Abstract
We critically examine the claim that identity is a fundamental concept. According to those putting forward this thesis, there are four related reasons that can be called upon to ground the fundamental character of identity: (1) identity is presupposed in every conceptual system; (2) identity is required to characterize individuality; (3) identity cannot be defined; (4) the intelligibility of quantification requires identity. We address each of these points and argue that none of them advances compelling reasons to hold that identity is fundamental; in fact, most of the tasks that seem to require identity may be performed without identity. So, in the end, identity may not be a fundamental concept after all.
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Notes
For instance, individuality could be characterized by requiring that an individual must exemplify an intrinsic property that discerns it from every other item (following Caulton and Butterfield 2012). In this case, the claim that quantum entities are non-individuals (that is, that they fail this specific condition) could be assumed also in quantum field theories, at least if we agree with Wolfgang Ketterle (Ketterle 2007), for instance when he says that "Electrons everywhere in the world are excitations of the same field and therefore they are absolutely identical.” Notice that here Ketterle uses “identical” in the physicists jargon, meaning “indiscernible”. In this case, of course, what Ketterle means is that no such intrinsic property to grant individuation can be found.
F. P. Ramsey has questioned Whitehead and Russell’s definition of identity in terms of indistinguishability in their Principia Mathematica, claiming that “the definition makes self-contradictory for two [different] things to have all their elementary properties in common. Yet this is really perfectly possible, even if, in fact, it never happens. Take two things a and b. Then there is nothing self-contradictory in a having any self-consistent set of elementary properties, nor in b having this set, nor therefore, obviously, in both a and b having all their elementary properties in common. Hence, since this is logically possible, it is essential to have a symbolism with allows us to consider this possibility and does not exclude it by definition.” (Ramsey 1950, p. 31).
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Krause, D., Arenhart, J.R.B. Is Identity Really so Fundamental?. Found Sci 24, 51–71 (2019). https://doi.org/10.1007/s10699-018-9553-3
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DOI: https://doi.org/10.1007/s10699-018-9553-3