In this article I present the problem of identity of objects (that persist in time and space) and their identification (also in time and space, when these objects persist and change their location) indicated in the title of the paper. I therefore present an outline of P.F. Strawson's proposal, but also a purely formal approach that can be found in formal sciences (logic and mathematics). In the final part I give some ontological solution to Strawson's research. It is a solution based on formal

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... on based on formal considerations within the so-called ontologically oriented versions of modal and temporal logics, which I proposed in my book Indywidua. Idee. Pojęcia (2008).