You haven't proven that it can't be proven that 2 + 2 = 5. All you have proven is that if 2 + 2 = 5, then mathematics are inconsistent. Which they could be; you can't just assume math and logic are consistent.

> you can't just assume math and logic are consistent.

What a bunch of bollocks.

Precisely my point. Wow, that guy really stepped in it.

Claiming that logic isn't valid is worse than a logical contradiction, because if logic isn't valid, you can't claim anything.

Nobody ever said logic isn't valid. We're talking about consistency.

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.

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.