Liz, that was enjoyable. In the back of it lurks the incompatibility of
'GOD with logics.
John
On Wed, Jan 29, 2014 at 5:51 PM, LizR lizj...@gmail.com wrote:
Would math make God obsolete?
If so, that remainds me of something...
I refuse to prove that I exist,' says God, for proof denies
On Mon, Jan 27, 2014 at 2:35 PM, Brian Tenneson tenn...@gmail.com wrote:
You could always just add it and its negation to the list of axioms
(though not at the same time, of course) and see where that leads,
Axioms should be simple things that are self evidently true, neither
Goldbach's
On Tue, Jan 28, 2014 at 3:20 AM, Bruno Marchal marc...@ulb.ac.be wrote:
A proof is a FINITE number of statements establishing the truth or
falsehood of something;
Not establishing the truth, but establishing the theoremhood.
I stand corrected; although it would be true if the axioms in
On 29 Jan 2014, at 18:12, John Clark wrote:
On Tue, Jan 28, 2014 at 3:20 AM, Bruno Marchal marc...@ulb.ac.be
wrote:
A proof is a FINITE number of statements establishing the truth
or falsehood of something;
Not establishing the truth, but establishing the theoremhood.
I stand
Would math make God obsolete?
If so, that remainds me of something...
I refuse to prove that I exist,' says God, for proof denies faith, and
without faith I am nothing.
But, says Man, The Babel fish is a dead giveaway, isn't it? It could not
have evolved by chance. It proves you exist, and so
On 27 Jan 2014, at 17:30, Brian Tenneson wrote:
Some basic.questions. When you say PA, do you mean the set of all
theorems entailed by the axioms of Peano arithmetic?
Yes. In some context it means only the axioms, but often I use the
same expression to denote the axioms and its logical
On 27 Jan 2014, at 19:55, John Clark wrote:
On Fri, Jan 24, 2014 at 2:23 AM, Brian Tenneson tenn...@gmail.com
wrote:
There are undecidable statements (about arithmetic)... There are
true statements lacking proof.
Yes.
There are also false statements about arithmetic the proof of
On 27 Jan 2014, at 16:12, Brian Tenneson wrote:
Yes, some day a computer might be able to figure out that the set of
rationals is not equipollent to the set of real numbers.
A Lôbian machine like ZF can do that already.
I saw somewhere that using an automated theorem prover, one of
Yes, some day a computer might be able to figure out that the set of
rationals is not equipollent to the set of real numbers. I saw somewhere
that using an automated theorem prover, one of Godel's incompleteness
theorems was proved by a computer.
The question I raised initially was this: will
Some basic.questions. When you say PA, do you mean the set of all theorems
entailed by the axioms of Peano arithmetic? Does this include the true
(relative to PA of course) wffs that are not provable from PA alone?
How can it be that PA+con(I) can prove its own consistency because it is
FWIW, under the usual definitions, the rationals are enumerable and so are
a smaller set than the reals. I'd suppose that if people can figure that
out with our nifty fleshy brains, then a well-designed computer brain
could, too.
-Gabe
On Friday, January 24, 2014 1:23:40 AM UTC-6, Brian
On Fri, Jan 24, 2014 at 2:23 AM, Brian Tenneson tenn...@gmail.com wrote:
There are undecidable statements (about arithmetic)... There are true
statements lacking proof.
Yes.
There are also false statements about arithmetic the proof of whose
falsehood is impossible;
A proof is a FINITE
You could always just add it and its negation to the list of axioms (though
not at the same time, of course) and see where that leads, if anywhere.
On Mon, Jan 27, 2014 at 10:55 AM, John Clark johnkcl...@gmail.com wrote:
On Fri, Jan 24, 2014 at 2:23 AM, Brian Tenneson tenn...@gmail.com wrote:
On 24 Jan 2014, at 08:23, Brian Tenneson wrote:
There are undecidable statements (about arithmetic)... There are
true statements lacking proof. There are also false statements about
arithmetic the proof of whose falsehood is impossible; not just
impossible for you and me but for a
There are undecidable statements (about arithmetic)... There are true
statements lacking proof. There are also false statements about arithmetic
the proof of whose falsehood is impossible; not just impossible for you and
me but for a computer of any capacity or other forms of rational
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