# Questions tagged [proof]

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

322 questions
Filter by
Sorted by
Tagged with
1k 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 ...
• 4,107
80 views

### 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 ...
85 views

### 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 ...
121 views

### 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 ...
269 views

### 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 ...
• 101
105 views

### 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.
89 views

### Why is the use of the ND rule ∃E not correct in this proof?

Is there anyone who could explain to me why these errors occur? It seems to me the rule was used properly.
136 views

### Prove the following theorem: Need hints to finish it

This is not homework. I do it for fun and learning. I use the Logic Book. Problem has to be done in SD+. How to prove the following argument : |- [~A =>(~B=>C)]=>[(A v B) v (~~B v C )] I ...
• 164
460 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 ...
104 views

### 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.
317 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....
• 123
499 views

### 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 ...
• 113
1 vote
193 views

### Is a game player winning against very long odds being a cheat, an example of the logical fallacy of personal incredulity?

There's this Minecraft speed-runner called Dream who has been accused of cheating due to his drop luck (ie receiving useful things in the game). A moderator team has calculated that the p-value of the ...
• 135
1 vote
62 views

### Looking for the correct english term for [closed]

I just remembered a conversation I had (in german) about 18 years ago and the other person used the (german) term "All Theorie", which in this context was not related to the theory of ...
• 111
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 ...
• 157
117 views

### How do I prove ∀x(A(x) -> B(x)) from ~∃x(A(x) ^ ~B(x)) using a fitch proof? [closed]

What would the formal fitch proof for this be? This question came up in my practice problems and I'm really stuck on how to proceed. I'm assuming that you start with an assumption, but I can't figure ...
104 views

### Is there any proof of assertion that "assertion can be proved"?

Here's some reason to doubt any proof: Dissent – The uncertainty demonstrated by the differences of opinions among philosophers and people in general. Progress ad infinitum – All proof rests on ...
• 401
117 views

### Soundness and Completeness of Tableaux

Tableaux to my knowledge are both sound and complete. The statement: "If P is valid then tableau for -P eventually closes". Does this statement prove that tableau is sound and complete or ...
• 23
43 views

### 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 ...
• 63
276 views

### How do philosophers answer a question like 'How do you know something exists?'

I recently watched a video from Rationality Rules titled "The Argument from Personal Experience - Debunked (Why Personal Experiences are NOT Proof)". As the title reveals, the video's goal ...
221 views

### 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 ...
27 views

### Rudimentary Proof in SL

So I'm currently being introduced to SL and asked to prove a statement. A simple question with the premise L & W and L ⇒ ¬ F. I am asked to prove W & ¬ F. Could someone verify my solution? So ...
107 views

### Prove that the following is a logical truth (tautology) using a natural deduction derivation: (B → C) ˅ (¬B → C) [closed]

Prove that the following is a logical truth (tautology) using a natural deduction derivation: (B → C) ˅ (¬B → C) How do I prove this using statement logic? I know I need to start with a supposition ...
147 views

### What is the difference between these two types of proofs?

While employing induction method for proving, is deriving the string(formula) "Fn → Fn+1 " any different from showing that if Fn holds true, then so does Fn+1 ? By showing I mean that we use ...
• 1,065
79 views

### Functional Abbreviation for Inst Expression in Turing's Paper [closed]

In Turing's 1936 paper On Computable Numbers Page 30-31, and its Correction Page 1-2 For a Turing Machine M, Inst(i,j,k,LEFT,l) means that if M scans symbol j under m-configuration i, then the symbol ...
• 1,065
107 views

### How does one prove (A->B)vC from the premise ~A? [closed]

Is the premise really enough to prove this?
85 views

### How to prove the following arguments [closed]

I'm trying to do a bunch of proofs to get better at them but it seems like I need some help with negation. Can anyone who has time prove the following arguments? I would really appreciate it! ¬(P ∧ ¬Q)...
• 9
42 views

### Validity of the Definiton of the Conditional [closed]

Can a proof for Premise (P→Q) ... Goal (¬P∨Q) be derived using only the following rules? Conjunction Introduction Conjunction Elimination Left Conjunction Elimination Right Disjunction Introduction ...
89 views

### 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!
1 vote
431 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 ...
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: ...
141 views

### 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 ...
70 views

### 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 ...
• 1,065
747 views

### How can a proof system be unsound?

I have recently started learning propositional logic. I stumbled upon the concepts of soundness and completeness. According to http://intrologic.stanford.edu/chapters/chapter_04.html, a proof system ...
• 35
1 vote
660 views

### can an argument containing a contradiction be valid argument

I know that validity has nothing with truth of the conclusion or with how good argument is in general, and an argument is valid iff the truth of its premises guarantees the truth of its conclusion. ...
500 views

### Question about fitch 6.19 proving A or C from premises A or B and -B or C

How to prove A or C from premises A or B and -B or C. Am using fitch and have been stuck on this for an hour
132 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 (●)...
• 9
187 views

### Negation of the Rule of Implication proof

tried forever to figure out a solution to this problem. It's based on the rule of Material Implication with a negation in front of both sides. Namely the premise is ~(A>B) with the goal solution ...
• 1
125 views

### First Order Languages [closed]

C1: ∀xWeakPref(x,x) C2: ∀xIndiff(x,x) C3: ∀x∀y(Indiff(x,y)↔Indiff(y,x)) C4: ∀x∀y∀z((Indiff(x,y)∧Indiff(y,z))→Indiff(x,z)) C5: ∀x∀y(StrongPref(x,y)→WeakPref(x,y)) C6: ∀x∀y(StrongPref(x,y)→ ¬StrongPref(...
124 views

### Actual and potential truth for neo-verificationists

Neo-verificationists such as Martin-Löf and Prawitz make a distinction between actual and potential truth of a proposition, roughly defined as follows: ... that a proposition A is actually true means ...
• 59
469 views

### 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 ...
497 views

### fitch proof chapter 13 (ex. 13.29) [closed]

how to proof exercise 13.29 without using taut con
337 views

### Logic – Deduction in Tarski's World (Fitch/LPL 13.22) [closed]

I am trying to use existential elimination to derive Brillig(a) & Tove(a). how would I do this? I have tried to do separate sub proofs to prove both Brillig(a) & Tove(a) but that doesn't work ...
46 views

Q ∧ S (Q ∧ ¬P) → ¬R Q → ¬P (S ∧ T) → (P ∨ R) The goal is:¬T
156 views

### To say that something is a logical consequence is always a subjective statement?

"A mathematically proven statement would be absolutely correct if all the axioms and inference rules used in the proof are first accepted as absolutely correct. That is the whole purpose of creating ...
• 355
1 vote
240 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 ...
180 views

### Solving a proof with 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. B ^ D (B^¬A) → ¬C B → ¬A (D^E)→ (A v C) GOAL: ¬E
422 views

### Deductive argument in which every step and premises are explicitly stated?

Is there in philosophy a word/term describing an argument in which all the premises and rules for derivation from those premises are stated explicitly so that even a computer can check it? I know that ...
• 355
118 views

### Predicate Logic

How do I derive this? Pr 1 ∀x(Fx -> ∀xGx) ∴ ∀x(Fx -> ∀x(Gx \ / Hx)) My attempt: However I cannot used universal derivation due to the free x. I think using ass id and qn would be better ...
• 15