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Questions tagged [paraconsistency]

A paraconsistent logic is an inconsistency-tolerant logic. Such a logic is not explosive, that is, contradictory premises do not explode into triviality.

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Discussion about Graham Priest's dialetheic views on Eastern and Western philosophy

Australian philosopher Graham Priest is famous for advocating Dialetheism, the view that there are true contradictions. Dialetheism goes against the law of non-contradiction. This gives rise to the ...
Dario Mirić's user avatar
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1 answer
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Liar's paradox, dialethism and law of excluded-middle [duplicate]

I've been reading about liar's paradox and its responses. I like Graham Priest, fantastic philospher and proponent of dialethism. Graham argues that liar's paradox is solved by claiming that statement:...
Dario Mirić's user avatar
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9 answers
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Why should I not believe there are true contradictions?

Kane Baker has a YouTube video in which he introduces the word 'wulture'. 'Wulture' applies to all things that are vultures, and excludes all things which are white. Delia is a white vulture. He asks: ...
edelex's user avatar
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Why can't the dialetheist say that the Curry sentence is both true and false?

In the SEP article for dialetheism, it is said that A dialetheist, though, cannot simply accept that the Curry sentence is both true and false, because if it is true then ⊥ follows. Dialetheists need ...
confusedcius's user avatar
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2 answers
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Do statements about borderline cases hold for both the vague term and its negation?

I read subvaluationists think that P can be both true and false (unlike supervaluationists, who think that P is neither true nor false), but it's completely unclear (because I can't read symbolic ...
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3 votes
4 answers
617 views

On the logical modeling of reality and human reason

What is the system of logic which models reality and, furthermore, which models human reason? Preface: Of course, objective reality (that is, reality as it is before it's perceived) may operate under ...
Joseph_Kopp's user avatar
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1 answer
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What is ⊥ called in paraconsistent logic?

I am building a weakened version of the intuitionistic logic. It wouldn't satisfy (p∧¬p)→⊥ as a tautology, but rather, (⊤→(p∧¬p))→⊥. In plain English, contradictions admit no proof, but there might ...
Dannyu NDos's user avatar
2 votes
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When does a conditional statement hold true according to Dialetheists?

I understand that for the consequent to really follow from the antecedent, it (the consequent) must be both relevant and necessary given the antecedent. So my question is: which types of conditional ...
help-me's user avatar
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Is there a rule/s for determining whether a contradiciton is a Dialetheia?

If not, is there a set of accepted properties or qualities that dialetheic statements have?
help-me's user avatar
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1 answer
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Paraconsistent logic for daily life

In everyday life, there can be evidence to support both a proposition and the negation of it. I guess paraconsistent logic is an appropriate way to model this. Is there any research in that direction?
user776490's user avatar
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"Should" there be multiple types of universal quantifiers?

Assumptions/presuppositions. I am trying to set up a logic where every connective/operator comes in at least two flavors. For example, with respect to disjunction, rather than hold the LEM rigidly ...
Kristian Berry's user avatar
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Laws of excluded however-many things

How strong is the difference between inclusive and exclusive disjunction? At least, let ∨0 be inclusive ("weak") disjunction, and ∨1 be exclusive ("strong") disjunction. Then take ...
Kristian Berry's user avatar
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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 ...
Kristian Berry's user avatar
1 vote
1 answer
118 views

Dialethic machines and incompatibilist free will

Preamble: although I believe in the LNC for Aristotelian/Quinean reasons and the argument from explosions to boot, and am not altogether adept at modal logic in general, much less counterpossible ...
Kristian Berry's user avatar
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1 answer
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Rehabilitating Zermelo's description of the universe of sets?

I was reading various essays about Cantor's doctrine of absolute infinity, and it came up again that Zermelo's doctrine, by contrast, was of V as an "unfinished totality." Initially, this ...
Kristian Berry's user avatar
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How is ~CH derived in paraconsistent set theory?

