Philosophy Stack Exchange
Philosophy Stack Exchange

Questions tagged [proof]

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

A proof is a chain of sentences (or wffs) that is formed according to the rules of a proof calculus. Calculi are specific to a given logic, but all have two properties in common: Firstly, it is algorithmically decidable whether a given chain of sentences constitutes a proof in it; secondly, proofs must be truth-preserving: If the premises are true, then so is the conclusion. This second property makes proofs a special kind of deductive reasoning. The most three common kinds of proof calculi are Hilbert style systems, natural deduction and sequent calculus.

In practice proofs are presented in natural language, yet in principle they are formalisable.

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Can you prove anything in philosophy?

I don't understand philosophy very well, and so I am wondering whether you can "prove" anything in philosophy. It always seems you can go a layer down, and find another question, almost endlessly until you get to the question of "why/how/are we…
John M.
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Does a negative claimant have a burden of proof?

I have often heard it said that the burden of proof is on the positive claimant but not on the one making a negative claim. A person claiming, "God exists" has a burden of proof but not a person claiming, "God does not exist." If I assert,…
user409
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What is the difference between "reductio ad absurdum" and "proof by contradiction"?

What is the exact difference between reductio ad absurdum and proof by contradiction? Wikipedia used to state that: Reductio ad absurdum (Latin: "reduction to the absurd") is a form of argument in which a proposition is disproven by following its…
loudandclear
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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 an atheist as A claims. So I was wondering - is…
easwee
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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 rather than mathematical truths. Can there be…
Lavie
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Is a proof still valid if only the author understands it?

Some time ago I was reading about the recent Shinichi Mochizuki's proof for the famous ABC conjecture. It's enormous and so incredibly difficult that at that time virtually nobody was able to comprehend it (now it seems to get better), and some…
machaerus
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What is the relation between proof in mathematics and observation in physics?

Recently in his 2015 Hirzebruch Lecture in Bonn, Arthur Jaffe re-amplified his famous perspective that finding proof in mathematics is analogous to making experimental observation in physics. In paraphrase: One observes that a proof exists, much as…
Urs Schreiber
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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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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 objects, none of which appear outside in the real…
user34467
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What is the correct, pragmatic, reasoning response to conspiracy theories?

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 videos, and say 'Look! Here's the proof! It's all…
dwjohnston
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Is watching an amputated limb regrow proof of the supernatural?

A typical challenge skeptics present when confronted with claims of alleged miracles is "why won't God Heal amputees?". But, would that do the job? Consider the following thought experiment: Let's suppose that God grants the miracle and multiple…
user48437
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What makes something mathematics?

Dictionary.com definition of math: (used with a singular verb) the systematic treatment of magnitude, relationships between figures and forms, and relations between quantities expressed symbolically. (used with a singular or plural verb)…
Tdonut
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Are there rules for dealing with self-reference "paradoxes" in logic?

My favorite paradox that leads to an endless regress, and also leads to a question: The sentence after this is true. The sentence before this is false. When contradictions appear in proofs, we have rules to finish out the proof. I believe that the…
hellyale
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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 from set B. Now if we make a list of natural…
user107986
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Why is Modus Ponens valid?

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 Therefore, Q My question is could we have…
Sniper Clown
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