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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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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 ...
PW_246's user avatar
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1 answer
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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 ...
Tim's user avatar
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7 votes
3 answers
1k views

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 ...
Kelvin Chan's user avatar
3 votes
2 answers
51 views

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 ...
Ken Presting's user avatar
-2 votes
1 answer
40 views

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?
DEE_GEE's user avatar
0 votes
1 answer
57 views

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.
Geremia's user avatar
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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/
DEE_GEE's user avatar
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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, ...
Noah Clarkson's user avatar
2 votes
1 answer
81 views

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 ...
Speakpigeon's user avatar
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6 votes
0 answers
67 views

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 ...
David Gudeman's user avatar
1 vote
3 answers
80 views

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 ...
Hopeful Whitepiller's user avatar
13 votes
12 answers
6k views

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 ...
adkane's user avatar
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2 votes
1 answer
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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 ...
Crest's user avatar
  • 21
4 votes
1 answer
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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 ...
Kristian Berry's user avatar
1 vote
1 answer
100 views

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 '=' ...
Confused's user avatar
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2 votes
1 answer
55 views

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 ...
csp's user avatar
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1 answer
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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&...
Kristian Berry's user avatar
0 votes
5 answers
133 views

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?
Leoucl's user avatar
  • 17
2 votes
1 answer
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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?
Ajax's user avatar
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2 votes
0 answers
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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," ...
Kristian Berry's user avatar
2 votes
2 answers
66 views

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 ...
user107952's user avatar
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6 votes
2 answers
298 views

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 ...
PW_246's user avatar
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1 vote
2 answers
88 views

"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 ...
UtilityMaximiser's user avatar
2 votes
3 answers
208 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 ...
Kamal Saleh's user avatar
1 vote
3 answers
84 views

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 ...
Dannyu NDos's user avatar
4 votes
2 answers
390 views

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 ...
Evi1M4chine's user avatar
2 votes
4 answers
462 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 ...
Mikayla Eckel Cifrese's user avatar
7 votes
9 answers
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?
user107952's user avatar
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0 votes
0 answers
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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 ...
Hopeful Whitepiller's user avatar
0 votes
2 answers
83 views

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 ...
user107952's user avatar
  • 4,198
4 votes
1 answer
117 views

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 ...
PW_246's user avatar
  • 299
0 votes
1 answer
67 views

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 ...
user65563's user avatar
3 votes
8 answers
7k views

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 ...
Eyeofpie's user avatar
  • 154
0 votes
2 answers
44 views

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 ...
eeqesri's user avatar
  • 127
1 vote
3 answers
123 views

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 (...
Frank's user avatar
  • 2,346
1 vote
1 answer
109 views

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 ...
Arian's user avatar
  • 263
0 votes
1 answer
106 views

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 ...
DarkNeos's user avatar
0 votes
0 answers
33 views

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 ...
Dennis Francis Blewett's user avatar
2 votes
2 answers
107 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 ...
Dennis Francis Blewett's user avatar
8 votes
3 answers
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 ...
Micrified's user avatar
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2 votes
2 answers
77 views

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 ...
David Gudeman's user avatar
-1 votes
2 answers
37 views

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 ...
Dennis Francis Blewett's user avatar
0 votes
0 answers
35 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 ...
Amin's user avatar
  • 37
5 votes
4 answers
1k 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 ...
John Forkosh's user avatar
0 votes
0 answers
38 views

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 ...
Kristian Berry's user avatar
2 votes
2 answers
105 views

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 ...
Firebirdofnercy's user avatar
1 vote
6 answers
149 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 ...
Hannah's user avatar
  • 19
5 votes
7 answers
460 views

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 ...
thecloud_of_unknowing's user avatar
0 votes
0 answers
72 views

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 ...
gradual_gradient's user avatar
4 votes
2 answers
175 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 ...
Hopeful Whitepiller's user avatar

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