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.
Brent
--
You received this message because you are subscribed to the Google Groups
"Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To post to this group, send email to [email protected].
Visit this group at http://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/d/optout.
