Questions tagged [proof]
For questions about the correctness of a proof or the nature of proofs in general.
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Language Proof and Logic 15.16 [duplicate]
This problem concerns the practice problem 15.16 of the textbook Language, Proof and Logic.
So I saw a similar post here, which gave most of the correct answer (Language proof and logic Chapter 15 ...
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1answer
44 views
Logical, semantic and self-referential paradoxes: The Truth teller and the Liar (draft) can an expert on the matter give feedback?
Title: Logical semantic and self-referential paradoxes: The Truthteller and the Liar (draft, informal)
(major) assumption: A statement is either true or not true (law of excluded middle, classical ...
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1answer
62 views
Fitch Proof - Arrow's logic of preferences
I've been stumped on this one question in particular for several days now and I'm hoping to get some help on where I'm going wrong.
Given the following premises:
∀x∀y(StrongPref(x,y)→ ¬StrongPref(y,...
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1answer
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Fitch Arrow Proofs [closed]
Using the FITCH program and the FITCH derivation rules you should make a proof or derivation of C10 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
66 views
Proof Tree to Fitch Proof
I was wondering if anyone could help me on a proof I've been working on:
I was able to check that it is valid with a proof tree generator (prooftools):
However, I still haven't figured out the proof....
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2answers
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Fitch Question Please Help Me [closed]
I'm having trouble understanding writing out a proof. The proof I'm trying to work with is :
[![enter image description here][1]][1]
How do I reach this goal? Which rules do I use and with which ...
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1answer
66 views
Fitch Questions Please Help Me
I'm having trouble understanding writing out a proof. The proof I'm trying to work with is :
How do I reach this goal? Which rules do I use and with which support steps to each rule (proofs to prove ...
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2answers
47 views
Fitch Proof Help
I'm having some trouble solving this proof in Fitch. How do the universals switch place from the premise to the goal? There is no negation in the goal so negation introduction is not the way to go, I ...
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3answers
658 views
How is Wittgenstein’s “notorious paragraph” about the Gödel's Theorem not obviously correct?
Timm Lampert quotes from Wittgenstein's "notorious paragraph" (§8 of Remarks on the Foundations of Mathematics, Appendix 3) in http://wab.uib.no/agora/tools/alws/collection-6-issue-1-article-6....
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2answers
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Fitch Question Help
I'm having trouble understanding quantifiers in proofs. The proof I'm working with is :
¬∀x Tet(x) -- Premise
¬∀x (Tet(x) ∧ Medium(x)) -- Goal
How do I reach this goal and also get to the goal ...
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2answers
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How to find a stance towards a controversial topic
When is a stance towards a topic "proven"?
To create this example I will take the anti vax topic.
My first impulse is:
anti vax people are stupid. They ignore basic science.
I myself would (...
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2answers
52 views
Structure of an if and only if proof
I am trying to get this proof to work out and so far I feel like I have the first part right but I'm stuck on how to get the A→B part.
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2answers
52 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 ...
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3answers
292 views
Fitch Proof Question
I'm having trouble with a proof and I'm not sure if it's valid or not. If it appears to be invalid, we are supposed to assign names to the letters in the proof and check it in a World, but when I do ...
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1answer
176 views
Using predicate logic, how to solve symmetric and anti reflexive
The networks is: A->B->C->D
The channels used by the network are: lo, med, hi
h-hi, l-lo, m-med
i) A network uses one, and only one channel.
ii) Networks within close proximity cannot both use the ...
4
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1answer
275 views
How to Prove P(a) → ∀x(P(x) ∨ ¬(x = a)) using Natural Deduction
How would a formal Fitch proof look like.
I am given P(a) → ∀x(P(x) ∨ ¬(x = a)) to prove using Natural Deduction of predicate logic.
I am confused on how to proceed with the proof.
Please advice me ...
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2answers
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Logical equivalence proofs
Trying to master logical equivalence proofs out of a textbook is proving to be difficult. I’m hung up on these four problems. I can make some progress, but usually get stuck towards the very end. Any ...
