I was thinking about the PSR. when it comes to the set of all contingent things, it seems that the set must also be contingent and could fail to exist because each member could fail to exist. but could there be a necessary proposition which says that some unspecified contingent things must exist, meaning that if any specific fact in the set had failed to exist another unspecified fact would have taken its place. first: is there an error in what I said? second: if there is no error would not the set of all contingent things be necessary?
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"Contingent" and "necessary" are just very ill-defined ideas. To decide what's contingent or what's necessary ultimately comes down to ad hoc appeal to intuition, but the "intuition" isn't backed up by anything clear. I don't think these ideas have ever been applied to produce any valuable philosophical result.– causativeCommented Jul 10 at 0:13
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If your set of all contingencies restrictedly built up even cumulatively from this actual world's beginning as a potentially uncountably infinite or even large cardinal sequence of atomic facts and it exists or exists as a class, then under the canonical PW semantics apparently such a perceived or conceived totality is still contingent as another PW could have different atoms. But per weak (modal) PSR the totality across all PWs could be said to be necessary, or equivalently any contingency causing you to time-travel back and change yourself in this actual world if you could is necessary...– Double KnotCommented Jul 10 at 3:19
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2 Answers
All sets exist in mind. They are discerned through the activity in consciousness. Mind and consciousness are impermanent. When consciousness itself is not there then there is no knowledge of sets. Nor there is any tendency to figure out the sets. There are no facts either. Therefore set of all contingent things is itself impermanent. It arises , changes and vanishes. We can say set of all contingent things is itself contingent. In other words , set of all contingent things are not necessary. There cant be a necessary proposition that unspecified contingent things must exist.
Sometimes it is said that the singleton of a contingent object is itself a contingently existing set.h On the other hand, by the foundation axiom, if there were a set of all contingencies and this set was itself one of the contingencies, then this set would be an element of itself, contrary to what foundation allows (I think). But so the set would necessarily exist, albeit not quite in the way that abstract sets are supposed to necessarily exist (by having the specific elements it has of necessity first).
Like, if you take the containment metaphor at face value, it'd be like saying you have the huge box of all contingencies regardless of the contents of the box (even down to zero content).
hAnd sometimes they associate singletons of objects with haecceities of those objects (and the association runs the gamut from involvement to identity of relation). But there is less pressure to conceive of haecceities as contingent upon the things that they are haecceities of (this is what makes for a whole metaphysics of possible worlds in terms of uninstantiated haecceities).
answered Jul 9 at 23:47
