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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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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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118 views

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
269 views

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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486 views

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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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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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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4answers
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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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1answer
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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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1answer
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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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1answer
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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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3answers
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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 ...
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1answer
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What is the name of the “undeserved profits” fallacy?

I see this type of inference made a lot, for example in the context of distributional justice: A makes an investment. He thinks this investment was a rational decision, until he learns that B also ...
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Is it possible that a question has only two answers?

□ yes □ no "no" implies that a closed system with only two options like the one above is impossible. If you accept that such a system is possible by the way, it generates paradoxical results, since ...
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Is the principle of non-contradiction self-evident?

The principle of non-contradiction is that contradictory propositions cannot both be true, e. g. the two propositions "A is B" and "A is not B" are mutually exclusive. However, whenever something is ...
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1answer
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How does a truth tree provide positive and negative effect tests for implication?

I'm trying to prove that the truth-tree method can be used to give a positive effect test for implication, and a negative effect test for non-implication. I've been given the fact that The truth-tree ...
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practical example of Limitations of Predicate logic [closed]

Discuss the limitations of predicate logic. Cite practical example to support your answer.
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1answer
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How would you describe it when someone uses the hypothetical to undermine an idea?

Here is the scenario. I'm working with a different technology for programming and I present it to my co-worker who is not up-to-speed on the new technology. He replies that there may be some ...
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1answer
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trouble with rules of inference practice problems [closed]

Prove the following symbolized arguments applying the appropriate rules of inference: 1) P ∨ Q = M ⊃ ¬ Q M =conjunction Therefore P 2) (P V Q) ∧ ¬ Q P ⊃ R =...
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Where is the fallacy here?

Where is the fallacy here: whatever is natural is not unnatural whatever is unnatural is not natural the phenomenon of cats being born into this world is natural the phenomenon of rabbits being born ...
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Why don't two equivalent propositions contribute to the same semantics?

We often have 2 propositions that have the same truth table, in that they are true and false given the same conditions. Nevertheless, we still feel as though there different semantics (i.e meaning..),...
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Inferring from (∃x)Fx to (∃x)(∃x)Fx using existential generalization?

I was introduced to EG as follows (for some name 'a'): One can infer from Fa to (∃x)Fx. But today within a proof my professor posted he used EG to infer from (∃x)Fx to (∃x)(∃x)Fx. I'm not sure how ...
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If turtles see everything, and nothing seen can see, does it follow that non-turtles exist?

Consider the following argument: Turtles see everything. Seeing is asymmetric (for the sake of argument). Therefore, something is not a turtle. I have problems symbolizing these statements. My ...
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Which logical fallacy is this: A is a C, B is a C, therefore A is a B?

Does this kind of logical fallacy have a name? Apples are fruit. Oranges are fruit. Therefore, apples are oranges. I'm guessing it's a particular kind of statistical syllogism?
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The illogical nature of want/motivation and its effects on free will

Are all the decisions and desires of humans made in order to stimulate pleasure centers and avoid pain? If so, could someone/thing which is unable to feel pleasure and pain, and only had the power of ...
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Is it a fallacy if someone claims they need an explanation for every word of your argument to the point where they don't understand common terms?

Is it a fallacy if someone claims they need an explanation for every word of your argument to the point where they don't understand common terms? For example, suppose someone said, "If a dog bites ...
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What are some of the paradigm shifts in how we think about logic and rationality in the history of philosophy [closed]

I am wondering if there was any shift or big revelations about logic that occurred in the history of philosophy. I am thinking it's highly likely, because if you read some of the thinkers during ...
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2answers
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Does this idea have a name: “A is a type of B, but B is not a type of A”

This question has been touched on in other questions but not answered in a way that fully answers my own question. Like here: Argument "a is b" but "b is not a" valid? What is ...
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I have trouble understanding this fallacy: “If A, then B. Therefore if not-B, then not-A.”

About "If A, then B. Therefore, if not-B, then not-A": From what I understand the conclusion is wrong, because it is not said that A is a sufficient condition for B, (and there may be other ...
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Multiple connectives using atomic sentences?

Can you use multiple connectives in atomic sentences? For example, consider the following transcription guide: A. The New England Patriots are the best team in the NFL. B. The New England Patriots ...
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2answers
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Proof with conditional introduction

Below is a screen-cap of part of a video where a proof using conditional introduction is shown, which is proving under certain assumptions that given A is true, then the adjacent sentence is also true....
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4answers
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A difficulty I've had with this “This sentence is false” and Russell's Paradox [closed]

I'm not sure if I'm engaging in some sort of circular logical trap but I don't really think "this sentence is false" is all that logically problematic. But it would be helpful if someone could fix up ...
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Are the “laws” of deductive logic empirically verifiable?

"Is Logic Empirical?" strongly suggests a question that I would like very much to get a handle on. That phrase is a title of an article by Hilary Putnam, and, according to synopses/reviews, the ...
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Is the following statement true, false, or can't be determined? Why?

"If it snows and we don't have school, then (x^3)<0 implies x is negative" (Assume x is a real number).
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What would be the negation of the following statement

"I sometimes work on Monday night" I'm struggling with the word 'sometimes'. Any advice on how to deal with this word?
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I need some help determining the validity of the following argument

“I got the highest grade on the last test and I have perfect attendance. If I get a cold, then I miss at least one class. I came down with a cold. Therefore, if I missed at least one class, then I ...
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Is an argument in natural language as logically valid as in formal logic?

Is a natural language philosophical argument which is argued strictly from first principles widely considered equally as valid as a proof written in formal logic?