Category Archives: Books

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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Jane Austen and moral philosophy

I’m one of the panelists on the Ask Philosophers website. And I’m amused to notice that three particular favourites of mine happen to be the topics of my last three responses, namely the philosophy of maths, wine, and Jane Austen. … Continue reading

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Cuts, consistency and axiomatized theories

In the Wednesday Logic Reading Group, where we are working through Sara Negri and Jan von Plato’s Structural Proof Theory, I today introduced Chapter 6, ‘Structural Proof Analysis of Axiomatic Theories’. In their commendable efforts to be brief, the authors … Continue reading

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Mary Leng’s Mathematics and Reality, Chs 5 & 6

We are reading Mary Leng’s book in the Thursday Logic Seminar for the second part of term. It fell to me to introduce discussion of Chapters 5 and 6, and I found myself yesterday writing (very rapidly indeed) these brisk … Continue reading

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Piling up on my desk

Term rattles on, leaving little time for doing much reading other than for the two logic seminars for grads (this term we looking at Mary Leng’s book on Mathematics and Reality in one, and Sara Negri and Jan von Plato’s … Continue reading

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A proper bookshop is a lovesome thing …

You would think that Cambridge, of all places, could sustain an attractive general bookshop. But sadly not so. The University Press shop is quite nicely done, but of course only sells CUP books, so doesn’t count. We are stuck with … Continue reading

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