On 27 Sep 2011, at 20:02, meekerdb wrote:
On 9/27/2011 5:28 AM, Jason Resch wrote:
On Tue, Sep 27, 2011 at 6:49 AM, Stephen P. King <stephe...@charter.net
On 9/26/2011 7:56 PM, Jason Resch wrote:
Okay, there may be other subjects, besides number theory and
arithmetical truth where other forms of logic are more
appropriate. For unambiguous propositions about numbers, do you
agree with the law of the excluded middle?
I think this an assumption or another axiom. Consider the
conjecture that every even number can be written as the sum of
two primes. Suppose there is no proof of this from Peano's
axioms, but we can't know that there is no proof; only that we can't
find one. Intuitively we think the conjecture must be true or
false, but this is based on the idea that if we tested all the evens
we'd find it either true or false of each one. Yet infinite testing
is impossible. So if the conjecture is true but unprovable, then
Undecidable does not entails the negation of the law of the excluded
Undecidable (by PA, say) = ~Bp & ~B~p. Law of the excluded middle = (p
(~Bp & ~B~p) -> ~(p V ~p) is NOT a theorem of G*.
You received this message because you are subscribed to the Google Groups
"Everything List" group.
To post to this group, send email to firstname.lastname@example.org.
To unsubscribe from this group, send email to
For more options, visit this group at