Skip to main content

Questions tagged [proof]

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

Filter by
Sorted by
Tagged with
-2 votes
0 answers
51 views

Why is the proof of Godel's incompleteness theorem wrong? [closed]

As for the proof of the incompleteness of the formal system, it is obvious that Mr. Godel has committed a low-level logical error, which is highly undesirable. First, he constructs a self-...
3 votes
1 answer
498 views

Why take Panpsychism seriously?

This question is about Panpsychism, but it is also a question I have more generally about the requirement for proof in philosophy. Panpsychism is the view that mentality is fundamental and ubiquitous ...
12 votes
16 answers
8k views

Can we logically prove that anything exists?

Suppose I want to prove that negative numbers exist. Well, I could easily do that using a mathematical proof. However, all I would be doing is adding another logical object to a list of known logical ...
5 votes
4 answers
845 views

Is it possible to show that something does not exist?

I am aware that I could show that something does not exist with the knowledge of an implication. If B is true if A exists, then A does not exist if B is false But if we have no implications, is it ...
4 votes
2 answers
128 views

Approaching the knowledge of knowing using premises

The only thing(knowledge) that I know is that I don't know anything/I know nothing. (Universal Quant.). Does this mean that I don't even know that I know to begin with? The only thing(knowledge) that ...
5 votes
6 answers
3k views

How to prove the world is real, and one isn’t just hallucinating everything? [duplicate]

I'm not asking whether other minds are real or not, I'm asking whether the whole shebang is "real". Google Gemini says it's impossible to know/prove it, and basically says to "move on&...
4 votes
1 answer
88 views

What is the Normal Form of Proofs in Intuitionist Logic?

I came across the concept of a normal form of proofs in Neil Tennant's A New Unified Account of Truth and Paradox (2015). I did a quick scan on SEP, and it seems to be a concept specific to his ...
0 votes
0 answers
79 views

Trying to prove ¬A ∨ B from A → B, but a bit stuck on how to end the proof

This is my first time trying out proofs, and I am not entirely sure what I am doing wrong, so criticism is happily received! My proof so far is as follows: A → B Subproof 1: 2. A ∨ ¬ A [Assumption ...
-1 votes
2 answers
77 views

How is this logic valid?

An excerpt from Logic 2010: In particular, what is confusing is that it permits assuming the conditional but then reaching a contradiction to prove the conditional. In my experience, that is not a ...
3 votes
1 answer
173 views

Converting a Euclidian proposition to a syllogism format

I am attempting to analyze Euclid's proof demonstrating that the interior angles of a triangle are equal to two right angles (book 1, prop 32). In particular, I'm looking for a way to convert the ...
0 votes
0 answers
55 views

Can someone help me with this? Logic using natural deduction

Does anyone know what I am doing wrong? I think I am missing how to pass line 12 of the subproof to the general proof. Can someone show me whats wrong? Thank you.
0 votes
3 answers
147 views

How do I prove the following? ¬(P → Q) ⊢ ¬Q

I am trying to prove this equation can anyone help?
2 votes
4 answers
256 views

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 ...
8 votes
19 answers
8k views

Do atheists bear the burden of proof in showing why/how the reasons presented by theists are unconvincing?

In conversations and debates between atheists and theists, is it enough for the atheist to assert that they are skeptical of theism without providing justification, or does the atheist bear the burden ...
3 votes
10 answers
288 views

Can science prove statements to be true?

I know that mathematics can prove certain statements to be true, which we call theorems. But what about science? Can science prove statements to be true? Note, just because a statement can't be proven ...
2 votes
2 answers
259 views

fitch proof. P v Q, Q→ ¬ R, ¬ P, ¬ R → ¬ S GOAL: ¬ S

Need help exercise using the FITCH program format. I'm stuck on where to start. The following 4 steps must be used to prove the goal. P v Q Q→ ¬ R ¬ P ¬ R → ¬ S GOAL: ¬ S Now I know: ¬ P and P v Q ...
4 votes
3 answers
588 views

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 ...
14 votes
8 answers
7k views

Does every truth have to be provable based on evidence?

