For, in many cases, whether or not a structural fact exists depends not only on the existence of its constituent facts but also on the absence of certain others (Armstrong 1997, 34ff).
However, if o were to bind with a further hydrogen atom h3, then, despite the fact that the constituent facts of W would still hold, W would not be water; there would be no such fact as W's being water.[47] Rather, W would exist only as a complex part of a hydronium ion; the new binding [B,o,h3] would, so to say, "spoil" the instantiation of Water.
Thus, the items categorized in Aristotle's categories are the constituents of facts.
The constituents of facts contribute to facts as the semantically relevant parts of a proposition contribute to its having the truth conditions it has.
Otherwise put, as simples exist only insofar as they are constituents of facts, there seems no reason why there couldn't have been a very small number of facts, indeed, just a single simple, atomic, monadic fact and, hence, a lone simple object and a lone simple universal.
More specifically, we could say that P relevantly entails Q only if the fact that would make P true is at least a constituent of the fact that would make Q true.
Nothing could be done about this short of devising entirely new repertories for all the constituent companies; in fact, one of them, but only one, was up to this challenge: the New York City Ballet, under George Balanchine's direction.
In laboratory experiments of similar phase transitions for example, the solidification of a liquid into a solid involving two or more substances, the final state may contain a very uneven distribution of the constituent substances, a fact exploited by industry to purify certain materials.
Russell did often speak about the constituents of atomic facts as independently existing entities.
Such a "logically ideal language", as Russell at times called it, would, besides logical constants, consist only of words representing the constituents of atomic facts.
That I have grey hair entails that someone has grey hair, but is my having grey hair a constituent of the fact that is someone's having grey hair?
