But even the most devoted Cartesian would have had a hard time understanding the full import of propositions one through fifteen.
Beside its own merits (mathematics is full of such propositions), this kind of analyticity is an intermediate step towards logical analyticity.
Daily religious belief is full of such implied propositions (e.g., "God is just"; "God saves my soul"; "Christ was God made man").
And a fist full of "No on Proposition 60" pamphlets.
So writing books upon books without the intention of sharing them with people is a proposition full of contradictory impulses and goals.
But its game-changing follow-up, Malibu, is a much deeper proposition, full of long-buried and painful childhood memories, transformed into bittersweet melodies and woozy, punch-drunk raps.
Unlike many of their small farmer colleagues who fear that legalization will depress prices or drive them out of business altogether, Chaitanya and Lastreto are full-throated supporters of Proposition 64, which will not only usher in an era of regulations and licensing, but also will give existing small growers a five-year head start before licenses for larger grows are granted.
(To see how a set of propositions could serve as a possible world, notice that if you believed in full-blown possible worlds — worlds that are just like the actual world in kind — then you would say that corresponding to each of these worlds, there is a set of propositions that completely and accurately describes the given world, or is true of that world.
Moreover, consistency for full belief derives from the concept of belief as holding propositions to be true and from the logic of propositions, without any such assumed tie to action, and although Ramsey thought that such a connection was necessary to clarify the idea of partial belief, it seems that a fully analogous characterization of consistency for partial belief should do without it.
More generally, when we reach necessity, haven't we reached the end of explanations?[15] Not always: mathematics is full of asymmetrical dependence relations among necessarily true propositions.
