Let's Learn Some Logic

[Gary Childress]

Under such circumstances I don't see how anything would be provable.
I've heard the opposite account: that from a contradiction, everything is provable. Though I don't know how such a proof would work.

Not sure if that is the case or not, but if everything is provable including arguments which are invalid and unsound, then it seems to me that all certainty has been removed and the ultimate result is also that nothing can be proved because everything can be proved including that which does not follow. And I suppose since both P and ~P can be correct, then even to say that both everything and nothing can be proved at the same time would be correct.

But at this stage in the thread it's a bit early to really tell what is at stake, so I of course encourage you to follow along as we progress and perhaps an answer will become clear.

 

[Ayatollah So]

There's a rule of disjunction introduction (use | for "or"):

From P, infer P | Q

And a rule (or two, if you look at it that way) of conjunction elimination:

From R & S, infer R
From R & S, infer S

And a rule of disjunctive syllogism:

From T | U and -T, infer U
From T | U and -U, infer T

Prove arbitrary statement A, starting with a contradiction:

1. P & -P
2. P (1, conjunction elimination)
3. P | A (2, disjunction introduction)
4. -P (1, conjunction elimination)
5. A (3,4, disjunctive syllogism)

 

[Borachio]

Argghh!

I remember this stuff, now.

Are you trying to fry my brains again?