William Tanksley writes:
Bill, you keep using the term "numerically identical", both when talking about the trinity and the incarnation. What do you mean by it?The phrase means nothing to me; it certainly doesn't communicate anything to me in the contexts in which you use it. I wish I could be clearer, but the best I can do is give an example: "a divine mind comes to be numerically identical with a human mind/body complex." What does this mean?
BV: Generally speaking, philosophers use 'numerically' in contrast with 'qualitatively.' If I tell you that I drive the same car as Jane, that is ambiguous: it could mean that Jane and I drive one and the same car, or it could mean that Jane and I drive the same type of car, say a 2004 Jeep Liberty Sport, but not one and the same car. Another example: six bottles of beer in a six-pack are numerically distinct but qualitatively identical. Suppose you want a beer from the six-pack. It won't matter which bottle of the six I hand you since they are all qualitatively the same (or identical), at least with respect to the properties that you would find relevant such as quantity of beer, taste, etc. If I hand you a beer and you say you want a different beer from the same six-pack, you mean a numerically different one. If I reply by saying that they are all the same, I mean they are all qualitatively the same.
If A and B are numerically identical, it follows that they are one and the same. If A and B are qualitatively identical, it does not follow that they are one and the same. (Exercise for the reader: Prove that this last sentence is not equivalent to saying: If A and B are qualitatively identical, it follows that they are not one and the same.)
The doctrine of the Incarnation asserts the numerical identity of the Second Person of the Trinity with a particular man, Jesus of Nazareth. Thus the doctrine does not say that Jesus is a God-like man, or the most God-like man, or the most God-like man possible, but that Jesus is (numerically identical to) God.
I use the phrase 'numerically identical' to underscore the fact that we are talking about one and the same being as opposed to two beings that share many or even all properties.