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7 votes
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What happens if we accept inconsistency?

We are asked to imagine the following conversation: Alice: I believe that X. Bob: Do you also believe Y? (Alice says yes) But that means you believe in Z. Alice: That's true, but I still don't ...
Frank Hubeny's user avatar
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7 votes
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What are the philosophical implications of using inconsistent mathematics?

Let me first address the issue of foundations, for a recent review see Azzouni's Is there still a Sense in which Mathematics can have Foundations? There is of course a legacy label "foundations ...
Conifold's user avatar
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3 votes
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Are quantum logics isomorphic to inconsistent logics?

One point of clarification first. To speak of 'inconsistent logics' is somewhat confused. A logic that proves P and not-P for any P would be of no use to anyone. But there are logics that permit a ...
Bumble's user avatar
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3 votes

Do contingent propositions about the world rely on the consistency of mathematics?

Not all those who assert contingent propositions believe that the consequence relation is classical (in relevant logic, for example, the consequence relation is paraconsistent, and so there's no proof ...
kuro's user avatar
  • 141
3 votes
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Do contradictions rule out holism and vice versa, and pluralism?

If you are asking specifically about Quine's position, he sticks rigidly to classical logic. He does not accept logical pluralism and does not allow that any contradictions are true. In Two Dogmas (...
Bumble's user avatar
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2 votes

Time as a transition from a whole which is constitutable by each of many sets of parts to the set of parts that generates the shortest path?

Quite the sophisticated question. I suspect there aren't a lot of people on this forum who speak McTaggert fluently and fewer who understand the mathematical physics of relativity and QM well enough ...
J D's user avatar
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2 votes

What happens if we accept inconsistency?

This answer has four parts. First, I'll analyze the specific example you give. Then I'll connect this to Alice's behavior, and follow up by talking about objections to paradox in general. I'll end ...
Noah Schweber's user avatar
2 votes

Do contingent propositions about the world rely on the consistency of mathematics?

In my opinion, sort of. My position on the philosophy of maths is a formalist one, that is, I believe mathematical truths are essentially constructed and evaluated from a set of rules, or axioms. ...
edelex's user avatar
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2 votes

Do contingent propositions about the world rely on the consistency of mathematics?

If we are some sort of mathematical realist and then distinguish our theories of mathematics from the "reality itself," then the reality itself will always be consistent anyway (supposing ...
Kristian Berry's user avatar
1 vote

Do contingent propositions about the world rely on the consistency of mathematics?

There are no great metaphysical insights into this question. First of all, contradictions aren't discovered. They're constructed, and a good explanation of this is Constructive Mathematics (SEP). You ...
J D's user avatar
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1 vote

Do contingent propositions about the world rely on the consistency of mathematics?

The case you describe already happened: Bertrand Russell’s antinomy in set theory from 1901, see Russell's paradox. After Cantor’s invention of set theory it took a while, until mathematicians learned ...
Jo Wehler's user avatar
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1 vote

Is philosophy about the resolution of mental conflict and disunity?

There is some precedent for this view in ethics, that is, the principle of reflective equilibrium. From SEP: The method of reflective equilibrium consists in working back and forth among our ...
emesupap's user avatar
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1 vote

Is philosophy about the resolution of mental conflict and disunity?

This is an odd, but not unproductive way of conceptualizing philosophy, one that approaches it from a standpoint of functional analysis. As you mentioned, however, this could describe a fairly large ...
Chris Sunami's user avatar
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1 vote

Is philosophy about the resolution of mental conflict and disunity?

This sounds like it could be Eleatic possibly. To Ancient Greek proponents, there is one thing, a unity of being. Thought is being. Nothing can be said about non-being. And humans are stuck by their ...
J Kusin's user avatar
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1 vote

Immorality of inconsistencies

It is odd to describe inconsistency as immoral, but perhaps you are asking about the normativity of logic. This is a fairly hot topic in the philosophy of logic at present. Traditionally, logical ...
Bumble's user avatar
  • 26k
1 vote

In a deductive reasoning system, what happens if we have unfounded axioms?

"Wrong" is not the correct term.  We'd simply rather axioms not be "Inconsistent". This happened to be the case with the axioms of Cantorian Set Theory.  It was found to derive several ...
Graham Kemp's user avatar
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