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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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Extreme examples for exploring the scope of statements - does this technique have a name? - Is it a fallacy?

When discussing opinions with friends, I often resort to making extreme scenarios out of their opinions in an attempt to investigate the limits within which their statements hold true (to them). ...
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How should we understand different knowledge attributions? (epistemic logic)

My main motivation is in terms of epistemic logic. In epistemic logic X knows that p if p is true in all states that X sees as epistemically indistinguishable from the current state. In this sense we ...
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Is there a limit beyond which mathematics, if used correctly, cannot be applied to reality?

And if so, why, and which? Take this case: If I've two apples and I believe that with two more I'll have four apples, then I implicitly believe that summation applies to reality. Yet there are ...
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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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How can we prove something ethical?

We as humans have ethics, giving us the ability to know what's good and evil, what's ethical what's not, yet what I consider ethical, others don't, so in theory how can we prove anything is ethical ...
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In a Descartes square are the statements just the negations of each other?

There is a decision making method based on wrapping problems into a Descartes square by answering 4 questions. I've tried to use it for my own decision process but I couldn't figure out what to place ...
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if philosophy didn't exist nor did psychology, could we prove that we think?

if philosophy and psychology didn't exist, could humans be able to prove that we think and are capable of coming up with inventions, I mean we create things because we need them(that used to be the ...
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166 views

Modus Ponens as Substitute for Syllogism

This is a pretty basic question, but I haven't been able to find a clear answer in the various sources I've looked at, including the Kneales' chapter on conditionals in 'The Development of Logic'. ...
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108 views

Could someone help me prove (P → Q) ↔ (~P ∨ Q) follows from (P ∨ Q) ↔ (~P → Q) in sentential logic?

I need to prove that (P → Q) ↔ (~P ∨ Q) follows from (P ∨ Q) ↔ (~P → Q).
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How does one judge “complexity” of assumptions for the purposes of “best explanation”?

The context for this question is from assessing theological arguments from the point of view of 'inference to the best explanation'. In philosophy (and science), we may wish to argue that some ...
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Using logic to exaggerate something

I am not sure if this is the best place for this question. Many times people in marketing or good at promoting things (and themselves) use sometimes a subset of similarities between 2 things to make ...
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Sentences and reality

Would sentences have meaning even if humans did not exist? For example, would "the earth is round" have meaning if humans did not exist? Would it be true?
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How are there at least 2 instances of Post Hoc in “I am opposed to charging tuition. Without tuition-free education, I could never have become mayor”?

Capaldi PhD Columbia, Smit PhD Catholic Univ. of Leuven. The Art of Deception (2007). Identify the fallacy, rhetorical technique, and potential difficulties in play with each of the following ...
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Understanding multiple values in a single cell of a truth table (P v ~Q) as (1 1 0 1) when P and Q are 1

This might seem basic to most here but I am struggling with a truth table for a disjunct. As I am looking at it further, I actually think the issue I am struggling with how to interpret truth values ...
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Could we develop a notion of conceivability that would allow us to imagine impossible/inconsistent/illogical things?

There are things that we cannot imagine because they are impossible (like a solution to Russell's set theory, since it is impossible to reach that solution because it is illogical.) Some months ago, ...
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Is Propositional Logic Sound and Complete

After reading Gödel's incompleteness theorem, I wonder if there are any systems whose axioms are sound and complete. I realize that Gödel's arguments (at least from my sources) only apply to ...
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What is the relationship between “truth” and logic?

I'm fairly new to logic. What I've surmised from the book I'm reading is that Logic is the science of evaluating arguments Arguments are composed of statements Statements are sentences that can be ...
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Where's the Red Herring in arguing that “I see it as a glass half full rather than as a glass half empty”?

Capaldi PhD Columbia, Smit PhD Catholic Univ. of Leuven. The Art of Deception (2007). p. 259. Exercise 1 Identify the fallacy, rhetorical technique, and potential difficulties in play with ...
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How's this Equivocation: IQ tests “measure not intelligence, but only the ability to comprehend and manipulate symbols”?

Capaldi PhD Columbia, Smit PhD Catholic Univ. of Leuven. The Art of Deception (2007). p. 259. Exercise 1 Identify the fallacy, rhetorical technique, and potential difficulties in play with ...
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How are “goals that we think can be achieved by a good-faith effort within the allotted timetables” fallacies of equivocation and creative thinking?

Capaldi PhD Columbia, Smit PhD Catholic Univ. of Leuven. The Art of Deception (2007). p. 257. Exercise 1 Identify the fallacy, rhetorical technique, and potential difficulties in play with ...
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How is this Appeal to Pity fallacious and a Red Herring: Our country should never war, because wars corrupt our troops?

Capaldi PhD Columbia, Smit PhD Catholic Univ. of Leuven. The Art of Deception (2007). p. 257. Exercise 1 Identify the fallacy, rhetorical technique, and potential difficulties in play with ...
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Is a barber a barber if he doesn't get paid?

For reference: The Barber Paradox. The Barber is he who shaves all those, and only those, who doesn't shave themselves. Now the question is: Who shaves the Barber? The paradox being that if ...
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Are syllogisms independent of humans?

For example, if "All a are b" and "All b are c" then "All a are c". To make this syllogism, does a conscious being need to exist? Or is it inferred from the sentences?
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Observing a zero probability event

I am not a philosopher. Just curious. From a philosophical point of view, if one observes an event with zero probability, does this immediately lead to a contradiction? For example, if you have a ...
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Why does one negative premise suffice to imply a negative conclusion?

