No infant is a man. But Lincoln was infant and man: "that infant'' and "that man'' picked Lincoln out at different points in his life. Now consider this argument:
7. that infant = Lincoln,
9. Lincoln = Lincoln, and so
10. that infant = that man.
Taking the descriptions as temporally rigid, the argument is sound, but of course does not prove that someone is both infant and man at once. Taking the descriptions non-rigidly, (7) ceases to be true when Lincoln ceases to be an infant, well before Lincoln is an adult. So the argument is never sound. One might think (10) true even so. But more precisely, what's true is that the person who was that infant = the person who is that man. Strictly speaking, reading the descriptions non-rigidly, (10) is false. For an identity statement is true only if the terms flanking "='' refer to the same item at once, and if we take them non-rigidly, "that infant'' and "that man'' never refer to the same item at once55: nothing is a man while* it is an infant. Let me now introduce a technical term, "phased sortal.''56 "Infant'' and "man'' are phased sortals: they pick out a substance under a description which essentially involves a particular phase of its life. Identity-statements linking temporally non-rigid descriptions involving mutually exclusive phased sortals cannot be true. So with the descriptions non-rigid, (7)-(10) is not only never sound but has a false conclusion.
In the Rockette case, "the leftmost Rockette'' and "the rightmost Rockette'' act as mutually exclusive phased sortals picking out Jane, if we're dealing only with Jane's own timeline. So too, on the account of the Trinity I've been suggesting, "Father'' and "Son'' are mutually exclusive phased sortals picking out God. (1) and (2) are never true at once*: God is not Father while* He is Son. And (4), like (10), cannot be true—though it is of course true that while* God is the Son, God is the God who is also the Father.
55 How about ''remember that infant I pointed out to you years ago? That man over there, the President, is that infant''? This is loose speech for ''that man was that infant,'' i.e. ''the person who is that man was that infant.''
56 See e.g. David Wiggins, Sameness and Substance (Cambridge, Mass.: Harvard University Press, 1980), 24ff.
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