[DSRP Evidence](https://dsrpevidence.org/)

# R3. Identity and other are co-defined within a distinction

On Distinctions

Can identity disappear when two or more instances lack intrinsic differences?

## Short answer

No. Identity and other are co-defined structural roles within a distinction. Two or more instances may occupy the identity role relative to one another even when they share every intrinsic property.

## Complete explanation

Anything can be an identity. Identity is not an intrinsic property that a thing must possess before a distinction can exist. Within a distinction, identity and other are co-defined by the special distinction relationship. The other may be global—everything not the identity—or local—a specific counterpart that gives the distinction explanatory content. When two or more instances exist, each can receive the identity role relative to the others. Numerical multiplicity is therefore sufficient for the structural polarity even when labels, haecceities, or classical individuality are unavailable. This does not claim that the instances have different intrinsic properties; it claims that identity and other are roles generated within the distinction.

## Why the apparent counterexample arises

The apparent difficulty arises because identity is assumed to be an intrinsic property of an object rather than a structural role co-defined with an other. Once the role structure is held constant, indiscernibility does not eliminate distinction.

## Cases this settles

- [Bosons in the same single-particle state](https://dsrpevidence.org/case/2)

- [Quasi-set m-atoms](https://dsrpevidence.org/case/5)

- [i and minus i in ante rem structuralism](https://dsrpevidence.org/case/15)

- [Objects eliminable by arrows alone](https://dsrpevidence.org/case/17)

- [Whether primitive identity is permitted](https://dsrpevidence.org/case/19)

[All cases and resolutions](https://dsrpevidence.org/counterexamples)