29 September 2013

Peregrin on "Logic and Reasoning"

I just finished listening to this talk; I quite liked it. Peregrin defends the view that logic is "constitutive" of rationality, and not merely normative for it: the laws of logic make the game of giving and asking for reasons possible, not what tells you which moves within the game are good ones or bad ones to make. This isn't a new idea, but I very much liked seeing someone defend it without leaning on the fact that they are also trying to exposit Kant's views on general logic, or the views of the author of the Tractatus.

There is one bit that struck me as odd, though, which is why I'm writing this post: at one point Peregrin is concerned to show that his view can still claim that logic is "a supreme arbiter of rationality" despite not allowing the laws of logic to be violated (in general -- he allows occasional violations by single members of linguistic communities, but says very little about the details of how even this could happen given that the laws violated constitute the act which is supposed to defy them). His reply seems odd, though: He says that being rational may be "having implications, negations, etc., not using them in an appropriate way."

This seems wrong for at least two reasons. One is that minutes earlier he'd allowed that there might be linguistic communities which don't have implication (a group in Siberia studied by a Soviet scientist is discussed as a possible example), and so don't have modus ponens because of this. So, what he put on his slide seems to contradict his own commentary on it, unless he wants those linguistic communities to fail to be rational (which is obviously undesirable). The other is a generalization of the point Peregrin made when he allowed for a linguistic community to lack "implication": Why should the material conditional, classical negation, exclusive disjunction, etc. be so important for being rational as such? They seem to be of fairly recent invention, and sit uneasily next to the ordinary-language terms often used to characterize them (as anyone who has ever had to teach undergraduates well knows). How could having them in one's language be so important as to constitute the game of giving and asking for reasons?

The remedy to this, I think, is just what Sebastian Rödl talks about in the first chapter of "Categories of the Temporal": we should retain the idea that logic is constitutive of thought as such, but not identify this logic with a calculus (and so in particular not with classical logic and its material conditional etc.): the possession of any particular logical calculus is an optional tool in reasoning, not constitutive of it. The kind of logic which is constitutive of thought as such is transcendental logic, not general logic: it essentially involves reference to thought's relationship to its objects (and so refers to inquiry, the process by which those objects are known). Being rational cannot plausibly be "having implications, negations, etc." but it is (at least plausibly) having distinctions of truth and falsity, of oneself as an inquirer who can err and be corrected by others or correct oneself, of the objects of inquiry as being capable (at least in many cases) of settling questions about them when some are in error or ignorant of them, etc. It is hard to see how one can be a rational subject without such notions; it is the task of a transcendental logic to outline them and give their laws, without which thought as such is impossible.

I think this sort of view also helps to make sense of so-called disagreements in logic (as between classical and intuitionist logicians, or dialetheists and everyone else): they are not expressing conflicting views on "the" logic constitutive of thought as such (which would have to be a transcendental logic), but expressing views which disagree with one another on which calculus captures the laws of thought as such (or which are normatively correct in describing how one should proceed if one wishes to think rationally, as they tend to think of it). Accepting or rejecting the law of excluded middle, or rejecting (and not merely accepting) the law of noncontradiction can then be seen not as doing the impossible (if laws of logic are constitutive of thought as such), but as advancing rival views on a distinct question -- one which the transcendental logician may reject as relying on a false assumption, that the logic of thought as such is the logic of a calculus, is general and not transcendental logic. So long as it is not among the laws of transcendental logic that one has a particular view of transcendental logic (which would be a surprising result), the disagreements in logic do not need to be seen as violating laws which are constitutive of thought as such, and can be regarded as genuine disagreements without overturning the view of logical laws as constitutive.

It might be thought that the existence of dialetheists still posed a problem: Didn't I say that a distinction between truth and falsity was (plausibly) involved in the laws of transcendental logic, and isn't this just what the dialetheists want to argue about? Are they not still seemingly violating the laws which are supposed to be constitutive of thought as such?

I think not: Even in the extreme case of Graham Priest's acceptance of every version of the denial of the law of noncontradiction he is presented with, one can find him affirming (in "Doubt Truth to Be a Liar") that one cannot both affirm and deny a proposition simultaneously. He views this as a psychological claim, and his ultimate evidence for it is phenomenological, but he recognizes that he needs something of this sort to make his own views so much as stateable: if he has access to no such distinction as this, then he can't intelligibly say that even dialetheists believe that there are monaletheias (propositions which are only true or false, and not both): without something in his system to keep two truth-values apart in the end, there is nothing to keep his opponent from asking "Yes, yes, you accept that P is true and not false, and is a monoletheia -- but how do I know you don't also hold it to be false and not true, and a dialetheia?" (The context in which Priest invokes an absolute psychological-phenomenological distinction between affirmation and denial is one in which he has rehearsed the many "revenge" Liars that a dialetheistical treatment of the Liar leads to; Priest needs some way to handle "This sentence is false and is a monoletheia", which on his treatment is both true and false and has both one and two truth-values, without undermining his own view that dialetheism is compatible with classical monoletheic logic "mostly" holding in everyday reasoning. I would look at my copy of the book to confirm this and find references, but I am lazy and as far as I know I'm the only person who feels a need both to defend the constitutive view of the laws of logic and to make sense of Graham Priest.) So I think that Priest can be seen as still abiding by (and affirming and not denying) the distinction between truth and falsity at the level of generality at which transcendental logic needs to deal with such truth-values: he just has peculiar views about how truth-predicates should be used in formal languages, etc. When it comes to knowing that when a question has been settled in inquiry it is not also still open, or that we can err when we hold that a question has been settled or not and might need reopening, Priest (and I think any other dialetheist who considers the issue) says nothing but what the transcendental logician says we all know qua rational beings: what is, is, and what is not, is not.

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