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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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Philosophy of Logic – Reexamining the Formalized Notion of Truth

Can we reformulate the formal proof to theorem consequences of symbolic logic to use the sound deductive inference model to make previously undecidable logic sentences become decidable?
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Can two different objects at the same time be the same?

Can two things be different and yet the same at the same time? For example, a chair (white) does not have one leg and another (black) has all of its legs. As in the question, these two things with ...
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Finite Alphabets

This is a question based on section 2.5.6 from the book Logic, laws of truth, by Nicholas J.J Smith, page 48. What does Nicholas mean when he says: Note that we can further specify exactly what we ...
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What is a good history of logic book that covers all logic?

Including inductive, formal and mathematical. I find them separated a lot and I don't know if I have the ability to sit through all the Handbook of the History of Logic series.
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Is it possible to mathematically define a hypercomputer-universe where things that could not be computed by it could exist? [duplicate]

There are a few physicists that propose that the universe is a hypercomputer. One example is Roger Penrose, who, basing in his quantum interpretation (https://en.wikipedia.org/wiki/...
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In predicate logic, does existential quantification (∃) include universal quantification (∀), i.e. can 'some' imply 'all'?

I am having a discussion wether 'some' can also imply 'all'. The definition for some, 'an unspecified number or amount of people or things' seems to leave room for this interpretation. Discussion ...
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What does odd and even mean? [closed]

Odds are against us. eg: If you say that the odds are against something or someone, you mean that they are unlikely to succeed. The sentence paints a picture of the word odds as something which is ...
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4answers
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Is the argument below valid?

If interest rates go down, then I will buy a house. If I buy a house, I will need a loan. Therefore, I will not need a loan if I do not buy a house. Is this argument valid?
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Hume's argument for the subjectivity of morality

I am trying to analyze the following argument by Hume in his Treatise of Human Nature: But can there be any difficulty in proving, that vice and virtue are not matters of fact, whose existence we ...
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Is it there any model of the universe or any (physical) cosmological theory or model completely compatible with trivialism? [duplicate]

Trivialism is a system that proposes that literally every proposition is true and false at the same time blatantly breaking the principle of no contradiction and triggering the principle of explosion (...
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2answers
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Is “If…then” not a truly logical connective?

Since you can completely fill out a truth table for "not A", "A and B", and "A or B", but not for "if A then B", can it really be a logical connective? The only thing that can be confirmed about the ...
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Is it there any trivialist model in physics (like in quantum mechanics)?

Trivialism is a system that proposes that literally every proposition is true and false at the same time blatantly breaking the principle of no contradiction and triggering the principle of explosion (...
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Recursive definitions (a couple questions based on them)

From the book Logic, laws of truth, by Nicholas J.J Smith: What does Smith mean by recursive definitions? Why does it matter? How do you make recursive definitions for something such as: a) the set ...
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Can hypercomputation compute the impossible?

There are things which are illogical/logically impossible (like saying that 2+2=4 and 2+2=5. Without changing anything in the axioms of mathematics or logic, this would be a contradiction and would be ...
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1answer
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Syntax of propositional logic

From the book Logic: The laws of truth by Nicholas J.J Smith, page 40, sub-heading: "Syntax of PL". What does the author mean by the syntax of PL? Can someone explain what the author is trying to ...
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1answer
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What is the difference between the resolution rule and the elimination in natural deduction?

I understand that elimination is: p v q ¬q then p and resolution is: q1 v q2 v q3...qn ¬q1 v q2 v q3...qn then q2 v q3...qn I see no difference, but my teacher is telling us don't use the ...
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Logic-related note-taking question

I have been thinking about note taking from a logical perspective recently. It started when I realized that note-taking is basically a process of extracting "statements" or "arguments" from a piece of ...
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To pass two time for the same place. Logic question [closed]

Let be the proposition: "To visit two times the same place is forbidden". It is forbidden to visit the same place three times? A says: "No, because it is forbidden to visit the place two times". ...
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What is the meaning of “comprehension” in logic?

I was reading about the axioms of Zermelo-Fraenkel set theory and the axiom of restricted comprehension. This led me to find out what the meaning of this word is and why it's called this. Then I saw ...
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Why is a square circle metaphysically impossible?

We have definitions for both a square and a circle. By definition, I understand that it's impossible to have a square circle. However, why does the word 'square' have to necessarily mean 'a plane ...
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If logical propositions aren't tautologies (a la Wittgenstein), then what could they be?

This is a historical question about philosophical views. I believe I understand the claim made by Wittgenstein and others that logical propositions are tautologies. I'd like to know what other views ...
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How is the claim “I am in New York only if I am in America” the same as "If I am in New York, then I am in America?

It makes absolutely zero sense to me. It would make sense if "I am in America" is the antecedent and the consequent is the former. Even though it wouldn't be sound, it would make logical sense. I ...
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3answers
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Relationship between entailment and equivalence with consistency

If A entails B, why is it not true that A is also consistent with B? Given the definition requires A and B to be able to be true at the same time.
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1answer
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Checking the validity of the logical conclusion gleaned from a heated conversation

I have two friends - call them John and Jane. I was recently privy to an argument concerning a book between John and Jane that went like this: John: This book did not make a single coherent, ...
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When is a connective truth functional?

