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Questions tagged [logic]

For questions about logic, whether it concerns syllogistic logic, mathematical logic or the nature of logic itself.

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can S5 be the weakest logic?

If we were to prove that an argument is a logical truth only in S5 logic out of (K, T, S4, and S5). does that make S5 the weakest of these four logics in which the argument is a logical truth?
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Does determinism prevent rationality?

If hard determinism is true, and our thoughts are merely the results of a causal chain of atomic interactions, are reason and logic illusory? This matter has likely been discussed in another thread, ...
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Is it fallacious to argue that something is correct, of good quality, or acceptable because a community of experts has established it as such?

Earlier today, I asked a programming question on a forum. I phrased the question as "What is the best way to do x?" Someone responded with something to the effect of, "the best way is ...
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2answers
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Why is this argument supposedly improved?

Hello to all philosophers! A while ago my professor was going through the First Cause Argument and formatted it as such: Everything has a cause. The chain of causes cannot reach back indefinitely; ...
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What Logic fallacy is Person 1 using in this?

Person 1: Vaccines can cause Autism Person 2: If it can cause Autism, why does all the Studies not support that in any way? Person 1: Actually I'm not saying it does but "Maybe" it can cause ...
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3answers
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Why do “subject” and “object” not have opposite meaning?

I am always confused by- and have to often look up the meanings of these words (it helps that English isn’t my first language). The word “subject” seems to imply that it is subjected to an action, ...
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How do logicians think of strength of proof systems?

I want to understand how logicians reason about strengths of proof systems and argue relative strengths of proof systems. I want to appreciate the validity of the reasoning by which we establish ...
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55 views

This logic is fine? [closed]

A banana is yellow, but A said the banana black. In this case, is “According to A, a banana is black” a true statement? I know “a banana is black” is false but there is “according to A.”
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Am I correct that tautologies and contradictions are NOT truth-functional?

We call a statement truth functional if its truth value depends on truth value of its parts. Like A⊃B can be true or false, depending on truth values of A and B. But, it's not the case with ...
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4answers
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Is imagination a sufficient condition for something to exist?

We can imagine a chair and build it, We can imagine the Starship Enterprise And given the neccessary technological knowledge build it. We can imagine a living flying elephant and it seems given the ...
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1answer
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A question on hypothetical syllogism

hypothetical syllogism is of the form: if a then b if b then c Therefore, if a then c . In one of the examples my book also says F ⊃ G ~ G ⊃ F Therefore ~G ⊃ G (by HS) I have a small problem of ...
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How to explain a logical joke like: A: "Do you do weight lifting or go jogging?" B: "Yes."

Example 1: A: Do you do weight lifting or go jogging? B: Yes. (or No.) Example 2: A: Does he have a Mercedes or a Porsche? B: Yes. (or No.) My understanding: A "logical disjunction" ...
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Why does a constructive dilemma use inclusive disjunction in its disjunctive premise, instead of exclusive disjunction?

Doesn't it contradict the whole point of having a dilemma? Even if the argument is sound it allows us to take both options, instead of just one. I don't think you're supposed to be able to do this, ...
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god is irrelevant? [closed]

I have this argument that god isn't relevant kind of along the lines of Epicurus'. Obviously it's impossible to prove anything doesn't exist but here is the next best thing in my opinion. Imagine 2 ...
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First-order semantics for plural logic

There are commonly thought to be two kinds of set-theoretic semantics for second-order logic: the standard one, where relation (and function) variables range over the entire power set of a model ...
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What does Carnap mean by the extensionality requirement in an observational language?

