Questions tagged [proof]

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

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Is a tree proof or natural deduction a semantic method of proof?

Peter Schroeder-Heister writes in an article on "Proof-Theoretic Semantics" the following: Proof-theoretic semantics is inherently inferential, as it is inferential activity which manifests itself ...
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De Morgan's Law Formal Proof [duplicate]

Does anyone know how to do this without the use of addition rules? We have not covered that in class, and all the info I can find online suggests that as a solution. Thanks]1
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1answer
278 views

Proof Using Model Universe

Suppose I am trying to prove the following argument (∀x)(Cx → Dx), (∀x)(Ex → ~Dx), /∴ (∀x)(Ex → ~Cx) Now, let's also assume that I don't know if this argument is valid or not. Because of this, I try ...
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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?
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What are some key differences between an argument in logic and a theory in mathematics?

Both are composed from rules and assumptions which enable us to deduce other inevitable truths that results from these rules and assumptions, right?
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Help with an existential natural deduction proof

From the assumption ∃x∃y R(x, y) I need to derive the conclusion ∃y∃x R(x, y) From the comments: I tried to use Existential Elimination but I can't figure out how to do it properly.
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1answer
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How does one go about this natural deduction proof?

From no assumptions derive the conclusion ∃x t = x (where t can be any term).
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1answer
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Are there rules for the following in the Open Logic Project's proof checker?

I'm using http://proofs.openlogicproject.org/ but can't find out what the translation of the rules are. I'm new at this, so when I try to make proofs, I know what I want the justification to be (which ...
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1answer
55 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
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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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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
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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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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
69 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
58 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
799 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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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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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
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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
58 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
332 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
194 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 ...
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1answer
324 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
170 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
287 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 ...
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1answer
86 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
43 views

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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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
221 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
114 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
166 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
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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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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
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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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2answers
246 views

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
162 views

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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2answers
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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
383 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
107 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
78 views

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
170 views

How to solve the derivation?

Derive the following without assumptions: ¬∃xFx↔∀x¬Fx How do I solve this derivation?
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2answers
190 views

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
429 views

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)...