Do philosophers use computers to find logical proofs? Or are there good reasons the task of programming a computer to do so is difficult (perhaps because of the complexity of proof required, or perhaps because you need a human for some sort of creative step)? Just from my experience of undergrad logic, it seemed to me there was a lot of repetition in what I was doing, and that it was a task I could learn and get better in -- ie, it wasn't down to pure creativity, but there were learnable, repeatable methods of searching that perhaps could be codified, made systematic.
Is this a decent argument (i.e. logical, sound)?
If God exists, God is an omniscient, omnipotent, wholly good being
If God is wholly good, God would want humans to posess free will
If God is wholly good, God could endow humans with free will
But, if any being is omniscient or all knowing, such a being would know human choices and actions before they are chosen
Under such conditions, free will would only exist as an illusion or in the mind as the human perception of having free will; true free will would not exist because God or some other power has predecided all human choices
Therefore, God, if God exists, cannot be both wholly good and omniscient
Therefore, God does not exist
This is a question about pure logic.
There are two theries: Theory A and Theory B. Theory A assumes AssumptionA. Theory B assume AssumptionB.
The two assumptions are mutually exclusive: if AssumpionA then not AssumptionB and vice versa.
I believe that a philosophical result is that Theory A and Theory B cannot prove anything about each other. All you can do is preface each result with the assumption. For example, if Theory A proves X and Theory B proves Y, then we can say "If AssumptionA, then X" and "If AssumptionB then Y".
Who first proved this? Where is it documented?
When you ask why people believe in logic, it seems to me that the commonest answer is, "It works." But that answer seems problematic to me; how do you know it won't stop working? I guess what I'm asking is -- are logical laws nothing more than empirical regularities, models of how things behave? Are logical laws any different from empirical laws? Is there any stronger reason to have faith in logic apart from the fact that it works and has always worked?