I don't have a clear answer for you on the actual origin of logic - other than from within. Humans can logically reason. However, not knowing the origin of it does not point me in the direction of any god.
Its good that you admit to not knowing where logic originates. I maintain that God is the originator of logic and I realize that the search for the answer to logic's origination does not necessarily lead to God. However, what the search does do is force one to realize that the non-material exists and governs. The next logical question is this: If a realm of the non-material (supernatural) exists, what is its definition?
Logic is only of this world in the sense that it is of the natural world - the natural universe - not supernatural. We landed on Mars because we understand the physics of our solar system. We didn't land on Mars because of any supernatural power.
I didn't say that a supernatural power directly enabled us to land on Mars. The point is, logic governs all natural laws. Natural laws must obey the laws of logic, the law of non-contradiction being one of those laws. The laws of physics work because they are non-contradictory and therefor are logical.
I do deny the existence of anything supernatural. I believe in things I can see and that are observable - that are able to be proven by scientific means. I am not angry at any god - how can I be when I don't believe in one? I am sure he is nothing more than a figment of many imaginations.
That said - I am open to proof in a god's existence, should there be any. But, I have not found any proof.
Don't turn away from the search for the origin of logic, but in the mean time there are a few things to consider.
One is the desire of yours to prove God exists. Johnnz is correct in his redirection to evidences. The chief evidence of God's existence is of course the historical life and works of Christ. Also, the evidences that meant the most to Ancient Israel were the fulfilled prophecies and these are also valuable to us.
Since 567/568 B.C. until 1948 A.D. Israel was not a sovereign nation and was scattered throughout the world. Hated reviled attempted to be obliterated from existence but still remains identifiable as a separate people by their religion and nationality. No other people group in the history of mankind can claim such a distinction. This existence of Israel today is exhibit A in the lineup of convincing evidences that the Bibles prophecies concerning the future ahead of us will be fulfilled. This, perhaps, is the most important blessing we can receive from the astounding history of the Jews. It reveals the reality of God-His overwhelming power, the authenticity of His promises, the certainty of His existence, the urgency of His call to us, and His claim on our very being.
I ask you to consider the book of Luke. Viewing Luke through a lens of context, he was a man of science; he was a physician. The book of Luke was written by Luke as an investigator with the intent of delivering a thoughtful and systematic report of the man called Jesus who is the Christ.
Luke 1:1-4 (ASV)
1 Forasmuch as many have taken in hand to draw up a narrative concerning those matters which have been fulfilled among us,
2 even as they delivered them unto us, who from the beginning were eyewitnesses and ministers of the word,
3 it seemed good to me also, having traced the course of all things accurately from the first, to write unto thee in order, most excellent Theophilus;
4 that thou mightest know the certainty concerning the things wherein thou wast instructed.
If you replace the name Theophilus with your name, the letter is written so you may know the certainty concerning the things wherein you were instructed.
