Friday, September 20, 2019

Certainty, Necessity, Sufficiency

As has been previously discussed, one inadequacy of Descartes' condition of Certainty to Truth is that it is merely Subjective, while the latter is Objective.  Accordingly, Necessity is a more accurate indication of Truth.  However, as even contemporary practitioners of Modal Logic acknowledge, Necessity is not the strongest Logical condition.  Rather, it is Sufficiency.  Nevertheless, Logicians seem to lack a direct representation of Sufficiency, usually defining it only indirectly, i. e. negatively.  Likewise, the usual standard of Necessity, the Principle of Contradiction, is inadequate as a direct determinant of Sufficiency.  In contrast, Necessity can be derived directly from Sufficiency, as a special case--Unique Sufficiency, i. e. if A is the only sufficient condition of B, then it is also its Necessary condition. Instead, only adequate in that regard is a Principle of Sufficient Reason, whatever that might entail.  Now, while Descartes' Method seeks to establish Certainty, it does involve Sufficiency in one respect--in that very task.  In other words, implicit in its operation is the supposition that it suffices to determine Truth, a supposition that, as has been previously discussed, becomes falsified when Descartes must resort to the adoption of other Methods to establish the Truth of propositions beyond 'I exist' and 'God exists'. Similarly, in a comprehensive Logical system, a means of generating new propositions out of an initial set of tautological propositions is required.  However, Sufficiency never becomes an explicit criterion in Descartes' seminal works of Modern Philosophy.

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