meekerdb wrote:
On 3/23/2015 5:11 PM, Bruce Kellett wrote:
LizR wrote:
On 24 March 2015 at 08:02, meekerdb <[email protected]
<mailto:[email protected]>> wrote:
That every number has a unique successor for one.
"Let's call the first number that doesn't have a unique successor n..."
Can you prove that n+1 exists and is unique? Just asserting it is not
sufficient.
Of course you can prove it from Peano's axioms. But that's the point:
that what you can prove is relative to the axioms you assume (and the
rules of inference too). So when someone asserts some propositions and
says see everyone believes these, they are very intuitive, and then he
proceeds to prove something implausible which counter-intuitive then one
is justified in wondering whether the axioms apply to the real world.
Right, that is what I meant. Proof is only within an axiom system -- the
hard problem is demonstrating that those axioms are the ones relevant to
the world we experience.
Bruce
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