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→Logical proof: clarif.
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.
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 would need to attempt to redetermine the thought-to-be "better-known" genus of "nuts" in the condition "eating nuts make me allergic" with the implied, qualified subject of the dubious conclusion, "soft-shelled nuts". So that, until that happens, the conditional premise, whatever use it eventually has, containing the genus "nuts" would no longer be better-known than the conclusion due to that premise having notions about the species "hard-shelled nuts" that contradict information alleged in the conclusion.
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 would need to attempt to redetermine the thought-to-be "better-known" genus of "nuts" in the condition "eating nuts make me allergic" with the implied, qualified subject of the dubious conclusion, "soft-shelled nuts". So that, until that happens, the conditional premise, whatever use it eventually has, containing the genus "nuts" would no longer be better-known than the conclusion due to that conditional premise having notions about the species "hard-shelled nuts" that contradict information alleged in the conclusion.
==Mathematical proof==
==Mathematical proof==