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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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1answer
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How to solve A ∨ (B ∧ C), A → C |— C using Natural Deduction? (Conclusion is C) [on hold]

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
37 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 ...
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0answers
30 views

Prove that if the truth tree method determines that a set of sentences gamma does not entail A then gamma does not entail A [on hold]

I’m on shaky ground right now in logic and I have no idea on how to start writing this proof. Please help. (It’s the third question) thank you!
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2answers
48 views

Fitch-style natural deduction

How to prove the following questions? (a) p from assumption ¬(p → q) (b) ¬¬p → p from no assumptions.
3
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1answer
79 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 ...
1
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1answer
45 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 ...
2
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0answers
42 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
166 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 ...
4
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0answers
63 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 ...
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0answers
93 views

How many logicians worldwide? [closed]

How many active researchers today have specialised in logic? I include in this population all mathematicians, philosophers, linguists and computer scientists (who else?) whose main activity is the ...
2
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1answer
70 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 ...
3
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1answer
771 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 ...
4
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1answer
81 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
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
58 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
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 ...
1
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1answer
62 views

trouble with rules of inference practice problems [on hold]

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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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 ...
2
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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..),...
5
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1answer
119 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 ...
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0answers
67 views

The Curry-Howard correspondence & Classical Logic

The Curry-Howard correspondence is supposed to show that a computer programme is effectively equivalent to a formal logical proof. However, I would expect that the correspondence is really between a ...
8
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1answer
382 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 ...
3
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2answers
131 views

Which logical fallacy is this: A is a C, B is a C, therefore A is a B?

Does this kind of logical fallacy have a name? Apples are fruit. Oranges are fruit. Therefore, apples are oranges. I'm guessing it's a particular kind of statistical syllogism?
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2answers
64 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 ...
35
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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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3answers
82 views

What are some of the paradigm shifts in how we think about logic and rationality in the history of philosophy [closed]

I am wondering if there was any shift or big revelations about logic that occurred in the history of philosophy. I am thinking it's highly likely, because if you read some of the thinkers during ...
2
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2answers
92 views

Does this idea have a name: “A is a type of B, but B is not a type of A”

This question has been touched on in other questions but not answered in a way that fully answers my own question. Like here: Argument "a is b" but "b is not a" valid? What is ...
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16answers
13k views

I have trouble understanding this fallacy: “If A, then B. Therefore if not-B, then not-A.”

About "If A, then B. Therefore, if not-B, then not-A": From what I understand the conclusion is wrong, because it is not said that A is a sufficient condition for B, (and there may be other ...
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0answers
94 views

If A is used to do x, when is x related to A? [migrated]

There is a meta aspect to this question. Let's say Stack Exchange A allows questions about A and its uses. The question may take the form of: is it legal to use A to do x? The answers can be: Yes No ...
0
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3answers
52 views

Multiple connectives using atomic sentences?

Can you use multiple connectives in atomic sentences? For example, consider the following transcription guide: A. The New England Patriots are the best team in the NFL. B. The New England Patriots ...
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2answers
40 views

Proof with conditional introduction

Below is a screen-cap of part of a video where a proof using conditional introduction is shown, which is proving under certain assumptions that given A is true, then the adjacent sentence is also true....
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4answers
166 views

A difficulty I've had with this “This sentence is false” and Russell's Paradox [closed]

I'm not sure if I'm engaging in some sort of circular logical trap but I don't really think "this sentence is false" is all that logically problematic. But it would be helpful if someone could fix up ...
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2answers
202 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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2answers
1k views

Is the following statement true, false, or can't be determined? Why?

"If it snows and we don't have school, then (x^3)<0 implies x is negative" (Assume x is a real number).
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1answer
55 views

What would be the negation of the following statement

"I sometimes work on Monday night" I'm struggling with the word 'sometimes'. Any advice on how to deal with this word?
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2answers
69 views

I need some help determining the validity of the following argument

“I got the highest grade on the last test and I have perfect attendance. If I get a cold, then I miss at least one class. I came down with a cold. Therefore, if I missed at least one class, then I ...
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5answers
161 views

Is an argument in natural language as logically valid as in formal logic?

Is a natural language philosophical argument which is argued strictly from first principles widely considered equally as valid as a proof written in formal logic?
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1answer
51 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 ...
2
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2answers
117 views

Prove or disprove ~◇◻p → ◇◇~p in system K

How to start with the following proof? Any help would be appreciated. I have tried by assuming the left side is true, however, I get confused with the negation. ~◇◻p → ◇◇~p
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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/...
0
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2answers
122 views

Known self-evident unproven logical truths

Is there any authoritative source for all known self-evident logical truths that most specialists would agree are true although they can't be proven? There are many different axiomatic systems, and ...
4
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2answers
374 views

Does S4 (and B) hold for the strongest interpretations of ♢ and □?

Suppose these are the interpretations we are working with: ♢Ψ iff no explicit contradiction can be deduced from Ψ in FOL or in other words it's not provable that ~Ψ in FOL. ~♢Ψ iff an explicit ...
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2answers
89 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 ...
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2answers
55 views

Truth-functional connectives - functions of what exactly?

In a recent piece of work I described sentences containing a specific natural language connective as ᴛʀᴜᴛʜ ғᴜɴᴄᴛɪᴏɴᴀʟ. More specifically, I wrote something along the lines of [wording changed to make ...
3
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1answer
49 views

Does 'until' imply a conditional with a negative consequent?

Suppose a father tells his kid that he can play video games whenever he wants. Then, one day, when the kid fell sick, the father told him that he can play video games until he recovers. Does this '...
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4answers
83 views

Illustration of Necessary & Sufficient Conditions [closed]

What is the clearest and most concrete illustration of the difference between Necessary & Sufficient Conditions found in an office setting?
2
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1answer
42 views

Null Hypothesis Appearing in Everyday Life [closed]

What are examples of a Null Hypothesis we use in everyday life but do not recognize?
2
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1answer
60 views

Who invented definitions?

Is an intensional genus–differentia definition an invention of ancient greek philosopy? "Chair is a seat typically having four legs and a back for one person" Have you seen definitions like this ...
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0answers
64 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 ...
6
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1answer
231 views

Why is a predicate of 0-arity considered as a sentence letter?

I often find that nullary functions are considered constants and 0-arity predicates are considered sentence letters. What is the intuition behind that notation?