TPF : Paradoxes & Fuzzy Logic

[Gnomon]

The Full Import of Paradoxes
https://thephilosophyforum.com/discussi ... ent/699216

1. Classical logic has to use Occam's broom (sweep paradoxes under the rug) otherwise, via ex falso quodlibet, concede that classical logic is trivial.

2. We're using some version of paraconsistent logic and we're not aware of it. — Agent Smith

Classical binary Logic is best used for problems that can be precisely defined with integer numerical values. But human contradictions are seldom concisely defined; instead loosely sketched with inexplicit subjective truth-values.

A formalized version of "paraconsistent logic" (logic of paradox) is the Fuzzy Logic that is used in computer science for complex puzzles that are hard to define numerically, such as human beliefs & intuitions. It is especially useful in Artificial Intelligence and Evolutionary Programming.

We're not aware of our sloppy logic because it is intuitive, so we don't normally examine it with classical rules in mind. That's why divisive emotional issues, such as Abortion & Racism tend to polarize people. And can only be resolved, to some degree, with critical (rational) thinking : to discover the inconsistencies in our beliefs.


Paraconsistent Logic :
A paraconsistent logic is an attempt at a logical system to deal with contradictions in a discriminating way. Alternatively, paraconsistent logic is the subfield of logic that is concerned with studying and developing "inconsistency-tolerant" systems of logic which reject the principle of explosion.
https://en.wikipedia.org/wiki/Paraconsistent_logic

Most if not all thinkers are under the impression that they're using classical logic - they don't take too kindly to contradictions. — Agent Smith

Actually, most thinkers have an ego-boosting impression of their own reasoning abilities. We find it easier to see the contradictions in other people's ideas than in our own thoughts. Intuition always seems true, even when it aint.

A great many people think they are thinking when they are merely rearranging their prejudices.
— William James.

[Gnomon]

If I'm not mistaken, there is work in combining formal paraconsistent logic with formal fuzzy logic. But fuzzy logic itself is not a formalization of paraconsistent logic. — TonesInDeepFreeze

Perhaps, I should have prefaced that personal opinion with "it seems to me, that . . .". Before Agent mentioned it, I had never heard of "paraconsistent logic". But a quick Wiki review sounded like a description of Fuzzy Logic, which I was already familiar with. For my general purposes, I prefer the more colloquial and less technical-sounding term. From my layman's perspective, both terms seem to reflect the Uncertainty Principle of Quantum Theory, as applied to other fields of investigation.

[Gnomon]

3. The LNC needs to be scrapped + a version of paraconsistent logic needs to be adopted — Agent Smith

Not so fast. The Law of Non-Contradiction is a good rule of thumb for most contexts. But there is one common circumstance where LNC does not apply : Holism. The reductive methods of science are appropriate for things-in-isolation. But when a thing participates in a larger System, it shares qualities of the system, which compromises some of its own properties. To a reductionist observer such holistic behavior may seem inconsistent and paradoxical.

For example : what Einstein called spooky-action-at-a-distance, Schrodinger called "entanglement". Which implies that some quantum particles in a holistic (waveform) system share some properties with other particles. Apparently, in their waveform state, electrons are connected to all other electrons in the universe, in such a way that a measurement of one instantly affects (e.g. flips the spin of) all similar particles. From that perspective, it's not a contradiction, but a feature of Holism : an emergent property.


Holism ; Holon :
Philosophically, a whole system is a collection of parts (holons) that possesses properties not found in the parts. That something extra is an Emergent quality that was latent (unmanifest) in the parts. For example, when atoms of hydrogen & oxygen gases combine in a specific ratio, the molecule has properties of water, such as wetness, that are not found in the gases. A Holon is something that is simultaneously a whole and a part — A system of entangled things that has a function in a hierarchy of systems.
BothAnd Blog Glossary

"The opposite of a profound truth is also a profound truth"
___Neils Bohr, baffled by apparent violations of LNC

"We are not only observers. We are participators. In some strange sense, this is a participatory universe. Physics is no longer satisfied with insights only into particles, fields of force, into geometry, or even into time and space." ___John A. Wheeler

SHARING IS PARTICIPATING (parts unite with the whole)
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[Gnomon]

My understanding of paraconsistent logic, from Graham Priest, is that things can contradict each other and still be true — Jackson

Yes. That is the implication of my personal BothAnd Philosophy. Some apparent "paradoxes" result from viewing only one side of the same coin.


Both/And Principle :
My coinage for the holistic principle of Complementarity, as illustrated in the Yin/Yang symbol. Opposing or contrasting concepts are always part of a greater whole. Conflicts between parts can be reconciled or harmonized by putting them into the context of a whole system.
BothAnd Blog Glossary

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