I've had many a discussion with contributors here who are convinced that ideas are essentially 'brain structures', and that the brain is shaped by evolutionary adaptation — Wayfarer
what we make of that math does seem to be a matter for philosophers (and everyone else, really.) — hanaH
The one we talked about:
[...] allowing contradictions in math is equivalent to dropping the law of the excluded middle from mathematical logic [...]
— Olivier5 — TonesInDeepFreeze
So , in sum , if one understands context in a formal categorical sense, then the LEM is applicable in some contexts
and not in others. — Joshs
But if one equates context with absolute situational and perspectival contingency , then the LEM can no longer find the minimal categorical identity over time in the idea of context necessary for it to contribute anything useful.
how would you write down the proposal that we allow contradictions in mathematics, syntactically and semantically? What sort of axiom would that translate into — Olivier5
You mean, one by one? — Olivier5
the LEM is different from the Law of Non Contradiction in that the "or" in LEM is inclusive and can accommodate (P & -P) which only the LNC excludes. — Olivier5
either P or non P — Olivier5
What's an event? Does it involve objects? 'Transformation' implies some thing that is transformed, maintaining its identity in some sense. As another poster has mentioned, this kind of point threatens to 'deconstruct itself,' which is not necessarily a bad thing. — hanaH
you're not a very eloquent writer — Olivier5
It would take you ages. — Olivier5
We have every reason to believe that because it is the best explanation for a shared world; in fact it is the only explanation apart from some form of idealism; some notion that all minds are somehow conjoined or that there is a universal mind we all partake in.. — Janus
Too slow, rather. You could have said a long time ago: "you must mean the LNC, because the LEM does not actually rule out contradiction."too ample. — TonesInDeepFreeze
You could have said a long time ago: "you must mean the LNC, because the LEM does not actually rule out contradiction." — Olivier5
the 'but not both' clause for exclusive or is demanded by the law of non-contradiction: ~(P & ~P). — TonesInDeepFreeze
It matters because the 'v' ('or') connective should never have been conflated with exclusive-or.
Also, your notion that exclusive-or has an advantage of elegance is ill-conceived, as I could explain also. — TonesInDeepFreeze
Since P and ~P are mutually exclusive, what difference does it make whether the disjunction is inclusive or exclusive? — T Clark
We started this discussion two or three days ago though. — Olivier5
Get involved in philosophical discussions about knowledge, truth, language, consciousness, science, politics, religion, logic and mathematics, art, history, and lots more. No ads, no clutter, and very little agreement — just fascinating conversations.