Questions tagged [proof]
For questions about the correctness of a proof or the nature of proofs in general.
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Proof of the existence of God?
Here it is, the long-awaited proof for the existence of God (for your consideration).
I have taken the liberty of defining discretely what God is, without which there is no question to be answered (...
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Does theism have the burden of proof?
I have heard that agnosticism seems to be the only position with respect to god that doesn’t have a burden of proof. What I find troubling about this is most people do not as a practical matter think ...
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Is there a way to confirm something material is infinite?
Mathematics is full of immaterial examples of infinities. However, is it possible to confirm or prove something material is infinite? Or, can we only conjecture they are?
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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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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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Would the imaginary unit be the truth-value of sentences formed using √𝐧𝐨𝐭?
Section 4.3 of "Sentence Connectives in Formal Logic" discusses a concept of demi-negation or what is (for the sake of the text) resolved to a concept of "the square root of negation&...
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Is the idea of weak and strong evidence incoherent?
Hypotheses are either true or not. Justin is either a murderer or not. There is either a God or not.
If statements are either true or false, how can it be the case that certain forms of evidence ...
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Why do some proof method feel more satisfying than others?
Let's say we are asked to show that 1+2+3.. =n(n+1)/2, then a very simple way to prove this is to use induction. The proof is simple, consider P(1) and show P(n+1) from P(n). However, it feels quite ...
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Is solipsism truly unprovable?
I know I’ve asked a lot of these but this one I’m hoping to be definitive.
I have heard pretty much everyone say that it’s unprovable, that you can’t know for sure if it’s true or not because of 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 ...
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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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Does this proof of God I made work? [closed]
I worked up this proof of God, and I want to know if the proof works. Here is the proof:
Something which is unlimited is limited by not having limits. If limits were to be imposed on something which ...
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Is game-theoretic semantics in logic more consonant with LEM than ~LEM?
When someone plays a game, they are minded to try, at least, to score points in the game (even if there is no final score but one can simply try for a higher score each time one plays), and often ...
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Why is Diogenes the Cynic's solution to Zeno's Dichotomy Paradox insufficient?
According to Wikipedia's discussion of Zeno's Dichotomy paradox (emphasis mine),
According to Simplicius, Diogenes the Cynic said nothing upon hearing Zeno's arguments, but stood up and walked, in ...
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Proving God and believing only provable things
This question has two, related, parts.
Part 1.
I recently have been on some discussions regarding proving God exists and proving that Jesus is really the son of God; intertwined with that, there was a ...
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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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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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Fitch Proof Help, Conclude ~B from ~(A > B) [closed]
I'm in the process of learning fitch proofs and I've come across one I'm having trouble setting up.
Premise: ~(A > B)
Goal: (A & ~B)
In other words, it looks something like this:
1 | ~(A > B)...
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How to argue statistics using logic?
Typically in logic, we have the axioms as facts which are 100% true but in statistics we have things which are true sometimes. For example, "the coin is heads" is true 50% of the time when ...
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What is the relationship between algorithms and logic?
Is an algorithm (cooking a dish, Grover's/Shor algorithm, etc.) a form of deductive reasoning or inductive reasoning, and if not what exactly is the relationship between an alogorithm and logic?
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Can we doubt all knowledge?
Can we doubt all knowledge from all sources (perception, reports, and reason)?
Regarding doubting reason, reason can't be proven, it is preceived and judged instantly by our logic, but what if our ...
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What, if any, are the most important claims to be considered proven in the absence of observation; ie: claims derived from logic alone?
This question arose during contemplation of whether free will and/or moral responsibility might ever be proven real or illusory.
Galen Strawson has proposed a proof for the impossibility of moral ...
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I've been working on this for way too long :/
I've made a lot of progress on the proof below, but I am stuck on the last steps where I need to add existential quantifiers back in: ¬∃x ∃y Smaller(x,y)
For context, I'm a logic novice, but I'm ...
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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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What is the Difference between a Claim and a Fact? [closed]
I know for a fact a computer must somehow add numbers but since I can only suggest it, it is forced to be a claim.
In that case, how could I ever state anything as a fact if I can only ever claim it?
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Is the debate on free will over? [closed]
I've never posted on here but I am interested in philosophy. I think a lot about free will / determinism / compatibilism. I always felt like I have some degree of free will. I know free will is ...
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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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Gödel’s Incompleteness Theorem: How can truth go deeper than proof?
My current understanding:
Math starts with a set of basic (purportedly self-evident) statements that are taken as a given without the need to prove them true, like e.g., a + b = b + a etc. Such ...
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Reading list to build a proof-based foundation in ethic
How to tell right from wrong, good from evil, and just from unjust? How to define what is moral, what is not? Given a situation, what actions is neither animal-like nor machine-like, but human? To ...
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Natural Deduction Proof with double quantifier (predicate logic) [closed]
Premise: (∃y)(∀x)(Px v Py)
Conclusion: ~(∀y)(~Py)
I'm starting out assuming the negation, i.e., (∀y)(~Py).
But then I'm unsure how to find a contradiction within that subderivation. Here's what I've ...
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How should we characterize the logical structure of wishes?
The motivation for this question is extraordinarily stupid, but it requires just enough thought and specific knowledge of formal logic that I think it still falls within the broad scope of "...
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Understandable definition of time
What is a thorough definition of time in terms of how it causes the universe to progress and only moves in one direction? Is something as abstract as time comprehendable to us beyond a measurement? ...
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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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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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How to understand a proof by contradiction in minute detail?
I am following the course "Language, Proof, and Logic" from Stanford on EdX. I am trying to understand proof by contradiction specifically. I understand the gist of this type of proof, and I ...
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Help me solve this predicate logic proof theory: -(∀z)(∃y)Tzy ⊢ (∃z)(∀y)-Tzy
-(∀z)(∃y)Tzy ⊢ (∃z)(∀y)-Tzy
Using Lande, (AI,EI,AE,EE,->E,->I,-I,--E,^I,^E,vI,vE) I cannot figure out the proof on this sequent.
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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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Does ◇◇A mean ~◻~~◻~A? If so is it by definition or it requires a proof?
In system K, ◇A is defined to mean ~◻~A. Therefore, it is very tempting to conclude ◇◇A means ~◻~~◻~A. But I am not certain whether this is valid conclusion to make, because in ◇◇A, the main operator ...
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Proving ~◻p → ~p in System K [closed]
I am working on a proof of ~◻p → ~p in System K. It says "If it is not the case that p is necessarily true, then p is not true". I have turned all the abbreviated symbols into their ...
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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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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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What are sufficient grounds for establishing a theory?
This question delves into the definition of a theory, but somewhat into the grounds of Set Theory as well. I was wondering on what grounds is theory established and accepted. To what degree do the ...
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Is the Categorical Imperative Simply Bad Math? :)
The title is clickbait, but the question is not.
First, The Categorical Imperative:
Act only according to that maxim whereby you can, at the same time, will that it should become a universal law.
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Proof for the absence of free will?
EDIT (17/08/2022): I have answered this question with an evolution of the argument. See accepted answer below.
There are a number of arguments which aim to prove the impossibility of free will.
The ...
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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 ...
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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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Why are there problems we don’t know how to solve?
For example, there is a simple deterministic algorithm for determining whether any given number is a perfect square. But why don’t we know how to solve things like the p vs np problem or the collatz ...
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When can we have certainty in what we claim to know?
This is a question that my friends asked me a few times. I am confused, because I have been trying to answer this question myself, but I can't seem to come up with any valid answer. For example, what ...
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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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