Posted: May 17, 2012 6:19 pm
amkerman wrote:Simply stunning shrunk. The arguments are analogous. That you can't see the contradiction in your first premise is simply due to language. You conditioned God's existence as being that which cannot exist, namely, a square circle. That you then go on to explicitly state that square circles can't exist might be confusing you.
They aren't. The logical forms are different:-
Shrunk wrote:If God exists, he is a square circle.
A square circle cannot exist.
Therefore, God does not exist.
The logical form of this is (broadly speaking*):
A -> B
¬B
therefore ¬A
This is a valid argument of the form Modus Tollens.
amkerman wrote:If a dog is all-black then that dog is all-white
All-White can't be all-black
Therefore the dog is not all-black.
The logical form of this is:
A -> B
B -> ¬A
therefore ¬A
This is as written not a valid form. We could have applied Hypothetical syllogism to the two lines, to conclude A -> ¬A, which is a contradiction and then applied Reductio ad absurdum to it.
*Actually if one wanted to include mention of existence then one would need to use first order logic and include some intermediate steps and lemmas, but that is confusing and beyond the scope of this discussion. I'm sure Shrunk won't object to my essential paraphrasing of his argument.