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
3 answers
111 views

How do you prove mathematical induction without the notion of a set?

In most books on mathematics, they state the principle of weak mathematical induction without proof. I have a book on logic, which proves weak and strong induction using the notion of infinity, and I ...
lee pappas's user avatar
  • 1,278
1 vote
4 answers
191 views

How can objects be nonexisting?

A square circle. Obviously, this is contradictory, but i feel odd saying it doesnt exist as well. thats not the bestw ay to say it. but, then again, whatg do we even mean in mathematics or logic by ...
Lawrence Lee's user avatar
3 votes
1 answer
505 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 ...
Aph002's user avatar
  • 141
4 votes
2 answers
130 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 ...
How why e's user avatar
  • 1,418
4 votes
1 answer
93 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 ...
confusedcius's user avatar
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&...
Artem S. Tashkinov's user avatar
-1 votes
2 answers
79 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 ...
user129393192's user avatar
3 votes
1 answer
176 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 ...
user73163's user avatar
0 votes
0 answers
57 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.
rosa_melano's user avatar
0 votes
3 answers
149 views

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

I am trying to prove this equation can anyone help?
rosa_melano's user avatar
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 ...
a complete thought's user avatar
1 vote
1 answer
52 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 ...
Kristian Berry's user avatar
3 votes
10 answers
293 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 ...
user107952's user avatar
  • 7,192
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 ...
Mark's user avatar
  • 6,037
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 ...
Meanach's user avatar
  • 2,385
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 ...
Mark's user avatar
  • 6,037
2 votes
2 answers
94 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 ...
Zachiel's user avatar
  • 123
1 vote
0 answers
90 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, ...
Kristian Berry's user avatar
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, ...
J D's user avatar
  • 28.5k
-1 votes
6 answers
495 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 (...
Jordan Cote's user avatar
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 ...
user avatar
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?
Jérôme Verstrynge's user avatar
0 votes
0 answers
55 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
Richard Gasquet's user avatar
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/...
Kristian Berry's user avatar
3 votes
1 answer
209 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&...
Kristian Berry's user avatar
-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 ...
user avatar
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 ...
Babu's user avatar
  • 2,188
2 votes
5 answers
833 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 ...
DarkNeos's user avatar
-1 votes
2 answers
65 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 ...
Dennis Francis Blewett's user avatar
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 ...
Kristian Berry's user avatar
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 ...
Kristian Berry's user avatar
-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 ...
Matt K's user avatar
  • 9
4 votes
3 answers
625 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 ...
Robert Columbia's user avatar
2 votes
4 answers
267 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 ...
Bernardo Benini Fantin's user avatar
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 ...
Bernard Eakins's user avatar
0 votes
0 answers
83 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, &...
GarretBobbyFerguson's user avatar
-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)...
Cam J's user avatar
  • 7
0 votes
2 answers
85 views

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 ...
Babu's user avatar
  • 2,188
6 votes
6 answers
2k views

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?
quanity's user avatar
  • 1,391
8 votes
16 answers
4k views

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 ...
AZeed's user avatar
  • 278
4 votes
8 answers
782 views

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 ...
Futilitarian's user avatar
  • 4,427
-2 votes
2 answers
128 views

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 ...
elemental123's user avatar
0 votes
0 answers
33 views

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 ...
J Kusin's user avatar
  • 2,794
1 vote
1 answer
1k views

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?
r0k1m's user avatar
  • 1,001
3 votes
6 answers
540 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 ...
kristian7's user avatar
1 vote
1 answer
378 views

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-...
Matthias Nehlfink's user avatar
2 votes
3 answers
823 views

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 ...
Matthias Nehlfink's user avatar
4 votes
2 answers
236 views

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 ...
Dick Grayson's user avatar
0 votes
1 answer
59 views

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 ...
qwerty1005's user avatar
3 votes
1 answer
127 views

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 "...
R. Burton's user avatar
  • 135

1
2 3 4 5
7