[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 
proper subgroups contains one of the i's.


For example, one can demonstrate the sentence


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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