In his article Methodological Character of Theoretical Concepts (Section II), he lists the requirements proposed for any language L to be meaningful. However, I don't understand what he means exactly ...
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A question about Transposition

Propositional logic Rules of Replacement Transposition (Trans): ( p ⊃ q) :: (∼q ⊃ ∼p) All i see here is some kind of a modus tollens case I don't see how did they get from ( p ⊃ q) To (∼q ⊃ ∼p) or why ...
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Understanding David Deutsch's assertion about the laws of physics as emerging from those of biology

In the Chapter 1 of the Fabric of Reality, David Deutsch says the following: There is no reason to regard high-level theories as in any way 'second-class citizens'. Each of them has implications for ...
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Does the "because" in a premise disrupt the validity of this argument?

One is good if and only if one does one's job well One does one's job well if and only if, and because, one is virtuous One is virtuous if and only if one is just From 1 and 2: One is good if and only ...
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Questions on Precise Meaning of Quine's Ontological Commitment Criterion

In a recent paper Ontological Commitment, Augustin Rayo tries to make the notion of ontological commitment more precise. He specifies: "Quine’s Criterion (Logical Version) A first-order ...
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2answers
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Is al-Farabi right that predicates must add information and existence is not a predicate?

Al-Farabi claimed that existence is not a predicate, because "exists" as in "Apple is red and exists." doesn't bring any new information, but does a predicate have to bring in a ...
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112 views

According to Wittgenstein, why are the laws of logic valid?

According to Wittgenstein's tractatus, A fact is composed of atomic facts. An atomic fact corresponds to an elemental proposition. (Picture theory) A proposition is a series of elemental propositions ...
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Relations and Properties

In predicate calculus there is no distinction between properties and relations---they are both just predicates. A property is a 1-ary predicate, and an n-ary relation is just an n-ary predicate. ...
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If I feel energetic, I play basketball or go boxing - how to illustrate it using an Euler diagram?

A: Me Playing basketball and me going boxing are disjoint events. B: If I feel energetic, I play basketball or go boxing. How do we draw an Euler diagram if both A and B are true? Can I draw it ...
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3answers
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Can a response to an unanswerable question that says that the question is unanswerable be considered to be answering the question?

Let's say someone has asked a question: "How can one do X?" But it turns out in fact that one cannot actually do X. So someone posts a response saying that X is impossible to do. Can this ...
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2answers
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Premises: 1. p & q 2. (q & p)→ r. Conclusion: ~~r

Can anyone help me to solve this: Premises: p & q (q & p) → r Conclusion: ~~r Premises: p & q p → r ~s V ~r Conclusion: ~s
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Does the logical conjunction of a false statement and a statement that doesn't make sense result in a false statement?

(This question was originally asked here, but I've decided to ask it in philosophy since it might be a better fit.) I kind of feel like this is a silly question, but does taking the logical ...
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5answers
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How can syllogisms with contradictory premises be valid?

A syllogism is valid if it is impossible for the premises to be true and at the same time the conclusion to be false. Consider the following syllogism: P1: This apple is red. P2: This apple is not red....
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Is an infinite passed time about universe a proof of 'violation of logic' or magic?

By human logic, either the universe has a beginning (Case1) or not (Case2). Examining Case1: If the universe has a beginning, it means it CAME INTO BEING FROM NOTHING. I think this is clearly a '...
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3answers
121 views

Is forcing someone to do something the same as forcing someone not to do something?

Would like to establish context first. The analogy of making it illegal to drunk drive after drinking vs vaccine mandates. The drunk driving analogy is used in many political cases such as abortion. I ...
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165 views

What are pro and contra arguments for considering syllogistic logic to be part of mathematics, instead of philosophy?

Of course, I reject naive notion that syllogistic logic isn't part of mathematics because it doesn't deal with numbers. There is more to mathematics than working with numbers. Also syllogistic logic ...
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What does the “ (∀y)(Py → x = y)" in “∃x(Px & ∀y(Py → x = y))” mean?

As known, Russell symbolise the statement , "The present King of France is bald", with a definite description in first order logic,"∃x(Px & ∀y(Py → x = y)&Bx)". Why not &...
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Questions about material implication

Propositional logic Rules of Replacement Material implication p ⊃ q :: ∼p v q Why it has the word " material " in its name? How does material is relevant to the term of implication, what is ...
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2answers
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Is there a name for this combination of generalization and the No True Scotsman fallacy?