This question on MathOverflow has been left unanswered. The respondents pointed mainly towards "Transfinite Numbers in Paraconsistent Set Theory", an article to which I don't have access. ...
Kristian Berry's user avatar
4 votes
2 answers
217 views

A variant question of the Liar paradox

This question is exercise 1 from Manuel Bremer's An Introduction to Paraconsistent Logics. The question Often the sentence given as the Liar example is "All Cretans are liars." said by a ...
MathematicalPhysicist's user avatar
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How do paraconsistent logicians resolve the 'Geach Paradox'?

Paraconsistent logic rejects the principle of explosion, which states that from a contradiction (both Y and ¬Y), any proposition 𝑍 can be inferred. However, within paraconsistent systems, we can ...
AnduinWilde's user avatar
4 votes
5 answers
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About Wigner's view on the relation between mathematics and physics?

Physicist Eugene Wigner argued that the enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and that there is no rational explanation for it ...
vengaq's user avatar
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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?
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Can Hegel's theory of logic be formalized?

For dialecticism, we have paraconsistent logic. Is it possible to formalize the logic of Hegel, other European philosophers' systems, or at least their arguments?
AnduinWilde's user avatar
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What is an example of a true contradiction in a paraconsistent logic?

While reading the Wikipedia article on trivialism I noticed the following: In classical logic, trivialism is in direct violation of Aristotle's law of noncontradiction. In philosophy, trivialism is ...
Frank Hubeny's user avatar
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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 (...
Sue K Dccia's user avatar
1 vote
0 answers
203 views

Can hypercomputation compute the impossible?

There are things which are illogical/logically impossible (like saying that 2+2=4 and 2+2=5. Without changing anything in the axioms of mathematics or logic, this would be a contradiction and would be ...
Sue K Dccia's user avatar
5 votes
1 answer
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Does Tegmark himself include paraconsistent mathematical structures in his mathematical multiverse hypothesis?

Tegmark postulates in his hypothesis that all possible mathematical structures would exist. But does he include also possible mathematical structures described by other types of logic like ...
Sue K Dccia's user avatar
8 votes
3 answers
336 views

Are there "partially explosive" logics?

Roughly speaking, I'm wondering if it's possible to meaningfully grade different systems on how explosion-tolerant they are. In classical sentential logic and intuitionistic sentential logic, a single ...
Greg Nisbet's user avatar
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Does Tegmark's Mathematical Universe hypothesis allow existence of alternative mathematics?

Tegmark's mathematical multiverse hypothesis assumes that all mathematical structures exist as universes But do you know whether his hypothesis also allows/accept universes described by other types ...
Sue K Dccia's user avatar
1 vote
10 answers
549 views

How could we get a world where only impossible things happen? [closed]

Imagine a universe where 1+1=3. This contradiction would trigger the effects of the principle of explosion, and thus, literally everything (possible and impossible things) could happen. If we lived in ...
Sue K Dccia's user avatar
3 votes
2 answers
1k views

Can paraconsistent or other logics make the impossible happen?

A paraconsistent logic system it is defined as "a logical system that attempts to deal with contradictions in a discriminating way. Alternatively, paraconsistent logic is the subfield of logic that ...
bautzeman's user avatar
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What paraconsistent logics are there?

Is there a non-dialetheist paraconsistent logic in which invalidating the law of non contradiction (someone is both stupid and not stupid and short ∃x(STUPID(x) ∧ ¬STUPID(x) ∧ SHORT(x))) in any ...
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What types of inconsistency are there that we know of?

Just trying to verify consistency of a system, I need to have a list types of inconsistency to look out for, so far I have the followings: 1.Anachronistic inconsistency (e.g. trying to read a file ...
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Is Belnap's four-valued logic technically a relevance logic?

Belnap, the American Logician, constructed a four-valued logic which is a form of relavance logic; interestingly the truth-values it takes are: true false both true & false neither true nor ...
Mozibur Ullah's user avatar
11 votes
2 answers
344 views

Is there a sheaf-theoretic description of para-consistent logics?

Paraconsistent logics drop the notion of global consistency, instead they have a notion of local consistency. In sheaf-theory, or categorical logic, as in topos theory, there is a notion of local ...
Mozibur Ullah's user avatar