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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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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1answer
36 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)....
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2answers
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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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2answers
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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.
...
4
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2answers
510 views
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 ...
2
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2answers
118 views
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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1answer
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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). ...
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1answer
294 views
Language, Proof, and Logic 14.11 Fitch Proof
Been stuck on this question for awhile now and I just don't know how to get Cube(x) so that I can use ^ intro with Cube(x) and ∀y (Cube(y) → y = a) and then use ∃ intro to get the conclusion. This is ...
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2answers
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Fitch Proof Exercise 6.20
I am working on a proof and am stuck on a step. I am not sure why I cannot assume the negation of B. Is it not allowed or am I missing something? Thank you]1
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4answers
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Language Proof & Logic 8.31 Fitch Proof
Been working on this one question for the past hours and I can't ever seem to get the last step working. Any help would be appreciated!
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8answers
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Does every truth have to be provable based on evidence?
I know the answer is "no" in general due to Gödel's Theory of Incompleteness, but I mean this question in a more real-world sense (i.e. scientific sense). In other words, I am talking about empirical ...
0
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1answer
96 views
What kinds of proofs can be given for axioms, e.g. the modal axiom S5?
From John Bigelow and Robert Pargetter's book, titled, 'Science and Necessity', they assert the following:
. . . . The resulting system, S5, contains all the theorems of S4 and all the theorems of ...
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1answer
58 views
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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1answer
43 views
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
293 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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9answers
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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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2answers
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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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2answers
81 views
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.
0
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1answer
30 views
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
74 views
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
60 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
85 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
100 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
66 views
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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2answers
87 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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votes
2answers
84 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
881 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
84 views
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 ...
3
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2answers
69 views
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
65 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.
2
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2answers
74 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
364 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 ...
0
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1answer
205 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 ...
3
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1answer
341 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
82 views
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
210 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 ...
2
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1answer
313 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
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
45 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
186 views
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
308 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
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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
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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 (...
