Suppose we have a thing A and a property F, and A has F. But suppose that A has F contingently: A could have lacked the property F even though A existed, even though F existed, or even though both existed together. And suppose that F is an intrinsic property: when something has F, that is entirely a matter of the nature of that thing itself, not at all a matter of its relations to other things. (Fill in an example if you like; but beware lest your example raise irrelevant questions about whether the property you chose really is a property in the fullest sense of the word, and whether it really is intrinsic.)

If we believe Armstrong, there must then exist a second thing, B. B is entirely distinct from A, and from F, and so from both together; yet B's existence is necessarily connected to whether or not A has F. Necessarily, if A has F, as it does, then B must exist; necessarily, if A had lacked F, as it might have done, then B could not have existed.

That is the central thesis of Armstrong's book. It is strange. If two things are entirely distinct, as A and B have been said to be, we want to say that questions about the existence and intrinsic nature of one are independent of questions about the existence and intrinsic nature of the other. Since Melbourne and Sydney are entirely distinct, Mel-bourne could exist without Sydney, or Sydney without Melbourne, or both of them could exist together, or neither.