The Conservation of Identity
2 October 2010
Now it is already fall, and I find myself harking back to some thoughts I had in the spring. I have mentioned previously that I planned to return to my post on The Loss of Objecthood, but was dealt a setback by the theft my computer which had my manuscript for this reflection by way of return. (Is it irony or destiny that this reflection upon loss should have been followed by a loss, demonstrating personally and poignantly the catastrophe of loss?) What I still hope to say about this needs to be said, but it is complicated and the exposition will therefore take some effort. In the meantime, I have another idea that I can relate in relatively brief compass.
In The Loss of Objecthood, Negative Organicism, and Submergent Properties I considered the possibility of wholes that are less than the sum of their parts, in contradistinction to the more familiar idea of wholes that are more than the sum of their parts. The distinction implicit in this recognition of negative organicisms also points to the possibility of a trichotomy: wholes that are more than the sum of their parts, wholes that are less than the sum of their parts, and wholes that are equal to the sum of their parts.
This mereological trichotomy in turn suggests the possibility of what we may call the conservation of identity. What do I mean by the conservation of identity? Allow me to attempt an explanation.
When a number of individual objects join together and become parts of a larger whole, it sometimes seems to be the case that the individual identities of the objects are lost within the unity of the whole. This would seem to be a straight-forward case of negative organicism, but it also seems to be the case that the loss of individual identity is often compensated by the simultaneous acquisition of a corporate identity derived from the whole into which the object has been absorbed as a part.
In this latter case, when the many become one, the loss of individual identities means that the total number of identities in the world has been decreased by the emergence of a whole that submerges these individual identities, and in this sense there is no conservation of identity. But in so far as every object that previously had an identity still possesses an identity, even if this identity has been substituted with another identity, then there is a conservation of identity at the level of a one-to-one correspondence between objects and their identities.
Contrariwise, when then one becomes many, and a corporate identity collapses, the objects that were the constituent parts of the whole re-gain their individual entities even as they lose the identity conferred upon them by the mereological participation in the identity of the whole. In this case there would appear to be an increase in the absolute number of identities in the world, but again the conservation of identity is maintained at the level of one-to-one correspondence between objects and identities.
This one-to-one correspondence between objects and identities could be understood to be a function of the famous Quinean dictum of “No entity without identity.”
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