Questions tagged [logic]

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

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1answer
315 views

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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4answers
586 views

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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1answer
365 views

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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6answers
1k views

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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3answers
108 views

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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4answers
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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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2answers
86 views

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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0answers
39 views

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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2answers
253 views

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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4answers
240 views

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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1answer
87 views

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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67 views

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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1answer
108 views

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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3answers
585 views

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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3answers
631 views

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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0answers
131 views

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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2answers
169 views

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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4answers
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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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12answers
15k views

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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1answer
102 views

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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0answers
102 views

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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1answer
202 views

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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48 views

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 (...
4
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3answers
234 views

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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2answers
73 views

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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1answer
98 views

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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72 views

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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1answer
148 views

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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1answer
57 views

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 ...
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1answer
111 views

Why cannot the following theory be refuted by logic but is rejected because of lack of empirical support?

The following statements are taken from a book: The man in the street, and also the philosopher K. Marbe, believe that after a run of seventeen heads tail becomes more probable. This argument has ...
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1answer
115 views

Can you imagine a completely different logical/mathematical system than that we have?

Can you imagine a different logic and mathematics? For example, with a different arithmetic, or even a universe with no logic or mathematics and contradictions? A non consistent system?...
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2answers
161 views

Quantum mechanics and the principle of bivalence

Does quantum mechanics, due to the phenomenon of superposition (Schrodinger's cat is both dead and alive), give reasons to alter the laws of logic, specifically the principle of bivalance (something ...
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1answer
618 views

Gödel's incompleteness theorems - what are the religious implications?

Apparently Kurt Gödel believed that his incompleteness theorems have some kind of religious implications. Despite Gödel's belief in a personal God, this was still somewhat surprising to me. ...
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Logic-related note-taking question

I have been thinking about note taking from a logical perspective recently. It started when I realized that note-taking is basically a process of extracting "statements" or "arguments" from a piece of ...
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1answer
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To pass two time for the same place. Logic question [closed]

Let be the proposition: "To visit two times the same place is forbidden". It is forbidden to visit the same place three times? A says: "No, because it is forbidden to visit the place two times". ...
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2answers
201 views

What is the meaning of “comprehension” in logic?

I was reading about the axioms of Zermelo-Fraenkel set theory and the axiom of restricted comprehension. This led me to find out what the meaning of this word is and why it's called this. Then I saw ...
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1answer
275 views

How to Prove P(a) → ∀x(P(x) ∨ ¬(x = a)) using Natural Deduction

How would a formal Fitch proof look like. I am given P(a) → ∀x(P(x) ∨ ¬(x = a)) to prove using Natural Deduction of predicate logic. I am confused on how to proceed with the proof. Please advice me ...
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1answer
44 views

How would you describe it when someone uses the hypothetical to undermine an idea?

Here is the scenario. I'm working with a different technology for programming and I present it to my co-worker who is not up-to-speed on the new technology. He replies that there may be some ...
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2answers
5k views

Is there a concept that relates to the idea of a “snuck premise”?

In this video around 6:00 into it, Charisma on Command channel, "7 Reasons Ben Shapiro Is So Dominant in Debates" https://www.youtube.com/watch?v=JY5t6iUzajk the concept of a "snuck premise" is ...
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8answers
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How is the claim “I am in New York only if I am in America” the same as "If I am in New York, then I am in America?

It makes absolutely zero sense to me. It would make sense if "I am in America" is the antecedent and the consequent is the former. Even though it wouldn't be sound, it would make logical sense. I ...
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3answers
71 views

Relationship between entailment and equivalence with consistency

If A entails B, why is it not true that A is also consistent with B? Given the definition requires A and B to be able to be true at the same time.
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0answers
89 views

If logical propositions aren't tautologies (a la Wittgenstein), then what could they be?

This is a historical question about philosophical views. I believe I understand the claim made by Wittgenstein and others that logical propositions are tautologies. I'd like to know what other views ...
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3answers
153 views

When is a connective truth functional?

I got this question from Logic, laws of truth, by Nicholas J.J Smith. He says (page 24) : "A connective is truth functional if it has the property that the truth or falsity of a compound ...
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2answers
995 views

Given P ∨ ¬ P prove (P → Q) → ((¬ P → Q) → Q) by natural deduction

I am very new to proof and logic and I would really appreciate a rundown of this proof. I use a program called Fitch to construct my proofs. I understand there are two types of proofs. Direct ...
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2answers
488 views

What is the difference between NTP and validity in Smith's “Logic: The Laws of Truth”?

The book I got this question from is "logic, the laws of truth" by Nicholas j.j smith. "Necessary truth preserving" (NTP in the book) is defined as the property that an argument has when it is ...
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5answers
1k views

Are there exceptions to the principle of the excluded middle?

It is inherent in our truth tables that we configure a statement to be either true or false, but it seems that this might have certain exceptions, especially in conditionals. For example, the ...
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2answers
224 views

What does Wittgenstein mean when he says “there are no numbers in logic”?

From the Tractatus: 5.453 All numbers in logic stand in need of justification. Or rather, it must become evident that there are no numbers in logic. There are no pre-eminent numbers. What does ...
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88 views

The illogical nature of want/motivation and its effects on free will

Are all the decisions and desires of humans made in order to stimulate pleasure centers and avoid pain? If so, could someone/thing which is unable to feel pleasure and pain, and only had the power of ...
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2answers
152 views

How can we be accountable if we are chemically programmed?

If we accept that molecular biology largely explains cognitive function deterministically, how can we be accountable? Is determinism not inherently nihilist in that a person is a victim of ...
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3answers
519 views

Is it a fallacy to claim someone is committing a fallacy without explaining why?

Making use of an argument about a subject X, Person 1 presents his view to Person 2. Then Person 2, who is against that position, simply makes the following claim: "Hey dude, you have committed the ...