A proof is a supported argument aiming at establishing a conclusion. There exist two types of evidence épistémologiquement considered as valid:

• the evidence based on the Déduction which is absolute or unquestionable in so far as one respects their starting assumptions
• the evidence based on the Induction which is not true that with some Probabilité whose estimate depends on knowledge available (an example to clarify this remark, the estimate which I will make of the probability that a part falls on its with dimensions face will not be the same one if I know that the part is faked).

In the real life, the majority of the evidence, if they can comprise deductive elements, contain despite everything inductive elements which thus confer a certain level of uncertainty to them. The often intuitive evaluation of this level will then determine the degree of confidence which one can bring to the proof. The majority of the evidence used in the everyday life are commonly allowed as being worthy of confidence.

If the degree of confidence of information is not sufficient, one will speak then about Soupçon, Présomption or Indice, but of the convergent indices can mutually reinforce their degrees of confidence and be then regarded as equivalents with a proof and accepted like such. One will speak then about beam of presumptions.

The Theory of probability makes it possible to show that the addition of conditions to a proof not some can increase or decrease its degree of confidence until the certainty or to the rejection (the addition of a part to a legal file can increase or decrease the estimate of culpability and even to guarantee it or reject it completely) but to in no case the addition of conditions to a proof some cannot change its unquestionable character. If that were to arrive, that would mean that the proof was not as certain as it was not thought.

History of the administration of the proof

What one calls a proof can vary during the history, as well as the way in which it is managed.

Composition of the pieces of evidence and evaluation of confidence

not = ¬ and = ∧ or = ∨

If ⇒ B has (has implies B) with a probability P1 and B ⇒ R with a P2 probability, then has ⇒ R with a probability P1*P2.

Different types of evidence

• In Mathematical and Data-processing theoretical, a proof is a demonstration of the truth of a statement. It is a Synonyme with Démonstration .

• In Philosophy, the ontological Proof of Gödel .
• In Right, the proof is used to establish the truth at the time of a lawsuit.
• Proof in civil law
• Proof in criminal law French
• In Data-processing, the electronic proof includes/understands collected data in an automatic way by computers and which are likely to prove the use which was made of an information system and to identify the user.

Simple: Proof

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