But, since you're familiar with reductio ad absurdum, perhaps you'd also like to read up on examples of ad hominems as well.
As used as a colloquial (and snobbish) synonym for insult? It's not the same thing as the 'informal fallacy' you know...
I just meant that you might like to add it to your repertoire.
That is NOT an axiom. But hey, keep redefining words, equivocating and the like.
You really don't seem to get it. Essentially ANYTHING that is unprovable (therefore not disprovable) can be postulated as an axiom.
And it is TRUE that they reject the classical principle of non-contradiction; at least within certain bounds.
Pussies. They don't even have the balls to completely reject it?
LOL. That's actually quite funny. I may have to adopt that. They reject it, in this sense: If the law of non-contradiction is stated as "No contradictions are true." They reject - or negate that, so: "Some contradictions are true." It therefore follows, that "Some contradictions are false." Paraconsistent logics are about discriminating true contradictions, from false ones.
So, combine (sum up or 'integrate') a bunch of linear operations and you get a curve. Recursive corner cutting is also a nice example of this. And what of it? The curve is STILL ruled by the 'linear' 'logic' used to create it.
This is your example of linearizing complexity? You consider piece-wise curve construction and integration complex? My lord, we have work to do. Sure - simple curves are differentiable, and expressed by approximations - and if taken to infinitely many terms, there is identity. So, fine - we have a Taylor series. Quite good. A Taylor series cannot be used to express a non-differentiable function, however. For that, we have to level up. Taylor series gives us sine/cosine, and we must create series of sine/cosine terms in Fourier series to approximate periodic, non-differentiable functions. And again, with infinitely many such terms, we get identity. All quite good - but none of this represents emergent behavior, feedback, or any type of complexity. It's trivial to find functions or data sets, that cannot be expressed by Taylor, or Fourier, approximation. A better example for you would have been one of Wolfram's cellular automata rules. This would illustrate some real unexpected behavior from simple rules and conditions. But that would also help prove my point: the methods and analysis and reasoning that one would use for simple automata systems -- mere logic -- are not useful to characterize the overall behavior. For that, the best we can do currently, is to describe them statistically. It's not a matter of constructing FORWARD. Yes, one can take simple things - functions, automata, or whatever .. and scale UP to create complexity. The point we began at was to DECOMPOSE the complex to the simple. To find the simple causes for the larger social/governmental/etc interactions.
Not subject to proof, as you claimed. Let's just be clear about that. You claimed that axioms can be proven. They cannot.
OK, let play your game. THey can't be proven. Are they still true? How THE FUCK do you know they are true?
Well, that is a deep philosophical question, in fact. There are different answers to it in different philosophical schools and ideas about epistemology. MY answer is: Axioms are not true, and are not false. The property of true and false doesn't apply to them. It is for this reason that they are able to PROVIDE that property of truth/falsity to other claims, when those claims are made in reference to a set of axioms. But because true/false doesn't apply does NOT mean they are arbitrary.
There ARE different systems of logic, with different axioms. The axioms cannot be PROVEN, and therefore it is a matter of CHOICE which system you're using. That choice may be for any reason,
So truth is a matter of choice? And Party 'Agreement' of course!
Yes, but no. Perhaps. But you know what, I'm not going to worry about the fact that you repeatedly made incorrect statements about axioms before, because you do it for me again:
Yes, I STATED that AXIOMS CNA BE PROVEN. So far so good?
No, because they can't. And since you won't accept reference citations of this, and since you're thick and obviously not listening to me. I'll listen to YOU. Completely open mind. No agenda. Prove some, then. Prove either the law of the excluded middle, or the law of non-contradiction. Your choice. Prove both? I'll shut up, leave the list, whatever you like, diety. It can't be done. You're a fool for thinking it can. IF it could be, the derived axiom would be eliminated from the set of axioms, and called a theorem. The axioms are the simplest set of unprovable propositions needed to prove other things. That's the way logic works.