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Questions tagged [proof]

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

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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. ...
philoque's user avatar
2 votes
2 answers
441 views

Is there anyway to prove things happen/exist if I'm not aware of them?

I don't even know how to properly ask this, but how can one prove things happen without them knowing? Things only exist for me when I'm aware of them, either by direct contact (I see it, I feel it etc....
yyyyyyyan's user avatar
  • 123
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 ...
Futilitarian's user avatar
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11 votes
10 answers
2k views

What makes something mathematics?

Dictionary.com definition of math: (used with a singular verb) the systematic treatment of magnitude, relationships between figures and forms, and relations between quantities expressed symbolically. ...
Tdonut's user avatar
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12 votes
8 answers
6k views

Is watching an amputated limb regrow proof of the supernatural?

A typical challenge skeptics present when confronted with claims of alleged miracles is "why won't God Heal amputees?". But, would that do the job? Consider the following thought experiment: ...
user avatar
10 votes
5 answers
18k views

How does one prove De Morgan's laws for quantifiers?

One of De Morgan's laws state that ¬∃x P(x) is equivalent to ∀x ¬P(x), but how would one go about formally proving this? Numerous attempts to find a solution have been futile, even proofwiki.org ...
DrDeanification's user avatar
5 votes
6 answers
3k views

Is any aspect of the supernatural testable? What level of proof is possible for the supernatural?

Assume the supernatural does exist, and consists of beings/forces that can interact with our natural universe in ways that are contrary to the natural laws of this universe (at least as we know them). ...
LightCC's user avatar
  • 1,026
2 votes
3 answers
872 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
6 votes
4 answers
965 views

Can something "count" as TRUE without support by logic and empirical data?

I was in an online debate and had this statement presented to me. I would note further that your apparent positivism rests on what is logically a faith claim - specifically, the unproveble claim ...
randomblink's user avatar
4 votes
2 answers
733 views

Can there be true conclusions without assumptions?

I was thinking of the sentence "I think therefore I am", which I had for a long time considered indisputable because it's self-evident. Then I considered the hypothetical situation where my ...
musedpony's user avatar
3 votes
1 answer
6k views

Use the Fitch system to prove the tautology (p ∨ ¬p)

I've scoured the math stackexchange and the philosophy one for some guidance on how to go about this while using the Fitch System. Anyone can attempt it here; http://logic.stanford.edu/intrologic/...
Alexander Michalak's user avatar
14 votes
9 answers
1k views

Is a proof still valid if only the author understands it?

Some time ago I was reading about the recent Shinichi Mochizuki's proof for the famous ABC conjecture. It's enormous and so incredibly difficult that at that time virtually nobody was able to ...
machaerus's user avatar
  • 321
12 votes
9 answers
13k views

How to prove (A v B), (A → C), (B → D) therefore (C v D)

Obviously since A → C and B → D then if A v B one of C or D must be true. My only idea is v must be introduced, but how would I use subproofs to show one of A /\ C or B /\ D is never false if A v B?
sumsum2's user avatar
  • 137
9 votes
4 answers
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Why is Modus Ponens valid?

I am having trouble understanding what defines Entailment operator. On Mathoverflow I posted this question on what I perceive to be paradox of entailment. Consider: Modus Ponens: P therefore Q P ...
Sniper Clown's user avatar
7 votes
5 answers
8k views

What is the difference between mathematical reasoning and philosophical reasoning?

Please see question in title. Why isn't philosophy considered to be a branch of mathematics? Is study of anything not a branch of mathematics, vague and imprecise?
John Sonderson's user avatar
6 votes
6 answers
889 views

What does it mean that a claim is a claim of nonexistence?

This question has devolved into a discussion. As I understand the discussion, everything is revolving around the veracity of statement Nonexistence can never be proven. and on what exactly ...
user avatar
6 votes
3 answers
3k views

In Fitch, how does one prove "(P → Q)" from the premise "(¬P ∨ Q)"?

