[javert]

If logic isn't consistent, then logic isn't valid.

I'm not assuming specialized definitions of "consistency" and "validity" here, just your normal everyday layman's usage.

[chris_wot]

Well, you were responding to someone who was using the correct formal terms. You, after all, don't dispute the second theorem - but given it uses the term "consistent" you can hardly complain when someone makes their argument using the same terminology as the theorem you agree with!

Interested in what you define "consistent" and "valid" as in laymans terms though.