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Questions tagged [inconsistency]

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What are the philosophical implications of using inconsistent mathematics?

Why mathematicians would prefer at times to work with inconsistent systems (from which I assume everything can be proven unless changing the logic used)? In particular, how could working with an inconsistent system be useful or advantageous? What…
L.M. Student
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What happens if we accept inconsistency?

(Philosophy novice here and not sure how best to phrase this question; if it's unclear please point out the problems). Imagine this conversation: Alice: I believe that X. Bob: Do you also believe Y? (Alice says yes) But that means you believe in…
Allure
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Did physicist Erwin Schrödinger propose that reality could have contradictions?

Did Schrödinger believe that contradictory or inconsistent things could exist in reality? Was Schrödinger some kind of dialetheist?
vengaq
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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?

Summary: Any entity E which is constituted by extrinsically indiscernible parts A and B remains extrinsically the same, in all stages of the change, even if A changes to B and B to A (concurrently). More generally, an entity E which is…
Morteza
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Do set theories have inconsistency strengths, on top of consistency strengths?

Caveat: this question is fairly technical in nature, and I have reason to believe it would be more fitting for the MathOverflow, especially in terms of potentially informative responses (there are some here who might be able to "put me in my place"…
Kristian Berry
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Transconsistency operators and degrees of logical explosivity?

So I noticed in an article I was reading that they talked about consistency and/or inconsistency or otherwise transconsistency operators. I don't recall the details, but they sound like propositional operators, though presumably on conjunctions? Let…
Kristian Berry
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How can the position of skepticism avoid becoming incoherent on the problem of the criterion?

Concerning the problem of the criterion, there has been said to be three traditional responses: methodism, particularism, or skepticism. Although other philosophers have proposed that there are more solutions to the problem than the three listed,…
Christian Dean
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Did Wheeler's "It from Bit" allow inconsistencies to exist?

Physicist John Wheeler proposed a model of the universe based on "It from Bit" asserting that the world is fundamentally information. I've been told both that Wheeler's It from Bit is compatible with inconsistency (for example, the bits in "It from…
inuflatze
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Is it there any trivialist model in physics (like in quantum mechanics)?

Trivialism is a system that proposes that literally every proposition is true and false at the same time blatantly breaking the principle of no contradiction and triggering the principle of explosion (https://en.m.wikipedia.org/wiki/Trivialism) I…
Sue K Dccia
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I'm so confused, why doesn't the foundation axiom allow us to derive ℘(ℵ₀) ≠ ℘(ℵ₁), or worse, why doesn't that axiom show that ZFC is inconsistent?

℘(ℵ₀) ≠ ℘(ℵ₁) is not provable in ZFC (this unprovability is an instance of Easton's theorem). I don't know why my mind decided to get hung up on this today, but I'm tired and this brain bee is buzzing like mad in my head. My confusion goes: Take…
Kristian Berry
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In a deductive reasoning system, what happens if we have unfounded axioms?

What if our axioms are false? What happens then?
asdfasfasdgf
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Immorality of inconsistencies

I am trying to find some arguments on the immorality of inconsistencies. To me it seems quite intuitive to conclude that an inconsistency is immoral (for example, 'Grass is green and grass is not green' is an odd result, so it must be immoral), but…
CowNerd
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Is it possible to mathematically define a hypercomputer-universe where things that could not be computed by it could exist?

There are a few physicists that propose that the universe is a hypercomputer. One example is Roger Penrose, who, basing in his quantum interpretation (https://en.wikipedia.org/wiki/Penrose_interpretation) and in spin networks…
Sue K Dccia
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