The pattern: When specific members of the Other Group display reprehensible behavior, they are cited as evidence that the Other Group as a whole is reprehensible. When specific members of My Group ...
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Is Russell's "(im)predicativity" terminology related to (or even derived from) Kant's "existence is not a predicate" argument?

I'm a mathematician who's generally ignorant of philosophy, so forgive me if my question is a bit sloppy. I'm really trying to ask about a historical connection/context. I recently encountered the ...
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Help with Sentential Logic Proof

everyone. I'm running into real trouble figuring out the following sentential logic problem. (S v T) ⊃ (S ⊃ ~T) (S ⊃ ~T) ⊃ (T ⊃ K) S v T What we're supposed to get: S v K Any help that anyone might ...
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Is categorical logic the same as predicate logic

In philosophical logic, categorical logic is the logic that deals with the logical relationship between categorical statements. I wonder if categorical logic is considered the same as predicate logic (...
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1answer
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Arguing / Pretending as an Opponent Speaker

What do you call a person or the strategy where the speaker acts as the opponent to know the issue at hand better (as an opponent). For instance, a Vegan (person X) can argue with another Vegan, ...
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Natural Deduction flagging system (Virginia Klenk)

I am wondering if anyone can clarify a detail that's been bugging me. Here are the flagging restrictions for Virginia Klenk's natural deduction system: RI. A letter being flagged must be new to the ...
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Is the following derivation of predicate logic correct?

I recently discovered https://proofs.openlogicproject.org/, except I'm still figuring out the appropriate rules that are needed for the system to check my proof. I thought it'd be quicker to turn to ...
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8answers
276 views

Is ancient indian philosophy outdated?

I know in the West one would be taught Western philosophy but even here in India generally, the colleges and unis don't teach ancient Indian philosophy (yes there are exceptions like IITs but very few)...
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How could Britannica's explanation of Venn diagrams work?

Britannica.com/biography/John-Venn says the rings on the left are a Venn diagram of the syllogism “Some mammals are carnivores; all mammals are animals; therefore, some animals are carnivores” but ...
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How to make this argument valid?

If Peter is virtuous, he manages a household with patience. If Peter is to be good, he needs patience. Here's my attempt to understand 1 and 2. I get confused by the wording and necessity-sufficiency ...
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1answer
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Checking translations of predicate logic

Let Dx = "x is a detective", U12 = "1 is the uncle of 2", and appropriate lowercase letters for names. If there are any detectives, John is the only detective. No detective is ...
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so im arranging these arguments from strongest to weakest, and am confused?

Either reublocrats are uninformed, or democrans or independents are uninformed it is not true that republocrats are uninformed someone is uninformed either republocrats are informed or they are not ...
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Checking the validity of an argument

Is the following argument valid? If A is to be good, they must be just If B is to be good, they must be just Therefore, if C is to be good, they must be just Therefore, if C is just, they become good ...
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If this world is the only possible world, what does that mean for validity in logical arguments?

Validity is usually defined in terms of possible worlds. More specifically, an argument with premise set S and conclusion C is said to be valid if and only if there is no possible world with all the ...
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Issue with the interpretation of Propositional Logic

I’m having an issue with the terminology and perception authors use. Some authors perceive PL as a branch of logic “with subsets” with classical or truth-functional PL as these subsets. Other perceive ...
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2answers
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What are some strong arguments for logical holism?

What are some strong arguments for logical holism? The idea that the world operates in such a way that no part can be known without the whole being known first seems extremely foreign to me. This is ...
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How to prove that ((~A->~(A->B)))->A is a theorem in Sentential Derivation

I've been banging my head against this question (HW) for the last few hours, and I'm not able to answer it. This is based upon the Logic Book 6th Edition I've been using negation elimination, in order ...

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