# Questions tagged [logic]

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

2,303 questions
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### I'm stuck and having trouble with ￢P ∨ Q Prove: P → Q

I am having trouble with this problem as I have just started doing logic. Is this the same as P → Q Prove: ￢P ∨ Q ?
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### Need some expert help on this proof problem [on hold]

Not sure how to do these problems and need some guidance on it 1. ￢(Y → X) 2. ￢(X → H) Prove: K
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### Philosophy of Logic – Converting formal proofs to the sound deductive logical inference model [on hold]

How do we convert the formal proofs to theorem consequences of symbolic logic to conform to the sound deductive logical inference model? What would be the benefits of doing this? PROPOSED ANSWER: ...
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### Logical analysis under Russell's theory of definite descriptions

My question stems from the two different logical forms for the following sentence under Russell's analysis. One in which the word 'not' has a wide scope and one where it has a narrow scope. 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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### How Do I start on Premise: B ↔ ￢B Conclusion: J ↔ ￢C?

I have started a new chapter and I do not quite understand how you start questions like these? Do i need to just keep doing contradictions to get an answer like this? Can someone point me in the right ...
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### Can anyone help me solve this problem?

Hi can anyone help me with this problem? Would greatly be appreciated. M → I ￢ I ∧ L M ∨ B Prove: B
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### Should only philosophy students study logic, ethics, axiology, phenomenology, epistemology, and aesthetics? [on hold]

E.g a physician. Should they not start in any univeristy studying these modules? Actually a lawyer most law schools teach philosophy of law as an elective module. And no social philosophy or ...
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### A physical thing to see [on hold]

Let's say people see round things. Other people from another dimension see square. The question is about physicality when touched, we know what shape it has. whether something can have a different ...
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### Where can I study this in more detail?

I am finding al-Farabi's Philosophy of Plato and Aristotle on pages 13-17, paragraphs 1-9, (pages 11-13 in the pdf file linked below), very interesting: http://traditionalhikma.com/wp-content/uploads/...
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### In predicate logic, does existential quantification (∃) include universal quantification (∀), i.e. can 'some' imply 'all'?

I am having a discussion whether 'some' can also imply 'all'. The definition for some, 'an unspecified number or amount of people or things' seems to leave room for this interpretation. Discussion ...
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### Is □(□A→B) v □(□B→A) provable in S5? If it's not, I am having trouble coming up with a countermodel

Modal Logic question about provability/ countermodels.
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### What formal logical systems “resolve” the Liar Paradox?

Short version of my question. What formal logical systems can represent, and seem robust against, the Liar Paradox? N.B. I would like to avoid reference to truth-values, except inasmuch as they ...
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### How did Aristotelian logic view this?

I am very interested in the logical aspect of Aristotelian philosophy, especially how it was used by al Farabi and Ibn Sina in explaining understanding and breaking this complicated process down ...
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### What should one know about term logic before studying propositional and predicate logic?

I'm hearing that predicate logic replaces term logic, but teaching of predicated logic assumes knowledge of term logic. What are essential to know from term logic before studying propositional and ...
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### What would happen if we saw an impossible thing? Would we see it? [on hold]

Consider there is a multiverse where all kinds of impossible worlds and things occur. Where illogical/logically impossible things exist. Where there are even, somehow, things that are logically ...
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### Is it possible to logically derive moral statements from factual statements?

Yes, this is essentially the is-ought problem posed as a question. The reason I am asking however, is that I have so far found absolutely no satisfactory arguments for this being the case anywhere ...
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### Can two different objects at the same time be the same? [on hold]

Can two things be different and yet the same at the same time? For example, a chair (white) does not have one leg and another (black) has all of its legs. As in the question, these two things with ...
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### Finite Alphabets

This is a question based on section 2.5.6 from the book Logic, laws of truth, by Nicholas J.J Smith, page 48. What does Nicholas mean when he says: Note that we can further specify exactly what we ...
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### Is Tarski's derivation of the Liar paradox valid?

First a link to his derivation: http://www.jfsowa.com/logic/tarski.htm Its a famous essay so you really should read all of it but at the moment its enough if you read section 7 where Tarski derives ...
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### How does catuskoti apply to everyday life?

An article on Aeon published the concept of catuskoti, a principle in use during the age of Buddha. It states that for any given statement, there are four possibilities i.e. it might be true (and ...
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### Logical expression that non-existent things don't do anything?

How could we express the idea that "something that doesn't exist cannot possibly do anything" using a logical argument? And if so, it is at all possible to prove that kind of proposition?
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### Is the argument below valid?

If interest rates go down, then I will buy a house. If I buy a house, I will need a loan. Therefore, I will not need a loan if I do not buy a house. Is this argument valid?
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### Is it possible to mathematically define a hypercomputer-universe where things that could not be computed by it could exist? [duplicate]

There are a few physicists that propose that the universe is a hypercomputer. One example is Roger Penrose, who, basing in his quantum interpretation (https://en.wikipedia.org/wiki/...
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### What is a good history of logic book that covers all logic?

