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A link to the paper is here:

https://www.theologie.uzh.ch/dam/jcr:ffffffff-fbd6-1538-0000-000070cf64bc/Quine51.pdf

So in the paper Quine gives two types of analytic statements:

  1. No unmarried man is married.
  2. No bachelor is married.

So for Quine, the second statement is problematic and the subject of the paper.

My concern is with the first statement, and specifically what he says about it here:

"' If we suppose a prior inventory of logical particles, comprising 'no,' 'un-' 'if,' 'then,' 'and,' etc., then in general a logical truth is a statement which is true and remains true under all reinterpretations of its components other than the logical particles."

But how could we make such an inventory of logical particles... and why wouldn't they be subject to the same issues of synonymy as bachelor? These logical particles arrive in language in an organic way just as words like bachelor do.

Now perhaps we could construct a purely artificial notation for logical operators for the sole purpose of logical deduction... but to use them we'd have to describe them in terms of words we already know.. But those words we know will have issues of synonymy. So we get an infinite regress...

So doesn't Quine have to throw out logical truths of any kind?

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    It sounds like you’d like to know about meaning postulates for logical operators. Would you accept that while it might be a synthetic issue whether any given language practice uses any particular logical semantics, it doesn’t need to be synthetic to describe a plurality of such logics in artificial models?
    – Sofie Selnes
    Apr 5, 2020 at 8:10
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    The issue is that, on the basis of syntax alone, we can "see" that the statement "No not-married man is married" is true, while for the "equivalent" statement "No bachelor is married" we need semantics. But your concern is right: it is not realistic that we can use (learn, etc.) natural language separating syntax from semantics.
    – Mauro ALLEGRANZA
    Apr 5, 2020 at 8:37
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    In other words: how we "understand" negation ? Obviously semantically: it reverses the truth-value.
    – Mauro ALLEGRANZA
    Apr 5, 2020 at 8:48
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    Quine does "throw out" logical truths of any kind, or rather he throws them in with everything else:"Revision even of the logical law 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?" It is just that there is a short agreed upon list of "logical particles", but nothing remotely so tractable for synonymy. So the problem with analyticity is much worse even in the plainly practical sense.
    – Conifold
    Apr 5, 2020 at 8:57
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    @AmeetSharma 1. What issues of synonymy? - 2. Logical words refer to things in the same sense that "bachelor" refers to something. In both cases, we can be mistaken as to what it is. If so, confusion ensue. But we use logical words to refer to a very small set of particular things that we think of as, well, logical things. There is usually no confusion. The distinction is clear. This is a pragmatic issue, not philosophy. The inventory is for us to decide what it is. Maybe we are missing some but so what? We only need is to know what we mean and understand each other. Much like for "bachelor".
    – Speakpigeon
    Apr 6, 2020 at 16:31

2 Answers 2

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To paraphrase your question, Quine allows himself to distinguish between 'logical particles' and other words. The logical particles (or constants) allow us to recognise sentences like "no unmarried man is unmarried" as logical truths because we do not need to understand the meaning of 'unmarried' or 'man' to know they are true. They are true under all uniform substitutions of the words other than the logical particles. By contrast the contentious claim that the sentence "no bachelor is unmarried" is analytic depends on understanding the meaning of 'bachelor' and 'unmarried'. Since Quine rejects the idea that there are sentences that are true purely in virtue of their meanings, why doesn't this rejection apply to logical truths as well? How are the logical particles distinguished from other terms?

It may help to read the answer I gave to this question about distinguishing logic from non-logic. There are many ways to ground and formulate the distinction. Quine himself sees logic as grounded in grammar. He expounds this view in his book "Philosophy of Logic" (Harvard, 1986). According to Quine, logic studies the truth conditions that hinge solely on grammatical constructions. The logical constants are those expressions that play a special structural or formal role in sentences.

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  • If seems pretty unreasonable not to consider semantics formalized syntactically such as this: Rudolf Carnap's (1952) Meaning Postulate: ∀x (Bachelor(x) → ¬Married(x)).
    – polcott
    May 4, 2020 at 0:33
  • "They are true under all uniform substitutions". But why? and by whose authority... I don't see the difference. By what mechanism do we know that "unmarried man" is the same as "man that is not married". The same "interchangeability" objection with meanings is there here also. "'Unmarried man' has 12 letters. ' I can't substitute 'Man that is not married' into this sentence and maintain truth.
    – Ameet Sharma
    May 4, 2020 at 3:55
  • The point, for Quine, is that in the case of logical truths we do not need to know the meanings of 'married' and 'man'. An un-F'd X is the same thing as an X that has not been F'd. This is a grammatical feature of how the logical particles work in English. There is no authority that makes it so, it is just a natural fact about how the English language works. Some features of a natural language are purely structural and some are not. It would be a fair point to say that on Quine's account the logical particles look like a laundry list, but I don't think this would have bothered Quine.
    – Bumble
    May 4, 2020 at 6:30
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This is the essence of the above question:

1. No unmarried man is married.
My concern is with the first statement, and specifically what he says about it...

This is a direct quote from Quine's paper:
(1) No unmarried man is married.
The relevant feature of this example is that it is not merely true as it stands, but remains true under any and all reinterpretations of 'man' and 'married.'

When Quine says:
remains true under any and all reinterpretations of 'man' and 'married.'

He means: Ameet Sharma quote of Quine:
"remains true under all reinterpretations of its components other than the logical particles."

Now perhaps we could construct a purely artificial notation for logical operators for the sole purpose of logical deduction...

Predicate logic already has all of those logical particles arranged together in a system of reasoning that is well understood and accepted.

Why wouldn't they be subject to the same issues of synonymy as bachelor?
∀x∀y (P(x) ↔ P(y)) is very well established in predicate logic and known to be true.

Rudolf Carnap's (1952) Meaning Postulate:
∀x (Bachelor(x) → ¬Married(x)) is not nearly as well established or accepted.

When we formalize the first sentence:"No unmarried man is married":
in predicate logic: ¬∃x (¬P(x) ∧ P(x)) (corrected by: Eliran) its basic logic structure proves that it is true under all reinterpretations of its components other than the logical particles (no matter what the predicate or bound variable is).

So doesn't Quine have to throw out logical truths of any kind?
The semantics of predicate logic is already very well established so Quine cannot simply throw it out.

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