# Proof (truth) > Mediated Wiki article. Canonical URL: https://mediated.wiki/source/Proof_(truth) > Markdown URL: https://mediated.wiki/source/Proof_(truth).md > Source: https://en.wikipedia.org/wiki/Proof_(truth) > Source revision: 1318962455 > License: Creative Commons Attribution-ShareAlike 4.0 International (https://creativecommons.org/licenses/by-sa/4.0/) {{Short description|Sufficient evidence/argument for truth}} {{Other uses|Proof (disambiguation){{!}}Proof}} A '''proof''' is [sufficient](/source/Necessity_and_sufficiency) [evidence](/source/evidence) or a sufficient [argument](/source/argument) for the [truth](/source/truth) of a [proposition](/source/proposition).''Proof and other dilemmas: mathematics and philosophy'' by [Bonnie Gold](/source/Bonnie_Gold), Roger A. Simons 2008 {{ISBN|0883855674}} pages 12–20''Philosophical Papers, Volume 2'' by Imre Lakatos, John Worrall, Gregory Currie, ISBN Philosophical Papers, Volume 2 by Imre Lakatos, John Worrall, Gregory Currie 1980 {{ISBN|0521280303}} pages 60–63''Evidence, proof, and facts: a book of sources'' by Peter Murphy 2003 {{ISBN|0199261954}} pages 1–2''Logic in Theology – And Other Essays'' by Isaac Taylor 2010 {{ISBN|1445530139}} pages 5–15 The concept applies in a variety of disciplines, Compare {{Bibleverse|1 Thessalonians|5:21|KJV}}: "Prove all things [...]." 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](/source/communication) such as [conversation](/source/conversation), [dialog](/source/Dialogue), [rhetoric](/source/rhetoric), etc., a proof is a [persuasive](/source/persuasive) [perlocutionary](/source/perlocutionary_act) [speech act](/source/speech_act), which demonstrates the truth of a proposition.[John Langshaw Austin](/source/John_Langshaw_Austin): ''[How to Do Things With Words](/source/How_to_Do_Things_With_Words)''. Cambridge (Mass.) 1962 – Paperback: [Harvard University Press](/source/Harvard_University_Press), 2nd edition, 2005, {{ISBN|0-674-41152-8}}. In any area of [mathematics](/source/mathematics) defined by its assumptions or [axioms](/source/axioms), a proof is an argument establishing a [theorem](/source/theorem) of that area via accepted [rules of inference](/source/rules_of_inference) starting from those axioms and from other previously established theorems.[Cupillari, Antonella](/source/Antonella_Cupillari). The Nuts and Bolts of Proofs. Academic Press, 2001. Page 3. The subject of [logic](/source/logic), in particular [proof theory](/source/proof_theory), formalizes and studies the notion of [formal proof](/source/formal_proof).Alfred Tarski, Introduction to Logic and to the Methodology of the Deductive Sciences (ed. Jan Tarski). 4th Edition. Oxford Logic Guides, No. 24. New York and Oxford: Oxford University Press, 1994, xxiv + 229 pp. {{ISBN|0-19-504472-X}} In some areas of [epistemology](/source/theory_of_justification) and [theology](/source/existence_of_god), the notion of [justification](/source/Theory_of_justification) plays approximately the role of proof,{{Cite book|chapter-url=http://plato.stanford.edu/entries/justep-foundational/|title=The Stanford Encyclopedia of Philosophy|chapter=Foundationalist Theories of Epistemic Justification|year=2018|publisher=Metaphysics Research Lab, Stanford University}} while in [jurisprudence](/source/jurisprudence) the corresponding term is [evidence](/source/evidence_(law)),{{Cite web|url=https://www.dictionary.com/browse/proof|title=Definition of proof | Dictionary.com|website=www.dictionary.com}} with "burden of proof" as a concept common to both [philosophy](/source/philosophic_burden_of_proof) and [law](/source/legal_burden_of_proof). In most disciplines, evidence is required to prove something. Evidence is drawn from the experience of the world around us, with [science](/source/science) obtaining its evidence from [nature](/source/nature_(science)),[http://www.fjc.gov/public/pdf.nsf/lookup/sciman00.pdf/$file/sciman00.pdf Reference Manual on Scientific Evidence], 2nd Ed. (2000), p. 71. Accessed May 13, 2007. law obtaining its evidence from [witness](/source/witness)es and [forensic investigation](/source/forensics),[John Henry Wigmore](/source/John_Henry_Wigmore), ''A Treatise on the System of Evidence in Trials at Common Law,'' 2nd ed., Little, Brown, and Co., Boston, 1915 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.{{Cite journal | doi = 10.2307/3052837 |author1=Simon, Rita James |author2=Mahan, Linda. |name-list-style=amp | year = 1971 | title = Quantifying Burdens of Proof—A View from the Bench, the Jury, and the Classroom| journal = Law and Society Review | volume = 5 | issue = 3| pages = 319–330 | jstor = 3052837 }}{{Cite web |url=http://www.valpo.edu/mcs/pdf/ReasonableDoubtFinal.pdf |title=Distributions of Interest for Quantifying Reasonable Doubt and Their Applications |access-date=2007-01-14 |author1=Katie Evans |author2=David Osthus |author3=Ryan G. Spurrier |archive-url=https://web.archive.org/web/20130317181559/http://www.valpo.edu/mcs/pdf/ReasonableDoubtFinal.pdf |archive-date=2013-03-17 |url-status=dead }} In law, the same evidence that may convince one [jury](/source/jury) may not persuade another. [Formal proof](/source/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.);[A. S. Troelstra](/source/A._S._Troelstra), H. Schwichtenberg (1996). ''Basic Proof Theory''. In series ''Cambridge Tracts in Theoretical Computer Science'', Cambridge University Press, {{ISBN|0-521-77911-1}}. for a [well-formed formula](/source/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](/source/formal_system) to the previous well-formed formulae in the proof sequence.