Proof (truth)

Source: Wikipedia, the free encyclopedia.
For other uses, see Proof.

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

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
law
.

In most disciplines, evidence is required to prove something. Evidence is drawn from the experience of the world around us, with

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] 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.);[15] 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.[16]

Proofs have been presented since antiquity.

rich patterns in nature as proof that nature is not ruled by chance.[18]

Proofs need not be verbal. Before

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
.

Proof vs evidence

18th-century Scottish philosopher David Hume built on Aristotle's separation of belief from knowledge,[21] 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, does one know the roommate did it.

In an absolute sense, one can be argued not to "know" anything, except for the existence of one's own thoughts, as 17th-century philosopher

Descartes addressed when saying cogito, ergo sum (I think, therefore I am). While Descartes was attempting to "prove" logically that the world exists, his legacy in doing so is to have shown that one cannot have such proof, because all of one's perceptions could be false (such as under the evil demon or simulated reality
hypotheses). But one at least has proof of one's own thoughts existing, and strong evidence that the world exists, enough to be considered "proof" by practical standards, though always indirect and impossible to objectively confirm.

See also

Wikiquote has quotations related to Proof.

References

  1. ISBN 0883855674
    pages 12–20
  2. ISBN 0521280303
    pages 60–63
  3. ISBN 0199261954
    pages 1–2
  4. ISBN 1445530139
    pages 5–15
  5. ^ Compare 1 Thessalonians 5:21: "Prove all things [...]."
  6. ISBN 0-674-41152-8
    .
  7. ^ Cupillari, Antonella. The Nuts and Bolts of Proofs. Academic Press, 2001. Page 3.
  8. ISBN 0-19-504472-X
  9. ^ "Foundationalist Theories of Epistemic Justification". The Stanford Encyclopedia of Philosophy. Metaphysics Research Lab, Stanford University. 2018.
  10. ^ "Definition of proof | Dictionary.com". www.dictionary.com.
  11. ^ Reference Manual on Scientific Evidence, 2nd Ed. (2000), p. 71. Accessed May 13, 2007.
  12. ^ John Henry Wigmore, A Treatise on the System of Evidence in Trials at Common Law, 2nd ed., Little, Brown, and Co., Boston, 1915
  13. JSTOR 3052837
    .
  14. ^ Katie Evans; David Osthus; Ryan G. Spurrier. "Distributions of Interest for Quantifying Reasonable Doubt and Their Applications" (PDF). Archived from the original (PDF) on 2013-03-17. Retrieved 2007-01-14.
  15. ISBN 0-521-77911-1
    .
  16. ^ Hunter, Geoffrey, Metalogic: An Introduction to the Metatheory of Standard First-Order Logic, University of California Press, 1971
  17. ISBN 0813521920
    p. 70
  18. ISBN 0872208052
    p. 198
  19. ^ Thomas S. Kuhn, The Copernican Revolution, pp. 5–20
  20. ISBN 159031767X
    page 47
  21. ^ David Hume
  22. ^ Locke: Knowledge of the External World
Retrieved from "https://en.wikipedia.org/w/index.php?title=Proof_(truth)&oldid=1162074535"