Category Archives: Truth Through Proof

TTP At long last, a short review

Very, very belatedly — and apologies for this in particular to Alan Weir — I’ve gathered together some of the thoughts from previous blog posts into a short review of Truth Through Proof. This is absurdly compressed, even though Mind … Continue reading

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TTP, 14. Worries about excluded middle

Weir’s formalist account of arithmetic in headline form comes to this: the arithmetical claim P is correct just in case that there is (or in practice could be) a concrete proof of P. (We’ll stick to considering the arithmetical case.) … Continue reading

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TTP, 13. Formalism and “pluralism”

In TTP 11, I emphasized that Weir’s position interweaves two separable strands. One strand I called “formalism about arithmetical correctness”: at a first approximation, what makes an arithmetical claim correct is something about what can be done in some formal … Continue reading

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Weir on colours, concepts, fiction, numbers, and more!

Alan has written a long reply to my reply to his comments on my last post.  This should be of particular interest to anyone who is reading his book, so I thought I’d flag it up at the top level … Continue reading

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TTP, 12. ‘The formal mode of assertion’

Weir himself distinguishes three model cases where a claim’s content is not transparently representational — to use my jargon for his idea — and I added a fourth case. (We are assuming, for the sake of argument, that the general … Continue reading

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TTP, 11. Disentangling neo-formalism

The introductory sketch in the last post reveals at least this much about Weir’s neo-formalism: it is the marriage of two independent lines of thought. One idea — call it “formalism about arithmetical correctness” — is that, at a first … Continue reading

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TTP, 10. Neo-formalism introduced

As you might remember, I’m supposed to be writing a review of Alan Weir’s Truth through Proof. I started blogging here about the book some time ago, intermittently discussing the first couple of chapters at length, and then I’m afraid … Continue reading

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TTP, 9. §2.IV A map of the terrain

Weir, to summarize once more, wants to develop a position that allows him to say sincerely, speaking with the vulgar mathematicians (and not having to cross his fingers behind his back, or do that little dance with the fingers that … Continue reading

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TTP, 8. §2.III Reduction

The projectivist about e.g. judgements of tastiness explains how “X is tasty” (as an ordinary judgement made in the restaurant, not the philosophy class) is an assertion that can be correct or incorrect even though there is no such property-out-there … Continue reading

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TTP, 7. §2.II Snapshot dispositions, correction, fiction

The projectivist’s root idea is that a judgement that “X is G”, for a predicate G apt for projectivist treatment, is keyed not to a belief that represents X as having a special property but to an appropriate non-cognitive attitude … Continue reading

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