Reductionism about people is the view that people exist but they are not a fundamental part of the world. On this reductionist view, personal persistence has to consist fundamentally in an impersonal continuity relation holding over time. Some standard candidates for this reductionist continuity are different kinds of psychological, physical, and phenomenal continuity. These continuity relations consist in overlaping chains of some basic form of connectedness, for example, psychological, physical, or phenomenal connectedness. The logical form of the relationship between the underlying basic connectedness and personal persistence is controversial, however. What happens when the contiuities branch? And what counts as branching? Below, you can explore interactively some of the most discussed proposals along with a new one.

Theory:

Add person-stages by clicking on the intersections of the grid. Connect two person-stages by clicking on one of them and then the other. The person-stages are represented by black dots and a connection between two person-stages is represented by a black curve between them. Remove a person-stage by clicking on it twice. Remove a connection by clicking on one of the connected person-stages and then on the other. You can also try some standard cases by pressing the buttons above the grid.

See which person-stages are part of the same continuant person according to different theories by pressing the buttons below the grid. That two person-stages are part of the same person is represented by a red curve between them.

**Personal Persistence***xIy* =_{df} *x* and *y* are parts of the same continuant person.

**Temporally Ordered Connectedness***xCy* =_{df} *x* and *y* are connected by the right kind of connection and *x* is present either simultaneously with *y* or earlier than *y*.

**Temporally Ordered Continuity***xRy* =_{df} either *xCy* or *yCx*, or there are person-stages *z*_{1}, *z*_{2}, … , *z _{n}* such that either

(i)

(ii)

**Temporally Unordered Connectedness***xC'y* =_{df} *x* and *y* are connected by the right kind of connection.

**Temporally Unordered Continuity***xR'y* =_{df} *xC'y* or there are person-stages *z*_{1}–*z _{n}* such that

**Locke***xIy* if and only if *xC'y*.

**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 1993***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*.

**Lewis***xIy* if and only if *xRy*.

**Shoemaker***xIy* if and only if *xRy* and there is no person-stage *z* such that

(i) *z* is not present before each of *x* and *y* is present,

(ii) *z* is not present after each of *x* and *y* is present,

(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***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*.

**My Proposal***xIy* if and only if *xRy* and there is no person-stage *z* such that

(i) *z* is not present before each of *x* and *y* is present,

(ii) *z* is not present after each of *x* and *y* is present,

(iii) *zRx*,

(iv) *zRy*, and

(v) there are two distinct and simultaneous person-stages *u* and *v* such that *zC'u* and *zC'v*.

John Locke was first attributed the memory criterion in Reid, Thomas Essays on the Intellectual Powers of Man, ed. Derek R. Brookes, Edinburgh: Edinburgh University Press, 2002, at pp. 275–276. Locke does not seem to have defended this view, however; see Gustafsson, Johan E. ‘Did Locke Defend the Memory Continuity Criterion of Personal Identity?‘ Locke Studies 10:113–129, 2010. David Lewis presents his proposal in Lewis, David ‘Survival and Identity’, in A. Rorty (ed.): The Identities of Persons, Berkeley: University of California Press, 3–30, 1976, at pp. 18–24. Derek Parfit presents an endurance version of the 1971 proposal in Parfit, Derek ‘Personal Identity’, The Philosophical Review 80 (1): 3–27, 1971, at p. 13, and the 1993 proposal in Parfit, Derek ‘The Indeterminacy of Identity: A Reply to Brueckner’, Philosophical Studies 70 (1): 23–33, at pp. 23–24. Sydney Shoemaker presents his proposal in Shoemaker, Sydney and Richard Swinburne Personal Identity, Oxford: Blackwell, 1984, at p. 90. Anthony Brueckner presents, but does not defend, his proposal in Brueckner, Anthony ‘Branching in the Psychological Approach to Personal Identity’, Analysis 65 (288): 294–301, 2005, at p. 295. Harold W. Noonan’s proposal is found in Noonan, Harold W. ‘Non-Branching and Circularity — Reply to Brueckner’, Analysis 66 (290): 163–167, 2006, at p. 167n. Finally, my proposal can be found in Gustafsson, Johan E. ‘Non-Branching Personal Persistence’, Philosophical Studies, forthcoming.