Questions tagged [logic]

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

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How the hell could it be a valid argument if the premise and conclusion are two different things [closed]

The premise is: John is a married bachelor The Conclusion is: Pigs can fly There is only one premise and one conclusion. Why are they connected and in what way can we say this argument is valid?
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Halting Problem Oracle

Halting problem is unsolvable. There is no method to solve it, so no human can solve it. So why is any theory utilising an oracle (which can solve halting problem) not simply nonsense?
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Is this a problem with verisimilitude talk, many-valued-logic talk, or something/nothing else?

A perhaps naive characterization of verisimilitude is "closeness to truth," the proximity coming from the similarity. At least, the SEP article uses, "The number of planets is 9," ...
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Are there conjunctive facts and disjunctive facts?

Facts are supposed to be the grounds for truths. However, consider a conjunctive statement like "Paris is in France and New York City is in the USA". What fact grounds that? Is there such a ...
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Identity in Quantified Modal Logic

Why is ¬(◇(a=b)∧◇¬(a=b)) a validity in Quantified Modal Logic (QML)? For example, let a:=“the present King of France” and b:=“the richest bald person alive”. Then, it seems ◇(a=b)∧◇¬(a=b) is not a ...
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"This seems to abolish logic, but does not do so."

If language is to be a means of communication there must be agreement not only in definitions but also (queer as this may sound) in judgements. This seems to abolish logic, but does not do so. -- It ...
225 views

Why not everything has an end

Consider this statement: “Everything has an end” I think many of you here can agree with this. But that means that the claim in this above statement also has an end. So one day, there might be some ...
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1 vote
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How be so sure that implications are bivalent? (An attempt to resolve paradoxes of material implication)

The material conditional, P→Q defined as ￢P∨Q, is usually thought not to match the usual linguistics, as seen by many paradoxes. The Wikipedia article gives few good examples. I tried to resolve them ...
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What do you call this type of logic?

What do you call a logic that is a gradient between a gradient between two extremes and a single point. So, for simplicity, let’s say an upside-down triangle (▼)… In my case, specifically, the top ...
494 views

How is scientific realism not an example of the fallacy of the converse?

Firstly, to be clear, I'm not trying to say that science is all nonsense or not useful or anything of the sort, since that's obviously not the case. If nothing else, it's incredibly useful for making ...
2k views

Is desire closed under logical equivalence?

Suppose some person P desires a statement S to hold. Also, S is logically equivalent to S'. Does this mean that P desires S' also? Basically, is desire closed under logical equivalence?
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Why do people speak as though "all" does not imply "some"? [closed]

Suppose someone asks whether some of the people in a classroom are over 20 years old, and then someone says, "No, all of the people are". Why would they say that? Why can't they say ...
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Natural Language and Implication

I understand that relevant logic deals with a natural-language interpretation of implication, but it seems too restrictive. It does seem a bit of a reach to say that there is a conceptual link between ...
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fitch-style proof C ∨ E , A ∨ M , A → ¬C , ¬S ∧ ¬M ⊢ E

I want to prove this statement using fitch-style : C ∨ E, A ∨ M, A → ¬C, ¬S ∧ ¬M ⊢ E This is what I have at the moment but I'm completely lost on what I should do next or if I've gone down the wrong ...
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Is this a fallacy: "A woman is an adult who identifies as female in gender"? [closed]

The phrase tries to avoid the overt circular definition found in the variant, "a woman is anyone who identifies as a woman", by swapping woman with female in gender. But is that still a ...
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If a then it cannot fail to be the case that b

I am studying logic in my free time from the book Logic: A very short introduction by Grahan Priest and I am currently encountering difficulties in chapter 6 about Necessity and possibility. In this ...
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Logic as an obstacle to knowledge

Has there been any philosopher making an argument along the lines that logic is an obstacle to knowledge about the world? The informal argument could go something like: logic is created by humans (...
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Relativism and common sense in ZFC

ZFC is the most well known set theory which is considered by many as the foundation of mathematics but I am confused to understand it intuitively. Most of us have a clear understating of empty set and ...
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Has this mathematically proven solipsism? [duplicate]

http://bc.upjp2.edu.pl/Content/5621/35_PDFsam_Ca%C5%82o%C5%9B%C4%87%20ze%20znakiem%20wodnym3.pdf It's not so much the math as it is these things in the link: More generally, there can be no deductive ...
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Would my argument of knowledge being a social construct be a resolution to The Problem of the Criterion?

Questions from https://iep.utm.edu/problem-of-the-criterion/: What do we know? How are we to decide in any particular case whether we have knowledge? I’ve been reading into The Problem of the ...
157 views

If an argument cannot be known as sound, can it still be claimed as sound?

I have read the the criteria to determine if an argument is sound is if its claim is valid and its premises are true. However, what if no one can know whether or not an argument is sound because no ...
2k views

Is there a term for a fallacy in which one believes something to be divinely inspired due to being improbable?

Consider the following argument: I have been born on Earth, during a time of relative prosperity. The probability that I was born at this moment, of all moments, is very small. Therefore, this is ...
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Is there a logic of non-universal class characteristics?

The proposition (1) Dogs have four legs is true, but if you tried to convert this proposition into predicate logic, the only reasonable candidate is the false (2) for all x, x is a dog implies x ...
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Jurisprudence and logic: Is it a necessary criterion for a claim to be declared sound that there be no evidence to the contrary as to its soundness?

So, I've been generating various arguments (such as related to the synthesis of legal arguments), and I have been doing my best to figure out how to declare that a particular claim is not sound. For ...
166 views

What truth value should be determined for statements that say something about something that has no meaning for it?

