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.

328 questions
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Does theism have the burden of proof?

I have heard that agnosticism seems to be the only position with respect to god that doesn’t have a burden of proof. What I find troubling about this is most people do not as a practical matter think they have no knowledge on whether 10,000 mermaids…
user62907
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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 "Ana-Con" feature, it does indeed suggest that this…
Sinthet
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Why are there problems we don’t know how to solve?

For example, there is a simple deterministic algorithm for determining whether any given number is a perfect square. But why don’t we know how to solve things like the p vs np problem or the collatz conjecture?
Måns Nilsson
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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 (unreflected) instantly agree that vaccines are…
Martin Eckleben
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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 solutions and breakdowns for these four, using…
A. Delarge
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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 almost all proofs I wonder that I would never…
Turkhan Badalov
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How can you prove I'm not a dog?

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 dog in disguise? I have tried these…
TigerGold
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Prove (P → Q) ↔ (¬Q → ¬P) using conditional elimination and negation introduction.

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
user17783
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How do I prove the following? ¬(P → Q) ⊢ ¬Q

I am trying to prove this equation can anyone help?
rosa_melano
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First Order Languages

C1: ∀xWeakPref(x,x) C2: ∀xIndiff(x,x) C3: ∀x∀y(Indiff(x,y)↔Indiff(y,x)) C4: ∀x∀y∀z((Indiff(x,y)∧Indiff(y,z))→Indiff(x,z)) C5: ∀x∀y(StrongPref(x,y)→WeakPref(x,y)) C6: ∀x∀y(StrongPref(x,y)→ ¬StrongPref(y,x)) C7:…
Daniel J.
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