FOM: naive or brainwashed?
rhersh at math.unm.edu
Thu Mar 19 13:42:40 EST 1998
I'm glad you brought up exists. It astonishes me how people
talk and argue about exists without saying what they mean by
the word exists.
As you know, Parmenides, Poincare and Hilbert says whatever isn't
inconsistent exists. Hilbert noticed that you might have to prove
the consistency, which Godel showed you can't. Not too satisfacgory.
Brouwer said whatever he personally (AKA the Creating Mathematician)
sees or thinks clearly exists. That's fine for him, but not so fine
for the rest of us.
I don't know what Frege says about it. Can you fill me in?
I use exist for anything that affects us, that we can somehow
sense, perceive, be aware of, repond to. I think Benacerraf
said pretty much the same thing.
This forces us to distinguish physical, mental and social existence
as three distinguishable modes of existence. Some would also
include transcendental or abstract existence; I do not.
The outrage that I say math exists in the same sense (socially)
as Donald Duck or Sherlock Holmes is understandable. But
sophisticated intellectuals can understand that sayinig two
different things share a common mode of existence does not
say they are equally important, interesting, or useful.
A spider and a whale are both oxygen-brathing animals, so what?
I must go. Will return later.
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