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→Logical proof: + corr. & examp.
5. Since premises are to be related to their conclusion through cause and effect, they must be as ''necessarily'' true as the desired necessary truth of the conclusion would demand: either ''rigorously proven'' themselves or ''self-evident'', without the truth or its necessity narrowing as it goes down the syllogistic chain to the point where it could no longer apply to the conclusion.
5. Since premises are to be related to their conclusion through cause and effect, they must be as ''necessarily'' true as the desired necessary truth of the conclusion would demand: either ''rigorously proven'' themselves or ''self-evident'', without the truth or its necessity narrowing as it goes down the syllogistic chain to the point where it could no longer apply to the conclusion.
However a state of "conditional necessity" may exist in the premises, so long as the condition is not determined by the subject of the conclusion as per requirement 4, but is rather an "assumption for a conditional proof", an assumption which would appear prior to the validly co-ordinated and soundly applied series of premises.
However, a state of "conditional necessity" may exist in the premises, so long as the condition is not determined by the subject of the conclusion as per requirement 4, but is rather an "assumption for a conditional proof", an assumption which would appear somewhere in the validly co-ordinated and soundly applied series of premises.
As an example, a conditional proof or demonstration would fail its "better-known" soundness criterion if one assumed as a condition "eating nuts make me allergic" and yet conclude in a simple way, "Walnuts are nuts with hard shells; I can eat walnuts and not get allergic." The would-be conclusion attempts to redetermine the thought-to-be "better-known" conditional genus of "nuts" in the condition "eating nuts make me allergic" with the subject of the dubious conclusion, "soft-shelled nuts", so that the genus of the premise would no longer be better-known.
==Mathematical proof==
==Mathematical proof==