Let the I-relation be the relation that holds between person-stages of a continuant person. On the psychological-continuity approach to personal identity, the I-relation is analysed in terms of psychological continuity, which is a relation that may hold from one to many. To avoid the possibility that different people share person-stages, the I-relation is often analysed as the holding of psychological continuity and a non-branching clause. There is, however, no consensus on what form this non-branching clause should take. Below, you can interactively explore some of the most discussed proposals.
First, create some person-stages by clicking on the canvas. Make person-stages psychologically connected by clicking on one and then on another. The person-stages show up as black dots and a psychological connection between two person-stages is represented by a black curve between them. Remove a person-stage by clicking on it twice. Remove a psychological connection by clicking on one of the connected person-stages and then on the other.
Second, see which person-stages are I-related according to different versions of the psychological approach to personal identity by pressing the corresponding buttons below the canvas. That two person-stages are I-related is represented by a red curve between them.
Psychological connectedness: xCy if and only if x and y are strongly psychologically connected with the right kind of cause.
Temporally ordered psychological continuity: xRy if and only if xCy or there are person-stages z1–zn such that xCz1, z1Cz2, … , zn-1Czn, znCy and these person-stages are temporally ordered so that they occur either in the order x, z1, z2, … , zn-1, zn, y or in the reverse order.
Temporally unordered psychological continuity: xR'y if and only if xCy or there are person-stages z1–zn such that xCz1, z1Cz2, … , zn-1Czn, znCy.
Lewis: xIy if and only if xRy.
Parfit 1971: xIy if and only if xRy, and there is no person-stage z such that either (i) xRz and y and z are distinct and simultaneous or (ii) yRz and x and z are distinct and simultaneous.
Parfit 1984: xIy if and only if xRy, and there is no person-stage z such that either (i) xRz and not yRz or (ii) yRz and not xRz.
Shoemaker: xIy if and only if xRy and there is no person-stage z such that (i) z does not occur before each of x and y occurs, (ii) z does not occur after each of x and y occurs, (iii) zRx, (iv) zRy, and (v) there are two distinct and simultaneous person-stages u and v such that zCu and zCv. xRz, yRz, and there are two distinct and simultaneous person-stages u and v such that zCu and zCv.
Brueckner (4): xIy if and only if xR'y and there is no person-stage z such that either (i) xR'z and not yR'z or (ii) yR'z and not xR'z.
Brueckner (5): xIy if and only if xR'y and there is no person-stage z such that either (i) xR'z and y and z are distinct and simultaneous or (ii) yR'z and x and z are distinct and simultaneous.
Noonan: xIy if and only if xRy, and (i) there are no simultaneous and distinct person-stages u and v such that uRx, uRy, and vRx, and (ii) there are no distinct and simultaneous person-stages u and v such that uRx, uRy, and vRy.
David Lewis presents his proposal in Lewis, David: 1976, ‘Survival and Identity’, in A. Rorty (ed.): The Identities of Persons, Berkeley: University of California Press, 3–30, pp. 18–24. Derek Parfit presents an endurance version of the 1971 proposal in Parfit, Derek: 1971, ‘Personal Identity’, The Philosophical Review 80 (1): 3–27, p. 13, and an endurance variant of the 1984 proposal in Parfit, Derek: 1984, Reasons and Persons, Oxford: Clarendon Press, p. 267. Sydney Shoemaker presents his proposal in Shoemaker, Sydney and Richard Swinburne: 1984, Personal Identity, Oxford: Blackwell, p. 90. Anthony Brueckner presents, but does not defend, proposals (4) and (5) in Brueckner, Anthony: 2005, ‘Branching in the Psychological Approach to Personal Identity’, Analysis 65 (288): 294–301, p. 295. Finally, Harold W. Noonan’s proposal is found in Noonan, Harold W.: 2006, ‘Non-Branching and Circularity — Reply to Brueckner’, Analysis 66 (290): 163–167, p. 167n.