Category Archives: Truth Through Proof

TTP, 6. §2.I Projectivism

Suppose we want to claim that some class of sentences that are grammatically like those of straightforwardly fact-stating, representational, belief-expressing discourse actually  have a quite different semantic function (and remember, this is going to be Weir’s line about mathematical sentences: … Continue reading

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TTP, 5. New readers start here …

So at long last, it’s back to discussing Alan Weir’s Truth Through Proof (henceforth, TTP). And apologies to Alan, and anyone else, who has been eagerly waiting for further  instalments. Let’s quickly, in this post, review where we’ve got to … Continue reading

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TTP, 4. §1.III: Sense, circumstance, world

In the present section, Weir says something about the kind of semantic framework he favours, and in particular about issues of context-sensitivity. Here I do little more than summarize. The basic idea is very familiar. “Utterances of declarative sentences are … Continue reading

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TTP, 3. §§1.I–II: Realisms

As we can see from our initial specification of his position, to get Weir’s philosophy of mathematics to fly will involve accepting some substantial and potentially controversial claims in the philosophy of language and metaphysics. The first two chapters of … Continue reading

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TTP, 2. Introduction: Options and Weir’s way forward

Faced with the Benacerrafian challenge, what are the options? Weir mentions a few; but he doesn’t give anything like a systematic map of the various possible ways forward. It might be helpful if I do something to fill the gap. … Continue reading

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TTP, 1. Introduction: Platonism vs ‘naturalized epistemology’

Let me begin by setting the scene, embroidering only a little on Weir’s opening pages. Consider then the following claims, ordinarily regarded as mathematical truths: 3 is prime. The Klein four-group is the smallest non-cyclic group. There is an uncountably … Continue reading

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Truth Through Proof, 0. Preamble

I am eventually going to be writing a (short) review for  Mind of Alan Weir’s new book  Truth Through Proof: A Formalist Foundation for Mathematics (OUP, 2010). The blurb on the publisher’s website gives  you an idea what of what … Continue reading

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