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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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2answers
15k views

How do I use the “Barbara, Celarent, … etc.” mnemonic?

Medieval logicians memorized this most famous logic mnemonic: Barbara, Celarent, Darii, Ferio ← direct first figure Baralipton, Celantes, Dabitis, Fapesmo, Frisesomorum ← indirect first figure Cesare,...
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5answers
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What are the practical applications of formal logic, outside of math and computer programming?

I am studying a bit of this and so far it seems that, apart from math and computer science, the discipline of Logic is very inward-facing...with logicians proving things for other logicians. This may ...
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3answers
769 views

Possible worlds in logic

In modern logic there is often talked about possible worlds. I understand this idea in this way: Every proposition may be true or false. Possible world W is a set of all propositions where there is ...
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2answers
778 views

Is there a deduction analog to the problem of induction?

Aren't deductive and inductive reasoning equally unjustified? So, inductive reasoning is going from specifics to general, whilst deductive reasoning is going from general to specific. But in deductive ...
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5answers
579 views

A Question Regarding Russell's Paradox

Consider the 'set' behind Russell's Paradox: R = { x | x is a set and x ∉ x } in light of Cantor's definition of set ("aggregate"/Menge) in his CONTRIBUTIONS TO ...
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247 views

What is the difference between depth and surface information?

I was looking for an answer to this question: Was Euclid's method of proof axiomatic? While doing so I ran across an abstract of Jaakko Hintikka for an article "What is the axiomatic method?" ...
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Was Kant anticipating Gödel's incompleteness in his antinomies?

Kant's attempts to prove that there's a limit to pure reason based on the existence of antinomies, i.e. pairs of propositions where each one is rational, but the propositions contradict each other. ...
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413 views

Why can't an algorithm understand incompleteness?

I've heard a lot of people say that Gödel's proof shows that human intelligence somehow goes beyond what a computer could ever do. It's only ever been articulated to me very badly, though not for want ...
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Syllogism from Lewis Carroll

I was reading Code by Charles Petzold, and on page 86 he references a syllogism from Lewis Carroll: All philosophers are logical; An illogical man is always obstinate; Therefore, some obstinate ...
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4answers
2k views

Do I need to read The Organon to understand Aristotle's philosophy?

I recently read through the collected works of Plato and really enjoyed learning about his philosophy and ideas. I'd like to do the same for Aristotle and have started reading through his works as ...
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6k views

What are the more complex/interesting examples of synthetic a priori statements?

The usual examples of synthetic a priori statements are – it seems at least since Kant: "Nothing can be simultaneously red and green all over" 7 + 5 = 12 (or any other basic arithmetic statements). ...
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What is the fallacy: “Nothing bad has happened, so nothing bad will happen”

I was talking to a small business owner the other day. When asked why they never incorporated in order to limit their liability, their explanation was, to paraphrase, "nothing bad has happened to us ...
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370 views

How does “higher-order logic” differ from “normal” (first order?) predicate logic?

How does “higher-order logic” differ from “normal” predicate logic? I assume the latter is consistently called ”first order logic”. So where are the differences between these? What kinds of statements ...
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3k views

Is reductio ad absurdum a valid logical proof?

It strikes me that atheists often in the religion debate will try to characterize religion in a funny or silly way, often comparing religion to belief in fairies or unicorns or flying spaghetti ...
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338 views

Where did Gödel write that first-order logic is the “true” logic?

In "On How Logic Became First-Order" Matti Eklund writes (p. 2/148): It appears to be widely held today that arguments from Skolem and Kurt Gödel, both alleged proponents of the thesis that ...
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344 views

Supervaluationism and Theories of Truth

How does the supervaluationalist defend his/her theory of truth since the correspondence theory of truth seems to presuppose bivalence? It would seem then that the only truth is Super-Truth. And, the ...
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4answers
2k views

Understanding Grice's Theory of (Non-Natural) Meaning

I am trying to understand Paul Grice's famous essay "Meaning". So consider a computer system which is fed a dictionary of every English word in existence. The computer system then randomly spits out ...
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5answers
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What are free variables and what does it mean for a statement to contain one?

I am puzzled a bit. I read the wiki page and an introductory book on logics, but I can't quite grasp it yet. The place where i came across them is Van Inwagens 'Material Beings'. Consider the ...
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465 views

What is Quine's response to Parmenides's argument against change?

I was recently reading Russell's chapter on Parmenides in The History of Western Philosophy, and I came across a fun little argument for the absence of change. Essentially, it says that word meaning ...
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164 views

Does fictional discourse pose special difficulties for logic?

Natural language is context-dependent, like the statement “My uncle is a plumber”, which is true or false depending on who asserts it. There has been lots of discussion about fictional entities and ...
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629 views

What would you call a counterfactual theory of Justified True Belief?

Ever since I heard the characterization of knowledge as justified true belief, the proper meaning of the word "justified" has always seemed clear to me: it should mean that you acquired the belief in ...
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Is it reasonable to arrive at a conclusion based on lack of evidence to the contrary?

I was having a discussion last night about my atheism, and it was suggested to me that agnostism is the only reasonable conclusion, as it leaves the door open for new information. This made me think, ...
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A bizarre question asked at a job interview about conditional probability [closed]

I was recently asked a "logic puzzle" type question at a job interview which seems to be a slightly mangled version of a N-coin puzzle (intended to test the subject's knowledge of conditional ...
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Are all non self-referential statements true or false?

