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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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3answers
193 views

What happens if we accept inconsistency?

(Philosophy novice here and not sure how best to phrase this question; if it's unclear please point out the problems). Imagine this conversation: Alice: I believe that X. Bob: Do you also ...
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1answer
44 views

Logic : steps to prove valid reasoning

I am very new to this and I can't figure out the steps to prove that these reasonings are valid. Thank you for your help. p ¬r p → (q→r) ___________ ¬q (¬p ∨ ¬q) → r p q __________ ...
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1answer
3k views

Zeno's arrow paradox

Zeno's arrow paradox: Zeno states that for motion to occur, an object must change the position which it occupies. He gives an example of an arrow in flight. He states that in any one (duration-less)...
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0answers
18 views

What did Nietsche mean?

What does, Nietzsche in Beyond Good and Evil, mean exactly when he states: Whoever fights monsters should see to it that in the process he does not become a monster. And if you gaze long enough into ...
5
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2answers
222 views

Are the “laws” of deductive logic empirically verifiable?

"Is Logic Empirical?" strongly suggests a question that I would like very much to get a handle on. That phrase is a title of an article by Hilary Putnam, and, according to synopses/reviews, the ...
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0answers
107 views

What is will and intelligence if we just obey chemical reactions? [on hold]

Suppose chemistry dictates our thoughts i.e cognition, learning, thinking, understanding, mood and behaviour are greatly affected and explained by molecular biology; what is “our” role, are we any ...
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0answers
53 views

Does ∀x True(x) ↔ ⊢ x complete Tarski: ∀x True(x) ↔ φ(x)? [on hold]

Philosophy of Logic – Reexamining the Formalized Notion of Truth Because formal systems of symbolic logic inherently express and represent the deductive inference model formal proofs to theorem ...
2
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5answers
106 views

Does the individual meaning of two propositions determine or constrain what kind of logical connectives can be formed between them?

What is the basis for the definition of logical connectives? Are they just arbitrary convention? Or does it depend on the meaning of the constituent propositions? Does the individual meaning of two ...
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7answers
12k views

What is the difference between Law of Excluded Middle and Principle of Bivalence?

Law of Excluded Middle: In logic, the law of excluded middle (or the principle of excluded middle) is the third of the so-called three classic laws of thought. It states that for any ...
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2answers
57 views

What irreducible functions constitute thinking?

Because all new knowledge, to be not illogical, must obey logic i.e. every thinking step must be consistent with rules of logic; so can we write an effective procedure/algorithm which may be followed ...
2
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4answers
121 views

Is math arbitrary?

Math at its core begins with calling something true or false and following logic. WE for example call an odd number 2n+1, but what if we called an odd number 2n and flipped it for it to become an even ...
16
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7answers
6k views

What's the name of the logical fallacy where a debater extends a statement far beyond the original statement to make it true?

Suppose that someone initially states that "fossil fuel consumption due to mobile phone usage is similar to that of private transportation, so if you think we should switch to electric/bike to fight ...
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0answers
35 views

Can you help me tackle this question by giving formal proof using natural deduction

Using the natural deduction rules, give a formal proof that the following three sentences are inconsistent: ¬P∨Q ¬P→Q ¬Q
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1answer
38 views
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2answers
356 views

Why is it logical to invoke an uncreated universe with no intelligent design?

How can an atheist invoke an uncreated universe with no intelligent design and assert its logical consistency? Why is it logical? By moving the goal post to aliens seeded earth from another universe,...
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6answers
3k views

Is God either immoral or not omnipotent?

The usual (Christian) justification for suffering/evil in the world created by a benevolent God is freedom of the will. However, the more interesting question is not about the source of evil (which ...
1
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1answer
58 views

Lists and predicates on lists in classical first order logic

I have to express some basic Prolog code in classical first order logic (FOL). In Prolog i use lists, together with member/2 and append/3 a lot. Could you give me some tips for writing clauses like ...
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2answers
463 views

We do everything for pleasure

I have been in debate for a while now with me friend. I come here looking for feedback and possible outlooks to related sources. The question we posed a long time ago is interesting one: why do we ...
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1answer
48 views

How to solve A ∨ (B ∧ C), A → C |— C using Natural Deduction? (Conclusion is C) [closed]

This question has been troubling me for days. Kindly help with it. The conclusion is C for A ∨ (B ∧ C) and A → C
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0answers
40 views

Please what do we call this type of hypothetical statement?:

"It is certain you have a nose when you can smell but not everyone with a nose can smell". Or "It is certain you have a brain when you can think. But not everyone with a brain can think" Note: As I ...
3
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1answer
66 views

Hume: excavating the is/ ought gap

Why does Hume believe that ought brings a new relation? If means-end reasoning, where we can say that one is ought to do X in order to get Y, does not bring a new relation, then in order to tell that ...
15
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4answers
774 views

Name for reverse Ad Hominem, (i.e. praising the defense)?

Is there a standard name for a fallacy of the same form as an ad hominem, except that instead of denouncing the opposition, it praises the defense? Typically an ad hominem ("against the man") fallacy ...
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2answers
54 views

Fitch-style natural deduction

How to prove the following questions? (a) p from assumption ¬(p → q) (b) ¬¬p → p from no assumptions.
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1answer
65 views

Trying to decide if the terms “proper education”, “real world education”, “successful life” are vague or ambiguous?

I feel like for all three of these terms, they can contain different meanings, but they are all vague as well. For example, proper education could mean a university education/college education/...
3
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1answer
87 views

Is b⊢C∧¬b⊢C∧b⇒C∧¬b⇒C possible?

