On 10/22/2013 6:19 AM, Bruno Marchal wrote:
"[]p -> p" is correctness. It is trivially true for the machine I consider, because they
are correct by definition/choice.
Consistency is correctness on the f: []f -> f. It is a very particular case of
correctness.
There are machines which are not correct, yet consistent. For example Peano-Arithmetic +
the axiom beweisbar('f').
Believing '0=1', does not make you inconsistent. Only non correct.
?? But in ordinary logic a false proposition allows you to prove anything. So if I prove
'0=1' then I can prove any proposition - which is the definition of inconsistency.
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 everything-list+unsubscr...@googlegroups.com.
To post to this group, send email to everything-list@googlegroups.com.
Visit this group at http://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/groups/opt_out.
