The Info List - Proof (truth)

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A proof is sufficient evidence or a sufficient argument for the truth of a proposition.[1][2][3][4] The concept applies in a variety of disciplines,[5] 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.[6] 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.[7] The subject of logic, in particular proof theory, formalizes and studies the notion of formal proof.[8] In some areas of epistemology and theology, the notion of justification plays approximately the role of proof,[9] while in jurisprudence the corresponding term is evidence,[10] with "burden of proof" as a concept common to both philosophy and law. On proof[edit] In most disciplines, evidence is required to prove something. Evidence is drawn from experience of the world around us, with science obtaining its evidence from nature,[11] law obtaining its evidence from witnesses and forensic investigation,[12] 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.[13][14][15] 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.);[16] 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.[17] 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.[18] On the other hand, Thomas Aquinas
Thomas Aquinas
used the observation of the existence of rich patterns in nature as proof that nature is not ruled by chance.[19] 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.[20] 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.[21] 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. See also[edit]

Wikiquote has quotations related to: Proof

Mathematical proof Proof theory Proof of concept Provability logic Evidence, information which tends to determine or demonstrate the truth of a proposition Proof procedure Proof complexity Standard of proof


^ Proof and other dilemmas: mathematics and philosophy by 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 ^ Compare 1 Thessalonians 5:21: "Prove all things [...]." ^ John Langshaw Austin: How to Do Things With Words. Cambridge (Mass.) 1962 – Paperback: Harvard University Press, 2nd edition, 2005, ISBN 0-674-41152-8. ^ Cupillari, Antonella. The Nuts and Bolts of Proofs. Academic Press, 2001. Page 3. ^ 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 ^ http://plato.stanford.edu/entries/justep-foundational/ ^ http://dictionary.reference.com/browse/proof ^ Reference
Manual on Scientific Evidence, 2nd Ed. (2000), p. 71. Accessed May 13, 2007. ^ John Henry Wigmore, A Treatise on the System of Evidence
in Trials at Common Law, 2nd ed., Little, Brown, and Co., Boston, 1915 ^ Simon, Rita James & Mahan, Linda. (1971). "Quantifying Burdens of Proof—A View from the Bench, the Jury, and the Classroom". Law and Society Review. 5 (3): 319–330. doi:10.2307/3052837. JSTOR 3052837.  ^ Katie Evans; David Osthus; Ryan G. Spurrier. "Distributions of Interest for Quantifying Reasonable Doubt
and Their Applications" (PDF). Retrieved 2007-01-14.  ^ The Principle of Sufficient Reason: A Reassessment by Alexander R. Pruss ^ 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. ^ Hunter, Geoffrey, Metalogic: An Introduction to the Metatheory of Standard First-Order Logic, University of California Pres, 1971 ^ Aristotle's Physics: a Guided Study, Joe Sachs, 1995 ISBN 0813521920 p. 70 ^ The treatise on the divine nature: Summa theologiae I, 1–13, by Saint Thomas Aquinas, Brian J. Shanley, 2006 ISBN 0872208052 p. 198 ^ Thomas S. Kuhn, The Copernican Revolution, pp. 5–20 ^ Trial
tactics by Stephen A. Saltzburg, 2007 ISBN 159031767X page 47

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Argumentation theory Axiology Critical thinking Logic
in computer science Mathematical logic Metalogic Metamathematics Non-classical logic Philosophical logic Philosophy of logic Set theory


Abduction Analytic and synthetic propositions Antinomy A priori and a posteriori Deduction Definition Description Induction Inference Logical form Logical consequence Logical truth Name Necessity and sufficiency Meaning Paradox Possible world Presupposition Probability Reason Reference Semantics Statement Strict implication Substitution Syntax Truth Validity



Mathematical logic Boolean algebra Set theory


Logicians Rules of inference Paradoxes Fallacies Logic

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Thomas Aquinas Augustine of Hippo William Alston Robert Audi A. J. Ayer George Berkeley Laurence BonJour René Descartes John Dewey Fred Dretske Edmund Gettier Roger Gibson Alvin Goldman Nelson Goodman Paul Grice David Hume Immanuel Kant Søren Kierkegaard Saul Kripke David Lewis John Locke G. E. Moore Robert Nozick Alvin Plantinga Plato Hilary Putnam Thomas Reid Gilbert Ryle P. F. Strawson Willard Van Orman Quine Bertrand Russell Baruch Spinoza Timothy Williamson Ludwig Wittgenstein Nicholas Wolterstorff Vienna Circle


Coherentism Constructivist epistemology Contextualism Determinism Empiricism Evolutionary epistemology Fallibilism Feminist epistemology Fideism Foundationalism Genetic epistemology Holism Infinitism Innatism Internalism and externalism Naïve realism Naturalized epistemology Phenomenalism Positivism Reductionism Reliabilism Representative realism Rationalism Skepticism Theory
of forms Transcendental idealism Uniformitarianism


A priori knowledge Analysis Analytic–synthetic distinction Belief Causality Common sense Descriptive knowledge Exploratory thought Gettier problem Justification Knowledge Induction Objectivity Problem of induction Problem of other minds Perception Proposition Regress argument Simplicity Speculative reason Truth more...

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