# Questions tagged [proof]

For questions about the correctness of a proof or the nature of proofs in general.

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### Testing the validity of syllogism argument

I came across a validation method for testing the validity of a syllogistic argument which seems quite easier to grasp: For example: To test the argument: no P is B some C is B Therefore, some ...
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### How to do indirect proof (reductio ad absurdum) using natural deduction for modal logic?

I have been using Garson's Modal Logic for Philosophers, 2nd edition, to learn how to use natural deduction with modal logic. (BTW, does anyone know where there's an answer key for chapters 1 and 2 of ...
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### Why not move from proof numbers to theories instead of theories to proof numbers?

In mathematics, they do this thing where they figure out what are called "proof-theoretic ordinals" (see this section of the SEP article on proof theory for background details) of theories, ...
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### Peirce cuts (mirrored) + demi-negation = demisets?

[Note: I found one essay, about Aristotle, that used the word "demiset," although at a glance it seemed like they might've been substituting this terminology for a counterpart to the subset/...
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### Can someone formulate John Pollack's argument in understandable terms for laymen?

http://www.strongatheism.net/library/atheology/ontological_argument_for_nonexistence/ By the way, I am not asking whether this argument is sound or not. I just want to have it formulated in ...
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### Nested Quantifiers Proof - Logic

When I prove this: -∃x.P(x) ⊢ ∀x.-P(x) [True] I did it like that: ∀x.-P(x) ⊢ ∀x.-P(x) because (negative ∃) -∃x.P(x) becomes ∀x.-P(x) so that we can say that it's true. However, I didn't ...
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### How do logicians think of strength of proof systems?

I want to understand how logicians reason about strengths of proof systems and argue relative strengths of proof systems. I want to appreciate the validity of the reasoning by which we establish ...
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### Axiomatic Proof of Symmetry and Transitivity of Identity

Given the axioms below and the rules of Modus Ponens and Universal Generalization, how can you prove that t=s → s=t for any terms s and t? Additionally, how do you prove that t = s → (s = r → t = r) ? ...
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### What are some active areas of research in proof theory?

Is there any research activity going on in the field of proof theory today? If so, what are some of the most active areas, what types of questions do they deal with, and where can I go to find out ...
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### Does Gödel’s findings boil down to part of classical mathematics (as opposed to computation) is flawed?

According to artificial intelligence researcher Joscha Bach, only classical mathematics is affected by Gödel’s incompleteness theorem however not computation where calculations are performed in a step-...
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### Proof for predicate logic

Prove the following formula in Fitch format: ∃x(∀y(P(y)→y=x)∧P(a)) |= ∀x∀y(¬(x=y)→(¬P(x)∨¬P(y))) I tried to use universal introduction as my main rule but didn't know how to proceed
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### 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 ...
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### Does the preface paradox undermine long mathematical proofs?

Descartes, IIRC, somewhere says something about the vagaries of memory influencing our justification for believing in our memory, and thence for believing in proofs involving many steps that we have ...
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### Need help with this Symbolic Logic Proof please

I am having trouble solving this proof. Line 5 is wrong, I know it's Demorgan's Law, but the proof machine doesn't accept that as an answer. I think it only accepts ~Elim, vElim, vIntro, ~Intro, &...
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### is there such a thing as non-constructive computational “proof”?

For the problems which can’t modified into a constructive proof, is there some useful notion of proving them to some computational approximation? I’m referencing: “Interpretations come at a cost: for ...
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### Proving validity/invalidity of a modal argument

□(A v B) → (□A v □B) ...(1) This symbolic argument is intuitively invalid. In (1), if we replace B with ~A, then we see that though the antecedent is necessary, the consequent is a contradiction since ...
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### Is the following derivation of predicate logic correct?

I recently discovered https://proofs.openlogicproject.org/, except I'm still figuring out the appropriate rules that are needed for the system to check my proof. I thought it'd be quicker to turn to ...
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### Proof truth is absolute and not relative

First of all, I want to point out I am not any expert in philosophy, so this question is not based in no further readings, but only my own knowledge in logic. Imagine I want to proof the truth is ...
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### Is the included derivation feasible? If so, would my proof be correct?

The simple derivation seems correct and intuitive, and yet I feel as if something is off. I would greatly appreciate it if someone could double-check the provided formal proof. Thank you in advance ...
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### Computing Premises from Consequence

We write 'If A, then B' to mean that if A is true, then B must be true because B is a logical consequence of A i.e. it is impossible for A to be true but B to be false. Let us consider one such ...
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### fitch arrow proof

using the FITCH program and the FITCH derivation rules you should make a proof or derivation of C7 from P5 through P11. P5: ∀x∀y(StrongPref(x,y)→ ¬StrongPref(y,x)) P6: ∀x∀y∀z((StrongPref(x,y)∧...
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### why are ∀x(P(x)→ ∃y(Q(y)∧R(x,y))) and ∃y(Q(y)∧∀x(P(x)→(R(x,y))) not logically equivalent?

been sitting here for hours and still can't figure this out. is the order of ∀x and ∃y important in this case? all I can think of now is "all P is R of some Q", but I don't think this is right.
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### Using predicate logic, how to solve symmetric and anti reflexive

The networks is: A->B->C->D The channels used by the network are: lo, med, hi h-hi, l-lo, m-med i) A network uses one, and only one channel. ii) Networks within close proximity cannot both use the ...
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### 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 ...
-1 votes
2 answers
429 views

### Predicate logic proof solve

Provide a proof for the following using FOL in forallx Use the natural deduction system and proof strategies in forallx to provide a formal proof for the following . Please provide a picture of your ...
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2 answers
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### Help with Sentential Logic Proof

everyone. I'm running into real trouble figuring out the following sentential logic problem. (S v T) ⊃ (S ⊃ ~T) (S ⊃ ~T) ⊃ (T ⊃ K) S v T What we're supposed to get: S v K Any help that anyone might ...
-1 votes
1 answer
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### Fitch proofs help?

I'm new to logic and can see how to write these out informally, but need some help seeing how they should be translated into formal proofs in Fitch.
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1 answer
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### Help with Fitch formal proof?

I'm having trouble solving this formal proof in Fitch. I've put together most of it, but I think I need to use disjunction elim(?) at some point and am having trouble doing that.
-1 votes
2 answers
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### How would an philosopher and scientist solve the following kidnapping - scenario?

I would like to hear your opinion as philosophers and scientists regarding how you would solve the problem of proof in the following scenario: "Plato" who has dementia and a damaged left ...
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1 answer
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### 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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2 answers
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### 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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1 answer
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### 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 ...
-1 votes
4 answers
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### 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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1 answer
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### Proofs of propositional logic truth tree rules in natural deduction?

It is a great irony of natural deduction that some of the most seemingly obvious inferences are also some of the trickiest to prove! So far, I haven't been able to prove the following, and I'd greatly ...
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1 answer
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### 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). ...