Capaldi PhD Columbia, Smit PhD Catholic University of Leuven. The Art of Deception (2007). Why's 2 true please? I can't intuit why, because 3 outwardly contradicts it. I prefer an intuitive ...
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In categorical logic, why must any argument with two negative premises be invalid?

Capaldi PhD Columbia, Smit PhD Catholic University of Leuven. The Art of Deception (2007). Why's 1 true please? I prefer an intuitive explanation, not one with Truth Tables or Formal Deduction.
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Implication in sentences

What implications do we get when we use the past tense? For example, if I say that when I was younger, I used to play football, does this imply that now I don't?
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Can the principle of sufficient reason be applied to the whole of existence?

Many philosophers (Leibniz and Heidegger, to name but two) consider "Why is there something rather than nothing" the most difficult and important question. Given that "nothing" is a possibility among ...
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How to prove ¬(p→q) ⊢ p &¬q

This is the first time I have posted anything on this forum. I am using Tomassi's Logic. Unfortunately I have been unable to solve some of the problems. One I can't solve is this one: ¬(p → q) ⊢ p &...
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Consciousness doesn't need your body - a thought experiment

1) During a deep sleep, your consciousness deactivates to reactivate upon awakening 2) During a deep sleep, you are narcotized and killed, to be replaced instantly by an identical copy, which wakes ...
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Do premises need to be valid conclusions themselves?

I'm pretty new to logic. I recently purchased "A Concise Introduction to Logic" by Patrick Hurley based on reviews. So far I'm liking the book. I'm really focusing hard on the first chapter to get a ...
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Do logic and reasoning need to be validated by an ultimate authority?

A lot of presuppositional appologists argue that the Abrahamic God is real because the Bible is self validating and that everyone "knows" God (except you have to presuppose sense perception and that ...
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Verum or T in dynamic epistemic logic models

I've been reading a paper on dynamic epistemic logic where they use T in a way that I'm not really familar with. The paper is here by Wesley Holliday, page 16: https://pdfs.semanticscholar.org/dae6/...
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How does philosophy advance despite irreconcilable background assumptions (“positions”) on every topic?

In philosophy there are always, and on almost everything, many "positions", many different possibilities to choose from, and there isn't mainly some decisive conclusion between positions as to what's "...
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Is logic logic because God defined it as such?

A popular argument that comes, by some theists, for attributes of God is: The argument that some of God's attributes, such as Omnipotence, are illogical cannot restrict God from having them since ...
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Given p ⇒ q and m ⇒ p ∨ q, use the Fitch System to prove m ⇒ q

I have spent about 6 hours now trying to prove this using the Fitch system and I just keep going in circles! Attached is one of the 500 attempts :) I have a feeling it's done fairly simply and ...
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Online (pdf) resources on doxastic logic

I would be interested in learning more about doxastic logic. The wiki entry is rather detailed but still obviously very summarised and references therein are either papers with a paywall or books ...
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Is causality a type of necessary and sufficient condition?

Does 'A caused B' mean that A is a necessary and sufficient condition for B? Imagine that we go to a shop and buy two items with a total cost 40 dollars (30 for 1st item and 10 for the 2nd). Is the ...
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Is calling an argument a fallacy, or is the notion of informal fallacy, just a method of manipulation?

Indeed, there are ways of thought which are not consistent with logic. I am not talking about such fallacies here. All of formal fallacies, statistical fallacies or fallacies of relevance (e.g. ad ...
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Why is faulty generalization called an informal fallacy?

According to wikipedia faulty generalization belongs to the class of informal fallacies. Also, a fallacy is called informal if it originates in a reasoning error other than a flaw in the logical ...
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Can you divide the natural numbers in half sequentially? [closed]

My brief stint on SE has been quite interesting because it forced me to make the premises of my inquiry more explicit. I resisted this initially simply for reasons of economy, but economy proved to be ...
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Does believing in a Christian God logically imply believing in miracles?

Assume you are a Christian and you believe that the descriptions of the life of Jesus are facts. Things like turning water into wine magically, walking on water and other miracles seem to be ...
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how do people pick the letters for syllogistic logic problems?

I encountered the following argument while I was studying syllogistic logic from a book: All red cars kill papers, (premise) All cars that kill papers are beautiful, (premise) All red ...
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Does the value of truth have an approximation threshold?

In other words, a truth value in a mathematical sense is binary, but human communication is fallible and runs the risk of fallacy, error, and distortion. The idea of being "close enough" to the truth ...
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What are the logical fallacies of this argument?

SCIENTIFIC FACT: Nothing in the universe, ceases to exist, it just appears in some other form. LOGICAL FACT: We can be absolutely sure that what we experience right now, exists. Let's mark ...
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How to show that (P & Q) v (~P v ~ Q) is a theorem in SD

I’m working on a practice question on my logic textbook. And I’m stuck at this question. This is what I have so far: 1. ~(P & Q) Assumption/ Negated Eelimination 2. P Assumption/...
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Learning Peano's notation

This is more a request than a question. I would like to read Russell's The Logic of Relations in which he uses Peano's notation. I'm looking for a text available online which would explain thoroughly ...
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Are arguments claiming the impossibility to prove or disprove anything themselves impossible to prove? [duplicate]

Could arguments claiming the impossibility to prove or disprove anything be flawed because if they were sound they would also be impossible to prove? Or could you just assume they must be right ...
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Defining 2 words with respect to each other

I apologize if this is in the wrong forum. I listen to a radio show where the host talks a lot about love & hate. He defines love as 'the absence of hate' and he says that hate is 'the absence of ...
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What's wrong with the following argument regarding temporal limits?

Let us suppose there is a limit: you cannot buy something after 10:00PM. From the position of law, of course "cannot" must be taken directly. But from the position of common thinking, people are less ...