Proof is a chain of reasoning using rules of inference, ultimately based on a set of axioms, that lead to a conclusion.

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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 ...
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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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44 views

Truth Tables and Venn Diagrams: Prove Contingent statement are consistent

I am trying to prove how consistent statements can be contigent. The problem i am having how to use a truth table to prove this.
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2answers
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LPL Q6.26 without --> or material implication

This is a repeated question: Language Logic and Proof Q. 6.26 "Using the natural deduction rules, give a formal proof of A ∨ D from the premises A ∨ (B ∧ C) (¬ B ∨ ¬ C) ∨ D" The LPL textbook ...
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3answers
157 views

Help with a proof in CSL

Premise: (A implies B) implies C Conclusion: (C implies A) implies A I had a logic exam a few hours ago, and this was one of the problems, but I really didn't know where to start. Since the ...
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1answer
56 views

Transitive Incompleteness of Logical WFF's Due to Godel's Incompleteness Theorem

If a set of theorems, or wff's, are used in conjunction with one another, does this have an impact on their completeness in terms of soundness? For example, I have five theorems of logic, or ...
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1answer
19 views

Are analogical middle terms sufficient for a valid demonstration?

William A. Wallace, O.P., in “Thomism and the Quantum Enigma,” The Thomist 61 (1997): 455–468, claims that analogical middle terms are sufficient for a valid demonstration and that this is a ...
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623 views

Mathematical versus philosophical reasoning (and the mathematics of philosophical arguments)?

What is the difference between mathematical reasoning and philosophical reasoning and why isn't philosophy just considered to be a branch of mathematics? Is any study not a branch of mathematics ...
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69 views

Burden of proof

Who has the burden of proof when trying to prove or disprove someones religious beliefs? I have always believed it belongs to the person who is making a claim but can there be exceptions?
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4answers
214 views

Does a statement exist which is its own proof?

In fake/pseudo mathematical notation: does there exist a statement S such that S = Proof(S)?
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2answers
161 views

An argument is valid if the premises CANNOT all be true without the conclusion being true as well

"An argument is valid if the premises CANNOT all be true without the conclusion being true as well." Argument_1: P or Q. not Q. Therefore, P. Argument_1 is valid. Argument_2: B or M. M or C. ...
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1answer
146 views

How to discharge an assumption?

I am proving the follow argument [(A ↔ B ) → C] ⊢ [ - ( A ^ B) V C ] Using the following set of rules I, ^E, vI, vE, →I, →E, ↔I, ↔E, --E, -I Here are my steps but I got to the point where I ...
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1answer
122 views

Help with a proof for the following arguments

I want to proof the following argument from both sides using the following rules ^I, ^E, vI, vE, →I, →E, ↔I, ↔E, --E, -I Argument [(A ↔ B ) → C] ⊢ [ - ( A ^ B) V C ] Please let me know ...
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1answer
82 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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7answers
202 views

The blur between proof and evidence

Consider this: Evidence is the foundations of proof. So, enough evidence creates proof. However, how much evidence is needed to make proof depends on the concerning persons' circumstances, ...
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3answers
189 views

How does one contradiction in argument makes the argument valid?

For any argument such as the following that we solve by "Proof by contradiction" method: (A v B) (A ⊃ C) (B ⊃ D) [ Therefore, (C v D) Assumption: ~(C v D) Therefore, ~C {from 4} Therefore, ~D {from ...
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0answers
197 views

Testing the validity of syllogism argument

I came across a validation method for testing the validity of a syllogistic argument which seems quite easier to grasp: For example: To test the argument: no P is B some C is B Therefore, some ...
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4answers
126 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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4answers
267 views

Rebuttal for modus ponens

Saw this (WP:"What the Tortoise said to Achilles") on the internet. A summary is as follows. The common argument is: A: If p then q B: p C: Therefore q. This raises the following question: what if ...
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1answer
45 views

help with deductive proof

∀x (Fx ∨ x=c), ¬Fb ∧ Gb |- ¬Fa → Ga So far I don't understand how to switch variables around to make it true. I've got a subproof set up assuming ¬Fa and concluding Ga In that proof I make F(b) ∨ b ...
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6answers
368 views

How do we know if a mathematical proof is valid?

Georg Cantor has showed there are more real numbers than natural numbers in his diagonal argument. Assuming that two sets have the same size if we can make a pair up elements from set A with elements ...
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1answer
49 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
105 views

Help with simple deductive proof

I am taking a class on natural deduction for the first time and we are currently on deductive proofs, I am having trouble with this one: Premise: A Premise: [(A&B) or (C&D)] Conclusion: not ...
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1answer
61 views

Help with a modal Hilbert-style proof of (□(a>b)&◊(a&c))>◊(b&c)

Can't grasp how it can be proved. To proof just propositional calculus formula (without modal operators) at first seems rather natural to me. Tried the law of importation scheme but it didn't work ...
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1answer
105 views

showing c=a v b=c from a=c v b=c?

I am currently using the book Language, Proof and Logic So far I have 1. a=c v b=c subproof 2. a=c =intro 3 c=c =elim 1,2 4. c=a =elim 2,3 end subproof new subproof 5. b=c 6. c=c =intro 7. c=b ...
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115 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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5answers
143 views

How to prove: (P v (P ^ Q)) iff P

How to prove (P v (P ^ Q)) ≡ P? I am not sure how to get rid of proposition Q. I am allowed to use Leibniz and apply Substitution. I already came across most calculation rules in the book: ...
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3answers
857 views

In what sense are proofs just arguments that convince us, not arguments that establish truth?

