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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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Is deduction based on induction?

I'm wondering if deduction is in the end based on induction. The problem of induction discovered by the Scottish philosopher David Hume is quite well known. On the other hand, it's commonly supported ...
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Is the problem of logical omniscience intractable?

Vincent Hendricks and John Symons notes the following about epistemic logic: Epistemic logic gets its start with the recognition that expressions like ‘knows that’ or ‘believes that’ have ...
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Interpretation and symbolic notations of operations in mathematics

As we know a mathematical operation is a function. And a function is a special type of relation. Ultimately a relation is a set of ordered pairs. For example, what is addition of natural numbers? At ...
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What's the fallacy of relevance here?

To know absolutely that there is no God one must have infinite knowledge. But to have infinite knowledge one would have to be God. it is impossible to be God and an atheist at the same time. Atheists ...
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How to prove : P v ( P → Q ) by Natural Deduction

Another of Tomassi's exercises I can't solve (Logic, page 109, Revision exercise III, 9) : P v ( P → Q ) I have to use natural deduction and the only rules I know are: • assumptions, • modus ...
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What's the difference between XY=F and XY=0 in Jeffrey's Logic of Decision?

I'm stuck solving problem 14 in Chapter 5 of Jeffrey's Logic of Decision. The first part of the problem says: Show that in presence of prob is nonnegative (prob X≥0) and prob is normalized (T=1)...
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What are the consequences of rejecting identity of indiscernibles

What kind of system are we in if we explicitly take its negation as an axiom? Here's the identity of indiscernibles. (1) ( ∀P.P(x)↔P(y) ) → x = y Here it is written in prenex normal form (2) ∀x∀y.∃...
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What is the premise and conclusion here?

"Half of the American population believes that the universe is 6000 years old. They are wrong about this. Declaring them so is not 'irreligious intolerance'. It is intellectual honesty." -Excerpt ...
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How do I input these statements into a truth table generator?

I have tried inputting my problems into several truth table solvers. I keep getting error messages. Which solver should I use and how do I change my statements on the homework in order to prevent ...
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3answers
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How do pragmatists avoid this modal argument against their view of truth?

I am reading Harry Gensler's Introduction to Logic (Routledge, 2002) and doing exercise 1 of 7.3b in the "Basic Modal Logic" chapter. I think I follow the steps. The answer is in the book. My ...
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Does anyone know how to prove ~ ∀x (Ax→Bx) from Ǝx(Ax & ~Bx)?

Ǝx(Ax & ~Bx) Premise SHOW: ~ ∀x (Ax→Bx) I really appreciate anyone who could help The instructions for the homework were to Prove that the obverse of a particular ...
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Has there been any philosophical guidance regarding when to use logic vs empirical testing?

One obvious disadvantage of testing a given claim with scientific constraints is that one may never know the number of possible constraints to try, in which combinations, and in which order to modify ...
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Does Reflective Set Theory “RfST” fulfill the requirements of founding Category Theory and Mathematics?

On mathoverflow I've posed the question in the title in connection to Muller's 2001 criteria for a founding theory of mathematics, which largely raised in connection to Category theory [see here]. ...
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Is using analogies a bad logic reasoning?

When discussing with someone, I like to take the argument they use and put it in another context, to see if it works, and if it doesn't, ask why the argument should be valid in one context but not in ...
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Is it scientific or a logical error to claim something is true because I can't think of another explanation

The situation Let's say, someone is wrong on the internet. She says The forums on that newspaper article is closed. Apparently the newspaper want to suppress public debate. I reply: That's ...
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1answer
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How to prove (PvQ) & (RvS) : ((P&R) v (P&S)) v ((Q&R) v (Q&S)) by Natural deduction

Another of Tomassi's exercises I can't solve (Logic, page 109, Revision exercise III, 3) (P v Q) & (R v S) : ((P & R) v (P & S)) v ((Q & R) v (Q & S)) I have to use natural ...
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1answer
97 views

What's the fallacy when someone asks a question and then answers it themselves?

Example: "Why didn't you compete in the annual sports event? It was because you knew that you'd lose anyway!" Or, "How did he run that fast? he must've taken steroids" It falls under unwarranted ...
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1answer
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Generating false statements in propositional calculus

Let p stand for the sentence "George is 6ft tall". Let q stand for "George is 5ft tall". Statement 1: ~(p → q) It is false that if George is 6ft tall, George is 5ft tall. It seems pretty obvious ...
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1answer
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Your irreducible ground truth [closed]

What is the ground you build your arguments on? By this I mean something that would be the ultimate base for your reasoning, something irreducible, a (self) evident and therefore unprovable fact, an ...
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2answers
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When are Accessibility Relations satisfied?

We can only "measure" (quantify) counterfactuals by an accessibility relation to our own world. Therefore how can we assert something as necessarily true in all possible world's if quantification of ...
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1answer
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Existential Quantifiers and Modal Logic

I have a question about predicate logic and modal logic. Namely, do any of them overlap with one another? To give an example, does existential quantification apply to counterfactual statements? A ...
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What is actual is a metaphysical necessity?

You look out of the window and it's raining. You grab a bottle and pour some water into a glass. You probably don't consider these events as necessary: it could have been a sunny day and you were free ...
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Are there any techniques for dealing with an arguer who continually denies facts?

Inspired by this question where individuals can't imagine something being possible, and somewhat similar to this. I've recently been in a debate where the debater had the very annoying habit of just ...
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1answer
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Are there useful logics that reject disjunction introduction?

Are there logics with fairly natural semantics that don't have disjunction introduction? Is there a good way of thinking about what "flavor of system" you're in when you don't take disjunction ...
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Is “I cannot imagine a mechanism for X to happen, so X can never happen” a named logical fallacy?

