On Nov 3, 4:15 am, Aatu Koskensilta <aatu.koskensi...@uta.fi> wrote:
> Indeed. I like to talk about "ways of thinking". (Others speak of > metaphors, conceptual pictures, what have you.) A way of thinking is > neither true nor false. Rather, ways of thinking are useful, confusing, > handy, what have you.
Yes, as I noted in my earlier reply.
> When first encountering Penrose's G delian > arguments I was baffled by the notion that there is any determinate > totality of "unassailably true" mathematical statements.
Yes; actually Penrose has got well out of his depth in that debate!
> I unassailably believe 1 + 1 = 2, perhaps.
It's an interesting point. Many of us would go along with that, and extend it as far as 2 + 5 =7, perhaps, and even a little bit further. And also maybe 2 x 3 = 6. But maybe not too much further?
Maybe not to 147 + 684 = 831 ? How sure are you of your ability to avoid mistakes in this kind of thing?
Probably it's a bit of a silly discussion; but I recall an earlier thread where Daryl McC remarked that he was totally happy with those baby ones, but just not *quite* so cavalier with the later ones.
It's an interesting subject for a coffee-room discussion.
> But do I unassailably believe the cut > elimination theorem for second-order logic? The existence of an > ineffable cardinal? I have no idea.
Those things are surely subject to a tincture of doubt, due to (if nothing else) the ability of the math world to accept mistakes for a great many years.
All this is fascinating epistemology, but scarcely mathematical!
-- Wondering Willy
** For every philosopher there is an equal & opposite philosopher.