In mathematics and logic, it seems that once a proof of some theorem is discovered, then it is taken to be "absolute truth" within the axiomatic system from which it was derived. My question is: are ...
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If there is anything that could behave like a god, is it then a real god?

Let's assume that the our universe's physics allows time travel. This is my main assumption! Let's further assume that there is an quite intelligent, invulnerable being, that found a way to achieve ...
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1answer
109 views

Showing b=a from a=b in Fitch Style System

I'm in the middle of completing a proof, and need to show that b=a. I already have a=b. I think this should be trivial, however, I cannot find a way to do it inside the system. Using the programs ...
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72 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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169 views

Is there such a thing as provability of provability?

Gödel says that there are true statements that can't be proved, given a sound axiomatic system. Does anyone says anything about the provability of the provability of statements? Is it still an open ...
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269 views

Evaluating proof of conspiracy theories is time consuming.

It's established that the burden of proof rests on the party making a claim. The problem I find, is that for any conspiracy theory - the proponent can point to a multitude of conspiracy websites or ...
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1answer
132 views

Is it possible to show that something does not exist?

I am aware that I could show that something does not exist with the knowledge of an implication. If B is true if A exists, then A does not exist if B is false But if we have no implications, is it ...
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1answer
163 views

Prooving ( ∃x Fx ∨ ∃x ~Fx) from no premises

I have a proof problem which I am stuck on. { } ⊢ ( ∃x Fx ∨ ∃x ~Fx) I already figured it out in order to get a∨b, I will have to do ~a→b or ~b→a. However, I have absolutely no idea how to get to ...
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2answers
278 views

Prove P v ~P using most basic rules?

Is there a way to prove P v ~P in basic inference rules? I can't think of where to start because nothing applies to this. I was thinking about usinig Conditional proof, but I don't know what should I ...
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51 views

What are Takeuti oridnal diagrams and how do they describe numbers?

I understand chiefly from writings of Solomon Feferman that Gaisi Takeuti invented ordinal diagrams for This is the following one line answer from Wikipedia: Takeuti (ordinal diagrams): Takeuti ...
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3answers
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Can we add to PA a new predicate T such that for every sentence A of the old vocabulary the new theory proves T(Godel numeric number of A) iff A

I am new to logic but I believe this is not a difficult problem, yet I am still soo confused, and the reason for that is because there are so many gaps in my knowledge or maybe I have overlooked so ...
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8answers
255 views

I've confounded myself with this formal logic “proof”

Let "r" mean "it's raining" and "s" mean "it's snowing." "->" is "implies"; "V" is "or" (inclusive); "~" is "not"; "^" is "and" Here's the "proof": (1) (r->s)V(s->r) is true because it's a ...
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What can suffice as a scientific proof for God? to what domain can such a proof belong to? [closed]

"Scientific" theories require proof, and there are certain guidelines and standards for the proofs to be acceptable to the "scientific" community in that domain (Algebra, Computer Science, etc.). ...
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1answer
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Establishing Incompletenes of Modal LPC

In Hughes and Cresswell A New Introduction to Modal Logic (1996 ed.) page 271, they attempt to establish the incompleteness of the system K + G1 + BF (where K is L(P->Q)->(LP->LQ), G1 is MLP->LMP, and ...
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2answers
213 views

Negative facts and truths

I know Russell and Wittgenstein argued about negative truths. It is easy to prove the existence of some property provided there is considerable empirical evidence for its existence, but what if we are ...
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2answers
555 views

Origin of the idea that something can't be proved, only disproved

Does anyone know if the idea that something can't be proved, only disproved has a specific origin? I often hear it and would like to make a reference to it in a term paper I'm writing. Is it from the ...
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334 views

How to check if this proof is valid?

I'm having some doubt if this proof is valid or invalid, especially regarding the line 4 derived from line 2. Do I need to change the letter in there? 1. (z)~Fz ∴ ~(z)Fz Using Indirect proof ...
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1answer
539 views

Does Descartes prove that he isn't dreaming?

I had a midterm question where this was relevant, essentially it was: "Assuming you're an atheist, how would you prove to Descartes that your last vacation wasn't a dream?" I put that since ...
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On validity of Modus Ponens

I am having trouble understanding what defines Entailment operator. On Mathoverflow I posted this question on what I perceive to be paradox of entailment. Consider: Modus Ponens: P therefore Q P ...
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How to prove you are an atheist?

I've been reading a conversation between two individuals - A claiming to be atheist and B asking him to prove it, since B does not believe that A is saying the truth and can't be sure if A is really ...
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Are there any known deficits of “relevant logic”?

The principle of explosion is the law of classical logic and similar systems of logic, according to which any statement can be proven from a contradiction. Some early formal systems like Frege's ...
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Claims that we know (virtually) nothing - can they be refuted?

Here's an argument that I've heard a number of times from friends and on the Internet: "The ratio of what we know about the universe to what we have yet to discover is so small - it is therefore ...
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1answer
213 views

Underlying logical structure behind Descartes' Ontological argument?

Quoting SEP: Version A: Whatever I clearly and distinctly perceive to be contained in the idea of something is true of that thing. I clearly and distinctly perceive that necessary ...