I am a bit perplexed by Wittgenstein' remarks in his book on the Philosophy of Mathematics.(adsbygoogle = window.adsbygoogle || []).push({});

I read this many years ago and found it almost impenetrable. Now I am trying again to make some assessment of Wittgenstein's view of numbers.

It seems he tried to remove many of the difficult problems of mathematics by merely saying that such ideas had no meaning. Thus he dismissed set theory as nonsense, and would not accept the continuum of real numbers. Indeed, in his attempt to finitise mathematics he would not accept that the decimal expansions of irrational numbers had any meaning, beyond whatever point one had actually calaculated it. Thus, for Wittgenstein, the question - is there any appearance of seven sevens (...7777777...) in the decimal expansion of PI ?, had no meaning - and one could only place a question as, is there any appearance of seven sevens (...7777777...) in the decimal expansion of PI up to the 10,000 digit (or whatever)?.

The mathematics which Wittgenstein could envigage, would appear to have to be considerably pruned - out goes set theory, topology, analysis of continuous functions, infinity, and so on.

Does anyone have any views on Wittgenstein's philosophy of mathematics ? Are there any ideas in his philosophy relevant to late 20th/ early 21st century mathematics, or should we merely see his work as a flawed critique of the mathematics of his era.

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# Wittgenstein's views of numbers

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