@morbiuswilters said:
The real problem is that you rely on ambiguity and deceit to make your point.
I have used one and only one definition of the word "axiom", which is an accepted definition; this is not ambiguous.
I have demonstrated that Godel's theorem does, in fact, contain language roughly synonymous with my statement; this is not deceitful.
My position has never changed. If we define an "axiom" as a "principle accepted without truth", as I have always defined it in this discussion, any such principle is an axiom - because the definition is not further qualified. No more specific requirement is necessary.
Godel's theorem outright states that there are true principles which cannot be proven. Logically, those principles - being true - must be accepted. Since they cannot be proven, we must accept them without proof. Being principles accepted without proof, they are axioms by the definition I have previously stated. Whether they are axioms by some other definition is irrelevant.
This is all true. It's not the least bit ambiguous. It's not the least bit deceitful. Read every post I've made in this thread; I do not contradict or alter any of the above.
The problem with correct principles and valid logic is that you have to accept the truth of the conclusion whether you like it or not. Godel's theorem does, in fact, say that there exist things you can't prove - principles which I can quite correctly call "axioms" in the English language. You have exerted a tremendous amount of effort trying to falsify something which is logically consistent and correct.
If you could not tell it was consistent and correct, I suggest that perhaps you are not so great at logic.
@morbiuswilters said:
you are just so hippy-dippy
Prejudicial language and ad hominem argument. I expect better from you. If you can't deliver, I claim my right to point at you and laugh.
@morbiuswilters said:
if you try to find refuge from the storm
I invite the storm, because my position is strong and will withstand any onslaught. Remember Jet Li atop the ziggurat at the end of "The One"? That's me. Can't touch this.
Let's look at this from another direction. Pretend Godel never wrote a theorem.
I say there exist things which are true, but that you cannot prove.
Is that an accurate statement? Forget Godel. Forget the word "axiom". Go directly to the substance of the argument.
Can you demonstrate that all things can be proven? That there does not exist even one thing which cannot be proven?
We both know you can't. All the argument about the word "axiom" and the domain of formal systems and whether Godel's theorem means what I said? Pointless. You have wasted all that time and energy on something which cannot possibly have a productive effect. Even if I were to accept your demand that I don't get to this conclusion with mathematics, I can get to it in myriad other ways, and it doesn't change.
But you knew that all along, didn't you? You weren't making a substantive argument in the first place. You just want me to give up. You think if you use big enough words to write long enough posts, I'll run away.
Not happening. See, I think this is fun. I think you're funny. Because I am right, and I have always been right, and the very principles you espouse will eventually force you to recant. The more you bitch and moan, the funnier that ultimate end becomes. The only way you can "win" this argument is to walk away.
But I don't think you can. I see you complaining about ambiguity and deceit and fallacy, all of which you employ in your own arguments, but which cannot be found in mine. And then I look back and see you proposing that I just don't want to admit I'm wrong.
I believe that's your own motivation. I believe you know you're wrong and are just trying like hell to complicate the issue so you won't have to admit it.
Which is simply hilarious.