let us look at (i) first: arguably, to the degree that beliefs about logic have been reflected in the literature on logic, the beliefs have clearly been revised from, say, Aristotle to Frege; although admittedly, this evidence is restricted to the specialists' beliefs. Another question, relating to (ii), is whether our norms of reasoning have been revised as well. Have some patterns of reasoning formerly valid now become invalid, or conversely? Presumably, this question is somewhat harder to answer, but I take it that one could explore the possibility by investigating historical evidence. Surely, some information about reasoning practice must be manifest in historical writings, say mathematical manuscripts.

Importantly, (1) and (2) may come apart, and probably to some extent are apart; i.e., our beliefs about our logic do not fit the actual practice. Thus, it is conceivable that we have been constantly revising our beliefs about logic while the logical practice has remained the same, or that we have revised our logical practice while the beliefs have remained the same. With philosophers suggesting that classical logic is a good model of our practice, it is made abundantly clear how frequent beliefs about logic fail to hit the mark.

In the above sense at least, I take it to be rather straightforward that there is a normative sense in which our beliefs about logic can be mistaken; but is it possible that the practice is mistaken as well? Dummett certainly argued that investigating the underlying meaning-theory could lead us to realise that our logical practice is indeed mistaken (as he thought was the case for classical mathematics). In particular, the practice could fail on account of certain (normative) semantic constraints, such as harmony (and presumably others as well). Since the negation rules for classical logic turned out to be disharmonious, it was up for revision.

However, it's not at all obvious that a similar position on normativity is open for Quine. The description of logic in Word & Object (§13) and the later remarks in Philosophy of Logic (pp. 82-83) does not seem to leave room for normativity - Quine's logic, as Quine's epistemology, is naturalized. Given that we apply radical translation even to our own language, logic is behavioural all the way home; there is no question of correctness and mistake over and above the practice (that is, the distribution of assent and dissent).

Returning to (i) and (ii), then, we could say that for Quine our beliefs are susceptible to revision but our practice is not. That Graham Priest's distinctions lead to such a division is perhaps no surprise, since his 1979 article 'Two Dogmas of Quineanism' applies precisely the distinction between the rules of logic (i.e., our practice) and their corresponding beliefs (so A |- B corresponds to |- A -> B; for Quine, the proponent of classical logic, it's no worry that this presupposes the deduction theorem) to stabilize a position with both the analytic/synthetic distinction and the web of belief type holism.

Before ending this everlasting post, let me briefly move on to (iii). What does it mean to revise logic per se? Well, here at least is one thing we could mean by such a revision. Suppose that you're a realist for logic, that is, you believe that there is fact of the matter of whether or not A is a logical consequence of Gamma, and this fact is mind-independent, language-independent, platonic, (potentially) verification-transcendent, or what not. Now, on such an account, is logic revisable? Surely not. For the realist, the consequence relation would be outside our reach, so to speak.

On the other hand, if you're some kind of anti-realist for logical consequence, it appears tempting to say that (iii) reduces to (ii), or maybe even (i) but I'm not sure how that would work. If reduced to (ii), we return to the disagreement between Dummettian and Quinean positions. In other words, the question of (iii) depends on what we take to be the validity-makers; conventions, language, the world, metaphysical facts, limitations of our minds, etc. Some of these are plausibly candidates for revision, others are not.

Obviously, giving a summary of the discussion is out of the question, so I'll just start a bit in medias res, at the point where I thought the discussion was at its most interesting. This - needless to say - has to do with Quine and normativity. In particular, I want to put down in writing some distinctions proposed by Graham Priest on the difficult issue of logic and revisability in Quine. Anyone familiar with Quine's texts on the philosophy of logic will recognize that it's not easy to find a stabel position on the revisability of logic that accomodates all the relevant passages. There is textual evidence both for the position that logic is revisable (it's just normally not practicle to do it - that is, logic is in the centre of our webs of belief) but also for the position that logic, in some sense or other, is (at least partially) exempt from revision. Priest and Shapiro dubbed the former "Radical Quine", so I'll simply call the latter "non-radical Quine".