It's all in the question really. I am working on a proof in Fitch for a class, but I am very much stuck. I am proving the tautology that "(P → Q) ↔ (¬P ∨ Q)", and I have already finished half of it, ...
Zenreon's user avatar
  • 61
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
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3 votes
6 answers
545 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
3 votes
1 answer
183 views

Are analogical middle terms sufficient for a valid demonstration?

William A. Wallace, O.P., in “Thomism and the Quantum Enigma,” The Thomist 61 (1997): 455–468, claims that analogical middle terms are sufficient for a valid demonstration and that this is a ...
Geremia's user avatar
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2 votes
6 answers
488 views

Is there anything a supernatural entity (e.g. God) could do to irrefutably prove its existence to humans? [closed]

I just posted a question in which I ask if spontaneously regrowing amputated limbs would constitute a proof of the supernatural, and several of the answers have presented interesting objections. This ...
user avatar
1 vote
7 answers
887 views

The blur between proof and evidence [closed]

Consider this: Evidence is the foundations of proof. So, enough evidence creates proof. However, how much evidence is needed to make proof depends on the concerning persons' circumstances, ...
woff's user avatar
  • 21
1 vote
4 answers
587 views

What can suffice as a scientific proof for God? to what domain can such a proof belong to? [closed]

"Scientific" theories require proof, and there are certain guidelines and standards for the proofs to be acceptable to the "scientific" community in that domain (Algebra, Computer Science, etc.). ...
Ali's user avatar
  • 135
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 ...
Lavie's user avatar
  • 269
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 ...
user34467's user avatar
  • 121
11 votes
8 answers
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What is the correct, pragmatic, reasoning response to conspiracy theories?

It's established that the burden of proof rests on the party making a claim. The problem I find, is that for any conspiracy theory - the proponent can point to a multitude of conspiracy websites or ...
dwjohnston's user avatar
11 votes
3 answers
3k views

Are there rules for dealing with self-reference "paradoxes" in logic?

My favorite paradox that leads to an endless regress, and also leads to a question: The sentence after this is true. The sentence before this is false. When contradictions appear in proofs, we have ...
hellyale's user avatar
  • 803
9 votes
6 answers
906 views

Claims that we know (virtually) nothing - can they be refuted?

Here's an argument that I've heard a number of times from friends and on the Internet: "The ratio of what we know about the universe to what we have yet to discover is so small - it is therefore ...
Salim Fadhley'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
6 votes
5 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
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6 votes
1 answer
9k views

The difference between argument, inference, deduction and proof?

I am trying to distinguish argument, inference, deduction and proof. First, let's look at the distinction between argument and inference (if there is one). This online source states: An argument ...
EthanAlvaree's user avatar
5 votes
3 answers
3k views

Are axioms tautologies?

My understanding is that axioms are the unprovable statements upon which systems are built. Tautologies are in essence things that can't be false. Godel's Incompleteness Theorem, though, shows that ...
Tatarize's user avatar
  • 171
5 votes
1 answer
2k views

Does anyone have a proof checker they prefer using for modal logic?

I am looking for a proof checker for modal logic using natural deduction or sequent calculus. I am trying to learn Isabelle, but I think there should be a simpler solution. Although I can rely on ...
Frank Hubeny's user avatar
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5 votes
2 answers
567 views

What is the difference between everyday realism and metaphysical realism?

At an everyday level, we seem to subscribe to a from of strong realism which doesn't leave any room for skepticism. We are certain that individuals who hear voices in their heads or who have ...
Alexander S King's user avatar
4 votes
2 answers
167 views

help with deductive proof

∀x (Fx ∨ x=c), ¬Fb ∧ Gb |- ¬Fa → Ga So far I don't understand how to switch variables around to prove the result. I've got a subproof set up assuming "¬Fa" in order to derive "Ga". In that proof I ...
John's user avatar
  • 153
4 votes
3 answers
690 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
4 votes
5 answers
521 views

Is there a way to prove the existence of choice and free will

It is practically impossible to "make" more than one decision at a point in time. Even if you "change" your mind later, it is at a later point. How do we know that those are decisions that sentient ...
dtech's user avatar
  • 230
4 votes
1 answer
238 views

Is it provable that epistemically possible (possible for all I know) does not imply possible?