Including inductive, formal and mathematical. I find them separated a lot and I don't know if I have the ability to sit through all the Handbook of the History of Logic series.
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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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### 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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### Alternate form of “all x are y”

It's typically correct to say something like "all cats are beautiful" as ∀x(CAT(x)->BEAUTIFUL(x)). It is incorrect to say ∀x(CAT(x) & BEAUTIFUL(x)) because you're effectively saying "everything ...
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### On Putnam's belief that we can choose a logic system based on the task at hand

I was reading "A Graphic Guide to Logic" and a little speech bubble from Hilary Putnam says that "I still believe that there are facts in the world that determine which logic it is appropriate to use ...
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### Formal logic to describe causation?

I'm looking for any formal work that has been done on describing causation the way people understand it. I am not looking for logical implication, more a way to talk about "Why?" questions. Basically, ...
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### How to find redundant premises?

Suppose I have this simple argument: ( P ⊃ Q ) R P Therefore, Q Here's the truth table I made in an excel worksheet: As you can see this comes out valid but in reality it isn't valid ...
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### Deduction vs Induction — are they equally valid?

I've been reading on deduction vs induction as two primary modes of reasoning. Can't exactly remember where but I have also seen deduction being described as backward and induction as forward thinking....
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### Is there modal logic without possible worlds?

Would it be desirable to carry out a deflationary research programme in modal logic? In other words, would it be desirable to re-think modal logic without the possible worlds semantics? The original ...
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### Is it there any trivialist model in physics (like in quantum mechanics)?

Trivialism is a system that proposes that literally every proposition is true and false at the same time blatantly breaking the principle of no contradiction and triggering the principle of explosion (...
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### Where can I learn about the philosophy behind mathematical and logical proofs?

I'm looking for something that dives into the philosophical idea of a "proof," and explains how the subjects of mathematics and logic deal with it. Does anyone have any book or article recommendations ...
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### Why is Modus Ponens valid?

I am having trouble understanding what defines Entailment operator. On Mathoverflow I posted this question on what I perceive to be paradox of entailment. Consider: Modus Ponens: P therefore Q P ...
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### Can you prove anything in philosophy?

I don't understand philosophy very well, and so I am wondering whether you can "prove" anything in philosophy. It always seems you can go a layer down, and find another question, almost endlessly ...
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### Are there “partially explosive” logics?

Roughly speaking, I'm wondering if it's possible to meaningfully grade different systems on how explosion-tolerant they are. In classical sentential logic and intuitionistic sentential logic, a ...
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### Hume's argument for the subjectivity of morality

I am trying to analyze the following argument by Hume in his Treatise of Human Nature: But can there be any difficulty in proving, that vice and virtue are not matters of fact, whose existence we ...
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### Omnipotence Paradox Defense and Meinongianism/Neo-Meinongianism

I was considering a solution to the omnipotence paradox in which excluding logical impossibilities from the definition of omnipotence is justified as follows. Consider the proposition, "God could ...
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### Is it there any model of the universe or any (physical) cosmological theory or model completely compatible with trivialism? [duplicate]

Trivialism is a system that proposes that literally every proposition is true and false at the same time blatantly breaking the principle of no contradiction and triggering the principle of explosion (...
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### How is the nature of logical principles commonly defined in contemporary philosophy?

In contemporary philosophy, how exactly is the nature of logical principles defined? For example, the way I've commonly seen logical principles construed are as true propositions which described the ...
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### Is “If…then” not a truly logical connective?

Since you can completely fill out a truth table for "not A", "A and B", and "A or B", but not for "if A then B", can it really be a logical connective? The only thing that can be confirmed about the ...
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### What is an example of a predictive conditional?

Can someone explain to me with an example what a predictive conditional is? Does this type of conditional have necessary and sufficient conditions?
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### Recursive definitions (a couple questions based on them)

From the book Logic, laws of truth, by Nicholas J.J Smith: What does Smith mean by recursive definitions? Why does it matter? How do you make recursive definitions for something such as: a) the set ...
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### Can hypercomputation compute the impossible?

There are things which are illogical/logically impossible (like saying that 2+2=4 and 2+2=5. Without changing anything in the axioms of mathematics or logic, this would be a contradiction and would be ...
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### Is the principle of non-contradiction self-evident?

The principle of non-contradiction is that contradictory propositions cannot both be true, e. g. the two propositions "A is B" and "A is not B" are mutually exclusive. However, whenever something is ...
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### Syntax of propositional logic

From the book Logic: The laws of truth by Nicholas J.J Smith, page 40, sub-heading: "Syntax of PL". What does the author mean by the syntax of PL? Can someone explain what the author is trying to ...