Good. You are at your most eloquent with emojis. — TonesInDeepFreeze
Could you give an example of a non-logical axiom — Tate
what makes it non-logical? — Tate
A non-logical principle is one that is not true in at least one model. — TonesInDeepFreeze
Classical binary Logic is best used for problems that can be precisely defined with integer numerical values. But human contradictions are seldom concisely defined; instead loosely sketched with inexplicit subjective truth-values.1. Classical logic has to use Occam's broom (sweep paradoxes under the rug) otherwise, via ex falso quodlibet, concede that classical logic is trivial.
2. We're using some version of paraconsistent logic and we're not aware of it. — Agent Smith
Actually, most thinkers have an ego-boosting impression of their own reasoning abilities. We find it easier to see the contradictions in other people's ideas than in our own thoughts. Intuition always seems true, even when it aint.Most if not all thinkers are under the impression that they're using classical logic - they don't take too kindly to contradictions. — Agent Smith
A formalized version of "paraconsistent logic" (logic of paradox) is the Fuzzy Logic — Gnomon
The diagonal argument is constructive and intuitionistically valid — TonesInDeepFreeze
The diagonal argument is constructive and intuitionistically valid
— TonesInDeepFreeze
The argument only goes to show that the continuum cannot be broken up in points. — Hillary
Leading to confused notions of infinitesimals or differentials. — Hillary
Smith is not ad confused as you suggest — Hillary
>. By definition, every real number is a point — TonesInDeepFreeze
glue two points together — Hillary
throw as many points in the bag — Hillary
How can you construct a continuum with points as building blocks? — Hillary
Your question suggests that you are not familiar with the basics of the subject. — TonesInDeepFreeze
A non-logical principle is one that is not true in at least one model. — TonesInDeepFreeze
On an unrelated, or at least only semi-related subject, does the fact that light has both a wave and particle nature constitute a valid example of a real-life, concrete paradox, which I just denied the existence of? — T Clark
You can throw as many points in the bag as you like. It's never filled. — Hillary
Those are your personal, impressionistic locutions. Real analysis doesn't have such terminology. — TonesInDeepFreeze
But how [do] you glue two points together — Hillary
Points come in sizes? — Hillary
particle-wave duality is only inconsistent in so far, that it doesn't mesh well with our typical view of the universe. it's however perfectly consistent, experiments will deliver consistently similar results. particle-wave duality is just a name to at least somewhat visualise what is happening in the equations of quantum mechanics — TieableCookie
How many points do I have to throw in the bag to fill it? — Hillary
Did Cantor's original set theory have non-logical axioms? — Tate
Cantor didn't have axioms. But of course he did use non-logical principles even if not formalized as axioms. — TonesInDeepFreeze
Does this mean you're sort of stretching the idea of non-logical axioms to address the problems associated with naive set theory? — Tate
It appears that axioms were created specifically to block the path to Russell's Paradox. — Tate
the pre-formal principles it uses are non-logical, — TonesInDeepFreeze
In the sense that these principles are untrue in some models? That doesn't make any sense to me. How can a principle be false? — Tate
It would be false in some models if it were formalized as a first order sentence, — TonesInDeepFreeze
What would that sentence be? — Tate
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