And so you presuppose the validity of logic. You believe logic is valid without proof and in effect, by faith. Do you not?
That particular axiom, as you call it, is known in philosophy as the law of identity or at least it is derived from it. It is one of the three laws of logic and thus it follows that it is a law of mathematics as well because as I mentioned earlier mathematics is simply a form of logic. So the point here is that your simply attempting to validate logic by describing what logic is but that doesn't help us determine whether logic is valid because what one is really asking is whether or not these axioms, or what I would call the three laws of logic, are valid and true. A question that you are completely incapable of answering in any rational manner.
Holy cow! :noway:
You get positive rep for this one! I don't recall anyone that wasn't a Christian ever being intellectually honest enough to come right out and say this! It's absolutely unbelievable!
You're absolutely correct! You have nowhere to start. The problem is a lot worse than you realize though because with this admission you've just thrown the baby out with the bath water. You don't realize it but you've just admitted that knowledge is impossible unless you assume without cause or reason that logic is valid. Logic is literally your god which you believe in by faith and faith alone. By your own admission you cannot verify by any rational means that ANYTHING is true.
It isn't a tautology it is one of the laws of logic. Let me just quote what those three laws are so that we all know what we're talking about here.
Here is a brief statement of each.
1. The law of identity states that if any statement is true, then it is true; or, every proposition implies itself: A implies A.
2. The law of excluded middle states that everything must either be or not be; or, everything is A or not-A.
3. The law of contradiction states that no statement can be both true and false; or, A and not-A is a contradiction and always false: thus, not both A and not-A.
These laws are irrefutable and are the basis of necessary inference. Without them necessary inference vanishes and any attempt to refute them, makes use of them. What's more, they are grounded in the 'Logos of God', the source and determiner of all truth. Moreover, the laws stand together as a trinity; to fault one, is to fault all, and to uphold one, upholds the others. Together, these laws establish and clarify the meaning of necessary inference for logic and all intelligible discourse.
source
And it is this basis for the three laws of logic that you and other non-theists miss it. You have no means by which to establish or even explain the existence of logic whatsoever. You insist on living your life based on reason and logic and all the while you are living by truly blind faith and as a result cannot truly know anything at all.
Resting in Him,
Clete