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Is Math Metaphysical? Math is not physical (composed of matter/energy), though all physical things seem to conform to it. Does this make Math Metaphysical and mathematicians Metaphysicians?

I have no problem at all with what Stephen says, but would add a couple of things. First, Stephen didn't address what might actually be the questioner's main concern, i.e. whether the fact that "all physical things seem to conform to it" makes mathematics metaphysical. What is "it" here? Mathematics keeps growing, and one of the main sources of growth is that new things keep coming along (such as new scientific findings) for which existing mathematics is no help. The formulation of general relativity, for instance, required new mathematics that had been developed to some degree (by Riemann and others) before 1915, but without any thought that it might someday actually apply to something in the world out there. The further development of differential geometry was largely in response to its employment in theoretical physics (though of course it then took on a life of its own, as mathematical ideas do). And these new developments invariably (perhaps inevitably) don't quite fit, in various ways,...

Does Quine's critique of the analytic-synthetic distinction also apply to circular definitions? For example: a 'bachelor' is an 'unmarried male' seems analytic, and 'bachelor' and 'unmarried male' are synonyms. But consider: 'condescension' means a 'patronizing' attitude. Of course, 'condescension' and 'patronizing' are defined in terms of each other. Are all definitions that are circular in this way still susceptible to Quine's critique of the analytic-synthetic distinction, because they trade on the synonymy of the definiens and definienda?

This question reflects what I think is a widespread conception of Quine's critique, which is that it applies to ordinary colloquial language. Quine actually went much further than that. He was fundamentally skeptical of synonymity as well, and thought he could cast doubt even on the idea that you could stipulate synonymity, by setting up, say, an axiom system or, on a less formal basis, local "meaning postulates." You can regiment all you like, but you can't control what becomes of your regimentations; the most eloquent recent articulation of this view, in endlessly fascinating scientific detail, is Mark Wilson's work (see esp. his book Wandering Significance ). So the answer to the question is "yes." Quine didn't think in the local "circularity" terms in which the question is posed; he considered all human knowledge, starting with the most elementary common-sense knowledge and reaching to the most abstract representations of theoretical physics, to be one gigantic reciprocally-supportive circle...

It's often said that we cannot predict which scientific discoveries will turn out to have practical value, and so we should encourage scientific curiosity and investigation even in cases where the subject matter seems frivolous or esoteric. To take one famous example, G.H. Hardy thought that number theory was perfectly useless, but it is now indispensable to cryptography. Could the same be said of philosophy? Are there philosophical theories that have had unforeseen benefits? Or is it safe to conclude that at least some philosophical pursuits really are just "useless"?

As useless as art, literature, music, or just about anything you do as an end in itself rather than a means toward some other end in itself. Most important science wasn't done for the purpose of achieving "practical" results, but to satisfy some inner compulsion, of the kind that Plato describes very well in his cave story. That said, just about all scientific disciplines have emerged, one way or another, from philosophy (though philosophy itself, if you consider Plato as an important milestone, seems to have been inspired by mathematics), so it's certainly been of very considerable practical use in that sense.