Here is an argument that it is not. Let's start with some equivalences: X is epistemically possible iff X is possible for all I know iff not (X is impossible given what I know) iff X is not ...
Tarkin's user avatar
  • 41
3 votes
1 answer
2k views

How to discharge an assumption?

I am proving the follow argument [(A ↔ B ) → C] ⊢ [ - ( A ^ B) V C ] Using the following set of rules I, ^E, vI, vE, →I, →E, ↔I, ↔E, --E, -I Here are my steps but I got to the point where I ...
cookie monster's user avatar
3 votes
2 answers
550 views

What makes an argument objectively more "compelling"?

If person A gives an argument to person B in order to convince them about the truth of claim X, how can B determine how compelling A's argument is in a way that is as objective as possible (i.e. in a ...
user avatar
3 votes
5 answers
340 views

Can any correct logical reasoning in natural language sentences be translated into a formal mathematical proof?

Since natural languages (e.g. English) are prone to ambiguities and misunderstandings due to their constant evolving nature and lack of rigorous formalization, and given an arbitrary philosopher X who ...
xwb's user avatar
  • 729
3 votes
1 answer
211 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
3 votes
3 answers
3k views

Prove A ∨ D from A ∨ (B ∧ C) and (¬ B ∨ ¬ C) ∨ D ( LPL Q6.26) without using --> or material implication

This is a repeated question: Language Logic and Proof Q. 6.26 Using the natural deduction rules, give a formal proof of A ∨ D from the premises A ∨ (B ∧ C) (¬ B ∨ ¬ C) ∨ D ...
Billy Bob's user avatar
  • 131
3 votes
2 answers
1k views

What's the difference (if any) between demonstration and description?

How do philosophers of various schools* explain the difference (if any) between demonstration and mere description? Are they synonymous, or are they different? How so? My first impressions: To ...
Geremia's user avatar
  • 8,270
2 votes
2 answers
732 views

How to check if this proof is valid?

I'm having some doubt if this proof is valid or invalid, especially regarding the line 4 derived from line 2. Do I need to change the letter in there? 1. (z)~Fz ∴ ~(z)Fz Using Indirect proof ...
cpx's user avatar
  • 537
2 votes
2 answers
303 views

Solving a proof in which the goal is the negation of a variable in Fitch

I'm working on an assignment and I'm stuck on this proof. I feel like I'm on the right track but I can't find the way to prove the goal. A ^ B (A ^ ~C) --> ~D A -> ~C (B ^ E) --> (C v D) ~E I ...
fitch-is-killing-me's user avatar
2 votes
2 answers
451 views

Negative facts and truths

I know Russell and Wittgenstein argued about negative truths. It is easy to prove the existence of some property provided there is considerable empirical evidence for its existence, but what if we are ...
glebovg's user avatar
  • 380
2 votes
4 answers
25k views

Does the famous Descartes quote "dubito, ergo cogito, ergo sum" suggests secure knowledge of ones existence?

After a discussion about the "difficulties to distinguish knowledge from faith" someone replied to me that the quote implies faith because it uses the word "think". But as it is generally understood: ...
John Am's user avatar
  • 1,324
2 votes
6 answers
2k views

Is logic built on assumptions?

I'm sorry if this sounds like a stupid question, but how can we know that our logical approach to ideas is not in itself based on assumptions. For example, how can we know that the workings of the ...
David Lalo's user avatar
2 votes
1 answer
1k views

Prove ◇(p ∨ q) → (◇p ∨ ◇q) and ◇(p ∧ q) → (◇p ∧ ◇q) in Modal Logic K

I would really appreciate a rundown of a proof of one of the formulas or both: 1) ◇(p ∨ q) → (◇p ∨ ◇q) 2) ◇(p ∧ q) → (◇p ∧ ◇q) I'm allowed to use following proof procedures of modal logic K: 1) ...
Pvniep Niepiniep's user avatar