It is well known that there exists self-referential statements which are neither true or false, such as "I am lying". Is it possible to have statements neither true or false which are not self-...
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What's the word for anything is true if the antecedent is false?

(1) If A then B. (2) A is false. Then B can be anything (true or false) and (1) remains true. So B is true by __. What's the word or words in the blank?
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If the universe is infinite, shouldn't I already have been contacted by a time and space travelling doppelgänger?

If the universe is infinite, by virtue of chance it means that every possible configuration of matter must exist somewhere (according to this documentary). Therefore, if the universe is infinite and ...
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Why are homologies evidence for evolution instead of common design?

I have seen some creationists arguing that when evolutionary biologists use homologies (anatomical or genetic) as evidence for evolution, they are committing the fallacy of affirming the consequent. ...
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7answers
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Is it possible to be truly unbiased?

I was pondering this question: Inductive Argument Against Believing Anything I his argument, the OP suggests that, in the position of choosing a system of belief where there are multiple, large ...
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708 views

Why might you not accept ¬(¬A) = A?

What motivates intuitionism's rejection of double negation: If A exists, then ¬(¬A) = A. I can't see what's wrong this statement or why someone would reject it.
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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 ...
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12k views

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 ...
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395 views

Are truth-claims inappropriate?

Strictly speaking, is it inappropriate to make a truth-claim? I am seeking an answer from Philosophy (Epistemology), and feel free to use logic I am speaking "theoretically", not "practically" I am ...
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994 views

What's the name for an argument that “this book or this person says P is true, therefore P must be true”?

People often claim P is true because a single book or person says P is true. This is most often the case when the book or the person is said to be divine. So is it a fallacy when people theorise the ...
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6answers
842 views

Is there a name for each individual's perceived sphere of reality?

Is it an acceptable idea that each individual carries their own model of reality in their mind? Is there a name for the model that each individual uses to perceive reality? Is there a name for the ...
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525 views

is “2+3=6, then 2+3+1=7” an example of the fallacy fallacy?

Is "if 2+3=6, then 2+3+1=7" an example of a fallacy fallacy or argumentum ad logicam? I believe it is an example of the fallacy fallacy, but I'm not able to show it. I only think it is a fallacy ...
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10answers
969 views

Does the Fallacy Fallacy make logic useless?

I should add that I'm not a formal student of philosophy and haven't studied it in any serious depth. I just like logic, and logical fallacies. I like to spot them, and I like to debate using them, ...
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462 views

What does it mean for an axiom to be logical?

I have recently been hearing the phrase logical axiom being thrown around in reference to the philosophy of mathematics and I'm having a hard time understanding what one might mean when they are using ...
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4answers
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Does the phrase “vacuous tautology” have specific meaning?

I just came across a use of the phrase "vacuous tautology" used in a piece of writing. Now, based on my understanding, by definition a tautology has no content and is therefore always vacuous. This ...
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5answers
2k views

What is the difference between identity and equivalence?

While the problems of identity seem to have more heft in philosophy, I am actually more interested in the meaning of "equivalence" as symbolized in the (=) sign and, in guilt by association,with ...
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356 views

Asymmetries in two opposite arguments from ignorance

Joe claims: "There is no proof that unicorns exist, therefore unicorns do not exist". Alice claims: "There is no proof that unicorns do not exist, therefore unicorns exist". Bob claims: "There is no ...
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What is the philosophical problem with Skolem's Paradox?

I guess there are two questions here. QUESTION 1: Skolem's Paradox shows that countability is relative in first-order logic, but where is the relativity? In this first question, I will do the ...
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353 views

What logical systems categorize A->~A as a contradiction.?

In the basic propositional logic I learned in school A->~A is not a contradiction because it is not false when ~A is true. What logical systems would hold this statement to always be false?
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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 ...
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5answers
2k views

Are “If P then Q” and “Q only if P” equivalent?

My textbook says "If P then Q" and "Q only if P" are logically equivalent, but consider this: "If it's green, it's poisonous." "It's poisonous only if it's green." Now say there's a purple ...
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4answers
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How does one prove De Morgan's laws for quantifiers?

One of De Morgan's laws state that ¬∃x P(x) is equivalent to ∀x ¬P(x), but how would one go about formally proving this? Numerous attempts to find a solution have been futile, even proofwiki.org ...
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830 views

Do all objects have properties?

Assumption: An object has no properties. I can think of that object as an object with the property that it has no properties, but this is a contradiction to my assumption. Hence all thinkable objects ...
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4answers
398 views

Can we do without Necessity?

It appears that necessity is a dead idea that, unfortunately, only philosophers still gush over. The association of epistemological and logical necessity with ontological necessity ran its course ...
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1k views

Is “Don't blame me; I voted for ___” a bad argument?

Is there a fallacy in the argument, "Don't blame me; I voted for ..."? Or is a voter's entire responsibility for their contribution to whatever current state of political affairs they experience ...
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808 views

Are there kinds of arithmetic that are decidable despite the Gödel theorem?

A proposition p in a consistent formal language is decidable when we can assert either the truth of p or the truth of not p (But not both, for then it would be inconsistent and we have already said ...
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916 views

Logical fallacy classification: comparing the best from one group with the worst in another

I am looking for the name for the logical fallacy that compares the best samples from one group with the worst samples from the second group and concludes that the first group is better than the ...