Questions tagged [logic]

Use this tag for general questions about logic that are not categorizable under some more specific tag, like "mathematical logic", "informal logic", "classical logic", etc.

Logic is the study of formal systems of reasoning, especially of the deductive variety. It is one of the fundamental philosophical subdisciplines.

The traditional approach to logic, starting with Aristotle, is syllogistic logic. The introduction of mathematical methods during the late 19th century and with it the formulation of first-order logic have resulted in a complete transformation of the field. This development allowed to raise and answer questions about the foundations of mathematics. During the second part of the 20th century many philosophical logics have been introduced in order to tackle many other questions in philosophy.

Key notions of logic are formal languages, proofs and truth.

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Why does "Daisy has four legs" not entail "Daisy has more than two legs"?

I have been going through one of the books and I found an example of conclusion C that is not entailed by a premise P. Daisy has four legs. So daisy has more than two legs. Surely though, the premise entails the conclusion as it's an analytical…
bodhihammer
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How is the argument "I love all logic, but I don’t love deductive reasoning. Therefore, the moon is made of green cheese." valid?

This example came up in class: I love all logic, but I don’t love deductive reasoning. Therefore, the moon is made of green cheese. I understand the premise is contradictory and the conclusion is false, but the prof said the argument is valid,…
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Are different values of nothing equivalent?

Are different values of nothing equivalent? Is 'no tigers' the same as 'no zebras'?
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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 hope someone could explain it in a way someone would…
MinigameZ more
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What is the difference between intensional and extensional logic?

Homotopy type theory talks is conjectured to be the internal language of (infinity,1)-toposes; it comes in two flavours: extensional and intensional - these aren't notions that I've come across before in logic. How are these terms defined and what…
Mozibur Ullah
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Semantic vs syntactic consequence

I see that the double turnstile ⊨ denotes the semantic consequence of some sentence of logic, and single turnstile ⊢ denotes the syntactic consequence of some model. This seems equivalent to me. Why do we need to make this distinction? Are there…
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What is the philosophical equivalent of mathematical proofs?

In mathematics, there seem to be five standard methods of proving or refuting an argument: a proof by induction, contradiction, counter example etc. Are there some typical proof methods that exist in philosophy as well (in some ways analogical to…
jimjim
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Why does the material conditional have the truth table it does?

Can someone provide me with the simplest possible argument for why the material conditional has the truth table it does? Googling doesn't help at all, providing only flimsy and clumsy arguments. I want the argument to be simple, and yet as…
Michael Smith
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What is the problem with using circular reasoning? Is it "invalid"?

What, specifically, is the problem with circular logic/reasoning? I think it's invalid. For some reason, everyone knows that it's wrong to use, but is there anything more to it than that? Additionally, where can I find journal articles or papers…
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Are we sinners because we sin or do we sin because we are sinners?

This question arose after I read a sentence like this : We are not sinners because we sin We sin because we are sinners. So "because it's carnivore then it eats meat" --vs-- "because it eats meat then it's carnivore"? To me it seems both are…
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Is 1=2 a logical contradiction, or merely a false statement?

I know that (1=2 AND NOT 1=2) is a logical contradiction, but what about 1=2 by itself? Is it a logical contradiction, or merely a false statement? And what about something like NOT 1=1?
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What is the difference between logic and reasoning?

What is the difference between logic and reasoning? I can makes sense of what logic is about. But when it comes to reasoning what does it do more than logic does? Can you give an example which shows the difference between logic and reasoning?
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Are there degrees of truth ?

I do not assume bivalence - that every proposition or declarative statement - is either true or false but not both. I do not raise the issue of 3-valued logics or offer or invite any theory of truth. But I do assume that at least some propositions…
Geoffrey Thomas
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What's an intuition for material implication?

The paradoxes of material implication show that the usual interpretation of implication as "if ... then" statements leads to counter-intuitive results. For example, from (P & Q) -> R we can derive (P -> R) v (Q -> R), which doesn't make much sense…
Xodarap
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Intuitively, why is ¬(P ↔ Q) ≡ P ↔ ¬Q?

Source: p 77. Sweet Reason: A Field Guide to Modern Logic (2010 2 ed) by Henle, Garfield, Tymoczko. I pursue only intuition; please do not answer with formal proofs or Truth Tables. I already comprehend, and so ask not about, the direct proof.…
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