Polytheism and the Euthyphro

In this reading of the Euthyphro, Socrates and Euthyphro are seen less in a primordial conflict between reason and devotion, than as sincere Hellenic polytheists engaged in an inquiry based upon a common intuition that, in addition to the irreducible agency of the Gods, there is also some irreducible intelligible content to holiness. This reading is supported by the fact that Euthyphro does not claim the authority of revelation for his decision to prosecute his father, but rather submits it to elenchus, and that Euthyphro does not embrace the ‘solution’ of theological voluntarism when Socrates explicitly offers it. Since the goal of this inquiry is neither to eliminate the noetic content of the holy, nor to eliminate the Gods’ agency, the purpose of the elenchus becomes the effort to articulate the results of this productive tension between the Gods and the intelligible on the several planes of Being implied by each conception of the holy which is successively taken up and dialectically overturned to yield the conception appropriate to the next higher plane, a style of interpretation characteristic of the ancient Neoplatonists

Transformation and Individuation in Giordano Bruno's Monadology

The essay explores the systematic relationship in the work of Giordano Bruno (1548-1600) between his monadology, his metaphysics as presented in works such as De la causa, principio et uno, the mythopoeic cosmology of Lo spaccio de la bestia trionfante, and practical works like De vinculis in genere. Bruno subverts the conceptual regime of the Aristotelian substantial forms and its accompanying cosmology with a metaphysics of individuality that privileges individual unity (singularity) over formal unity and particulars over substantial forms without sacrificing a metaphysical perspective on the cosmos. The particular is individuated as a unique site of desire, continually transforming but able to entrain itself and others through phantasmatic ‘bonding’, the new source of regularity in Bruno’s polycentric universe. Bruno thus tries to do justice to the demands of intelligibility as well as transformative eros. The essay concludes with a note on Bruno’s geometry as it relates to his general conception of form

Plotinian Henadology

Plotinus’ famous treatise against the Gnostics (33), together with contemporary and thematically related treatises on Intelligible Beauty (31), on Number (34), and on Free Will and the Will of the One (39), can be seen as providing the essential components of a Plotinian defense of polytheism against conceptual moves that, while associated for him primarily with Gnostic sectarians overlapping with Platonic philosophical circles, will become typical of monotheism in its era of hegemony. When Plotinus’ Gnostics ‘contract’ divinity into a single God, they not only devalue the cosmos for its multiplicity and diversity, but also multiply intelligible principles unreasonably. This is because they have foreclosed the distinction, which is to become increasingly explicit in the later antique Platonists, between the intelligible and that which is given existentially, the domain belonging to Plotinus’ indeterminate multiplicity of ‘intelligible Gods’, as opposed to the dialectically determinate number of intelligible principles. Plotinus is prescient in recognizing that incipient monotheism threatens to erase the distinction between philosophy and theology, and between both of these and psychology, the final outcome of which can only be solipsism or nihilism. The defense of polytheism is seen in this fashion to be essential to the preservation of the space for philosophical discourse

Beyond endoscopy for the Rankin-Selberg L-function

We try to understand the poles of L-functions via taking a limit in a trace formula. This technique avoids endoscopic and Kim-Shahidi methods. In particular, we investigate the poles of the Rankin-Selberg L-function. Using analytic number theory techniques to take this limit, we essentially get a new proof of the analyticity of the Rankin-Selberg L-function at $s=1.$ Along the way we discover the convolution operation for Bessel transforms.Comment: 27 pages; accepted to Journal of Number Theor