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Unread 01-02-2018, 07:54 AM
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Michael F Michael F is offline
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Yes, John – I just read that in Tony’s thread and it indeed is very funny. And I adore the gray bearded sage!

I did not mean to be dismissive of any comments earlier in the thread; rather, I meant to turn the discussion to why I found the GKC quote provocative. In particular, I’ve felt I should reply to Walter on infinities. It’s a line of thought that interests me, though it’s well outside my intellectual dominion, and I know that a little knowledge is a dangerous thing…

Walter, I once dabbled in our favorite gay Austrian’s book on the foundations of mathematics, and, while much of it was beyond me, I think I did understand that LW banished infinities from the realm of meaningful discourse in mathematics. I believe the term for LW’s view of mathematics is ‘finite constructivism’. Anyway, he says this regarding infinities:

They are a piece of mathematical architecture which hangs in the air, and looks … let us say, like an architrave, but not supported by anything and supporting nothing.

It is of no use… the picture is one with which we cannot do anything.


LW further asserts that it is the calculus that bestows a meaning on ∞, rather than the other way around.

I suspect LW had Cantor, at least, in mind with these remarks; it seems to me that LW thought Cantor could as well have been talking about manipulating sets of unicorns: that there is nothing in the real, observable world that corresponds to the term, or to speculations about it. As I recall, the mature LW (post Tractatus) also thought Russell’s project of establishing a secure intellectual 'foundation' for mathematics had failed. I'm not qualified to opine on that point, but LW has my very highest esteem as a thinker.

Pardon this excursion, which takes me rather far out to sea. I post these thoughts belatedly out of respect and curiosity, and I hope that's how they come across.

Last edited by Michael F; 01-10-2018 at 08:30 AM. Reason: clean up and precision
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