[Michael F]

That is nicely put, Andrew, and I'm very glad to hear your thoughts.

One of the things I admire about GKC is his remarkable egalitarianism, something that reminds me a bit of Simone Weil, a writer and person whom IIRC we both admire -- and not one I have seen tied to GKC. I'm still a novice on GKC, admittedly, but I'm fascinated by how these two very different personalities share something, an intuition, call it, of compelling beauty. At least to me.

Happy New Year, brother!

[John Isbell]

My new favorite thing about GKC is his parody of Walt Whitman, which I'd forgotten and which is wonderful. Nice to be reminded of it!

John

[Michael F]

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.

[Orwn Acra]

Michael, thanks for the Wittgenstein. I especially like his architrave image. I wonder if the question is actually one of philosophy in that Cantor was a mathematical Platonist and Wittgenstein was apparently not (but about this I am not so sure; it sometimes seems like he is). It didn't matter whether it was real to Cantor since to Cantor none of it was real, or at least whether it was real or not was not the concerning question. Wittgenstein, however, was always tormented by meaning, and I guess his rejection of Cantor comes from his belief that mathematical theorems express truth and that something that is meaningless cannot express truth and is therefore not mathematical... or something. Wittgenstein was right about Russell's failure to build a logical foundation for math; ironically, it was that other mathematical Platonist, Godel, who proved Russell wrong.

[Michael F]

Yes, Walter. I remember reading somewhere (now I can’t remember where) that most mathematicians and scientists tend toward Platonism wrt numbers. I, too, think that LW does not. And you are quite right on LW’s obsession with meaning; his whole philosophical career turned around showing what does and doesn’t make sense to say, and why. This obsession with meaning is surely one of the reasons I love him, well … not to distraction, but quite recklessly.

I think it’s good to love that way, at least a few times in life!

M

[Michael F]

I ran across this article this morning on “Quantum Poetics” and thought it worth adding to (and perhaps concluding) this thread. It discusses in more depth some of the ideas touched on above. A bit heady, but appearances by LW, Borges, Bohr, Bohm, Joyce and even David Foster Wallace keep it rolling along, I think.

The final paragraph is worth quoting in full, IMO:

The authority of physics is entirely justified for the kinds of explanations and powers it affords. But the idea that the language of physics alone speaks the ultimate truth about the world, dispelling the illusions produced by our everyday experience, for instance of space and time, or of consciousness, seems difficult to defend when that language itself depends on ways of speaking that belong fully to everyday experience. Talk of illusions is surely overrated and often no more than sensationalistic silliness. It would be wiser to say that the physical world, whatever it is like when expressed in the full complexity of mathematical physics, is unlike what it seems to us. And that is the point: The physical world isn’t like that to us, which means that if it matters that we understand human experience as fully as we might, including how we shape our personal, moral, and political lives, then the hope that mathematical physics alone discloses ultimate reality is misguided. This is so even while — and this is no small thing — physics offers one of the richest opportunities for wonder, to which the most deeply human response, besides seeking to understand, may well be either poetry or silent awe.

I hope others find it interesting.