Questions tagged [logic]
For questions about logic, whether it concerns syllogistic logic, mathematical logic or the nature of logic itself.
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Why shouldn’t I be a skeptic about the Necessitation Rule for alethic modal logics?
Alethic modal logics for metaphysical possibility and necessity usually have the Necessitation Rule:
From ⊢P, infer ⊢□P.
Doesn’t this commit us to the meta-notion that logical necessity modulo some ...
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What logical differences are between "if" in conditional clauses and "provided that" in proviso clauses?
In Keller's Learn to Read Latin:
The conjunction dum, sometimes strengthened by the adverb modo, "only", may introduce a subordinate clause stating a provision under which the event of the ...
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Is there a system of logic which denies DNI?
From what I know, the law of double negation is often simplified as p <=> ~~p. Intuitionist logic splits the biconditional into DNI and DNE.
DNI: p -> ~~p
DNE: ~~p -> p
and denies DNE ...
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Why does no modal logic use an anti-symmetric (partial order) accessibility relation?
Several sources includes catalogs of many modal logics, often arranged into a lattice of inclusion, showing increasing power, from K to S5. Naturally, for each logic there is a corresponding ...
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https://proofs.openlogicproject.org/ - Double negation introduction - [duplicate]
How can we introduce double-negation? For example, p is the same as ~~p.
I am not able to find how to introduce ~~ in https://proofs.openlogicproject.org/
Is there anything like DNI, similar to DNE?
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What logical fallacy is made in this argument that seems to prove that learning is futile?
To learn is to gain more knowledge.
Having more knowledge means having more that one can forget.
∴, the more one learns, the more one forgets.
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Double-negation deduction rule in https://proofs.openlogicproject.org/
How can we use double-negation deduction rule?
For example, ~~p is the same as p.
I am not able to find how to eliminate ~~ in https://proofs.openlogicproject.org/
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Proof of A & B from ¬(A → ¬B) using rules of inference
I have been tasked with proving A & B from −(A → −B). However, I'm only allowed to use the following rules:
ModusPonens,
ModusTollens,
ConditionalProof,
DoubleNegation,
AndIntroduction,
...
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What are the arguments of philosophers against the reasoning which justifies the horseshoe from truth-functionality?
There is a reasoning in mathematical logic which is meant to prove that the horseshoe is the only logical operation which fits our notion of conditional.
The reasoning starts from the idea that the ...
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Essentialism and concepts
I've been reading an old logic text (Deductive Logic. George Stock. 1888) and he describes something very like Aristotle's notion of a definition, but in his description, it is clearly a matter of ...
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Modelling glass half full vs half empty using logic
Suppose we have a glass of water, and it is filled till half. One could either say, it is half full or it is half empty. These are two distinct propositions, but are complement to each other in some ...
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Do computers use logic?
I know we refer to computers as using logic, logic gates and the like, but is this just us ascribing human capacities to the machines? It sounds like a case of us giving more meaning to the machines ...
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Natural language into logic and proof
I'm working through Logic by Paul Tomassi, and there is one particular problem I'm stumped with. The problem is on pg 186 and involves representing an argument in English as a sequent and then ...
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Is there a logic with negation as (primarily) a binary relation?
The only search results I got for the exact phrase "negation as a binary relation" were a cryptic essay and/or book about "Chinese opposites." Now, what I have in mind is something ...
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ls elementary mathematical equality essentially a self-identity statement?
In a lot of places equality is defined that for two expressions A=B, A=B means that A and B have the same value (A=B). This relationship seems strange as we are slightly abusing use/mention, if '=' ...
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What to make of properties as unary relations?
Take for example the property or the unary relation, Man(x). It seems to "really" be a binary relation between x and {true, false} "under the hood." So would this make the notion ...
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Would the imaginary unit be the truth-value of sentences formed using √𝐧𝐨𝐭?
Section 4.3 of "Sentence Connectives in Formal Logic" discusses a concept of demi-negation or what is (for the sake of the text) resolved to a concept of "the square root of negation&...
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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 ...
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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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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 ...
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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 ...
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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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How is the common understanding of implication related with the logical one? [duplicate]
If I say $A=>B$ in real life, then one would think that from the antecedent, we can through some sequence of steps show that $B$ is true. That is, there is some theoritical connection between A ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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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