Questions tagged [logic]

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

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Logic Philosophy question [duplicate]

I am looking for help in answering the full question with a full conditional proof (cp). This will help me understand this question and others that I am trying to understand. Thank you. Would ...
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Which came first, the semantic approach or the syntactic approach?

Logic is today developing in many, very different directions. But the basic distinction between the semantic approach (truth, "⊨") and the syntactic one (provability, "⊢") is still important and ...
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Aristotelian vs Boolean, trying to determine the exact difference

Good afternoon, I've looked at some other answers and I feel those don't quite answer what I'm trying to ask, so I'll just ask it here. I'm in a logic course and I'm either misunderstanding ...
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Formalisation of an Argument

I just came across the following passage in the Appendix B of "Why Race Matters" by Michael Levine: Let $G$ be a genotype expressed by phenotypic variable $P$, and lets $G$'s home organism $O$ ...
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Existential import: 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 is the origin of the truth table in logic?

Specifically for the material implication if possible. Who was the first to use a truth table for this and justify its validity?
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can we reason about logic?

People who study mathematical logic make arguments about logic itself. So it seems that people take for granted an "intuitive logic" (otherwise, how would they form arguments?). So the observation is ...
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Rhetoric: How to frame redundancy in an argument as deficiency?

How can we categorize redundancy in an argument as deficiency? That is, weaken the argument because of its redundancy? Suppose X is an argument that boasts coherence and clarity, but it has various ...
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1answer
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Did William of Soissons prove the law of explosion in the 12th century?

In the 12th century, William of Soissons attempted to prove that any proposition can be inferred from a contradiction. I've adapted his proof into a logical system I'm more familiar with: Let E ...
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Help with a Predicate Logic homework proof

I have a Predicate Logic argument I need to translate into the symbolism of predicate logic first and then I need to construct a proof in CP. The argument is "Some wars are just. No war of ...
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Does a biconditional necessarily imply a causal relationship?

Supposing A if and only if B, is it necessarily true that either A causes B or B causes A? I'm considering this question where the truth values of A and B are both True, not both false. In theory, ...
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Natural deduction proof help!

I've gone through about 40 natural deduction proofs in the past couple days, and mostly they are no problem. For some reason, I've been stuck on 1 tedious problem for an entire day. I just can't seem ...
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Rewriting a set of propositions that includes a circular proposition

"For any proposition P, if I believe that P then this paragraph (everything that is written between the quotes) entails that I believe that P. I believe that I exist. For any proposition P, if I ...
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Is There a Maximally Consistent Set That is Not $\omega$-complete? [on hold]

I was going back through Mates 2nd edition Elementary Logic and am having a bit of trouble on one of the exercises; it says, "Find a counter example to the following assertion: for any set of ...
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1answer
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Does a pattern constitute evidence, logic or something else? [on hold]

Powerful groups (e.g. tribes and states) often exploit or attack weaker groups. That's a historical pattern suggesting that people will continue to prey on each other. Many wars have begun with ...
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How might I notate that an entity either cannot have a quality or has all of it?

I have two friends, Charles and Louis. I want to state that given one of the following conditions then Charles and Louis are identical: Charles does nothing. Louis does nothing. Charles does ...
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What is a predicate according to Aristotle's Organon?

There is of course predicate as in predicate logic; but I'm asking about the notion in Aristotle's Organon. Consider the proposition: Socrates is a man. Man is a universal, Socrates is a ...
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Who first proposed that A → (B ∧ ¬B) ⊢ ¬A was the principle of proof of some theorems?

The proof of various theorems are nowadays routinely described as "proof by contradiction". For example, the following theorems: https://en.wikipedia.org/wiki/Proof_by_contradiction The ...
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Can death be given meaning through the theory of evolution?

Disclaimer: I haven't seen any other posts about this anywhere and one night, I was just thinking and scribbled this down, so I don't know where this could be found otherwise. What if, there is no ...
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Could philosophers via Logic prove the validity of some holy books, then use them as a source of trustful knowledge?

Could philosophy or philosophers or some philosophers prove the validity of the text of a holy book, e.g: Qur'an or the Bible, or some holy books, using logic and philosophical means, then use these ...
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What counts as a logically necessarily true statement and what is not?

"If an existing population contains both mortal and immortal beings, some members of that population are not subject to death." Is this statement considered logically necessarily true? I personally ...
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Infinity - Sizes vs Types

Suppose there is a line, infinitely long in both directions. Make arbitrarily "uniform" cuts or "integers". Obviously there are infinitely many of these. And there are arbitrary "lengths" BETWEEN ...
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How do I show that using NOR one can express NOT and OR?

The answer given in the texbook is as follows: ¬A: (A↓A)≡¬(A∨A)≡¬A A∨B: (A↓B)↓(A↓B)≡¬(¬(A∨B)∨¬(A∨B))≡¬¬(A∨B)∧¬¬(A∨B)≡A∨B However, its not clear to me how to go about finding this solution.
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Are Wittgenstein's propositions analytic or synthetic?

