# Questions tagged [proof]

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

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236 views

### Classification of deductive reasoning types

Please, could you help me make sense of/classify types of deductive reasoning? When studying mathematical logical, I have noticed there is this Hilbert's axiomatic system (Hilbert calculus) with its ...
123 views

### Predicate Logic Proof Help! ∃xAx ∨ ∃yFy , ∀x(Ax → Fx) |= ∃xFx [closed]

I am unable to prove it :( I think I need to assume - ∃xFx but what follows later on? 119 views

### fitch arrow proof

using the FITCH program and the FITCH derivation rules you should make a proof or derivation of C7 from P5 through P11. P5: ∀x∀y(StrongPref(x,y)→ ¬StrongPref(y,x)) P6: ∀x∀y∀z((StrongPref(x,y)∧...
95 views

### How would I create a proof In SL

H Therefore, S ⇒(B ⇒H) How would I create a proof in SL which shows the following argument is valid in SL.
572 views

### Complete a formal proof of ~(~A&~B) from A in as few lines as possible

Prove ~(~A&~B) from A in as few lines as possible. ~ = negation & = conjunction v = disjunction | = line in a subproof Here's what I have: A - Premise |~A - Assume |~B ...
183 views

### 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 ...
352 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)....
245 views

### 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), ...
1 vote
234 views

### 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. ...
600 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 ...
1k 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 ...
69 views

### 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.
598 views

### 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). ...
873 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 ...
1k views

### 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
578 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!
7k views

### 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 ...
228 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 ...
1 vote
104 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 ...
703 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
413 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 ...
12k views

### 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?
101 views

### 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?
1 vote
280 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.
46 views

From no assumptions derive the conclusion ∃x t = x (where t can be any term).
463 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 ...
361 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,...
294 views

### 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)∧...
602 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....
98 views

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 ... 1 vote
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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 ... 287 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 ...
1k 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-...
299 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 ...
82 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 (...
1 vote
141 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.
254 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 ...
1 vote
650 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 ...
268 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 ...
426 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 ...
1 vote
245 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 ...
1 vote
775 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 ...
448 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 ...
108 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.
82 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....
1 vote
94 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 ...
462 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?
243 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