beta: "Not 'guesswork' this time but insight"
teacher: "I abhor your pretentious insight. I respect conscientious
guessing because it comes from the best human qualities, courage and modesty."
-Proofs and Refutations, Lakatos
Thesis
In my thesis I propose a partly empiricist strategy for simultaneously solving a
problem of access (why should there be any relationship between stuff people are
inclined to believe about numbers sets etc. and the truth about these subjects?) and a
problem of applicability (how can mathematical truths be so spookily helpful in
predicting certain kinds of observations?) More specifically: Math says (somewhat
vacuous sounding) things about the world like: 'if a computer runs this program then
it
wont output a 3', or 'if there are two apples and two oranges there are four fruit'
and these turn out to be both more helpful and more possible to be ignorant of
then you might think. Thus various kinds of selection (evolutionary, cultural,
psychological) in favor feeling compelled by specific mathematical methods that lead
one to get these
concrete mathematical statements right result in people like us, who find certain kinds
of
good (truth-preserving or at least no-false-consequences-about-concrete statements
preserving) mathematical methods psychologically compelling and relatively few bad
ones. Now that people have these inclinations to be convinced by good arguments
rather than bad ones they can create and be convinced by proofs and thereby there by
acquire mathematical knowledge.
Some very rough thesis chapter drafts, appendix drafts etc are on this wiki now so I don't spend endless
time messing with presentation. Comments are always welcome though some of the sections
are still quite sketchy and poorly explained
Thoughts in Progress:
philosophy of math
(older stuff)
, my prospectus and
related stuff ,
perception's content, and why *exactly
because* the mind is like a computer there probably isn't a
language of thought
and some amateur vaguely sentimentalist
moral philosophy
as well as past present and future Win Sharon's
Money info
tidied-up papers: