Proof (logic)
A proof is a series of logical inferences that are supposed to reduce the truth of a proposition to what is assumed to be true.
Proof in the strict sense
In a strict sense, the assertion is inferred with certainty from sentences recognized or accepted as true. In this case one speaks of strict or deductive or progressive proofs. or from apodictic evidence. A fully formalized proof in a calculus consisting of individual formal derivation steps is called a derivation .
Proof in the weak sense
In a less strict sense, what has been said does not follow with certainty, but it is very likely . The less strict forms of proof include proof by analogy, regressive proof, and inductive proof. In this sense, every argument is evidence. These proof procedures are usually not accepted as proof in mathematics and mathematical logic.
Regressive evidence
In the case of regressive proof, as many conclusions as possible are drawn from what is to be proven. If these are all true, one can assume with a high degree of probability that the proposition to be proved is also true.
Inductive proof
In an inductive proof, one inferred from a part of a whole about the whole. If all ravens observed so far were black, it is concluded that all ravens are black.
Individual evidence
- ^ Veit Pittioni: Proof . In: Peter Prechtl / Franz-Peter Burkard (Hrsg.): Metzler-Philosophie-Lexikon: Terms and Definitions Stuttgart / Weimar: Metzler 1996, 70
- ↑ Friedrich Kirchner: Dictionary of basic philosophical terms . Heidelberg: Weiss 1890 (2nd edition), p. 62
- ^ Veit Pittioni: Proof . In: Peter Prechtl / Franz-Peter Burkard (Hrsg.): Metzler-Philosophie-Lexikon: Terms and Definitions Stuttgart / Weimar: Metzler 1996, 70