Aliases: [ Types of atemporal collection in which membership is necessarily essential ]
A collection of collections. Each instance COL of type of atemporal collection in which membership is necessarily essential (ANECT) is a collection satisfying three conditions: (1) COL is disjoint with (see Disjoint With) thing that exists in time, (2) every instance INST of COL is an instance of COL essentially (i.e. INST is an instance of COL, and could not exist without being an instance of COL), and (3) condition (2) is a necessary truth about COL.
Positive examples of ANECTs include type of thing, integer, and relationship (each of which is a collection of atemporals and is such that, necessarily, all of its instances are in it essentially). Negative examples include spatial thing (though arguably it is necessary that all of its instances are essentially instances of it, it is not disjoint with thing that exists in time) and type of unique anatomical part (which, though disjoint with thing that exists in time, has instances, such as heart, that could exist even if they weren't instances of it; e.g. it might have been the case that every creature with a heart had at least two hearts). There are no known examples of Cyc-reified collections satisfying conditions (1) and (2) but not (3), but one can be contrived. Suppose that all of today's winning lottery numbers were primes. Now consider the collection:
This collection is clearly disjoint with thing that exists in time and, by hypothesis, all of its instances are in it essentially (as each prime number is essentially a prime number). But this last fact is not necessarily true of this collection: the collection might have had instances that belonged to it only contingently (i.e. not essentially), as it might have been the case that one of today's winning lottery numbers was non-prime, and no number is such that it is essentially one of today's winning lottery numbers.
When asserting that something is an instance or specialization of a given instance of ANECT, it is appropriate to do so in the things known independent of context (q.v.). Indeed, ANECT was specially defined to facilitate the movement of appropriate assertions to that microtheory.
COLof type of atemporal collection in which membership is necessarily essential (ANECT) is a collection satisfying three conditions: (1)COLis disjoint with (see Disjoint With) thing that exists in time, (2) every instanceINSTofCOLis an instance ofCOLessentially (i.e.INSTis an instance ofCOL, and could not exist without being an instance ofCOL), and (3) condition (2) is a necessary truth aboutCOL.Positive examples of ANECTs include type of thing, integer, and relationship (each of which is a collection of atemporals and is such that, necessarily, all of its instances are in it essentially). Negative examples include spatial thing (though arguably it is necessary that all of its instances are essentially instances of it, it is not disjoint with thing that exists in time) and type of unique anatomical part (which, though disjoint with thing that exists in time, has instances, such as heart, that could exist even if they weren't instances of it; e.g. it might have been the case that every creature with a heart had at least two hearts). There are no known examples of Cyc-reified collections satisfying conditions (1) and (2) but not (3), but one can be contrived. Suppose that all of today's winning lottery numbers were primes. Now consider the collection:
(Collection Union Fn (The Set prime number TodaysWinningLotteryNumbers))
This collection is clearly disjoint with thing that exists in time and, by hypothesis, all of its instances are in it essentially (as each prime number is essentially a prime number). But this last fact is not necessarily true of this collection: the collection might have had instances that belonged to it only contingently (i.e. not essentially), as it might have been the case that one of today's winning lottery numbers was non-prime, and no number is such that it is essentially one of today's winning lottery numbers.
When asserting that something is an instance or specialization of a given instance of ANECT, it is appropriate to do so in the things known independent of context (q.v.). Indeed, ANECT was specially defined to facilitate the movement of appropriate assertions to that microtheory.
Cf. pragmatically decontextualized collection.