On Wed, 5 Oct 2016 21:04:32 -0000
No, one simply denies them. But, even if one HAD to USE them, that would not prove them. I might use several axioms to derive a contradiction.
So one or more of your 'axioms' are not true and not really axioms. The method is called reductio ad absurdum.
No, it just means the axioms are incompatible. And, reductio ad absurdum is quite a bit more general than proof by contradiction, but I won't quibble.
But this all began not with a disagreement over the law of identity, but over the law of non-contradiction.
Which are closely related. And no, this all began with you being a cheap charlantan who can't write a semi consistent rant. Since your rants are laughably inconsistent you embarked in even more stupid rants trying to 'prove'...who knows what about the 'logical' status of contradictory nonsense.
But, since you're familiar with reductio ad absurdum, perhaps you'd also like to read up on examples of ad hominems as well. Are they related? Yes, they are among the three classical laws of logic. That is their relation. Other than that, they do not depend on each other whatsoever. Holding to them as in some way objective is a matter of tradition, convenience, and little more than that.
I am well aware that you ignored my reply to your nonsensical example with iran and nukes for instance, So fuck off.
I did ignore it. Because replying was futile with someone who doesn't even have a grasp of axioms, and proof. But, if you insist:
From the USA/Iran's individual points of view, it is logical and rational to pursue the stated goals. It is rational for USA to prevent Iran from obtaining a nuke.
It is rational from Iran's POV to try to acquire one. Having nukes forces other countries to the negotiating table rather than invasion. Sure, as you point out, it might speed up invasion -- in to Tehran before they get a nuke. But if an axiom that Iran is operating by is that sooner or later, given USA's historical performance in the region, they WILL get invaded regardless, it is quite rational to try to obtain a nuke to prevent that. Individually, from different perspectives, and different goals it is possible to reason to quite different conclusions. You seem to be taking the position that there is Rational/Logical (note caps) that somehow transcends these individual frameworks. I don't see it, and if you really had a clear idea of it on any sort of firm basis, you ought to write a book -- because no one else has such an idea either.
The principle of non-contradiction IS denied, by example, in the philosophical school of dialetheism.
Nonsense.
What is nonsense? The philosophical school of dialetheism? Fine, that is your opinion. I'll wager you couldn't argue against any of it, successfully though. But in any case, it is TRUE that this school of thought exists. And it is TRUE that they reject the classical principle of non-contradiction; at least within certain bounds.
These, and other multi-value logics, generally, are useful in a wide area of mathematics, physics, electronics and so on.
I already dealt with the fact that 'complex' systems are made up of simpler 'linear' bits. You seem to have ignored it. I don't need to add anything.
I didn't ignore it, I was waiting to get some more ground-work covered. You're right. Some complex systems can be simplified, and linearized and dealt with that way. But not all can: hence the reason multi-value logics exist in the first place. But, more generally, in complex systems there is emergent behavior. One might state the notion with the old phrase "the whole is greater than the sum of its parts." The whole can develop properties that none of its parts have. Moreover this can happen spontaneously, or at least accidentally apart from the human design. So, the type of thinking or analysis that is sufficient for a smaller part will not be sufficient for the whole. You can use quite simple mathematics -- nothing more than algebra, to characterize an audio amplifier, and an audio microphone. Under the right conditions, those components will generate feedback -- and at that point, algebra is entirely insufficient to characterize the system's performance. In the same way, with governments, social systems, and so on where emergent behavior and feedback are at play, one needs a wider view than merely the algebraic philosophical notions that gave rise to a government, or simple economic modeling only according to one view, and so on.
I don't either. I've explained several times that axioms are assumptions,
There you go again...Axioms are NOT suppositions.
Wait for it...
r if you prefer, propositions, and are not subjected to PROOF. You disagreed, so I quoted sources.
There we go.. right. So PROPOSITIONS, then. Statements that ARE REGARDED (but not necessarily) as self-evidently true. Not subject to proof, as you claimed. Let's just be clear about that. You claimed that axioms can be proven. They cannot. 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, really. Utility is a good one, and I've said above with regard to complex systems, but ignorance and simply not knowing of more than one equally valid. But that must be set out. There is no objective criteria of which to use.
Your statement about axioms was quite wrong. They are not subject to proof. You're now trying to walk that back and play a different angle -- one that I handed to you -- that of self-evidence.
Don't make up stuff . I provided my version (correct) and even went with your defination.
Denial #1.
And in any case, in philosophy, and informal logic, axioms cannot be proven, as you have stated.
I didn't state that. But it's beside the point anyway.
Denial #2. Refutation: On Wed, October 5, 2016 6:11 am, YOU said:
Again, truth is NOT a matter of agreement. And axioms are not to be 'agreed' upon. Also, AXIOMS CAN BE PROVEN. If axioms couldn't be proven then any statement based on them would be...unproven, meaningless, useless, et cetera.
Emphasis mine.