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3answers
151 views
Is anything not proven impossible therefore possible?
Is it a truism that, except for that which is proven impossible, everything is or must be considered possible? If so, why? It seems to me to be an argument from ignorance to say that just because we ...
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1answer
258 views
How does a truth tree provide positive and negative effect tests for implication?
I'm trying to prove that the truth-tree method can be used to give a positive effect test for implication, and a negative effect test for non-implication. I've been given the fact that The truth-tree ...
2
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1answer
84 views
How to prove or disprove validity of ◻◻p → ◻p in the frame (Q,<) of the rational numbers with the usual less-than ordering?
I was wondering if someone can perhaps help with this proving. I am not sure how to handle a temporal frame that is not a set of only natural numbers. Any suggestions?
Thank you.
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2answers
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Proof with conditional introduction
Below is a screen-cap of part of a video where a proof using conditional introduction is shown, which is proving under certain assumptions that given A is true, then the adjacent sentence is also true....
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2answers
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I need some help determining the validity of the following argument
“I got the highest grade on the last test and I have perfect attendance. If I get a cold, then I miss at least one class. I came down with a cold. Therefore, if I missed at least one class, then I ...
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5answers
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Is an argument in natural language as logically valid as in formal logic?
Is a natural language philosophical argument which is argued strictly from first principles widely considered equally as valid as a proof written in formal logic?
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2answers
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Prove or disprove ~◇◻p → ◇◇~p in system K
How to start with the following proof? Any help would be appreciated.
I have tried by assuming the left side is true, however, I get confused with the negation.
~◇◻p → ◇◇~p
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3answers
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Do picture proofs of the Pythagorean theorem make it empirical?
As I understand it, the Pythagorean Theorem, which defines the metric for Euclidean space, is said to be strictly mathematical in the sense that it is derived from a set of purely theoretical axioms (...
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1answer
177 views
De Morgan for Quantifiers Formal Proof: ∀∃-intro and -elim Questions
I have a problem reading existing question's answers. I've successfully encoded the proof of one of De Morgan's Laws, ¬∃x P(x) → ∀x ¬P(x), for Quantifiers formally via cubicaltt type-checker via Curry-...
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2answers
105 views
De Morgan for Quantifiers Formal Proof: Inhabitance Question
I have a problem reading existing question's answers. I've successfully encoded the proof of one of De Morgan's Laws, ¬∃x P(x) → ∀x ¬P(x), for Quantifiers formally via cubicaltt type-checker via Curry-...
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3answers
162 views
Modal validity & vagueness
(2nd version to make explicit my implicit assumptions about A, B and C, and the definitions of the non-logical constants "⊂" and "≡".)
Intuitively, the following modal argument seems valid to me and ...
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4answers
292 views
Is the Kalam cosmological argument scientifically provable?
Kalam Cosmological Argument:
(1) Everything that has a beginning of its existence has a cause of its existence.
(2) The universe has a beginning of its existence.
Therefore:
(3) The universe has a ...
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2answers
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How to get the refutation of (OP ⊃ OQ) ∴ O(P ⊃ Q) in Deontic Logic
In Deontic Logic, one could easily infer "If it is obligatory that P, then it is Obligatory that Q", from "It is obligatory that if P then Q"
O(P ⊃ Q) ∴ (OP ⊃ OQ)
Where the ⊃ is an implication (...
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2answers
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Language Proof and logic Chapter 13 problem 31
I have been working on this problem for over an hour and I think I have simply missed something. I need some help. I don't see how this is supposed to work out
Here are the premises:
∀x ∀y[Likes(x,...
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2answers
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If I saw UFOs, and I was of sound mind and body, does that give the right to say that it is true? [closed]
Around a year ago I saw some spectacular things in the skies above me, on three separate occasions. I believe I was of sound mind and what I saw really did exist.
Given that what I saw was so out-...
