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20 votes
Accepted

Why should I not believe there are true contradictions?

You may cancel from ordinary logic the prinicple of non-contradiction and admit at least one contradictory statement ’A and non-A’. But then you get for arbitrary statements B the valid statement A ...
Jo Wehler's user avatar
  • 33.6k
17 votes

Why should I not believe there are true contradictions?

Frame challenge: This is based on a false premise Your problem is a lot simpler than you think, and your YouTube reference is trivially wrong. You're only confused because they're talking rubbish, and ...
Graham's user avatar
  • 2,360
8 votes

Can paraconsistent or other logics make the impossible happen?

Logic, paraconsistent or not, does not exactly make something happen, it is applied to reshuffle information already contained in a system. Paraconsistent logic does not even have to be applied to ...
Conifold's user avatar
  • 43.5k
7 votes

Does Tegmark's Mathematical Universe hypothesis allow existence of alternative mathematics?

Pigliucci gives an interesting review of the Mathematical Universe based on personal conversations with Tegmark. Apparently, Tegmark does admit plurality of mathematical structures, at least ...
Conifold's user avatar
  • 43.5k
7 votes

Can Hegel's theory of logic be formalized?

Hegel's logic has already been formalized by physicist and mathematician Urs Schreiber. However, there are likely only a few dozen people on earth who can understand it due to the formalization being ...
helloimhamid's user avatar
5 votes
Accepted

A variant question of the Liar paradox

There are, in fact, two problems with the "All Cretans are liars" paradox. The first is that a liar is not a person who tells nothing but lies, it's a person who tells (some) lies. If all ...
Mary's user avatar
  • 1,988
5 votes

Why should I not believe there are true contradictions?

This got me thinking: How does one really justify the law of non-contradiction without just appealing to intuition? If you accept logic, but specifically deny the law of non contradiction, the ...
TKoL's user avatar
  • 3,462
3 votes

On the logical modeling of reality and human reason

Reality, from a realist perspective, is just what exists, independently of us observing it. It doesn't operate under a logic, though it may be possible to describe it using the help of a logic. ...
Bumble's user avatar
  • 26.4k
3 votes

How do paraconsistent logicians resolve the 'Geach Paradox'?

Below I'll refer to the paradox - namely, the problem arising from sentences of the form "If this sentence is true, then X" - as Curry's paradox, which I believe is standard. Note that this isn't ...
Noah Schweber's user avatar
3 votes

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

A very interesting question. I think that you are not committed to the existence of both the worlds, because you are looking at the impossible world (IW) from the perspective of the possible one (PW). ...
Francesco D'Isa's user avatar
3 votes

Why should I not believe there are true contradictions?

Perhaps we should first check whether the statement, "No contradiction can be true," can be made more precise. We will say, "Propositions (A) and (not A) cannot both be true." But ...
Kristian Berry's user avatar
2 votes

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

One serious possibility for understanding entropy and the arrow of time, given that all events in quantum field theory (QFT) seem to be reversible (equally workable forwards and backwards in time, ...
CriglCragl's user avatar
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2 votes

Are there "partially explosive" logics?

The three-valued logic of Lukasiewicz can be viewed as a paraconsistent logic, since ¬(P ∧ ¬P) is not a universal law that applies to all statements, but a contingent statement, applicable to some ...
Confutus's user avatar
  • 614
2 votes

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

A few points that didn't get enough attention: The deductive reasoning invoked by OP has been proven (by Kurt Gödel) to be insufficient to describe our world. Specifically he proved that any Formal ...
christo183's user avatar
  • 2,475
2 votes

What is an example of a true contradiction in a paraconsistent logic?

Long comment (but I'm not sure to fully understand your question...) Some definitions from Walter Carnielli & M.E. Coniglio, Paraconsistent Logic : Consistency, Contradiction and Negation (...
Mauro ALLEGRANZA's user avatar
2 votes

On the logical modeling of reality and human reason

On the "description of human reason" side of things, there's the defeasible-reasoning research program to consider. This is related to logics of belief revision and dialogical or dynamic ...
Kristian Berry's user avatar
2 votes
Accepted

How is ~CH derived in paraconsistent set theory?

On the basis of a full axiom of comprehension, Weber shows that there is a set of all sets, which he denotes V, and a set of all ordinals, which he denotes On. He uses von Neumann’s definition of a ...
Bumble's user avatar
  • 26.4k
2 votes

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

The question seems to be based on the elimination rule for contradiction or explosion. Imagine a universe where 1+1=3. This contradiction would trigger the effects of the principle of explosion, ...
Frank Hubeny's user avatar
  • 19.5k
2 votes

What is ⊥ called in paraconsistent logic?

In a logic system that accepts true contradictions but not the law of noncontradiction, the symbol ⊥ (usually called "bottom" or "falsum") may represent something different than a ...
280's user avatar
  • 46
1 vote

Do statements about borderline cases hold for both the vague term and its negation?

The comments here are quite good, but I want to pick up on something that I was interested in. Consider the quantifier exchange rules: ¬∃xPx ↔ ∀x¬Px (there's not some P iff everything is not P) ∃x¬...
GreenPricklyCactus's user avatar
1 vote
Accepted

On the logical modeling of reality and human reason

What is the system of logic which models reality and, furthermore, which models human reason? On a nominalist (SEP) reading, 'reality' is a linguistic entity that describes by way of representations, ...
J D's user avatar
  • 28.5k
1 vote

Paraconsistent logic for daily life

Yes, there is research in the field of paraconsistent logic, which is a type of logic that allows for the coexistence of contradictory statements. In everyday life, it is often the case that there is ...
Yoel Schvarcz's user avatar
1 vote
Accepted

"Should" there be multiple types of universal quantifiers?

In English, the quantifiers 'all', 'any', 'every' and 'each' are somewhat different, though all of them would qualify to be called universal quantifiers. In simple cases, they are interchangeable, for ...
Bumble's user avatar
  • 26.4k
1 vote

"Should" there be multiple types of universal quantifiers?

In the appendix to Blok and Pigozzi it is explained that the algebraization of first-order logic impacts the "standard" (ahem, a nonsense word for mathematics) quantifier rules associated ...
mls's user avatar
  • 11
1 vote
Accepted

Laws of excluded however-many things

I cannot speak to any of the concerns which led to your question. However, I can say something. With regard to material connectivity, inclusive disjunction is linearly separable whereas exclusive ...
mls's user avatar
  • 36
1 vote

Dialethic machines and incompatibilist free will

SUMMARY -- I don't have references for you for whether a dialethic quantum computer could model, approximate, emulate, or achieve free will What I can offer is a reasoning path that brings rationalism ...
Dcleve's user avatar
  • 14.6k
1 vote

About Wigner's view on the relation between mathematics and physics?

A paraconsistent logic is a logic that does not validate the principle of explosion ("from a contradiction, anything follows"). A paraconsistent plurality of worlds will therefore be open to ...
Kristian Berry's user avatar

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