Are there any cases where b and C are real world statements where b⊢C∧¬b⊢C∧b⇒C∧¬b⇒C where b and C are not tautologies? It may seem like a silly question, but after searching hard and deep, I couldn't ...
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1answer
46 views

A Problem With Kripke's Rule-Following Paradox Example?

It seems that there is a problem with the example that Saul Kripke gives in "Wittgenstein on Rules and Private Language" to explain Wittgenstein's rule-following paradox. I'm not asking about the ...
4
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1answer
84 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 ...
2
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1answer
73 views

What is the name of the “undeserved profits” fallacy?

I see this type of inference made a lot, for example in the context of distributional justice: A makes an investment. He thinks this investment was a rational decision, until he learns that B also ...
2
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0answers
43 views

Prove that if the tree method determines that a set of sentences T implies a sentence A, then T does in fact imply A

Having trouble wrapping my head around how to prove this. My first question about this is what it means for the tree method to determine that the set of sentences implies A. I'm taking it to mean that ...
2
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3answers
172 views

Logic. Truth of a negation

If I say: If I am paid today I'll go to the party tonight I am saying that if I receive a payment today I will go to the party tonight. But if I am not paid, can we conclude that I am not going ...
8
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1answer
149 views

What is the difference between depth and surface information?

I was looking for an answer to this question: Was Euclid's method of proof axiomatic? While doing so I ran across an abstract of Jaakko Hintikka for an article "What is the axiomatic method?" ...
3
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1answer
191 views

Is the problem of logical omniscience intractable?

Vincent Hendricks and John Symons notes the following about epistemic logic: Epistemic logic gets its start with the recognition that expressions like ‘knows that’ or ‘believes that’ have ...
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0answers
69 views

Given the principle of innocence, how shall we explain logic's usefulness?

I have been reading Florian Steinberger's dissertation (Harmony and logical inferentialism) and I come across the following on p60: ...two fundamental assumptions (the other one being the principle ...
3
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1answer
780 views

Is it possible that a question has only two answers?

□ yes □ no "no" implies that a closed system with only two options like the one above is impossible. If you accept that such a system is possible by the way, it generates paradoxical results, since ...
1
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1answer
65 views

De Morgan for Quantifiers Formal Proof: Inhabitance Question

I have a problem reading existing question's answers. I've successfully encoded the proof of one of De Morgan's Laws, ¬∃x P(x) → ∀x ¬P(x), for Quantifiers formally via cubicaltt type-checker via Curry-...
1
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1answer
69 views

De Morgan for Quantifiers Formal Proof: ∀∃-intro and -elim Questions

I have a problem reading existing question's answers. I've successfully encoded the proof of one of De Morgan's Laws, ¬∃x P(x) → ∀x ¬P(x), for Quantifiers formally via cubicaltt type-checker via Curry-...
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11answers
7k views

Where is the fallacy here?

Where is the fallacy here: whatever is natural is not unnatural whatever is unnatural is not natural the phenomenon of cats being born into this world is natural the phenomenon of rabbits being born ...
4
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1answer
153 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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1answer
59 views

practical example of Limitations of Predicate logic [closed]

Discuss the limitations of predicate logic. Cite practical example to support your answer.
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1answer
164 views

How does a truth tree provide positive and negative effect tests for implication?

I'm trying to prove that the truth-tree method can be used to give a positive effect test for implication, and a negative effect test for non-implication. I've been given the fact that The truth-tree ...
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1answer
32 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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1answer
64 views

trouble with rules of inference practice problems [closed]

Prove the following symbolized arguments applying the appropriate rules of inference: 1) P ∨ Q = M ⊃ ¬ Q M =conjunction Therefore P 2) (P V Q) ∧ ¬ Q P ⊃ R =...
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2answers
90 views

When is reasoning with “unknown” knowledge permissible?

When is reasoning with "unknown" knowledge permissible? E.g. when can one "legitimately" formulate political beliefs or laws based on knowledge, which contains unknowable, unpredictable parts? If ...
2
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0answers
148 views

Why is Psychologism invalid according to Husserl?

I am having a difficult time understanding the critique of psychologism. From Dan Zahavi's book Husserl's Phenomonology: Logic (as well as, for instance, mathematics and formal ontology) is not ...
4
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5answers
458 views

Validity stemming from contradictory premisses

I'm a student new to the study of logic, and having had my first tutorial on it yesterday, while I generally understand the characterisation of logical validity, there were a couple of examples my ...
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0answers
92 views

Why don't two equivalent propositions contribute to the same semantics?

We often have 2 propositions that have the same truth table, in that they are true and false given the same conditions. Nevertheless, we still feel as though there different semantics (i.e meaning..),...
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11answers
14k views

Is it a fallacy if someone claims they need an explanation for every word of your argument to the point where they don't understand common terms?

Is it a fallacy if someone claims they need an explanation for every word of your argument to the point where they don't understand common terms? For example, suppose someone said, "If a dog bites ...
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1answer
120 views

Inferring from (∃x)Fx to (∃x)(∃x)Fx using existential generalization?

I was introduced to EG as follows (for some name 'a'): One can infer from Fa to (∃x)Fx. But today within a proof my professor posted he used EG to infer from (∃x)Fx to (∃x)(∃x)Fx. I'm not sure how ...
8
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1answer
390 views

If turtles see everything, and nothing seen can see, does it follow that non-turtles exist?

Consider the following argument: Turtles see everything. Seeing is asymmetric (for the sake of argument). Therefore, something is not a turtle. I have problems symbolizing these statements. My ...
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4answers
2k views

What is the role of common sense in logic?

In Logic by Wifred Hodges he says [..] you must rely on your common sense - as always in logical analysis. So i'm confused (again!). What has common sense to do with logical reasoning? My previous ...