Questions tagged [proof]
For questions about the correctness of a proof or the nature of proofs in general.
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questions
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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 ...
3
votes
2answers
264 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 ...
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1answer
39 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.
0
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1answer
58 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....
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0answers
69 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 ...
1
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1answer
73 views
Is the DREAM controversy 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. A moderator team has calculated that the p-value of the chance you'd get the same drops as Dream ...
1
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0answers
57 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 ...
4
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1answer
2k 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 ...
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2answers
94 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 ...
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2answers
80 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 ...
2
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1answer
65 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 ...
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0answers
41 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 ...
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1answer
114 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 ...
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2answers
184 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 ...
0
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1answer
25 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 ...
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2answers
70 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 ...
0
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2answers
130 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 ...
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1answer
72 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 ...
0
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1answer
65 views
How does one prove (A->B)vC from the premise ~A? [closed]
Is the premise really enough to prove this?
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1answer
72 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)...
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1answer
38 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 ...
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1answer
31 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!
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6answers
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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 ...
11
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8answers
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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: ...
2
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0answers
112 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 ...
0
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0answers
67 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 ...
2
votes
1answer
189 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 ...
1
vote
3answers
146 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.
...
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2answers
82 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
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2answers
101 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:
1.(A ∨ B) ⊃ (C ∨ D)
C ⊃ E
C ∨ ~F
A ● ~E
F ∨ (D ⊃ Z)
.: Z
KEY:
Tilde (~) forms negations (“...
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1answer
58 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 ...
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1answer
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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(...
3
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1answer
77 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 ...
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2answers
96 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 ...
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2answers
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2answers
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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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1answer
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3answers
137 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 ...
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2answers
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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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votes
1answer
74 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
3
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2answers
359 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 ...
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votes
2answers
102 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 ...
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1answer
71 views
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 ...
0
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1answer
160 views
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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1answer
61 views
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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0answers
106 views
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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1answer
62 views
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.
0
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1answer
204 views
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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2answers
137 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 ...
0
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1answer
86 views
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)....
