Proof (truth)

Formal languages | Automated theorem proving | Computational complexity theory | Formal systems | Proof theory

A proof is sufficient evidence or a sufficient argument for the truth of a proposition. The concept applies in a variety of disciplines,with both the nature of the evidence or justification and the criteria for sufficiency being area-dependent. In the area of oral and written communication such as conversation, dialog, rhetoric, etc., a proof is a persuasive perlocutionary speech act, which demonstrates the truth of a proposition. In any area of mathematics defined by its assumptions or axioms, a proof is an argument establishing a theorem of that area via accepted rules of inference starting from those axioms and from other previously established theorems. The subject of logic, in particular proof theory, formalizes and studies the notion of formal proof. In some areas of epistemology and theology, the notion of justification plays approximately the role of proof, while in jurisprudence the corresponding term is evidence,with "burden of proof" as a concept common to both philosophy and law. In most disciplines, evidence is required to prove something. Evidence is drawn from the experience of the world around us, with science obtaining its evidence from nature, law obtaining its evidence from witnesses and forensic investigation, and so on. A notable exception is mathematics, whose proofs are drawn from a mathematical world begun with axioms and further developed and enriched by theorems proved earlier. Exactly what evidence is sufficient to prove something is also strongly area-dependent, usually with no absolute threshold of sufficiency at which evidence becomes proof. In law, the same evidence that may convince one jury may not persuade another. Formal proof provides the main exception, where the criteria for proofhood are ironclad and it is impermissible to defend any step in the reasoning as "obvious" (except for the necessary ability of the one proving and the one being proven to, to correctly identify any symbol used in the proof.); for a well-formed formula to qualify as part of a formal proof, it must be the result of applying a rule of the deductive apparatus of some formal system to the previous well-formed formulae in the proof sequence. Proofs have been presented since antiquity. Aristotle used the observation that patterns of nature never display the machine-like uniformity of determinism as proof that chance is an inherent part of nature. On the other hand, Thomas Aquinas used the observation of the existence of rich patterns in nature as proof that nature is not ruled by chance. Proofs need not be verbal. Before Copernicus, people took the apparent motion of the Sun across the sky as proof that the Sun went round the Earth. Suitably incriminating evidence left at the scene of a crime may serve as proof of the identity of the perpetrator. Conversely, a verbal entity need not assert a proposition to constitute a proof of that proposition. For example, a signature constitutes direct proof of authorship; less directly, handwriting analysis may be submitted as proof of authorship of a document. Privileged information in a document can serve as proof that the document's author had access to that information; such access might in turn establish the location of the author at certain time, which might then provide the author with an alibi. (Wikipedia).

Proof: What is it, and how does it work?

From playlist The Nature of Proof

Proof by Contradiction: Arithmetic Mean & Geometric Mean

From playlist The Nature of Proof

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More resources available at www.misterwootube.com

From playlist The Nature of Proof

Proof by Contradiction (Example: Smallest Positive Rational Number)

From playlist The Nature of Proof

How to determine the truth table from a statement and determine its validity

👉 Learn how to determine the truth or false of a conditional statement. A conditional statement is an if-then statement connecting a hypothesis (p) and the conclusion (q). If the hypothesis of a statement is represented by p and the conclusion is represented by q, then the conditional stat

From playlist Conditional Statements

A Brief Introduction to Proofs

This video serves as an introduction to proofs.

From playlist Summer of Math Exposition Youtube Videos

How many subsets in a set? (1 of 2: Induction proof)

More resources available at www.misterwootube.com

From playlist The Nature of Proof

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Lec 1 | MIT 6.042J Mathematics for Computer Science, Fall 2010

Lecture 1: Introduction and Proofs Instructor: Tom Leighton View the complete course: http://ocw.mit.edu/6-042JF10 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

From playlist MIT 6.042J Mathematics for Computer Science, Fall 2010

7. Ch. 3, Sections 3.1 & 3.2. Introduction to Logic, Philosophy 10, UC San Diego - BSLIF

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From playlist UC San Diego: PHIL 10 - Introduction to Logic | CosmoLearning.org Philosophy

What are the basics of mathematical logic? | Intro to Math Structures VS1.1

So you want to prove things? Where do you start if you haven't ever written a proof before? In most cases, a course on discrete mathematics or mathematical structures is where someone writes their first proof and that starts with propositional calculus. In this video section, we go through

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From playlist Summer of Math Exposition 2 videos

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I'm not a native English speaker, sorry about my pronunciation and fluency in English. If there is any kind of mistake in the video, please inform me in the comments section.

From playlist Summer of Math Exposition Youtube Videos

Proof-of-Work — Waste of energy or useful?

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From playlist Summer of Math Exposition Youtube Videos

Foundations - Seminar 2

Billy Price and Will Troiani present a series of seminars on foundations of mathematics. In this seminar Billy introduces natural deduction as a proof system. You can join this seminar from anywhere, on any device, at https://www.metauni.org. This video was filmed in Deprecation (https:/

From playlist Foundations seminar

The Mathematical Truth | Enrico Bombieri

Enrico Bombieri, Professor Emeritus, School of Mathematics, Institute for Advanced Study http://www.ias.edu/people/faculty-and-emeriti/bombieri October 29, 2010 In this lecture, Professor Enrico Bombieri attempts to give an idea of the numerous different notions of truth in mathematics.

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Inference: A Logical-Philosophical Perspective - Moderated Conversation w/ A.C. Paseau and Gila Sher

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From playlist Conditional Statements

How to determine the truth of a statement using a truth table

From playlist Conditional Statements

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I'm sorry I had to do it because of the memes. Crash course educational look of propositional logic with the motivation to show how to prove things through proof by contradiction and proof by contraposition. Honorable shoutouts to @blackpenredpen and @drpeyam. God bless Toby Fox! Timel

From playlist Summer of Math Exposition 2 videos

Proof (truth)

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