I have seen some argue that any relative identity claim can be reduce to an absolute identity claim in the following manner:
1) x and y are the same F ≝ x is an F, y is an F, and x = y.
However, I don’t think this works. Part of the motivation for relative identity is that there may be circumstances like:
2) x and y are the same F, but x and y are not the same G.
But (1) and (2) are not compatible, since we would have to affirm and deny absolute identity between x and y. So the relative identity theorist should reject (1) given his commitment to (2).
Relative identity is not just absolute identity, plus the idea that x and y fall under the same sortal. Moreover, this would be to suggest that relative identity is derivative, and absolute identity is the more primitive notion. I would argue that is it the other way around. So I would define absolute identity in terms of relative identity in the following manner:
4) x = y ≝ for any sortal, S, if x is an S or y is an S, then x and y are the same S.
In other words, the absolute identity between x and y is derived from the fact that for any sortal which belongs to either x or y, it is the case that x and y count as the same S. I say “either x is an S, or y is an S” as opposed to “both x is an S and y is an S” to avoid situations where x can be counted as an S and some y cannot, but they are the same S for any sortal underwhich both can be counted. For there to be absolute identity, it must be the case that all sortals that belong to x must also belong to y. I believe (4) captures this.
So to say x and y are absolutely identical is to say that for any sortal underwhich x or y can be counted, x and y are the same sortal.
Following the death of his wife Helen Joy, C.S. Lewis wrote some reflections which were gathered up into A Grief Observed. In one section he wrote,
If H. ‘is not,’ then she never was. I mistook a cloud of atoms for a person. There aren’t, and never were, any people. Death only reveals the vacuity that was always there. What we call the living are simply those who have not yet been unmasked. All equally bankrupt, but some not yet declared.
But this must be nonsense; vacuity revealed to whom? Bankruptcy declared to whom? To other boxes of fireworks or clouds of atoms? I will never believe–more strictly I can’t believe–that one set of physical events could be, or make, a mistake about other sets (1989, 41)1
It seems to me that this is a powerful objection to a naturalistic worldview. I do not understand how it could be that the physicalist accounts for the identity and individuation of persons. In fact, I think that if physicalism is true, there could be no persons to know it is true. I would argue as follows:
1. If physicalism is true, then there are no objective criteria for individuating and identifying persons.
2. If there are no objective criteria for individuating and identifying persons, then no persons exist.
3. If no persons exist, then I cannot experience love for my wife.
4. If I experience love for my wife, then there must be persons.
5. I experience love for my wife.
6. Therefore, physicalism is false.
In other words, if the physicalist is to convince me that my experiences belie reality, they still must appeal to me and “my experiences”. If my experiences are to be false and I am mistaken, then there must be criteria for individuating and identifying me from the rest of the physical universe. These criteria cannot be subjective, arbitrary, and ad hoc. Rather, they must be objective, essential, and real. But, I think we have good reason to think premise 1 is true. Organisms constantly change in that which they are physically composed. The physicalist might say that the pattern remains the same, but they really mean that patterns are similar. Consider the physicalist who supposes that a transporter might copy a human, decompose the matter at one location and reproduce the pattern perfectly elsewhere. The physicalist might say that the human has been transported like a faxed message. But if the original is not destroyed when the copy is produced, the physicalist struggles to explain what has happened. Are both the copy and the original the same person? The struggle reveals the point that even if all physical facts of a person are copied and reproduced in matter elsewhere, there is still something non-physical through which a person is identified and individuated as the self-same person. So, I would challenge the physicalist to supply these objectively real criteria. For, without such an account, I could hardly be faulted for thinking that these real and objective criteria are found in non-physical realities–in what the supernaturalist calls the “soul”.
1C.S. Lewis. (1961). A Grief Observed. New York: Harper Collins Publishers.