Distinguishable

Distinguishable is an adjective that describes the ability to be distinguished from another object or to be identified as different. In everyday language, two items are distinguishable if a person can recognize a feature that sets them apart, such as color, shape, or size. The term contrasts with indistinguishable or with being difficult to distinguish.

In logic and mathematics, distinguishability can be formalized. Two objects in a structure are distinguishable if there exists a property, or a first-order formula, that holds for one and not the other. In model theory, an element is definable over a set if a formula uniquely identifies it; non-definable elements may be indistinguishable from others under the given language. Distinguishability relates to separability and to equivalence relations that partition objects into indistinguishable classes.

In physics, the concept matters for counting states. Classical particles are often treated as distinguishable, whereas quantum particles of the same type are indistinguishable, meaning that permuting identical particles does not produce a new state. This distinction affects entropy calculations and the form of statistical distributions.

In measurement and data analysis, discriminability expresses how well different categories can be separated by a classifier or measurement system. High discriminability implies clear, robust identification of differences; low discriminability implies overlap and ambiguity.

Overall, distinguishable indicates that a given context provides criteria by which differences can be recognized.