Questions tagged [logic]

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

279 questions with no upvoted or accepted answers
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102 views

If-then statement and time between antecedent and consequent

Suppose the following statement. "If I kick the ball then the ball will hit the wall." Can this sentence have a truth value? I mean the time that I kick the ball, it hasn't reached the wall so the ...
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5answers
283 views

Does it hold that everything exists necessarily?

In Quantified modal logic, "constancy’s defenders can point to certain powerful arguments in its favor. Here’s a quick sketch of one such argument. First, the following seems to be a logical truth: ...
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How do I complete the remainder of this quantified Fitch proof?

This is where I get stuck, how do I finish this proof? I only have access to intro and elif rules, not DS or anacon or others.
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1answer
65 views

What counts as a logically necessarily true statement and what is not?

"If an existing population contains both mortal and immortal beings, some members of that population are not subject to death." Is this statement considered logically necessarily true? I personally ...
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2answers
126 views

Liar paradox from a different view/resolved?

Informally, the statement T: T: "this statement is not both true and not true" a) T is not true if and only if it is both true and not true b) T is true if and only if it is not both true and not ...
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0answers
80 views

Any minimal axiom systems that produced interesting mathematical theorems?

Hilbert was interested in minimal axiom systems for parts of mathematics, probably inspired by the debate over Euclid's parallel postulate and non-Euclidean geometries. Are there any examples outside ...
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1answer
30 views

Modal Logic Proof in System T

I need to provide an axiomatic proof of the following formula in System T of modal logic: ◇(A→□B)→(□A→◇B). Any advice on how to start would be great!
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1answer
66 views

Can you give other examples of skeptical hypotheses that haven't been mentioned yet?

I need some help with my philosophy homework. We were told to formulate our own skeptical hypothesis and use it as part of a radical skeptical argument, and that the skeptical hypothesis needs to be ...
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2answers
92 views

How to prove A<—>not A

So basically there are no premises, but the file I have received to start this problem has a contradiction symbol as step one. I’m not sure if this was a mistake or purposeful, and if it was ...
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1answer
50 views

prove using natural deduction truth functional logic

can someone help me with my practice problems pls prove using natural deduction truth functional logic A → (B → C), D → B ∴ A → (D → C) 1 A → (B → C) 2 D → B 3 A 4 D 5 ...
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1answer
80 views

Distinguishing arguments and explanations

For this question suppose that an argument is a rationale in which the reason presents evidence in support of a claim made in the conclusion, and an explanation is a rationale in which the reason ...
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1answer
38 views

Is RAA just MT?

If I say P and it leads to ~ Q then I have a false conditional . So imagine I want to prove ~ P then I show that Q is false as in If P then Q ~ Q ~ P We can do it the other way too If ~ P then ...
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1answer
126 views

Use the Fitch system to prove the tautology (p ∨ ¬p). Stalled for days (NOT duplicated)

First of all, please don't close this question cause I don't get the explanation given in: Use the Fitch system to prove the tautology (p ∨ ¬p) I have been trying to solve this exercise for days ...
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1answer
50 views

A Classical Notion of Dividing Travel Up into Infinite Divisions

1) A man wants me to go from a to b in a straight line. 2) Suppose he can, first he needs to go to (a-b)/2. 3) Suppose he can, secondly he needs to go to (a-b)/4. 4) There are infinitely many integers....
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1answer
365 views

Which problems do you consider as most important open problems in philosophy of mathematics?

At the "intersection" of mathematics and philosophy, or, rather, within their "union", surely some problems are still open and no general consensus is attained when those problems are discussed. ...
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1answer
591 views

Language, Proof, and Logic 14.11 Fitch Proof

Been stuck on this question for awhile now and I just don't know how to get Cube(x) so that I can use ^ intro with Cube(x) and ∀y (Cube(y) → y = a) and then use ∃ intro to get the conclusion. This is ...
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1answer
53 views

Existential Elimination in Fitch (Barber of Seville)

To be clear, I'm just struggling to understand why Fitch won't let me use EE. From other examples I've seen, I've set it up correctly for EE. I've also tried using BotE and EE on the desired sentence, ...
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3answers
70 views

A question about possibility

If A, then B ~ A So, possible that B Valid or not? My take: Not valid. Reason: Valid means if all the premises are true, the conclusion must be true That means adding new information should not ...
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1answer
211 views

Can something end which never began?

I was thinking that if life is infinite then it has no meaning. But if life began then the meaning of life must be for it to end. The meaning is in the future and since the last thing that will ...
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1answer
951 views

Can a sentence without a truth value be true?

I was doing some very, super, light reading on self reference. It seems to me that the statement nothing that I say is true both: cannot be understood with the T-schema; is self referential. - ...
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4answers
335 views

Language Proof & Logic 8.31 Fitch Proof

Been working on this one question for the past hours and I can't ever seem to get the last step working. Any help would be appreciated!
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1answer
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Should we define truth (given it exists)?

Should we, human-beings, try to define truth (given truth exists in reality)? Personally, I don't think we should reduce truth to symbols and syllables because I think it will take us into weird ...
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2answers
95 views

Fundamental Weakness in math?

Every proof in mathematics is an implication of the form A -> B where B is the proven statement and A is the premise (which can consist itself of many conjuncts like axioms, inference rules, theorems ...
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1answer
449 views

What is the difference between class and concept?

What is the difference between class and concept? − I am not sure whether, for instance, “chair” is typically a class or rather a concept, or both. I would say that it is only a class, though it is ...
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3answers
194 views

Is a 'creatio ex nihilo' logically impossible?

Please look if my following argument is correct, otherwise point to my mistakes! I distinguish two cases: We have nothing but logic, i.e. we have an empty set of premises. And here the answer seems ...
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1answer
491 views

Language, Proof and Logic Exercise 14.13 (Fitch)

Having trouble proving this. I know how to prove the first conjunct of the conclusion, but not the second one. Picture shown is the attempt proof of the second conjunct (rules haven't been added yet). ...
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0answers
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I need help to Derive F & G

Derive F & G F=G. Assump. F v G. Assump. ? G. F & G. & I 1-? Should l use disjunction elimination or biconditional elim. next? I am flubbered Help
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2answers
248 views

Is Classical Logic the proper model of the deductive logic of human reasoning?

Which mathematicians and philosophers unambiguously claimed that Classical Logic was the proper model of the deductive logic of human reasoning, and when did they say it? The expression "Classical ...
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2answers
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how to prove ‘¬∃xP(x)→(P(a)→Q(a))’ from no premises? fitch

I am totally lost on how to do this... can anyone help? What does it mean? I tried to understand what it means before proof but am totally clueless

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