Questions tagged [logic]

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

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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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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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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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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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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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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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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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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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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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624 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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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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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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687 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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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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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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371 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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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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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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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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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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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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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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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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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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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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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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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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317 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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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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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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767 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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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 ...
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What's a good source for refreshing my formal logic skills prior to graduate school?

I need to flex my formal logic muscles prior to graduate school--I've had a dry spell in my logic practices while finishing my mathematics degree, particularly since the logic used in analysis, ...
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How to justify the use of logic?

I would like to hear some Philosophical arguments which justify the use of logic. Additionally, if a justification of logic takes the form of an inference, this inference itself makes use of logic. ...
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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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542 views

In logic, do propositions default to true or false when objects in them do not exist?

In this hypothetical: Firefighters always tell the truth, while politicians always tell lies. Suppose three people, who are either a mix of firefighters and politicians, all politicians, or all ...
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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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How does Logic define “true” and “false”?

"Truth", "Falsehood" are pretty axiomatic expressions, but even axioms need to be defined in common language terms. What are the "official" definitions of these in Informal logic, Formal logic, ...
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What is an 'argumentum ad lapidem'? [closed]

I've seen philosophical arguments descriped as 'argumentum ad lapidem', but never quite understood what the criticism is trying to indicate. As best I can tell, it's a dismissal of an argument with ...
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How many people can know a secret? [closed]

I'm not sure if this is a question with a clear answer, and if this is the correct stack to ask it, but is there a limit for how many people can know a secret? An entire goverment can keep a secret, ...
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What's the difference between :=, =, and ≡?

I understand that ≡ is logical equivalence, "iff". = is a symbol for numerical equivalence. And := is an identity claim. I often only see = and := used with variables and names, while ≡ only appears ...
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What exactly is the value of completeness and decidability in logic?

I understand why consistency and soundness are important. It would undermine the purpose of reasoning if we can make conclusions that contradict our assumptions. At some level, when we desire to ...
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Logic and Computation : a philosophical viewpoint

The link between logic and computation is stronger than ever, especially since the establishment of the Curry-Howard isomorphism specifying that proofs can be seen as programs and formulas as program'...
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369 views

What name or label applies to a statement the very act of making which contradicts its truth?

Consider a proposition stating something to be true that by the very act of stating denies truth to the speaker. This is not a fallacy, which is an argument incorrect by virtue of its form. But I am ...
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How do I check if two logical expressions are equivalent?

For example: Is (A ∨ B ∨ C) ∧ (D ∨ E ∨ F) the same as (A ∧ D) ∨ (A ∧ E) ∨ (A ∧ F) ∨ (B ∧ D) ∨ (B ∧ E) ∨ ( B ∧ F) ∨ (C ∧ D) ∨ (C &...