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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
6 votes
Accepted

Does Gödel's argument that minds are more powerful than computers have the inconsistency loophole?

As such, Turing machines are not consistent or inconsistent - formalized systems are. However, once we fix a coding of (e.g.) the syntax of the language of arithmetic, we can view some Turing machines ...
Panu Raatikainen's user avatar
4 votes
Accepted

Reference needed: why is the Liar Paradox regarded as not important/fringe by some?

To give you an example (a few more are cited in that paper of Weaver) those who hold it as unimportant generally do not write in usual academic venues about it, but it goes something like: As the ...
got trolled too much this week's user avatar
4 votes
Accepted

Is there a difference between contradictory and the opposite?

Yes. Contradiction just means that not both can be true at the same time. Opposite means the other extreme of the scale. (Of course, if there is no scale and just two possible states, contradiction ...
Natalie Clarius's user avatar
4 votes

Why shouldn’t I be a skeptic about the Necessitation Rule for alethic modal logics?

Modal logics that include the necessitation rule are called normal. Not all modal systems are normal. Some of the non-normal logics are S1, S2 and S3, which are consistent with the necessitation rule, ...
Bumble's user avatar
  • 26.7k
3 votes

Has anyone recast Aristotle's Law of Noncontradiction as a law of recontextualization?

Resolving a contradiction is an issue that arises in dialectic: there is an apparent inconsistency in my/your/their beliefs and I want to resolve it. In the Metaphysics Aristotle isn't coming from the ...
b a's user avatar
  • 622
3 votes

Has anyone recast Aristotle's Law of Noncontradiction as a law of recontextualization?

Fuzzy logic maps degrees of truth over the otherwise conventional logic membership relations (MATLAB - What Is Fuzzy Logic?): https://youtu.be/__0nZuG4sTw Call it recontextualization or whatever term.
SystemTheory's user avatar
  • 2,213
3 votes
Accepted

Do contradictions rule out holism and vice versa, and pluralism?

If you are asking specifically about Quine's position, he sticks rigidly to classical logic. He does not accept logical pluralism and does not allow that any contradictions are true. In Two Dogmas (...
Bumble's user avatar
  • 26.7k
3 votes
Accepted

A philosophy of suspending disbelief. What is it called?

Are you thinking of a case where : S that not-p but intends to bring it about that s/he acquires the assumed [or known] to be] false belief that p           ? In your ...
Geoffrey Thomas's user avatar
  • 35.8k
3 votes

Does many valued logic hold in unambiguous cases?

I'm not sure to correctly interpret your question... The relevant discussion is about the difference between truth-value gaps and truth-value guts: see G.Priest, An Introduction to Non-Classical ...
Mauro ALLEGRANZA's user avatar
2 votes

Is there a difference between contradictory and the opposite?

Short Answer Opposite in logic is generally taken to mean logical negation. A contradiction in logic is generally taken to be two propositions whose truth values are opposites. Example: P and ~P are ...
J D's user avatar
  • 28.7k
2 votes

? as a logical connective

This was a misprint of the pdf. I checked other pdfs of the text and it the law of identity reads "it is necessary that a implies a" in the first case. If you've got the same rendering of ...
melembroucarlitos's user avatar
2 votes

A philosophy of suspending disbelief. What is it called?

What's missing is a notion of subjective truth, as opposed to objective truth. A nice example of this is winking. Usually, when done effectively, only one person is aware when another person winks ...
elliot svensson's user avatar
2 votes

Reference needed: why is the Liar Paradox regarded as not important/fringe by some?

Appearances being deceiving here, consider that the liar sentence (and the truth-teller sentence too, for that matter) could only be as they say they are in the effective equivalent of a private ...
Kristian Berry's user avatar
2 votes

What is the exact form of law of non-contradiction that dialetheism rejects?

I believe that it is not so much a case of dialetheism rejecting a form of LNC, but rather a case of where LNC is applicable. For the dialetheist, the Liar sentence has a literal meaning, but it has ...
nwr's user avatar
  • 3,535
2 votes
Accepted

Semantic rules overdetermine the truth value of Liar Paradox

Recall that (see also your previous post) Graham Priest is a dialetheist, i.e. a proponent of the view that there are true contradictions. Priest's discussion of the Liar starts rejecting the view ...
Mauro ALLEGRANZA's user avatar
1 vote
Accepted

Why can't the dialetheist say that the Curry sentence is both true and false?

I found the following information in JC Beall (a dialetheist)'s Spandrels of Truth (chapter 2). Beall notes that if we interpret the Curry sentence's conditional as LP's barebones conditional (the ...
confusedcius's user avatar
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

Can Hegel's theory of logic be formalized?

No, Hegel's notion of logic is directly against formal logic (even contemporary paraconsistent logic). For example, in §119 of his Shorter Logic, Hegel said that "6 miles to the west" and &...
Anduin Wilde's user avatar
1 vote

Motivations for dialetheism?

If you accept dialetheism, you have to develop some new logical systems to make it work out. We don’t need people running around like, “The Liar’s Paradox! Therefore, it follows that NASCAR is a sport!...
user38224's user avatar
1 vote

Dialetheias in the absence of contraction/absorption?

Since asking this question I have realized that even if contraction-free logic does not reproduce any literal dialetheias of the form "P and not-P", it gets pretty close. For instance, in naive set ...
Mike Shulman's user avatar
1 vote

Dialetheias in the absence of contraction/absorption?

Russell's paradox (set theory) does not depend on contraction. However whether it can be used as an argument for dialetheism is doubtful. The standard interpretation is that it is a demonstration that ...
AnotherSmellyGeek's user avatar

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