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Notes on the Academicians: Xenocrates
May. 18th, 2014 01:36 pmXenocrates, like Speusippus, a woefully underrated Platonist. Xenocrates says soul is a "self moving number," where "number" expresses the parataxis by which the soul makes time concrete. The stream of association woven by the soul and constitutive of it, that is the soul as "number".
For Platonists, a "number" in the primary sense is a configuration of incomparables, an individual with only peculiar traits. Xenocrates takes this henadological concept of "number" and integrates self-motion to arrive at his definition of soul.
There is so much more to Platonic "number" talk than mathematics as we usually understand it. As I've remarked before, as far as I can see, it's not even about numbers as we know them, but about arithmos in the sense of seriality.
To be sure, Xenocrates talks about numbers, triangles, lines, but these are playing a role like formal logic does for us. What if, instead of the symbols of formal logic, we just used geometry to express arguments? Xenocrates says that gods are equilateral triangles, daimones are isosceles, mortals scalene. These are three ways of forming a basic manifold, three possible relations between the terms in the association: a God equalizes the terms, a daimon subordinates, hierarchizes, a mortal expresses the inequality.
Xenocrates also identifies the three Fates with the three kinds of substance, which are in turn determined epistemologically. Substances are determined as the objects of intellect, sensation and opinion, and these are Atropos, Clotho and Lachesis respectively. This ties in nicely with the definition of soul as self-moving number, its destiny expressed directly in its cognitive processes. The Moirai or "Fates" are literally "partitioners": how do we divide a whole? The Xenocratean scheme concerns how sensation, intellect and "opinion" (i.e., judgment), woven together, are lived time.
To this threefold epistemological scheme we must presumably in turn apply the Xenocratean scheme for triangles generally. The divine perspective will equalize the three modes of cognition, the daimon will establish a hierarchy, while the mortal will experience the real lack of fit between these cognitive powers—which is why we do philosophy.
The triangle scheme must be applicable to the basic ontological elements of monad, dyad, mixture, to yield three kinds of mixture. The equality of the elements is not abstract, like amounts in a recipe, but equality of value. In a way, this means that for the God, all three moments are "monadic", i.e. "authentic", "in virtue of themselves", while for the daimon, they are inherently dyadic, that is, adequately determined by systemic relations, while the mortal has the aporetic or relativistic side of holistic determination—each is "mixed". There is no totalizing viewpoint in this system: I say the God "equalizes", because the mortal *must* assume such a process.
For Platonists, a "number" in the primary sense is a configuration of incomparables, an individual with only peculiar traits. Xenocrates takes this henadological concept of "number" and integrates self-motion to arrive at his definition of soul.
There is so much more to Platonic "number" talk than mathematics as we usually understand it. As I've remarked before, as far as I can see, it's not even about numbers as we know them, but about arithmos in the sense of seriality.
To be sure, Xenocrates talks about numbers, triangles, lines, but these are playing a role like formal logic does for us. What if, instead of the symbols of formal logic, we just used geometry to express arguments? Xenocrates says that gods are equilateral triangles, daimones are isosceles, mortals scalene. These are three ways of forming a basic manifold, three possible relations between the terms in the association: a God equalizes the terms, a daimon subordinates, hierarchizes, a mortal expresses the inequality.
Xenocrates also identifies the three Fates with the three kinds of substance, which are in turn determined epistemologically. Substances are determined as the objects of intellect, sensation and opinion, and these are Atropos, Clotho and Lachesis respectively. This ties in nicely with the definition of soul as self-moving number, its destiny expressed directly in its cognitive processes. The Moirai or "Fates" are literally "partitioners": how do we divide a whole? The Xenocratean scheme concerns how sensation, intellect and "opinion" (i.e., judgment), woven together, are lived time.
To this threefold epistemological scheme we must presumably in turn apply the Xenocratean scheme for triangles generally. The divine perspective will equalize the three modes of cognition, the daimon will establish a hierarchy, while the mortal will experience the real lack of fit between these cognitive powers—which is why we do philosophy.
The triangle scheme must be applicable to the basic ontological elements of monad, dyad, mixture, to yield three kinds of mixture. The equality of the elements is not abstract, like amounts in a recipe, but equality of value. In a way, this means that for the God, all three moments are "monadic", i.e. "authentic", "in virtue of themselves", while for the daimon, they are inherently dyadic, that is, adequately determined by systemic relations, while the mortal has the aporetic or relativistic side of holistic determination—each is "mixed". There is no totalizing viewpoint in this system: I say the God "equalizes", because the mortal *must* assume such a process.
