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The short answer is that Quine is not a mathematical realist as intended in the question (on my reading of it). Why does he call himself a realist? Because he practices what he preaches. Indeterminacy of translation, and hence meaning, implies that words only mean as relata in a scheme, not as individual references to raw reality or mental content. Holism of ...


8

"Conventionalism" was the original position of positivists, which came to be seen as a failure after Quine's criticisms of truth by convention and the analytic/synthetic distinction. Wittgenstein abandoned it even earlier. The idea was that science uses what Carnap called "linguistic frameworks" based on conceptual schemes, axiomatizing ...


7

The notion of a priori changed a lot since Kant, see Did Kant consider Newtonian mechanics a priori? Today they are seen as potentially fallible, even if not empirical. The Austrian school, including Brentano’s pupils Stumpf, Husserl and Reinach, and more recently "Manchester three" Mulligan, Simons, and Barry Smith, focused on more immediate and ...


7

Quine's attack on the analytic/synthetic distinction is contained in a series of papers: Truth by Convention, Two Dogmas of Empiricism, Carnap on Logical Truth, and in the early chapters of Word and Object. In broad brush terms he argues: Attempts to establish that some sentences are true by virtue of their meanings is either vacuously true or viciously ...


6

It would be to argue against meanings as mental or objective entities. Grice and Strawson rely on meaning as something propositional statement "inherently" has, Quine's position, like late Wittgenstein's, is to replace reified meanings with linguistic roles in social use when interpreting language. In Word and Object, that came out about a decade after the ...


4

The OP is very close to Quine's considered view of necessity, as e.g. in Pursuit of Truth: "In respect of utility there is less to be said for necessity than for the propositional attitudes. The expression does serve a purpose in daily discourse, but of a shallow sort. We modify a sentence with the adverb 'necessarily' when it is a sentence presumed ...


2

I. I do agree with Barcan and Kripke: if two things are actually one and the same, then they are necessarily one and the same. As far as my judgment can discern, this is just the statement that, for all possible worlds or scenarios, x exists if and only if x exists. So when we say that "Hesperus is Phosphorus," or that "the morning star is the evening star,"...


2

"Blue + Yellow = Green." It's basically a reformulation of 7+5=12, but it helps get the point across for beginners. There's by definition nothing "green" about "blue," nor anything by definition "green" about "yellow," so there's no way to logically deduce this (i.e., it's not a tautology). However, when you add them together you get green, and you get it ...


1

Your post seems to involve two question. A first shallower and a second deeper one. The first question: "Why does the very mathematics work that has been axiomatically developed in the 20th century"? The semi-obivous answer: Because it has been axiomatized exactly in order to render mathematical results which were in use in the empirical sciencies for ...


1

A statement like "analytical" is just an indicator of a new approach. The holders of such ideas are suggesting they have something better than before. They do though have to prove it and probably you will discover it is just rebranding the product. Why rebrand the old product if you have fundamentally changed it? Because you have not, you are just window ...


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