Numerical identity
The concept of identity originally comes from logic, where it designates the relationship in which each object stands to itself and to no other. In this sense one speaks of "numerical identity", because this relation forms the basis of the operation of counting, in which identical objects are counted as one object, as opposed to objects that may be arbitrarily similar but are numerically different. The relation of the numerical identity does not allow gradual increments: Two objects are either identical in the numerical sense, when they are actually one and the same object, or they are not. If, on the other hand, a person is said to have undergone a more or less profound change in their identity, then the gradual nature of this change alone suggests that claims of this type are not based on a numerical understanding of personal identity. If interpreted as statements about numerical identity, formulations such as "P's identity has changed" or "P has lost his identity" are even contradictory, because they obviously presuppose the continued existence of the person whose identity has changed or who has lost their identity. After all, the assertion of a change of numerical identity implies precisely that a new person takes the place of the original one.
Apart from its origins in logic, the concept of numerical identity can be found in the context of ethics and applied ethics, particularly in the areas of enhancement, ageing, diseases such as dementia, but also organ donation (see module Controversy about the concept of personhood and module Literature on enhancement and identity).
For further information on the concept of numerical identity, see:
Locke, J. (1690): An Essay Concerning Humane Understanding. London: Thomas Basset.
Kant, I. (2002): Groundwork of the Metaphysics of Morals [1785]. Transl. by M. J. Gregor, with an introd. by C. Koorsgard. Cambridge: Cambridge University Press.
Parfit, D. (1984): Reasons and Persons. New York: Oxford University Press.
Quante, M. (Hg.) (1999): Personale Identität. Stuttgart: UTB.
Quante, M. (2007): Person. Berlin/New York: De Gruyter.
For further information on numerical identity in an ethical context, see:
Knell, S. (2022): Demenz: Ethische Aspekte. In: Sturma, D. / Lanzerath, D. (Hg.): Demenz. Naturwissenschaftliche, rechtliche und ethische Aspekte. Sachstandsberichte des DRZE 23. Baden-Baden: Nomos. Online Version (German)
Gasser, G. (2022): Personale Identität, Verkörperung und Personentransfers: Eine identitätstheoretische Skizze. In: Willmann, T. / El Maleq, A. (Hg.): Sterben 2.0: (Trans-)Humanistische Perspektiven zwischen Cyberspace, Mind Uploading und Kyronik. Berlin/Boston: De Gruyter. Online Version (German)
Sturma, D. (2021): Identität der Person. In: Fuchs, M. (Hg.): Handbuch Alter und Altern. Stuttgart: J. B. Metzler, 348–354.
Segawa, S. (2020): Der Begriff der Person in der biomedizinischen Ethik. Paderborn: Brill/Mentis
Dufner, A. (Hg.) (2018): Schwerpunkt: Philosophie der Demenz. In: Zeitschrift für Praktische Philosophie, 5 (1), 73–230. Online Version (German)
Quante, M. (2017): Personal Identity as a Principle of Biomedical Ethics. Cham: Springer.
Therein in particular: Dufner, A. (2018): Einleitung: Demenz und personale Identität. In: Zeitschrift für Praktische Philosophie, 5 (1), 73–80. Online Version (German)