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2answers
159 views
Language proof and logic Chapter 15 question 21 how?
I'm really not understanding the set up of how to go about solving this problem any help is welcome
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Language proof and logic Chapter 15 question 16 help
I'm trying to go about solving this problem but I'm having problems even knowing how to approach it. Can someone help me to set it up?
Here is the premise: ∀x∀y(x ⊆ y ↔️ ∀z(z ∈ x ⟶ z ∈ y)
Here is ...
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2answers
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language proof and logic chapter 13 question 49 Help
Premises:
∃xP(x)
∀x∀y((P(x)∧P(y)) → x = y)
Prove:
∃x(P(x)∧∀y(P(y) → y = x))
I've started it but the end is starting to get super muddy and not work out and I don't know where I went wrong.
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In Fitch, how does one prove “P” from the premise “(¬P ∨ Q)→P”?
I can't figure out how to prove that formally. Please, help!!
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4answers
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How to prove ‘∃xP(x)’ from ‘¬∀x(P(x)→Q(x))’
What would a formal Fitch proof for this look like?
I am given ¬∀x(P(x)→Q(x)), and need to derive ∃xP(x) from it.
I started with this, but I don't know if I am doing the right thing, and where to go ...
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2answers
309 views
Fitch Proof by Contradiction help
Hi, I'm pretty new to writing formal proofs and I was wondering if I could get some help solving this question.
I've set up the problem and I was thinking of perhaps proving it by contradiction that ...
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2answers
96 views
Fitch Biconditional Proof Help?
Hi, I'm starting to learn formal proofs using Fitch, but I'm having a bit of trouble figuring out my arguments. I've generally mapped out the subproofs I was considering to use, but I'm unsure how to ...
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2answers
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Can results be predicted?
I wanted to know that, what can we assume as the result of some experiment which we have not conducted on the basis of mathematical proofs? I mean, in general, equations are created after analyzing ...
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1answer
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How to solve the derivation?
Derive the following without assumptions:
¬∃xFx↔∀x¬Fx
How do I solve this derivation?
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2answers
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How does one prove ‘(B→C)→¬A’ from ‘(A→B)∨C’ and ‘(A→¬C)’ in Fitch?
I am trying to work my way through this Fitch proof, and I am not sure what I am doing wrong, but I keep getting stuck no matter what I try.
First attempt:
Second attempt:
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3answers
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2 simple Formal Fitch Proofs
I'm having difficulty proving these. They seem obvious, but I can't figure how to set up formal proofs for them. Could anyone give me clues on how to start them?
¬(P∧¬Q) from the premise P→Q;
¬Q→(R→P)...
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1answer
296 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 ...
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1answer
61 views
Does this symbolic logic proof work?
So, I have this proof:
Let a be an open sentential variable.
Let K and C be prepositional variables asserted of sentences.
Given
K(a) <=> C(a) & a
C(a) <=> C( C(a))
C(a & b) <=> C(...
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1answer
112 views
Why cannot the following theory be refuted by logic but is rejected because of lack of empirical support?
The following statements are taken from a book:
The man in the street, and also the philosopher K. Marbe, believe that after a run of seventeen heads tail becomes more probable. This argument has ...
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1answer
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Is Frankenstein's monster tantamount to positive proof in Science?
Specifically Biology presents some problems for me. For instance, now that we have Evolution we know what to look for. Thus we are bound to observe some adaptations, and over time even new species. ...
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12answers
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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 ...
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Are arguments claiming the impossibility to prove or disprove anything themselves impossible to prove? [duplicate]
Could arguments claiming the impossibility to prove or disprove anything be flawed because if they were sound they would also be impossible to prove?
Or could you just assume they must be right ...
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1answer
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Correct Way of Handling A Corollary of A Corollary?
I have a conclusion S that is moderately interesting. While the corollary of S is more interesting, the corollary of the corollary of S is extremely interesting. Should I just label them corollary 1 ...