{{Hunter 1996|p=7}} Proofs have been presented since antiquity. [Aristotle](/source/Aristotle) used the observation that patterns of nature never display the machine-like uniformity of [determinism](/source/determinism) as proof that [chance](/source/chance_(Ancient_Greek_concept)) is an inherent part of nature.''Aristotle's Physics: a Guided Study'', Joe Sachs, 1995 {{ISBN|0813521920}} p. 70 On the other hand, [Thomas Aquinas](/source/Thomas_Aquinas) used the observation of the existence of [rich patterns in nature](/source/law_of_nature_(science)) as proof that nature is ''not'' ruled by chance.''The treatise on the divine nature: Summa theologiae I'', 1–13, by Saint Thomas Aquinas, Brian J. Shanley, 2006 {{ISBN|0872208052}} p. 198 Proofs need not be verbal. Before [Copernicus](/source/Copernicus), people took the apparent motion of the [Sun](/source/Sun) across the sky as proof that [the Sun went round the Earth](/source/geocentric_model).Thomas S. Kuhn, The Copernican Revolution, pp. 5–20 Suitably incriminating evidence left at the scene of a [crime](/source/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](/source/signature) constitutes direct proof of [authorship](/source/authorship); less directly, [handwriting analysis](/source/handwriting_analysis) may be submitted as proof of authorship of a document.''Trial tactics by Stephen A. Saltzburg'', 2007 {{ISBN|159031767X}} page 47 [Privileged information](/source/secret) 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](/source/alibi). ==Proof vs evidence== 18th-century Scottish philosopher [David Hume](/source/David_Hume) built on [Aristotle](/source/Aristotle)'s separation of [belief](/source/belief) from [knowledge](/source/knowledge),[https://plato.stanford.edu/entries/hume/ David Hume] recognizing that one can be said to "know" something only if one has firsthand experience with it, in a strict sense proof, while one can infer that something is true and therefore "believe" it without knowing, via evidence or supposition. This speaks to one way of separating proof from evidence: If one cannot find their chocolate bar, and sees chocolate on their napping roommate's face, this evidence can cause one to believe their roommate ate the chocolate bar. But they do not ''know'' their roommate ate it. It may turn out that the roommate put the candy away when straightening up, but was thus inspired to go eat their own chocolate. Only if one directly experiences ''proof'' of the roommate eating it, perhaps by walking in on them doing so, would one have certain ''knowledge'', in Hume's sense, that the roommate did it. In a more strict sense of sure knowledge, one may be unable to prove anything to a rational certainty beyond that of the existence of one's immediate sensory awareness. [Descartes](/source/Descartes) famously raised a similarly strict standard with his first principle ''[Cogito, ergo sum](/source/Cogito%2C_ergo_sum)'' (I think, therefore I am). While Descartes' larger project in [Meditations on First Philosophy](/source/Meditations_on_First_Philosophy) has knowledge of God and the external world—founded on the certainty of the cogito—as its aim, his legacy in doing so is to have shown that one cannot have such proof, because all perceptions could be false (such as under the [evil demon](/source/evil_demon) or [simulated reality](/source/simulated_reality) hypotheses). One nevertheless can still have clear proof of the existence of one's thought, even if belief in the external world lacks the certainty of demonstration beyond that of one's own firsthand experience. == See also == {{wikiquote|Proof}} * [Mathematical proof](/source/Mathematical_proof) * [Proof theory](/source/Proof_theory) * [Proof of concept](/source/Proof_of_concept) * [Provability logic](/source/Provability_logic) * [Evidence](/source/Evidence), information which tends to determine or demonstrate the truth of a proposition * [Proof procedure](/source/Proof_procedure) * [Proof complexity](/source/Proof_complexity) * [Standard of proof](/source/Standard_of_proof) * {{annotated link|Proving a negative}} * {{annotated link|Proof of impossibility}} == References == {{Reflist|2}} {{logic}} {{epistemology}} {{Law}} {{DEFAULTSORT:Proof (Truth)}} Category:Automated theorem proving Category:Computational complexity theory Category:Concepts in epistemology Category:Evidence Category:Formal languages Category:Formal systems Category:Legal reasoning Category:Logical truth Category:Metatheory Category:Proof theory --- Adapted from the Wikipedia article [Proof (truth)](https://en.wikipedia.org/wiki/Proof_(truth)) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Proof_(truth)?action=history)). 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