Has Logic always existed? everywhere?
Logic is usually seen as a tool with which our minds operate, for the purpose of orientation in the environment, and this for the purpose of survival.
It is strange to say that "logic is inherent to the Universe", or that "logic exists everywhere". We just like to see things with the tool of logic, this much is sure.
Has there been something that always exists, irrespective of form?
This is hard to say.
Sometimes, nonexistence is understood as a mere philosophical construct, used in some arguments. But this is all nonexistence is: a construct, as such, nonexistence does not exist.
An atheist would be unable to trust in possibility of illogic, which would mean even his contention is in doubt.
I take you mean that an atheist would be unable to trust in the possibility of *incosistency* of the Universe.
To think that the Universe is inconsistent -- that would be insanity. What may be inconsistent, and often is, is someone's thinking about the Universe, but not the Universe itself, at least it doesn't seem to be inconsistent.
Yet if illogic does not exist in the material world, then surely it exists in the mind. We really have no logical reason for believing in the existence of logic, but for the inductive notion of our apparently logical world.
Sure.
But this is not so different from a theist who defends his own existence after death. Both theist and atheist would like to perserve the ideals of logic, of thought, and of life. The theist extends these ideals to the realm of the next life, whle the atheist does not. The question to the atheist is why?
I think the answer is blatantly simple, and has little to do with logic. We should ask at this point, why does atheism exist? I'm afraid that the reasons for that lie in the history of religion and the way religion was, and still is practised by many religionists -- "If you don't believe what I do, I'll kill you." Such a stance easily provokes a distaste for anything religious.
An atheist, however, would have a difficult time explaining how something could not exist yet know that it does not exist. Their knowledge of this implies that they have complete knowledge of the universe.
Yes, dreadful, huh? Some atheists lack consistency and humility.
To prove that there is no God, one would first have to have a definition of God -- and vice versa!
That there are apples I know because I have a definition of what an "apple" is, and I know what that definition of "apple" applies to because there are apples.
It is a two-way inductive reasoning: the theory you've made enables you to see the evidence this very theory is based on. In other words, insight.
Before you make that theory, you don't see that evidence (that is, you don't see certain phenomena as evidence for something), and as long as you don't see that evidence, you can't make that theory.
That is, you make a bold hypothesis, and test it, and if it turns out to be true, you have insight. But once it comes to matters of the Universe, this bold little method seems somehow ... too simple, to dismal. I wonder why.