[FOM] Constructivism and physics; Absolute truth vs. relative meaning
joeshipman@aol.com
joeshipman at aol.com
Sat Feb 11 20:02:17 EST 2006
My last long post had some typos which may create unnecessary
confusion, so let me restate the technical statements involved with the
typos corrected:
***********************
What I proved is that (AF&[i1]&[i2]&...&[i_m])-->[n] is a logical
tautology (and therefore provable in pure first-order logic) iff the
following condition holds:
For every subgroup G of Sn which acts without fixed points on
{1,2,...,n}, the additive semigroup generated by the indexes in G of
its
proper subgroups contains one of the i's.
***********************
For example, one can demonstrate the sentence
([2]&[15])-->[6]
by specializing to the case m=6 one of Gauss's proofs of the
fundamental theorem of algebra, which reduced the case of polynomials
of degree m = (2^k)*r, for r odd, to the case of polynomials of degree
m(m-1)/2, which has one fewer power of 2, with the base case handled by
the fact from analysis that odd-degree real polynomials have roots.
************************
-- Joe Shipman
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