Questions tagged [proof]
For questions about the correctness of a proof or the nature of proofs in general.
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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
237 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
56 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
143 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
185 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
79 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
40 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
70 views
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
178 views
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
122 views
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
133 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
92 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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1answer
69 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
155 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
264 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
82 views
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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1answer
73 views
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
109 views
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
109 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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2answers
137 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
110 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
115 views
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
1k views
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
196 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
58 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
72 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
88 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
119 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
301 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)...
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1answer
230 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
57 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
108 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
80 views
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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11answers
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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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0answers
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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
66 views
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 ...
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3answers
181 views
Proofs in math and physics
Suppose we have the case of a proof in math or physics and we want to compare the status of the derived information. I know that in math mostly all derived information or deduced details are a priori. ...
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3answers
134 views
Symbolic Logic - Negation Introduction
I am working on a problem for an online class that I'm struggling to figure out.
I'm given these premises:
1. (H > (A > B)) (The > sign here represents conditional)
2. (~K & ~B)
3. (~A > K)
The ...
2
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3answers
224 views
Prove ¬∃x ∀y (E(x, y) ↔ ¬E(y, y)) given no premises
The only way I could think of to do this problem is reductio, but since the two biconditional terms are not contradictory, I am pretty stuck.
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2answers
183 views
Natural deduction proof help!
I've gone through about 40 natural deduction proofs in the past couple days, and mostly they are no problem. For some reason, I've been stuck on 1 tedious problem for an entire day. I just can't seem ...
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5answers
189 views
Is there a way to prove the existence of choice and free will
It is practically impossible to "make" more than one decision at a point in time. Even if you "change" your mind later, it is at a later point.
How do we know that those are decisions that sentient ...
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5answers
182 views
Can any correct logical reasoning in natural language sentences be translated into a formal mathematical proof?
Since natural languages (e.g. English) are prone to ambiguities and misunderstandings due to their constant evolving nature and lack of rigorous formalization, and given an arbitrary philosopher X who ...
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1answer
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What's the name of this kind of fallacious proof to refute an idea?
In an argumentation where speaker A suggests an idea, we sometimes encounter this kind of fallacious proof from speaker B that speaker A's idea is bad (a very common form is known as passive-agressive ...
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3answers
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Deriving “(p.q) v (p.r) from ”p.(q v r)"?
I am new to logic. and here are my tryouts for deriving deriving "(p.q) v (p.r) from "p.(q v r)", and further I want to show that ”p.(q V r)” is equivalent to ”(p.q) V (p.r)”, by using natural ...
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1answer
165 views
How to prove the tautology ¬(P↔¬P) using Fitch?
Just as the question proposes, I'm having trouble with proving this tautology. I know one should use proof by contradiction however I am currently stuck.
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2answers
277 views
Sentential logic derivation: ~(A ≡ B) ├ (~A ≡ B)
I am doing some practice sentential derivation proofs for an upcoming test and have attempt the following proof many, many times without success.
~(A ≡ B) ├ (~A ≡ B)
The logic system I am using is ...
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2answers
82 views
How to prove using higher abstractions instead of diving into axioms or a little bit deeper?
Sorry for the bad formulated question, feel free to edit it. I will explain my question here.
I try to reflect on my abilities of proving theorems to become better at this. That is why after reading ...
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1answer
63 views
Doubt in Searle's Mind: A Brief Introduction
I have been reading Searle's Mind: A Brief Introduction, Oxford UP (2004).
In it I came across the passage in Chapter 2:
if we believe that p and if we believe that if p then q we will
believe ...
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0answers
76 views
Does anyone know of a philosophy which rectifies or considers the following question?
Let's imagine that I began to doubt the validity of one of my arguments, which leads me to question my ability to make rational arguments. And so begin to distrust my intuitive ideas about logic, then ...
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4answers
240 views
In fitch, S → (R ∨ P), P → (¬R → Q) ∴ S → (Q ∨ R)
Construct a proof for the argument: S → (R ∨ P), P → (¬R → Q) ∴ S → (Q ∨ R)
I have gotten to the point in the illustration, but I am unable to figure out where to go from here. I get tricked up on ...
