[FOM] inconsistency of P
meskew at math.uci.edu
Wed Oct 5 01:34:02 EDT 2011
On Tue, Oct 4, 2011 at 2:13 PM, Studtmann, Paul
<pastudtmann at davidson.edu> wrote:
> And why would an empiricist draw such a line? For the simple reason that such facts are accessible through ordinary experience, while experience of the infinite is beyond the ken of finite creatures like us who are embedded in a small portion of space and time.
Could this skepticism easily creep in to throw much of empirical
science into doubt? For how could be possibly be justified in saying
that we know the chemical composition of distant stars, the mass of
Jupiter, the structure of proteins, or the radius of an electron?
These are only "known" through elaborate systems of hypotheses and
generalizations which interpret things we can see and hear. They are
far beyond our ability to experience in a direct way. Terence Tao's
lecture on the "cosmic distance ladder" seems relevant-- our knowledge
of distances (even just distances!) on a cosmic scale is obtained in a
very indirect way, and different methods apply to different orders of
Our human limitations are pretty severe. We are very small creatures
with puny computational abilities and poor senses. In my opinion, a
beautiful thing about math and science alike is how we permit
ourselves to transcend our limitations through abstract reasoning and
big, creative ideas.
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