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# Monthly Archives: December 2008

## Parsons’s Mathematical Thought: Sec. 49, Uniqueness and communication, continued

In sum, then, we might put things like this. Parsons has defended an ‘internalist’ argument — an argument from “within mathematics” — for the uniqueness of the numbers we are talking about in our arithmetic, whilst arguing against the need … Continue reading

## Parsons’s Mathematical Thought: Sec. 49, Uniqueness and communication

Parsons now takes another pass at the question whether the natural numbers form a unique structure. And this time, he offers something like the broadly Wittgensteinian line which we mooted above as a riposte to skeptical worries — though I’m … Continue reading

## Advances in education

Stuff the “Season of Goodwill”. The only decent reaction to this kind of thing remains anger: “Female education is against Islamic teachings”.

Posted in This and that
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## RAE 2008 again

Discussions of the RAE 2008 results for philosophy rumble on inconclusively. One thing I’d be rather interested to know is how much the need to make a show in RAE returns (and so get promotion) constrains — an even distorts … Continue reading

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## Another great day for obscurantism and stupidity

Well, we expect no other from the crazed geriatric Pope. But we might have hoped for better from science teachers than from some dingbat Muslim loony. Meanwhile, in Saudi Arabia …

Posted in Rants
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## Parsons’s Mathematical Thought: Sec. 48, The problem of the uniqueness of the number structure: Nonstandard models

”There is a strongly held intuition that the natural numbers are a unique structure.” Parsons now begins to discuss whether this intuition — using ‘intuition’, of course, in the common-or-garden non-Kantian sense! — is warranted. He sets aside until the … Continue reading

## RAE 2008

Well, the RAE results for UK philosophy departments are out (here’s the Guardian’s summary page: the two Cambridge entries are for HPS, ranked higher, and for the smaller Philosophy Faculty ranked at equal 12th).1 The results for us, and our … Continue reading

Posted in This and that
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## Parsons’s Mathematical Thought: Sec. 47, Induction and the concept of natural number (continued)

To continue. Parsons now takes up three more issues about his self-styled “justification” of induction. 1. His ﬁrst question is: “What is the range of the first-order variables?” over which we can apply the rules which ground his “justification” of … Continue reading

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## Parsons’s Mathematical Thought: Sec. 47, Induction and the concept of natural number

Why does the principle of mathematical induction hold for the natural numbers? Well, arguably, “induction falls out of an explanation of the meaning of the term ‘natural number’”. How so? Well, the thought can of course be developed along Frege’s … Continue reading

Posted in Math. Thought and Its Objects, Phil. of maths
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## Parsons’s Mathematical Thought: Secs. 40-45, Intuitive arithmetic and its limits

Here, as promised, are some comments on Chapter 7 of Parsons’s book. They are quite lengthy, and since in writing them I found myself going back to revise/improve some of my discussions of earlier sections, I’m just posting a single … Continue reading