I got this question from Logic, laws of truth, by Nicholas J.J Smith. He says (page 24) : "A connective is truth functional if it has the property that the truth or falsity of a compound ...
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1answer
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How to Prove P(a) → ∀x(P(x) ∨ ¬(x = a)) using Natural Deduction

How would a formal Fitch proof look like. I am given P(a) → ∀x(P(x) ∨ ¬(x = a)) to prove using Natural Deduction of predicate logic. I am confused on how to proceed with the proof. Please advice me ...
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Quantum mechanics and the principle of bivalence

Does quantum mechanics, due to the phenomenon of superposition (Schrodinger's cat is both dead and alive), give reasons to alter the laws of logic, specifically the principle of bivalance (something ...
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What is the difference between NTP and validity in Smith's “Logic: The Laws of Truth”?

The book I got this question from is "logic, the laws of truth" by Nicholas j.j smith. "Necessary truth preserving" (NTP in the book) is defined as the property that an argument has when it is ...
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Gödel's incompleteness theorems - what are the religious implications?

Apparently Kurt Gödel believed that his incompleteness theorems have some kind of religious implications. Despite Gödel's belief in a personal God, this was still somewhat surprising to me. ...
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What does Wittgenstein mean when he says “there are no numbers in logic”?

From the Tractatus: 5.453 All numbers in logic stand in need of justification. Or rather, it must become evident that there are no numbers in logic. There are no pre-eminent numbers. What does ...
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How can we be accountable if we are chemically programmed?

If we accept that molecular biology largely explains cognitive function deterministically, how can we be accountable? Is determinism not inherently nihilist in that a person is a victim of ...
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Wittgenstein argues in the Tractatus that the laws of logic lack sense, say nothing about reality, and are analytic [duplicate]

1) What does this mean? and what's his argument? 2) What do you think of this view?
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Formal proof errors

I am trying to prove A ^ B from the premises shown in the screenshot. As you can see in the screenshot I am struggling with the second sub-sub proof. Do you have recommendations for how to continue/...
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Why do there exist “logical fallacies” that are not really consistent logical fallacies?

Why do there exist "logical fallacies" that are not really consistent logical fallacies? By logical fallacy, consider e.g. ad hominem. By consistent logical fallacy I refer to a type of logical ...
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What did Nietzsche mean? [duplicate]

What does, Nietzsche in Beyond Good and Evil, mean exactly when he states: Whoever fights monsters should see to it that in the process he does not become a monster. And if you gaze long enough into ...
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1answer
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Logic : steps to prove valid reasoning [closed]

I am very new to this and I can't figure out the steps to prove that these reasonings are valid. Thank you for your help. p ¬r p → (q→r) ___________ ¬q (¬p ∨ ¬q) → r p q __________ ...
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What happens if we accept inconsistency?

(Philosophy novice here and not sure how best to phrase this question; if it's unclear please point out the problems). Imagine this conversation: Alice: I believe that X. Bob: Do you also ...
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Can you help me tackle this question by giving formal proof using natural deduction

Using the natural deduction rules, give a formal proof that the following three sentences are inconsistent: ¬P∨Q ¬P→Q ¬Q
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Is math arbitrary?

Math at its core begins with calling something true or false and following logic. WE for example call an odd number 2n+1, but what if we called an odd number 2n and flipped it for it to become an even ...
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Fitch Proof and Logic prove A V D given premises 1. A V B 2. ¬C ∨ ¬B [closed]

I have to prove this in Fitch without using any of the cons
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Why is it logical to invoke an uncreated universe with no intelligent design?

How can an atheist invoke an uncreated universe with no intelligent design and assert its logical consistency? Why is it logical? By moving the goal post to aliens seeded earth from another universe,...
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What's the name of the logical fallacy where a debater extends a statement far beyond the original statement to make it true?

Suppose that someone initially states that "fossil fuel consumption due to mobile phone usage is similar to that of private transportation, so if you think we should switch to electric/bike to fight ...
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Please what do we call this type of hypothetical statement?:

"It is certain you have a nose when you can smell but not everyone with a nose can smell". Or "It is certain you have a brain when you can think. But not everyone with a brain can think" Note: As I ...
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Fitch-style natural deduction

How to prove the following questions? (a) p from assumption ¬(p → q) (b) ¬¬p → p from no assumptions.
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Is b⊢C∧¬b⊢C∧b⇒C∧¬b⇒C possible?

Are there any cases where b and C are real world statements where b⊢C∧¬b⊢C∧b⇒C∧¬b⇒C where b and C are not tautologies? It may seem like a silly question, but after searching hard and deep, I couldn't ...
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A Problem With Kripke's Rule-Following Paradox Example?

It seems that there is a problem with the example that Saul Kripke gives in "Wittgenstein on Rules and Private Language" to explain Wittgenstein's rule-following paradox. I'm not asking about the ...
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Prove that if the tree method determines that a set of sentences T implies a sentence A, then T does in fact imply A

Having trouble wrapping my head around how to prove this. My first question about this is what it means for the tree method to determine that the set of sentences implies A. I'm taking it to mean that ...
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Logic. Truth of a negation

If I say: If I am paid today I'll go to the party tonight I am saying that if I receive a payment today I will go to the party tonight. But if I am not paid, can we conclude that I am not going ...
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Given the principle of innocence, how shall we explain logic's usefulness?

I have been reading Florian Steinberger's dissertation (Harmony and logical inferentialism) and I come across the following on p60: ...two fundamental assumptions (the other one being the principle ...