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.

Theory:

**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 *z*_{1}–*z _{n}* such that

**Temporally unordered psychological continuity:** *xR'y* if and only if *xCy* or there are person-stages *z*_{1}–*z _{n}* such that

**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.