Is there a criterion of identity, a standard by which identity is to be judged?
For example the criterion of identity for directions is parallelism of lines, that is, the direction of line a is identical with the direction of line b if and only if line a is parallel to line b etc
Let us look at identity over time
Identity over time is a controversial notion, however, because time involves change.
If a thing changes, your body/mind set something is true of it at the later time that is not true of it at the earlier, so it is not the same.
For identity to be certain there has to be a belief that there is a homunculus in one's brain which is unchanging, the essential you and not subject to the vagaries of your phsyiology, politic, culture
economics etc. And where would this homunculus reside and how was this homunculus constituted
We often talk about people as if they have particular attributes as 'things' inside themselves -- they have an identity, for example, and we believe that at the heart of a person there is a fixed and true identity or character (even if we're not sure that we know quite what that is, for a particular person). We assume that people have an inner essence -- qualities beneath the surface which determine who that person really 'is'. We also say that some people have (different levels of) power which means that they are more (or less) able to achieve what they want in their relationships with others, and society as a whole.
Foucault rejected this view. For Foucault, people do not have a 'real' identity within themselves; that's just a way of talking about the self -- a discourse. An 'identity' is communicated to others in your interactions with them, but this is not a fixed thing within a person. It is a shifting, temporary construction