According to the principle of excluded middle, every statement is either true or false. It might sound a little ridiculous, but consider the following statement: Mountains believe in God. Believing ...
2k views

What is the difference between a "question" and an "answer"?

All I was able to find through Google regarding the subject is from The Blind Spot, where it says, in part, The question at stake is the nature of mathematical knowledge and the difference between a ...
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Can, "This problem is unsolvable," be used to formulate the first incompleteness theorem in erotetic logic specifically?

Assumptions/definitions: the Gödel sentence is informally equivalent to, "This sentence can't be proved in system X," where X is appropriately specified. Since that sentence can itself be ...
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Is circular reasoning always wrong?

I was wondering if circular reasoning is always a problem I was thinking about something like this if A then B, And If B then A. Premise. A is true Conclusion. B is true. All this shows is that B ...
1 vote
202 views

Can circular reasoning be logical, and can it provide support for the Bible?

Circular reasoning is a type of logical fallacy where the premise is used to prove the conclusion. A basis example would be: This historical movie is creditable. Why? Because it says so. In this ...
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Is this the correct usage of "consensus"?

[See updated question below] I'm debating someone who is making this argument: "Most religions believe all other religions are wrong, and their religion is right. Therefore the consensus is that ...
1 vote
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From English Sentence to Symbolic Logic: "The Happiest Person is not named John"

Suppose that x is over the domain of all things and I have the following predicates: H(x) = x is a person, J(x) = x is named John, F(x,y) = x is happier than y, a = John Smith My interpretation of ...
210 views

What are examples of non classical formal logic being used to solve practical questions?

Algebraic logic is something which exists both in Mathematics and Philosophy. However, I've been feeling discontent with the number of examples presented of using logic to solve work through ...
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Would a "disagreement operator" break down if iterated too much?

Let D(S) read as, "I disagree that S." It is possible to iterate this, so that DD(S), "I disagree that I disagree that S." Then we can go on to DDD(S), and so on. (For a peer-...
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Fundamental equations in Philosophy and Logic

For the natural sciences it is easy to indicate the most important fundamental equations. If I want to explain Philosophy and Logic to a physicist or a chemist, what are considered the most important ...
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Do models of Cartesian closed logic physically exist?

Cartesian closed logics, also known as simple type theories or simply-typed lambda calculi, are ubiquitous; we use sentential logic (WP, nLab) all the time in philosophy and law, and doxastic logic to ...
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The massive problem with regarding string manipulations as the foundation of mathematics

Formalists believe that mathematics is just a game of string manipulation, not much different from other games like Ludo or chess. I think string manipulation is an extremely useful way to think about ...
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Question regarding the stipulated 'domain of discourse' for models of first-order sentences

Assume 'S' is a first-order sentence about a subject 'Z'. When one stipulates a Model for 'S' with a domain 'D' does one always assume that the domain will contain all the objects within the subject '...
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Intuitionism, the law of excluded middle and mental construct

I don't get why LEM is rejected in intuitionistic logic. The basic idea behind intuitionism is that math is a mental construct. But how does this make LEM not acceptable? I've seen some similar posts ...
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1 vote
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How does one test their credences of belief?

Suppose I feel that event A is more plausible than event B. How can I test, verify, or falsify this? For example, suppose I have a belief that my partner is cheating on me. Suppose I have another ...
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How does logic deal with objects that change?

Say I have an object that is currently red, but in one day will be painted green. If I put it in my formal language with a constant symbol 's' and define the colours green and red using 'g' and 'r' ...
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How can we prove that the supernatural or paranormal doesn't exist?

Agnostic theists and atheists believe themselves to be hopelessly ignorant concerning the existence of the supernatural or paranormal. To them, gnostic atheism isn't adequately supported by evidence, ...
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An introductory book on philosophy of language and logic?

I tried self teaching philosophy of language, logic, modal logic but I am lost as a headless chicken. Can anyone help me please? I have a full time job, but I can take an hour everyday and learn a bit....
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Books similar in nature to Logic and Theism by Jordan Sobel?

I've recently been reading "Logic and Theism" by Jordan Sobel and have found it to be fascinating. The two primary things I like about it are: The book primarily focuses on analyzing the ...
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Logic of hypothesis testing

The logic of hypothesis testing is this: State the hypothesis (called the null hypothesis) Get some data If the data is very unlikely under the assumption that null hypothesis is true then conclude ...
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Bias type based on achievement of goals

What type of bias is it if I favour an idea because the implementation of the idea will benefit me? Example: I favour limited gun control despite reading contrary arguments because my livelihood is ...
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Why was intuitionist logic abandoned?

I have seen many questions discussing intuitionist logic (Brouwer, Weyl etc.) on the site. However, this whole area of logic seems to be dead, and it also looks like philosophers / mathematicians / ...
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Reference request : Defining concepts

Shafi Goldwasser's interview In the video attached, Goldwasser talks about course(s) on abstract subject matter like definition of concepts, definienda, etc. I am looking for a link to course/book ...
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1 vote
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Does a definite description such as "the train" or "the student" always signal uniqueness of the referent?

Some authors claims that a definite description such as "the king" does not necessarily signal uniqueness. Examples given: (1) I’ve got this data from the student of a linguist. — Poesio (...
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What is ⊥ called in paraconsistent logic?

I am building a weakened version of the intuitionistic logic. It wouldn't satisfy (p∧¬p)→⊥ as a tautology, but rather, (⊤→(p∧¬p))→⊥. In plain English, contradictions admit no proof, but there might ...
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