A system for use with a multi-valued semantics can be paraconsistent or not.
However, as far as I know, a paraconsistent system can't have a classical 2-value semantics. — TonesInDeepFreeze
(1) I don't know your meaning of 'homological' applied to relationships between a mathematical theory and empirical observation. — TonesInDeepFreeze
If we must use the word 'signifier' here, I would say that the signifier is not a model but rather a theory. — TonesInDeepFreeze
I put it this way: There is no model of a contradictory theory. (That's for classical logic. We may find other things pertain in other kinds of logic.) — TonesInDeepFreeze
Thus a math expression homological to a state-of-affairs, as specified in our example here, expresses contradictory conclusions that are both valid. — ucarr
You're telling me that a math expression that asserts a claim is nonetheless considered theoretical? — ucarr
classical logic parameters categorically exclude contradiction — ucarr
this is an example of a mathematician modulating axioms to fit a metaphysical principle (LNC) — ucarr
a mathematician can re-jigger axioms to admit contradictions — ucarr
paradoxes; they're an existential threat — Agent Smith
That's true! I cannot understand why more people don't lie awake at night about it! It requires a global response. We need the World Bank, the World Heath Organization, the International Court of Justice, Interpol, the United Nations Security Council, and the entire cast of 'Glee' on this!
Either that, or Agent Smith just doesn't know the meaning of 'existential threat'. — TonesInDeepFreeze
paradoxes; they're an existential threat
— Agent Smith
That's a paradox itself. — jgill
Paradoxes are an existential threat to epistemology (truth) & logic. When these two are assaulted (successfully), our world comes crashing down around our ears! — Agent Smith
financial markets will all collapse, followed by all the populations lapsing into chaos and war? — TonesInDeepFreeze
There have been controversial puzzles in epistemology for centuries. I don't see any crashing down of the world related to this. What do you think will happen, the media will announce that philosophers still haven't reached agreement on solutions to the logical and linguistic paradoxes and then the financial markets will all collapse, followed by all the populations lapsing into chaos and war? — TonesInDeepFreeze
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