To provide some context it is perhaps wise to check out some of the interesting papers. In 'Two Dogmas', the tension between Radical Quine and Non-radical Quine surfaces: early on in the paper he distinguishes between two types of analytic statements, namely (1) those that are logically true and the other (2), statements that "can be turned into a logical truth by putting synonyms for synonyms". In the subsequent attack on the notion of analyticity, Quine's focus is on (2), a focus which stays the same throughout the the first part of the paper. Only in §6. Empiricism without the Dogmas, do we see the contours of Radical Quine. Here he says:

"[...] no statement is immune to revision. Revision even of the logical laws of the excluded middle has been proposed as a means of simplifying quantum mechanics; and what difference is there in principle between such a shift and the shift whereby Kepler superseded Ptolemy, or Einstein Newton, or Darwin Aristotle?" (p. 43 in From a Logical Point of View)In Philosophy of Logic (1970; 1986 2nd ed.), Radical Quine is challenged by the famous passages on logic in translation. 'Change of logic, change of subject' says Quine, alluding to the radical translation situation where the translator must impose his own logic on the translation in order to make sense of the native. "[L]ogic", says Quine, "is built into translation more fully than other systematic departments of science." (p 82) The reason for this is supposed to captured by the Quinean slogan 'save the obvious' (of course, it's highly contentious to claim that logic is obvious, but I won't go into that now. It suffices to say that Quine related obviousness to completness, and thus perceived this to be a crucial advantage of first-order classical logic).

It is not altogether easy to square this translatory picture with revision of logic. Shapiro gave the following problem (attributing it to one of his students): Suppose that you are a classicist but become convinced by relevantist arguments, thus revising your logic. Since radical translation 'starts at home', upon changing the logic it would appear as if you had always been reasoning according to relevant logic. Consequently, you could not revise your logic and know about it, although the logic could perhaps change without you noticing. To settle whether such a situation would count as revision of logic, it's time to introduce the distinctions promised above.

Graham Priest laid out the following three versions:

(i) Revision of logical beliefs;

(ii) Revision of logical practice;

(iii) Revision of logic (per se, whatever that means)

So what is the difference? Let us look at (i) first: arguably, to the degree that beliefs about logic have been reflected in the literature on logic, the beliefs have clearly been revised from, say, Aristotle to Frege; although admittedly, this evidence is restricted to the specialists' beliefs. Another question, relating to (ii), is whether our norms of reasoning have been revised as well. Have some patterns of reasoning formerly valid now become invalid, or conversely? Presumably, this question is somewhat harder to answer, but I take it that one could explore the possibility by investigating historical evidence. Surely, some information about reasoning practice must be manifest in historical writings, say mathematical manuscripts.

Importantly, (1) and (2) may come apart, and probably to some extent are apart; i.e., our beliefs about our logic do not fit the actual practice. Thus, it is conceivable that we have been constantly revising our beliefs about logic while the logical practice has remained the same, or that we have revised our logical practice while the beliefs have remained the same. With philosophers suggesting that classical logic is a good model of our practice, it is made abundantly clear how frequent beliefs about logic fail to hit the mark.

In the above sense at least, I take it to be rather straightforward that there is a normative sense in which our beliefs about logic can be mistaken; but is it possible that the practice is mistaken as well? Dummett certainly argued that investigating the underlying meaning-theory could lead us to realise that our logical practice is indeed mistaken (as he thought was the case for classical mathematics). In particular, the practice could fail on account of certain (normative) semantic constraints, such as harmony (and presumably others as well). Since the negation rules for classical logic turned out to be disharmonious, it was up for revision.

However, it's not at all obvious that a similar position on normativity is open for Quine. The description of logic in Word & Object (§13) and the later remarks in Philosophy of Logic (pp. 82-83) does not seem to leave room for normativity - Quine's logic, as Quine's epistemology, is naturalized. Given that we apply radical translation even to our own language, logic is behavioural all the way home; there is no question of correctness and mistake over and above the practice (that is, the distribution of assent and dissent).

Returning to (i) and (ii), then, we could say that for Quine our beliefs are susceptible to revision but our practice is not. That Graham Priest's distinctions lead to such a division is perhaps no surprise, since his 1979 article 'Two Dogmas of Quineanism' applies precisely the distinction between the rules of logic (i.e., our practice) and their corresponding beliefs (so A |- B corresponds to |- A -> B; for Quine, the proponent of classical logic, it's no worry that this presupposes the deduction theorem) to stabilize a position with both the analytic/synthetic distinction and the web of belief type holism.

Before ending this everlasting post, let me briefly move on to (iii). What does it mean to revise logic per se? Well, here at least is one thing we could mean by such a revision. Suppose that you're a realist for logic, that is, you believe that there is fact of the matter of whether or not A is a logical consequence of Gamma, and this fact is mind-independent, language-independent, platonic, (potentially) verification-transcendent, or what not. Now, on such an account, is logic revisable? Surely not. For the realist, the consequence relation would be outside our reach, so to speak.

On the other hand, if you're some kind of anti-realist for logical consequence, it appears tempting to say that (iii) reduces to (ii), or maybe even (i) but I'm not sure how that would work. If reduced to (ii), we return to the disagreement between Dummettian and Quinean positions. In other words, the question of (iii) depends on what we take to be the validity-makers; conventions, language, the world, metaphysical facts, limitations of our minds, etc. Some of these are plausibly candidates for revision, others are not.

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