# Questions tagged [proof]

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

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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### Proving (P → Q) ↔ ¬ (P ∧ ¬ Q) in Fitch with no premise [duplicate]

I am struggling with this one for days and keep getting stumped |_ | |_ P → Q | | |_ P ∧ ¬Q | | | : | | | # | | ¬(P & -Q) | (P → Q) → ¬(P ∧ -Q) | |_ ¬(P ∧ ¬Q) | | |_ P | | | : | ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### How does one prove (A->B)vC from the premise ~A? [closed]

Is the premise really enough to prove this?
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### 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)...
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### 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 ...
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### 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!
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### 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 ...
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### 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: ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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. ...
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### 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
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### 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: 1.(A ∨ B) ⊃ (C ∨ D) C ⊃ E C ∨ ~F A ● ~E F ∨ (D ⊃ Z) .: Z KEY: Tilde (~) forms negations (“...
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### 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 ...
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### 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(...
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### 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 ...
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### 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 ...
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### fitch proof chapter 13 (ex. 13.29) [closed]

how to proof exercise 13.29 without using taut con
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### 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 ...
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Q ∧ S (Q ∧ ¬P) → ¬R Q → ¬P (S ∧ T) → (P ∨ R) The goal is:¬T
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### 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 ...
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### 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 ...
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### 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
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### 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 ...
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### 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 ...
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### How to solve this Predicate logic derivation

I want to derive the following: ∀x(Fx ↔ (¬Gx ∨ ¬Hx)). ¬∀x(Gx ∧ Hx) → ∃x(Ix ∧ ¬Gx) ∴ ∃xFx → ∃x(Ix ∧ Fx) This is my attempt: Any suggestions as to how I continue and derive this? I cannot figure out ...
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### Classification of deductive reasoning types

Please, could you help me make sense of/classify types of deductive reasoning? When studying mathematical logical, I have noticed there is this Hilbert's axiomatic system (Hilbert calculus) with its ...
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### Predicate Logic Proof Help! ∃xAx ∨ ∃yFy , ∀x(Ax → Fx) |= ∃xFx [closed]

I am unable to prove it :( I think I need to assume - ∃xFx but what follows later on?
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### fitch arrow proof

using the FITCH program and the FITCH derivation rules you should make a proof or derivation of C7 from P5 through P11. P5: ∀x∀y(StrongPref(x,y)→ ¬StrongPref(y,x)) P6: ∀x∀y∀z((StrongPref(x,y)∧...
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### How would I create a proof In SL

H Therefore, S ⇒(B ⇒H) How would I create a proof in SL which shows the following argument is valid in SL.
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### Complete a formal proof of ~(~A&~B) from A in as few lines as possible

Prove ~(~A&~B) from A in as few lines as possible. ~ = negation & = conjunction v = disjunction | = line in a subproof Here's what I have: A - Premise |~A - Assume |~B ...
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### 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 ...
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### How do I prove :((A ⊃ B) ⊃ C) ⊃ (B ⊃ C)?

How do I prove, :((A ⊃ B) ⊃ C) ⊃ (B ⊃ C), using symbolic logic derivations where ⊃ represents a conditional i.e. A ⊃ B = A implies B? The first line of my derivations is the assumption, (A ⊃ B) ⊃ C)....
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### How do proofs about logic fit into a logical framework?

I'm learning logic from Michael O'Leary's A First Course in Mathematical Logic and Set Theory. In chapter 1 he carefully explains the meaning of logical implication (p ⊨ q), logical inference (p ⟹ q), ...
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### Proving A ⊨ B iff ⊨A → B

Let A and B represent arbitrary formulas. Also let 1 ≡ True and 0 ≡ False Prove that A ⊨ B iff ⊨A → B For my proof, I break down the biconditional into two conditionals and prove each conditional. ...
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### How to show (in a hand waving manner) that the Godel sentence is true

I have been reading Graham Priest's The Logic of Paradox, and there is a section where he tried to show that our informal proof argument (in Priest's terminology, naive proof procedure) is more ...
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### I could prove: Solipsism is wrong. Is my argument acceptable?

Solipsism is the idea that one cannot be sure of anyone's existence but only themself. I think that one can assume this idea to be right and then prove that this is wrong. This self-inconsistency ...
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### why are ∀x(P(x)→ ∃y(Q(y)∧R(x,y))) and ∃y(Q(y)∧∀x(P(x)→(R(x,y))) not logically equivalent?

been sitting here for hours and still can't figure this out. is the order of ∀x and ∃y important in this case? all I can think of now is "all P is R of some Q", but I don't think this is right.
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### Language, Proof and Logic Exercise 14.13 (Fitch)

Having trouble proving this. I know how to prove the first conjunct of the conclusion, but not the second one. Picture shown is the attempt proof of the second conjunct (rules haven't been added yet). ...