Wittgenstein provides a logical analysis of propositions in the Tractatus. Does he there admit the Kantian distinctions between analytic/synthetic and a priori/a posteriori divisions; or does his ...
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1answer
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Does Tegmark himself include paraconsistent mathematical structures in his mathematical multiverse hypothesis?

Tegmark postulates in his hypothesis that all possible mathematical structures would exist. But does he include also possible mathematical structures described by other types of logic like ...
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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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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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Where can I find logical fallacies in action?

I'm looking for a website that gives logical fallacies in action. Not a video that explains logical fallacies, but a video, say a debate between two people where one of the debators uses a logical ...
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Was Russell's purpose in Principia Mathematica to formalize all the possible constructions of logic?

In writing Principia Mathematica, was one Russell's purposes to formally describe all the possible variations of logical concepts and reasoning that can be used in mathematics? For example, suppose ...
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What are the objections to the axioms of modal logic?

I am looking for good/classical references on objections/criticism of modal logic. I am a bit familiar with the work of Quine but find his objections around the paradoxes of material implication or ...
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Modal essence of potentiality

What is the modal essence of Aristotelian potentiality? Why and how potentiality seems to be inherently modal?
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Why de re modality is a problem for Quine?

I have read that Quine "accepts" de dicto modality because he is able to extensionalize it. But I have also read that Quine rejects de re modality because it is not extensionalizable and because in ...
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If F is a sufficient condition for G, is lacking G a sufficient condition for lacking F?

If having feature F is a sufficient condition for having feature G, then lacking G is a sufficient condition for lacking F. I think this statement should be "If having feature F is a sufficient ...
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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 &...
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Tableaux for normal modal logics

Does ⊢ ◻p ⊃ ◻◻p hold in Kρ? Check with tableaux and if the tableau does not close, define and draw a counter-model.
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In Fitch, how does one prove “(P → Q)” from the premise “(¬P ∨ Q)”?

It's all in the question really. I am working on a proof in Fitch for a class, but I am very much stuck. I am proving the tautology that "(P → Q) ↔ (¬P ∨ Q)", and I have already finished half of it, ...
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How to prove ~(~A v ~B) |- A & B by natural deduction? [closed]

Help with proof please. I can't seem to see a proper way to go about this specific proof.
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How to derive P > (Q > R) from (P > Q) > R in Fitch?

I am having a little bit of difficulty coming up with a Fitch-style natural deduction proof. Presumably, I need to use a few conditional introduction rules, but I am not sure what I can get out of ...
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What is the justification for the claim that observing something that is both a raven and black increases the likelihood that all ravens are black?

Suppose that I have access to a machine that allows me to input a positive integer (perhaps up to ten decimal digits) and the machine will -- depending only on the input -- output a statement. If the ...
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Which problem is Russell focusing on while providing a solution, in his introduction to the Tractatus?

In the final part of his introduction to the Tractatus Logico-philosophicus, Russell provides a possible solution to the problem of the impossibility of self-reference of logic: There is one ...
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Is every sentence we write or utter either true or false? [closed]

Please read the complete description before putting any answer / comment, Thank you. I've been just thinking through this question which I can frame it like this: Can I write or utter any sentence ...
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In classical model theory, how does one represent the one-place predicate R(x) where for all x, R(x) iff (x∉x)? [closed]

If we try to represent the predicate by means of the set of values that satisfy it, then of course we run into Russell's paradox. Now, in ZF, we could simply use the whole domain of the theory, but ...
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How would I go about proving P>Q from the premise (notP v Q)? [duplicate]

A similar question had already been asked, but the solution involves steps I am unfamiliar with. in class, we have only been exposed to intro and elim rules, as well as contradiction rules. Here is ...
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Fitch Proof - Logic LPL 6.31

I am trying to complete the following proof in Fitch but am completely clueless on how to approach it. Any help would be appreciated! Thanks
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Why doesn't one assert in metamathematics that a sentence S is a logical consequence of the conjunction of a set of sentences?

In other words, why isn't there -- at least in standard textbook presentations of things like the deduction theorem and the compactness theorem -- a conjunction connective that is applied to sets of ...
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How can a undecidable theory be complete?

I don't understand how a theory can be undecidable (there is no effective procedure for determining if a sentence of the language is a theorem) and also be complete. How do we know all sentences are ...
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Descartes's *Cogito* from a modern, rigorous perspective

In Descartes's Meditations, in order to establish a firm foundation upon which he could build a framework to determine philosophical and material truths, he begins by removing all of his then-current ...
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Is Herbrand semantics a kind of term formalism?

Michael Genesereth and Eric Kao describe Herbrand semantics as follows: Herbrand semantics is an alternative semantics for First Order Logic based on truth assignments for ground sentences rather ...
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Contrapositive Fitch Proof

I can't seem to figure out how to get past this step. Any suggestions?
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To connect or to disconnect mathematics and platonism?

How [do philosophers] strongly support or refute the view that: mathematics is a bag of tricks for real-world problem solving; undecidable statements are an irrelevant and harmless side-effect of an ...