Construct · 2 fields · 5 citations

Where does proof collide?

One name. Different field. Different construct. One map.

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proof2 CONSTRUCTSMathematical proofEUCLID · DEMONSTRATIONLegal proofPAULUS · ONUS PROBANDI

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1898Legal proof1908Mathematical proof
2026

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Mathematics and logic

A deductive demonstration of a theorem

In mathematics a proof is a finite chain of deductions that establishes a statement with certainty from accepted axioms and earlier results. Euclid's Elements (c. 300 BCE) fixed this pattern by deriving each geometric proposition step by step from a small set of postulates and common notions, and Hilbert and Ackermann's 1928 Grundzüge der theoretischen Logik later recast a proof as a formal object: a sequence of formulas each of which is an axiom or follows from earlier ones by stated rules. Rav's 1999 Why do we prove theorems? examined how working mathematicians use such arguments to convey understanding and not only to certify truth. Here the referent is a deductive argument that compels assent, unlike a fact weighed to a legal standard or a trial sheet pulled from a press.[1][2][3]

Unit
One valid proof of a single theorem, a finite sequence of justified steps
Recovery means
Not applicable
Measured by
Judged by whether each step follows from axioms and prior results under accepted rules of inference, and increasingly checked by proof assistants

Law

Establishing a fact to a required standard

In law proof is the process of establishing a disputed fact to the standard a tribunal requires, together with the question of which party must do the establishing. The Roman jurist Paulus stated the governing rule in Justinian's Digest (533 CE, Book 22, Title 3): the burden of proof lies on the one who asserts, not on the one who denies. Thayer's 1898 A Preliminary Treatise on Evidence at the Common Law traced how the common law separated the burden of producing evidence from the burden of persuasion, and set out thresholds such as the balance of probabilities and proof beyond reasonable doubt. Here the referent is the persuasion of a fact-finder to a fixed threshold, not a deductive certainty in mathematics or a corrected sheet in a print shop.[4][5]

Unit
One disputed fact established, or not, against a stated threshold by the party who bears the burden
Recovery means
Not applicable
Measured by
Assessed by whether the evidence meets the threshold, such as the balance of probabilities or proof beyond reasonable doubt

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Nearby collisions

burden3 fields · 6 citationsjingle · one word, three constructsargument3 fields · 3 citationsjingle · one word, three constructsdeduction3 fields · 4 citationsjingle · one word, three constructs

References

  1. Euclid. (c. 300 BCE). Elements (T. L. Heath, Trans., 1908). Cambridge University Press.
  2. Hilbert, D., & Ackermann, W. (1928). Grundzüge der theoretischen Logik. Springer.
  3. Rav, Y. (1999). Why do we prove theorems? Philosophia Mathematica, 7(1), 5–41. https://doi.org/10.1093/philmat/7.1.5
  4. Justinian. (533). Paulus, Digest 22.3.2 (De probationibus et praesumptionibus). In A. Watson (Ed. & Trans., 1985), The Digest of Justinian. University of Pennsylvania Press.
  5. Thayer, J. B. (1898). A Preliminary Treatise on Evidence at the Common Law. Little, Brown.

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