Re: Godel's proof, truth, reality, self-awareness, and all that jazz

On 16 Sep., 15:18, "T.H. Ray" <thray...@xxxxxxx>
wrote:
On 16 Sep., 14:24, "T.H. Ray" <thray...@xxxxxxx>
wrote:

I think part of the problem may be a
failure to
understand
what constitutes a "proof." Proof theory
itself
has rules
for compelling correspondence between
theorem
and
proof,
and some strategies are more compelling
than
others.
Constructivists found that strategies
relying
on
double
negation (proving a statement true by
assuming
it
is
false)are logically equivalent to proving A
by
showing it
is not-not-A. Because A and not-not-A are
identical,
the tautology is unconvincing to many who
would
rather
see the proof proceed by some other
strategy.

You have not understood constructivism. The
identity
would not bother
any constructivist. What bothers them is the
non-identity:
A ==> non-non-A but not the other way round
(because
of the fact that
in infinite sets only finite subsets can be
subjected
to proofs). This
is one example where your belief in some
absolutely
true proof theory
turns out to be a subjective belief without
any
scientific foundation
(as you granted).

Regards, WM

You are the one who profoundly fails to
understand
constructive proof.

Really?

Really.

Infinite sets are no problem for any philosophy
of
mathematics;

They are a problem for finitism, no?

Mathematics is not identical to "finitism."


But finitism is a branch of mathematics. Further
constructivism is a
branch of mathematics, and also denying the axiom of
infinity. For
these branches there are no finished infinities and
hence one cannot
apply some operations to all numbers (but only to
those yet
constructed). That is the reason for non-non-A being
not identical to
A in much of math.

Oh, please do teach me Brouwer.

See above, for a start.

Regards, WM


Nope. This is complete nonsense. Finitism and
constructivism are philosophies of mathematics, not
branches of mathematics. Platonism is also not a
branch of mathematics, nor is formalism.

Please, give me another lesson in Brouwer. And do
cite your source.

Tom
.

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