To the modal concept of possibility is nowadays paid an always growirg attention. The realism of Roderick M. Chisholm - one of the top re- pre sentatives of American analytical philosophy and a deep expert of Middle-European thought - constitutes an important attempt made in the direction of the refusal of reductionism and nominalism, by means of the acknowledgment of irreducibly abstract properties. Abstract objects are properties, that could reasonably be attributed to contingent things. This kind of attribution, i.e. the exemplification, is a form of Platonic participation. The category of possibility is read through the relation of exemplification, that Chisholm links to his theory of intentionality and pushes until the extreme point of self-reference.