Furthermore, even though necessary truth can be determined in polynomial time, possible truth is NP-hard.
Latent in this distinction for Kant is the antithesis between necessary truth and contingent truth.
As Wittgenstein had already shown, the necessary truth of tautologies simply amounts to their being true under all conceivable circumstances.
(ii) Although the MTC for necessary truth is correct, the MTC for possible truth is incorrect: it provides necessary but insufficient conditions for ensuring possible truth.
From his pessimistic perspective, Mr. Berlusconi's outburst at the European Parliament was a moment of bracing and necessary truth.
Among them areLp ⊃ LLp, Mp ⊃ LMp, and p ⊃ LMp.The first of these means that if a proposition is necessary, its being necessary is itself a necessary truth; the second means that if a proposition is possible, its being possible is a necessary truth; and the third means that if a proposition is true, then not merely is it possible but its being possible is a necessary truth.
The modal system known as T has as axioms some set of axioms adequate for PC (such as those of PM), and in addition Lp ⊃ p L(p ⊃ q) ⊃ (Lp ⊃ Lq) Axiom 1 expresses the principle that whatever is necessarily true is true, and 2 the principle that, if q logically follows from p, then, if p is a necessary truth, so is q (i.e., that whatever follows from a necessary truth is itself a necessary truth).
That was a hard but necessary truth, and Mr. Bloomberg must now steel himself for months of wrestling with the city's powerful unions.
Alan Sidelle (1989) advocates conventionalism about necessary truth.
But (4) does not seem to be a necessary truth.
On the other hand, (3) is clearly a necessary truth.