I know the answer is "no" in general due to Gödel's Theory of Incompleteness, but I mean this question in a more real-world sense (i.e. scientific sense). In other words, I am talking about ...
1 vote
1 answer
51 views

Do the incompleteness theorems need the provability predicate to be expressed, or can they be expressed via just ⊢?

In his "Epistemic Set Theory," William Reinhardt says: It is the purpose of this paper to formulate axioms for Gödel's modal operator B for provability (see [3], [8]) in the context of set ...
2 votes
5 answers
761 views

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 ...
9 votes
9 answers
4k views

Do people who "withhold judgement" also have a burden of proof?

I will illustrate my question with several examples involving 3 individuals: A, B, C. Example 1: The shape of the Earth A defends the claim that the Earth is round. B defends the claim that the Earth ...
3 votes
9 answers
3k views

What is the burden of proof? Has this principle ever been challenged?

I have been surprised to find that some people doubt this principle. Onus probandi incumbit ei qui dicit, non ei qui negat - the burden of proof lies with the speaker, not with the one who negates. I ...
2 votes
2 answers
93 views

Can fatalism be disproved by fate-changing magic?

In a world where magic exists, fate-spinners are people with supernatural powers that influence the chances of events happening. Their power has been proven by countless experiments where they compare ...
4 votes
1 answer
3k views

Does software exist to automatically validate an argument?

I'd like to Derive logical arguments from English, and test their validity using a program. Does software exist for step 2? It would be fine if it were to give up because The validity isn't ...
1 vote
0 answers
86 views

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, ...
1 vote
3 answers
1k views

Is non-deterministic automated reasoning a viable strategy for solving problems in mathematical logic?

EDIT 2023/10/06 There are objections that this is too technical to be philosophy, and while I've seen questions on this forum go far beyond what I'm asking here in set theory, computability theory, ...
3 votes
1 answer
207 views

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&...
-1 votes
6 answers
479 views

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 (...
8 votes
10 answers
4k views

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 ...
5 votes
2 answers
610 views

Philosophical interpretation of the cut rule of Sequent Calculus

It seems that the cut elimination theorem of Sequent Calculus has some interesting consequences. Quote from Alain Lecompte, La logique linéaire et la question des fondements des lois logiques (French)...
1 vote
1 answer
90 views

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?
0 votes
0 answers
54 views

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
1 vote
0 answers
23 views

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/...
0 votes
2 answers
99 views

Fitch Question Please Help Me [closed]

I'm having trouble understanding writing out a proof. The proof I'm trying to work with is : How do I reach this goal? Which rules do I use and with which support steps to each rule (proofs to prove ...
-1 votes
4 answers
128 views

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 ...
0 votes
1 answer
89 views

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 ...
0 votes
3 answers
183 views

In what contexts or disciplines does "One may assume X" imply "One may ignore the possibility of any statement contrary to X being true"?

In computer programming, it has become fashionable for compilers (processors of computer language) to apply the following form of reasoning: A language standard would permit a compiler to assume that ...
2 votes
4 answers
3k views

How to prove ‘∃xP(x)’ from ‘¬∀x(P(x)→Q(x))’

What would a formal Fitch proof for this look like? I am given ¬∀x(P(x)→Q(x)), and need to derive ∃xP(x) from it. I started with this, but I don't know if I am doing the right thing, and where to go ...
-1 votes
2 answers
64 views

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 ...
0 votes
0 answers
43 views

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 ...
0 votes
0 answers
53 views

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 ...
3 votes
6 answers
533 views

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 ...
-3 votes
1 answer
135 views

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 ...
3 votes
15 answers
2k views

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 ...
4 votes
3 answers
1k views

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. ...
-1 votes
2 answers
431 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 ...
-2 votes
2 answers
136 views

I need help using the rules of implication/inference to construct a proof for the following argument: [closed]

I need help using the rules of implication/inference to construct a proof for the following argument: A ⊃ C D ~C ~A ● D KEY: Tilde (~) forms negations (“not,” “it is not the case that”). Dot (●)...
1 vote
0 answers
83 views

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 ...
0 votes
0 answers
82 views

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, &...
-2 votes
1 answer
50 views

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)...

1
2 3 4 5
7