I have encountered this reasoning quite frequently: Somebody posits the hypothesis that an event X can happpen. A recent example I encountered was "vinegar and salt in the boiling water make eggs ...
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John Earman and Time Travel

Time travel and grandfather paradox: Earman suggests in his 1995 paper that physical possibility should be considered similarly with the laws of nature (i.e. logical possibility). Does this mean that ...
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Logic and resolving a modus tollens

Wasserman presents a common argument against time travel: (P1) If backward time travel were possible, it would be possible to perform a self-defeating act. (P2) It is impossible to perform a self-...
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Justification for axiom OB-RE in deontic logic

Let OB p denote "p is obligatory". Axiom OB-RE is (p ↔ q) → (OB p ↔ OB q). This axiom seems false to me (under the interpretation of obligation). For example, let p denote "don't lie to me" and q ...
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62 views

Grandfather Paradox and Causal Loop

How does the grandfather paradox cause a causal loop (and therefore a bootstrap paradox)? https://en.wikipedia.org/wiki/Grandfather_paradox
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Is Ross' paradox really a paradox?

Consider the following disjunction introduction: Your room is clean. Therefore, your room is clean or your house is burnt down. Ross' paradox allegedly arises when applying this inference to ...
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Is there anything wrong with this argument?

The Constitution of the Russian Federation says, in Chapter 1, Article 1: The Russian Federation - Russia is a democratic federal law-bound State with a republican form of government. The ...
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proof for relational predicate logic

I have been working on this problem for over an hour and I think I have simply missed something. I need some help. The rules I am allowed to use are the Basic Inference rules (MP, MT, HS, Simp, Conj, ...
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Why can't existence be expressed in linear temporal logic?

In some circumstances, existence cannot be expressed in linear temporal logic. I don't understand why it can't be constructed with negations and global quantifiers. For example, the wikipedia page (...
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What is the difference between inference and deduction?

This question contains my question, but tries to accomplish too much at once; I would like a clear answer to the distinction between inference and deduction. What is the difference between coming to ...
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~(~P&Q) & ~(P&Q) : Prove ~Q

This must be proved using only negation, double neg.Intro, double negation Elimination, indirect proof, conj.Intro, and conj.Elim.
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Language proof and logic Chapter 15 question 21 how?

I'm really not understanding the set up of how to go about solving this problem any help is welcome
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In Fitch, how does one prove ¬(B ∧ C) from two premises (A → ¬B) and (¬A → ¬C) [closed]

Help me out please!! I have been trying to solve it for hours
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Language proof and logic Chapter 15 question 16 help

I'm trying to go about solving this problem but I'm having problems even knowing how to approach it. Can someone help me to set it up? Here is the premise: ∀x∀y(x ⊆ y ↔️ ∀z(z ∈ x ⟶ z ∈ y) Here is ...
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What would be an intuitive understanding of Peirce's law?

Wikipedia describes Peirce's law as In propositional calculus, Peirce's law says that ((P→Q)→P)→P. Written out, this means that P must be true if there is a proposition Q such that the truth of P ...
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language proof and logic chapter 13 question 49 Help

Premises: ∃xP(x) ∀x∀y((P(x)∧P(y)) → x = y) Prove: ∃x(P(x)∧∀y(P(y) → y = x)) I've started it but the end is starting to get super muddy and not work out and I don't know where I went wrong.
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language logic and proof chapter 12 question 49 and question 50

I've been working on this and I can't seem to figure out what exactly is going wrong can anyone help?
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In Fitch, how does one prove “P” from the premise “(¬P ∨ Q)→P”?

I can't figure out how to prove that formally. Please, help!!
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1answer
174 views

What is the best proof that 1+1=2 by a person who was not Bertrand Russell?

The question says it all. Besides Russell and Whitehead, who are the philosophers and mathematicians who demonstrated successfully that 1+1=2? Extra bonus (i.e., a warm feeling inside) awarded for ...
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How to prove ‘∃xP(x)’ from ‘¬∀x(P(x)→Q(x))’

What would a formal Fitch proof for this look like? I am given ¬∀x(P(x)→Q(x)), and need to derive ∃xP(x) from it. I started with this, but I don't know if I am doing the right thing, and where to go ...
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Difficulty with understanding the semantics of the following equivalences

I know that the rules for removing quantifiers from the antecedent of a conditional are as follows: (∀x)φ(x) → ψ ⇔ (∃x)(φ(x) → ψ) and (∃x)φ(x) → ψ ⇔ (∀x)(φ(x) → ψ), provided that x is not free in ψ. ...
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Can the conclusion of an inductive argument be that there is only one exception to the list of evidentiary claims?

Can this be an example of an inductive argument? Premise 1: Country A rejected idea Z. Premise 2: Country B rejected idea Z. Premise 3: Country C rejected idea Z. Premise 4: Country D rejected ...
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What argument styles have only recently been labelled fallacies?

While reading Douglas Walton's "Historical Origins of Argumentum ad Consequentiam", I realized there is at least one argument style that appears reasonable but which has been labelled as a logical ...
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What's wrong with the logic in the following ''paradox''?

The apparent paradox pertains to the homesteading principle. This isn't a question about the morality/immorality of homesteading, or ownership, or use, etc, just the logic behind it. The concept: ...
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Fitch Proof by Contradiction help

Hi, I'm pretty new to writing formal proofs and I was wondering if I could get some help solving this question. I've set up the problem and I was thinking of perhaps proving it by contradiction that ...
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Is there a logical fallacy for rejecting “A not B, because A precludes B?”

I'm not sure if I'm asking the right question here, but I'm wondering if there is an actual fallacy to describe this situation.