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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.

The following are some sources for paraconsistent logic.

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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 truth. Is it possible to think of paraconsistent…
Mozibur Ullah
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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 contradiction P ∧ ¬P lets you conclude any…
Greg Nisbet
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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 of mathematics? Even mathematics that allow…
Sue K Dccia
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Can Hegel's theory of logic be formalized?

In paraconsistent logic, we have dialecticism. So is it possible to formalize the logic of Hegel, like Anton Friedrich Koch in "Hegel's on the logical big bang and the evolution of logical space", and formalize all the European philosophers' system,…
AnduinWilde
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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 false This, of course, reflects the Buddhist…
Mozibur Ullah
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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 still be true contradictions anyway. (Of course,…
Dannyu NDos
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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 before it is been written). 2.Type inconsistency…
jimjim
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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 Cretan. Why does this not work as an antinomy if there is…
MathematicalPhysicist
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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 as it it indicated in his essay “The Unreasonable…
vengaq
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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 paraconsistent…
Sue K Dccia
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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 a logic which is not conceivable or…
Joseph_Kopp
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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 over every disjunction, we confine its primary…
Kristian Berry
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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 is concerned with studying and developing…
bautzeman
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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 statements actually hold true under dialetheism?…
help-me
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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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