§15 [108-110]

"It seems that it is something great and very difficult to grasp place for what it is, because along with it there always is given the body, in what it is made of and in its outward look, its form," so that one is tempted to take the extension of the material or the limit of the form as the place. And, further, it is difficult to see place as such, because the μετάστασις of what is in motion comes to pass in each case in such a way that the place itself does not thereby move. And what is in motion has a privilege with regard to perceptibility.

In summary, a first understanding of the concept of place can be acquired if we keep in mind that place has a δύναμις: ἔχει τινὰ δύναμιν.4 Place is the possibility of the correct appurtenance of a being. The correct appurtenance refers to that presence which belongs to beings as such according to their objective constitution. It belongs to fire to be above, to the earth to be below. The beings of the world, as "nature" in the largest sense, have their place. Place belongs in each case to the being itself and constitutes the possibility of the proper presence of the being there where it appertains. This possibility is not intended as empty conceptual (logical) possibility, as arbitrariness, such that it would be left freely to the body to be here or there, but instead the δύναμις is a possibility which is determinately prescribed and which always harbors in itself a direction. This determinateness of δύναμις belongs to the τόπος itself. Δύναμις is understood as an ontological basic category. The possibility is itself a being. Place is something belonging to beings as such, their capacity to be present, a possibility which is constitutive of their Being. The place is the ability a being has to be there, in such a way that, in being there, it is properly present.

β) The genesis of geometry and arithmetic from τόπος. The acquisition
of geometrical objects by extraction of the πέρατα
(τόπος) of the φύσει ὄντα. The determination of their site
(θέσις). Analysis situs. Μονάς: οὐσία ἄθετος.

Geometrical objects can serve to clarify the distinction between τόπος and θέσις. If we abstract from the peculiar mode of being of τόπος, a mode which is determined φύσει, and retain simply the multiplicity of possible sites, the moments of orientation, we are then in a position to understand how the specifically geometrical objects are constituted. What is extracted from the αἰσθητά and becomes then the θετόν, the posited, is the moment of place, such that the extracted geometrical element is no longer in its place. Indeed the moments of place, which ἀφαίρεσις withdraws from the σῶμα, extracts from it, are the πέρατα of a physical body; but insofar as they are extracted from it they are understood mathematically and no longer as limits of the physical body.

4. Cf. p. 73.