/sci/ - Science & Math

>>9364218
I see- I think I may have misunderstood you, and as it's the early morning before an exam, I think I was unclear in my own original writing.

What I mean to say is that if somebody makes an argument that is not sound, which contains one or more contradictions in their premises, instead of resolving the contradiction and reforming their own argument (in a debate like setting), it is possible to logically derive wacky things from their own argument.

I've been erroneously using "derivation" and "proof" interchangeably, when it's not the case- I'm just used to thinking of them as such because often I only have to do a derivation if the premises are all valid/sound.

The part that is particularly non-intuitive to me is the idea that proving a contradiction doesn't have to do directly with the negation you are trying to prove. A good example is in the image attached. In lines 8-11, you're essentially taking the negation of ~F (which is just F), and then showing that it must be the case with a contradiction that you would already have at your disposal (~M & F)- You don't NEED the assumption to be F in order to then produce the result contradiction used to support ~F.

Though, maybe the reason this is so un-intuitive is because t occurs within the assumption of A to prove not A, and that things that aren't valid will create these moments of fuckery at multiple instances within the purposefully assumed invalid premise.