GA19:69-70 – mathematika (μαθηματικά)

The μαθηματικαὶ ἐπιστήμαι have as their theme τὰ ἐξ ἀφαιρέσεως, that which shows itself by being withdrawn from something and specifically from what is immediately given. The μαθηματικά are extracted from the φυσικὰ ὄντα, from what immediately shows itself [Cf. Met. XI, 3,1061a28f; De Caelo III, 1,299a15ff; Met. XIII, 3; Met. XII, 8,1073b6ff]. Hence Aristotle Aristoteles
Aristote
Aristóteles
Aristotle Para Heidegger, Aristóteles é com efeito toda a filosofia, por esta razão passou sua vida a situar, demarcar, mensurar, em resumo questionar em sua dimensão mesma de lugar, este lugar comum a toda humanidade. says: ὁ μαθηματικός χωρίζει (cf. Phys. II, 2, 193b31ff.). Χωρίζειν, separating, is connected with χώρα, place [Platz]; place belongs to beings themselves. The μαθηματικός takes something away from its own place, […] What is peculiar is that the mathematical is not in a place: οὐκ ἕν τόπῳ (Met. XIV, 5, 1092a17ff.). Taken in terms of modern concepts, this has the ring of a paradox, especially since τόπος is still translated as “space.” But only a σῶμα φυσικόν has a τόπος, a location, a place. This χωρίζειν, which we will encounter in Plato Platon
Plato
Platão
Platón O pensamento de Heidegger é um diálogo a todo instante com aquele de Platão. Presente em todos os escritos de Heidegger desde Ser e Tempo, Platão é o pivô a partir do qual o pensamento de Heidegger se engaja prospectivamente a entrar em correspondência com outros Matinais. (LDMH) ’s theory of the χωρισμός of the Ideas, where Plato Platon
Plato
Platão
Platón O pensamento de Heidegger é um diálogo a todo instante com aquele de Platão. Presente em todos os escritos de Heidegger desde Ser e Tempo, Platão é o pivô a partir do qual o pensamento de Heidegger se engaja prospectivamente a entrar em correspondência com outros Matinais. (LDMH) indeed explicitly assigns to the Ideas a τόπος, namely the οὐρανός, this χωρίζειν is for Aristotle Aristoteles
Aristote
Aristóteles
Aristotle Para Heidegger, Aristóteles é com efeito toda a filosofia, por esta razão passou sua vida a situar, demarcar, mensurar, em resumo questionar em sua dimensão mesma de lugar, este lugar comum a toda humanidade. the way in which the mathematical itself becomes objective.

[…] Insofar as the φυσικά ὄντα are κινούμενα, i.e., insofar as motility is a basic determination of their Being, the mathematical can be considered initially as appertaining to beings that move. The mathematical as such is removed from things characterized by motion, […], the mathematical, e.g., a point, is “extracted from beings insofar as they move,” (b34) i.e., insofar as they change, turn around, increase and decrease. And specifically the mathematical is χωριστά τῇ νοήσει, “discerned,” extracted simply in a particular mode of consideration. Κίνησις itself, however, is initially and for the most part κίνησις κατά τόπον, change of location […] [GA19EN:69-70]