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Questions tagged [proof]

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

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3answers
168 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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2answers
426 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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1answer
59 views

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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2answers
241 views

Predicate logic proofs - how to split a disjunction bound by two quantifiers

I need to complete the following proof using only primitive rules (the introduction and elimination rules for each connective and quantifier). (∃x)(∀y)(Py ∨ Qx) ⊢ (∀y)Py ∨ (∃x)Qx I've only been able ...
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1answer
339 views

Given proofs of A → B and A, when do we get a proof of B?

In intuitionistic mathematics, a proposition is true only when a proof of it has been experienced. Following the BHK semantics, a proof of A → B is an algorithm that, when given a proof of A, will ...
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3answers
2k views

Fitch Formal Logic Help 6.26

6.26 Premise: A v (B ^C) Premise: ~B v ~C v D Goal: A v D Prove it formally without using DeMorgan's Law.
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1answer
205 views

Is a proof still valid if many people say that is true? [duplicate]

A proof is some explanation to convincing others that a statement is true (or false in case of a counterexample). As Yuri Manin once wrote: "A proof becomes a proof only after the social act of ...
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2answers
64 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
77 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
182 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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2answers
127 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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1answer
63 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
113 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
104 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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2answers
1k views

Can a true statement also imply the opposite of itself?

It's unlikely that there could be a thesis that also is its own antithesis. Similarly, a formula usually isn't the "opposite" of itself if we use well-defined terminology. Somehow I have a notion ...
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1answer
2k views

Logic – Deduction in Tarski's World (Fitch/LPL 13.36)

I am working on proving the following question: | ∀x [Dodec(x) → LeftOf(x, a)] | ∀x [Tet(x) → RightOf(x, a)] |––– | ∀x [SameCol(x, a) → Cube(x)] The question has the following rules: […] give a ...
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5answers
330 views

If you're the smartest person on earth, how do you know if you're making logic errors? [closed]

In any logical argument, there is the practical step of verifying that it is sound. When there are experts in that particular area, they can check the argument for soundness. For two examples: A math ...
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1answer
260 views

Proof validity methods other than truth tables

I have read or heard some time ago that truth tables cannot be used to validate arguments which involves the use of quantifiers i.e. in predicate or quantificational logic where you can find ...
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2answers
216 views

How are 'proof of inexistence' and 'proof of impossibility of existence' different?

What is the difference between proof of inexistence (A) and proof of impossibility of existence (B)? Does A implies B? Does B implies A? I know that there is a scientific axiom that says 'proof lies ...
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0answers
53 views

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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3answers
186 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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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
236 views

Axiomatic Proof of Symmetry and Transitivity of Identity

Given the axioms below and the rules of Modus Ponens and Universal Generalization, how can you prove that t=s → s=t for any terms s and t? Additionally, how do you prove that t = s → (s = r → t = r) ? ...
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0answers
248 views

What are some active areas of research in proof theory?

Is there any research activity going on in the field of proof theory today? If so, what are some of the most active areas, what types of questions do they deal with, and where can I go to find out ...
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0answers
102 views

Using the conception of 'reliable, unchanging' does 'truth' exist?

An 'archaic' definition for TRUE,TRUTH implies constancy, reliability, unchanging, fidelity. Using this concept of TRUTH is the following valid? There exists either that which is TRUE or that which ...
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1answer
59 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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4answers
286 views

Are the limitations of language proof against the divinity of holy books? [closed]

Many religions like Islam and Hinduism have holy books(the Quran and the Vedas, respectively) which claim some kind of superhuman origin. However, are the limitations of languages then counter to ...
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2answers
1k views

Is there something in the real world that cannot be proved nor disproved? [closed]

It is often said that you cannot prove nor disprove God. People who bring forward this kind of reasoning often try to persuade you that there is a kind of balance, a truce; you can't prove your point (...
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6answers
291 views

How can you prove I'm not a dog? [closed]

This is a general question that proves you have no way of knowing anything. How can you prove, that if you see me (assume I look like you exactly, because you don't have a picture of me), I am not a ...
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4answers
276 views

If supposing that a statement is false gives rise to a paradox, does this prove that the statement is true?

If supposing that a statement is false gives rise to a paradox, does this prove that the statement is true? Let me attempt to be a little more precise: Suppose you have a proposition. Furthermore, ...
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1answer
88 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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2answers
193 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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1answer
29 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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73 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 ...
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2answers
188 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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248 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
170 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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1answer
60 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
237 views

Prove (P → Q) ↔ (¬Q → ¬P) using conditional elimination and negation introduction. [closed]

I'm trying to prove that (P → Q) ↔ (¬Q → ¬P) using Fitch. I know I have to prove two subproofs. 1) P → Q 2)¬Q → ¬P
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2answers
221 views

The Customer is not Always Right [closed]

This issue has always been a philosophic issue to me, sense I have worked at McDonalds for the last six years of my life. On minute one of my first day of training, I was told "the customer is always ...
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1answer
30 views

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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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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63 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
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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1answer
208 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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1answer
95 views

Has any philosopher ever argued succesfully that anything at all does not exist?

Is it possible to prove that something does not exist? I'm asking because I find it very difficult to think of any such idea.
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285 views

What is it mean by “to be meet with in space” by Moore?

I was reading the Moore's proof of external world, and I am completely stuck with an idea/phrase of "to be meet with in space." It is on page 130 on the following pdf philosophical papers, collier ...
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1answer
64 views

If many people show positivity, is that irrefutable proof of no negativity?

I want to know how we can analyze the number of preferences versus lack of preferences, or dislikes versus likes, and determine if the balance or lack thereof signifies a truly positive affirmation or ...
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1answer
39 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
198 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 ...