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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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28 views

What are 'counterfactual definiteness'?

Without much gibberish, I am wondering what are 'counterfactual definitive statements' made across possible worlds? And, most importantly how do they obtain?
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What kinds of proofs can be given for axioms, e.g. the modal axiom S5?

From John Bigelow and Robert Pargetter's book, titled, 'Science and Necessity', they assert the following: . . . . The resulting system, S5, contains all the theorems of S4 and all the theorems of ...
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Possible worlds and accessibility relations [on hold]

Is there anything preventing possible worlds from meeting one another in a plane of existence that intersects both possible worlds? And if not, how would you describe such a plane that intersects ...
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1answer
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In logic, 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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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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1answer
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Aristotelian vs Boolean, trying to determine the exact difference [duplicate]

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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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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1answer
42 views

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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2answers
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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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Is There a Maximally Consistent Set That is Not $\omega$-complete? [closed]

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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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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1answer
60 views

Does a pattern constitute evidence, logic or something else? [closed]

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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34 views

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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49 views

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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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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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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1answer
58 views

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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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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1answer
51 views

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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3answers
84 views

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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29 views

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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2answers
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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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1answer
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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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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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1answer
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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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1answer
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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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2answers
123 views

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 ...
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67 views

Complement of “at least two people share the same birthday”

Suppose a room contains 𝑛 people. What is the probability that at least two people share the same birthday? So this is actually a question on probability, but I'm really confused in the logic and ...
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77 views

Is every reason reducible to a sequence of tautological statements? [closed]

I think of tautological statements as those statements which when explained should repeat themselves, and should intuitively explain the reason. For example, A = A because 'A is equal to A'; Dog is ...
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2answers
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Do Aristotle's three laws of logic apply to statements about the future?

I have just read about Aristotle's Three Laws of Logic. I was wondering if statements such as "There is a chance of it raining in the next hour" can be evaluated using the three laws. Can you apply ...
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1answer
24 views

Logic Question in a fitch style system - disjunction elimination

I am having difficulty in formally proving two arguments. Firstly, given the premises A ∨ (B∧C) ¬B∨¬C∨ D derive A v D. I can see why it has to be either A or D, because if it's B and C, ...
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278 views

Proof Using Model Universe

Suppose I am trying to prove the following argument (∀x)(Cx → Dx), (∀x)(Ex → ~Dx), /∴ (∀x)(Ex → ~Cx) Now, let's also assume that I don't know if this argument is valid or not. Because of this, I try ...
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102 views

Difference between “neither true nor false” and “either true or false.”

What is the difference between "neither true nor false" and "either true or false."? I was reading about definitions And I read a line saying "Lexical definitions are either true or false". After ...
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Clarification on what is and isn't a logical statement

After reading the article from Wikipedia I feel more confused on what the scope of the definition of a 'logical statement' or proposition is. First, is the statement "It is raining" considered to be ...
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1answer
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What is the difference between a function and a relation in first-order logic?

Consider this definition of first-order (or Herbrand) logic syntax. Here is the vocabulary: Definition (Vocabulary): A vocabulary V consists of: A set of relation constants {r1, ...,...
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The perfect definition of impossible [closed]

When i think about the true impossible, for me is a very dark area, that causes depression, because when we think about this simple question that begins whit, an example, "God creates the Human ...
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1answer
67 views

What's the difference between a second-order relation and a relation between objects?

I was reading an article in philosophy and found this: Some philosophers have denied that there is such a relation as identity. Thus Ludwig Wittgenstein writes (Tractatus 5.5301): "That ...
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How should one symbolize “and then” in logic?

Graham Priest observed that not all uses of "and" in English commute: (page 15) ...according to the truth table for &, 'a and b' always has the same value as 'b and a', namely, they are both ...
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What's the difference between “All A are B” and “A is B”?

I'm having trouble catching the difference between these two forms. I tried to draw some Venn diagrams but it's not helping. "All A are B" means A is contained in B. Does "A is B" mean A is also ...
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1answer
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logical fallacy (or pseudo-logical, or rhetoric) corresponding to unduly extending my argument to make it false

This is probably similar to my preceding question: What's the name of the logical fallacy where a debater extends a statement far beyond the original statement to make it true? but I'm not sure ...
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How to prove (A v B), (A → C), (B → D) therefore (C v D)

Obviously since A → C and B → D then if A v B one of C or D must be true. My only idea is v must be introduced, but how would I use subproofs to show one of A /\ C or B /\ D is never false if A v B?
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What is an example of a true contradiction in a paraconsistent logic?

While reading the Wikipedia article on trivialism I noticed the following: In classical logic, trivialism is in direct violation of Aristotle's law of noncontradiction. In philosophy, trivialism is ...
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4answers
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Is metaphysics justified in its conclusions?

I'm curious of the modern meta-philosophical viewpoints on metaphysical knowledge. That is, is it possible for arm-chair theorizing or rational pure thought alone to gain true knowledge about any ...
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What is the logical distinction between “the same” and “equal to?”

We all understand that Given A = C, and B = C, Then A = B. However, A is not “the same as” B. Example: A is the question, “What animals have feathers and can fly?” B is the question, “What was the ...
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4answers
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Is there any exception that proves or suggests that the law of non-contradiction does not always apply?

Is there any exception that proves or suggests that the law of non-contradiction does not always apply? I am thinking, because the law of non-contradiction is very similar to the law of excluded ...
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3answers
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Is this ad hominem or in general acceptable behavior during an argument?

Person A: What is considered socially acceptable should be common sense regardless of outside influences. Person B: What is considered common sense or obvious can be very different depending on ...
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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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265 views

Is there a difference between equality and identity?

Is there any difference between equality and identity, or are they the same concept?
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Is there any exception that proves or suggests that the law of identity not always apply?

The law of identity is rather simple, so I feel like there can be absolutely nothing that can contradict it or suggest it to be false, it's like a tautological truth that doesn't say anything. But is ...