Questions tagged [non-classical-logic]

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Implication as an Explanatory Relation Reference Request

Has there been anyone in Academia lately who has proposed the following form of logic: Implication is interpreted as an explanatory relation between two propositions, so that implication is not ...
• 459
118 views

Act and Potency in Logic and Mathematics

Presently, has there been an attempt to incorporate the Aristotelian-Thomistic notions of Act and Potency into Logic and Mathematics? Also, how would the current interpretation of the principle of ...
• 459
82 views

Interpretation of the Implication Sign

According to @DanChristensen: “Smoking has been scientifically proven to cause cancer. We cannot infer from this that smoking implies cancer.” To this I would reply with the following: First, if we ...
• 459
65 views

Is Peirce’s Law seen as a principle for relevance logics?

As far as I can tell, ‘relevance’ is a bit of a nebulous term depending on which logicians you ask, but that each of them has a rigorous view of what it means. Consider the formula known as Peirce’s ...
• 1,431
4k views

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: ...
• 1,079
60 views

Vacuous truth in non-classical logics

Does the notion of a vacuous truth exist in non-classical logics as well? I'm thinking of logics inspired by intuitionism, which assign great importance to constructive proofs.
155 views

Relationship between Structural Contraction and the Absorption theorem?

Edit: Originally I called the absorption theorem “contraction theorem” which makes everything needlessly wordy and confusing. I will call the left structural contraction rule simply LSC rule, and the “...
• 430
72 views

Question about a presentation on substructural logic (negation modulo two kinds of residuation)

I've been reading through this slide-based presentation on substructural logic and I'm delightfully perplexed by the following section: What is the use to which the two given flavors of negation can ...
• 16.2k
1 vote
54 views

Infinitesimals and plural quantification

In reply to, "Does nature jump?" Mikhail Katz notes that: There is a different idea in Leibniz called the Law of Continuity. One of its formulations is the rules of the finite are found to ...
• 16.2k
45 views

How would demi-conditionals work?

Let 𝒜 = an actuality operator and √→ be demi-if. Which, if any, of the following conversions would go through? 𝒜A √→ 𝒜B = √𝒜A → √𝒜B 𝒜A √→ 𝒜B = √𝒜A → 𝒜B 𝒜A √→ 𝒜B = 𝒜A → √𝒜B 𝒜A √→ 𝒜B = √�...
• 16.2k
1 vote
130 views

The square root of evil (the demi-forbidden = the suberogated?)

Pursuant to the general question of demi-operations in logic, I wondered today about demi-forbidding, √FR. So luckily enough, my question is simple enough: Via Fregean conceptual analysis, or ...
• 16.2k
31 views

If we used √OB and √𝓐 operations, could we have a demi-is/demi-ought proposition that bridged full "is" with full "ought"?

The insight that the teleological ethicist seems to have is that final causality is a type of the moral law in the Kantian sense (from the second Critique): ... the moral law has no faculty but the ...
• 16.2k
259 views

Quantum probability theory and the idea of a "truth-value sphere"

A while ago I asked a question about using imaginary numbers as truth-values for a peculiar concept known as "the square root of negation"; I just found out that apparently this concept is ...
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80 views

√◊ (or generally √M, for whatever modal operator(s) M)

I tried Googling "demi-possibility demi-negation" and got nothing (just "demi-possibility" gave results mostly related to demisexuality). And my analysis of demi-negation didn't ...
• 16.2k
414 views

Let's consider the famous liar paradox's statement: This statement is false Now, in classical logic, principle of bivalence could be stated as "All statements can either be assigned a value of ...
614 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 ...
• 551
422 views

What are borderline cases?

What is a borderline case, and its relationship with vagueness? I have googled a lot but didn't quite find anything that suits my understanding.
48 views

? as a logical connective

I am reading Doubt Truth to be a Liar by Graham Priest. In it he uses the symbol ? as a logical connective, and I am unsure of it's meaning. Given his use of ? (a ? a) to denote the Law of Identity, ...
75 views

What is the "logic of ejaculations"?

I was looking through a paper on one valued logic and it references something called the "logic of ejaculations", shocked by the name, I tried to find another reference to it in which I ...