Why does Quine's argument threaten logical truths?

Question

At the end of this video on Quine's critique of the analytic/synthetic distinction, there is an argument about why logical truths are suspect, because of Quine's critique:

Quine's argument also threatens the idea of logical truths -- what Quine called analytic statements of the first class [...] [Quine] grants logical truths. But we might think that there is a bit of a problem here. Let's take a logical truth of the form $∀x (Vx → Vx)$ or "if x is a vixen then x is a vixen" or more colloquially "all vixens are vixens"... but this only works if each instance of "vixen" has the same meaning. If the first token of vixens means female foxes and the second token of vixens means attractive women, then obviously this statement is false.

Ordinarily, we would say that this kind of thing is not a counter example to logical truths because it would be equivocating on the term vixen. When we characterize logical truths we have to specify the different tokens of the same expression have the same meaning. It must be the first token of vixen is synonymous with the second token of vixen. Without sameness of meaning it is not quite so obvious how we are to understand logical truths.

I have a bit of a trouble interpreting what is being said above. Specifically, what does the speaker mean when he says If the first token of vixens means female foxes and the second token of vixens means attractive women, then obviously this statement is false? What is the first and second token in the sentence "all vixens are vixens", and why they can have different meanings? I understand how in general in our language the word "vixen" might have different meanings, but how can it change in a sentence such as "if x is a vixen then x is a vixen"? To me, when I read the sentence the word "vixen" represents a label of some category, it doesn't matter how the category is defined or whether the definition is correct. What matters is that there is a definition and it has the label "vixen" slapped on it and x might match that definition or not.

Answer 1

One thing to keep in mind is Quine's behaviorism about language. Per Roth[03]:

Quine emphasizes that language learning, to be explained at all, must be explained behaviorally. "I hold further that the behaviorist approach is mandatory. In psychology, one may or may not be a behaviorist, but in linguistics one has no choice."

For Quine, then, logic per se is not quite a study of necessary, if ethereal, truths, i.e. a logical truth is not a pure a priori necessity.^M The expectation that, "A is A," is "always" true is more relative than that: we expect it to be true when we are engaging with texts written by members of the community of logicians, because this community has a recognized standard of behavior, a commitment to "clarity." It would be unclear behavior, for a normal logician, to change the value of a variable "mid-stream," so if we are linguistically reasoning in a context where this behavior is unexpected, we can tentatively or experimentally assume that normal logicians don't tend to do such things.

Alternatively, Quine was (to put it aggressively) inconsistent with respect to his theory of intension-vs.-extension, or (less aggressively) he did not have an unalterably settled theory of these things. There is something seemingly intensionalistic about his saying, "Change the logic, change the subject," and he indulges in a bit of poesy when he claims that second-order logic is "set theory in sheep's clothing" while himself being the progenitor of the most bizarre family of set theories there is (NF studies). His willingness to countenance a peculiar kind of Platonism about mathematics might seem out of line with his aversion to "creatures of darkness" (what could be darker than the unlight of a realm beyond causal relationships with us?), but it could just be, again, that he wasn't often looking for absolute certainty, nor did he overestimate himself as having achieved such certainty.

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To put this all in terms of my interpretation of Quine's thinking in "Two Dogmas":

1. If the justification of, "The concept of A can be decomposed into the concepts of B + C," is equivalent to the justification of, "The word A is defined in terms of the words B and C," then this fact of definition is not itself true "by definition." It is not necessary that I use the word A to refer to compositions of B's and C's; "By A, I mean B + C," is synthetic (it can be denied without contradiction that I mean one thing by another).

2. By contrast, the statement, "I define A as A," seems off-key. It's like the scene in the old cartoon where the pig and the duck are trying to sleep in the same bed, and the pig is absentmindedly saying, "Good night," in two different languages. From the duck's point of view, there is no nontrivial point-of-entry into the intended semantics of the pig's words. This circularity is even worse if we say, "'Bonsoir' means what 'bonsoir' means," or schematically, "'A' means A."

Insofar as Quine "accepts" logical truths like, "A = A," then, he doesn't need to be accepting them as substantive or important. Given the caliber of his mathematical knowledge, I assume he was both intellectually and practically familiar with the distinction between trivial and nontrivial solutions to formal problems, so I would venture to guess that he might've been willing to attribute trivial verity to logical truths, but then per his indeterminacy-of-translation and "changing logics changes subjects" attitudes, even this verity need not be more than conjectural in the limit.

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^MIn "Quine on Modality" (Føllesdal[68]), the author remarks:

Answer 2

Quine's arguments against analyticity do not apply to logical truths - at least from Quine's perspective on the subject.

For Quine, logic is rooted in grammar. Logic is concerned with structural features of language. Some words or phrases can be identified as 'logical particles' and are distinguished from other words and phrases that are not. We can recognise that a sentence such as "no unmarried man is married" is a logical truth without having to understand the meaning of 'married' or 'man'. What makes it a logical truth is not some fact about meanings, but the fact that the sentence is true if we uniformly subsitute other words for 'married' or for 'man'.

Quine prefers not to speak of meanings, since he considers the concept to be too vague to provide a foundation for logic. He thinks of logic in terms of substitutivity. Logical truths remain true under uniform substitution of words other than the logical particles. By contrast, the sentence, "no bachelor is married" is not a logical truth since it does not remain true if we substitute 'bachelor' or 'married' separately. Hence his criticisms of analyticity do not carry over to logical truths.

While it might be possible for someone to utter the sentence, "all vixens are vixens," with the intended sense that all female foxes are bad-tempered women, it would be a very odd thing to do. I suspect Quine would say that the sentence is being used in a specific contextual fashion that the audience would recognise as different from the conventional logical truth through its inferential consequences.

Answer 3

From Conifold:

The point of Quine's critique is that meaning is an ephemeral notion that cannot be pinned down in a non-circular way, i.e. without appealing to equivalents like synonymy or analyticity. And if we cannot pin down "the same meaning" then what sense does it make for the "meaning" of different instances of "vixen" to be the "same"? It is not even clear what "changing the meaning" is about considering that there is no tangible entity to do the changing in the first place. "Defining a category" does not help because the "defining" is done in terms of other categories with the same problem.