The unit can be regarded either as the limit of its relations to all other units, or as the point of origination of the unique agency or causality associated with it.
Project Statement (After Aristotle, Metaphysics 987b18 & sq.):
The One and the Dyad are the causes of forms, that is, the unit in relation is the cause of form. Thus when we compare units, we discern properties in them that are the same, and from this become aware of forms.
Forms and the Dyad are the causes of sensibles, that is, forms in relation are the causes of sensibles, which are bundles of form-instances.
Intermediate between the forms and the sensibles are the mathematicals, that is, intermediate between philosophy, which concerns units in relation, and the study of phenomena, which concerns forms in relation, comes mathematics, which concerns abstract, indifferent units.
Theory of Multiplicities (Manifolds)
There are two primary structures of multiplicity, polycentric and monocentric. The polycentric multiplicity cannot be generated out of the monocentric multiplicity, and so the polycentric multiplicity should be regarded as prior and the monocentric multiplicity as emergent.
In the polycentric multiplicity, all units are in each unit; this is what makes each unit in a polycentric multiplicity the center for itself and the periphery for another. In the monocentric multiplicity, all units are in one unit, and all units are in this respect “for another” in the monocentric multiplicity.
There are many ways of constituting a monocentric multiplicity, whereas there is only one way of constituting the polycentric multiplicity in the strict sense. In the strict sense, the polycentric multiplicity is the set of existing unique individuals. For this reason, it may also be referred to as the “existential” multiplicity, and monocentric multiplicities as “ontic” or “formal” multiplicities.
The Status of Being
Being is the result of henadic activity; or the system of relations among henads; or the idea of a power belonging to a henad—these expressions are essentially equivalent.
The Modes of Unity
The personal (animal) mode of unity is the most comprehensive, and thus has primacy in the generative hierarchy in this respect, but such a unit may in its activity project itself into a subordinate mode, resulting in different hierarchical dispositions of units and/or principles.
“The Second Intelligible Triad and the Intelligible-Intellective Gods,” Méthexis Vol. 23, 2010, pp. 137-157. [Corrected PDF with journal pagination in brackets.]
“Hercules of the Surface: Deleuzian Humanism and Deep Ecology,” in An (Un)Likely Alliance: Thinking Environment(s) with Deleuze/Guattari, ed. Bernd Herzogenrath (Cambridge Scholars Publishing, 2008), pp. 139-158.
“Animal and Paradigm in Plato,” Epoché: A Journal for the History of Philosophy, forthcoming.
Bound hardcover and softcover copies of my dissertation are also available from ProQuest.
“The Metaphysics of Polytheism in Proclus,” MS Word file [NOTE: Pagination does not correspond to the PDF, which is the version of record. This version is provided for those who cannot download the PDF successfully.]
“The Henadic Structure of Providence in Proclus,” Department of Classics, Dalhousie University, 3/11/10.