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The Different Origins of the Affects in the Preface to the Theological-Political Treatise and in the Ethics

Chantal Jaquet

in Affects, Actions and Passions in Spinoza: The Unity of Body and Mind

Once Spinoza's thought has been situated with respect to Descartes, it is necessary to understand the stages of how the concept of affect is constructed in his corpus. The aim of Chapter III is to ... More

Once Spinoza's thought has been situated with respect to Descartes, it is necessary to understand the stages of how the concept of affect is constructed in his corpus. The aim of Chapter III is to compare and contrast the relevant texts in the Preface to the Theological-Political Treatise and in the Ethics in order to measure the evolution of Spinoza's thought. This approach is divided into three parts: – The principles of the comparison between the affects in the Preface to the Theological-Political Treatise and in the Ethics – The origin and definition of the affects in the Theological-Political Treatise – The differences between the Theological-Political Treatise and the Ethics Whereas the Theological-Political Treatise offers an analysis of the affects in the historical context of humankind living under the guardianship of theological and political authorities, the Ethics approaches the affects geometrically, and studies them like lines, surfaces, and bodies, removed from historical context. Beyond this methodological approach, a more and more dynamic conception of the affects is gradually sketched out. Whereas in the Theological-Political Treatise affect is essentially passive and contrary to reason, the Ethics establishes a new approach by distinguishing action-affects from passion-affects, thus ceasing to systematically pit the affective and rational worlds against one other.Less

On the Singularities of the Pluricomplex Green’s Function

D. H. Phong and Jacob Sturm

Charles Fefferman, Alexandru D. Ionescu, D. H. Phong, and Stephen Wainger (eds)

in Advances in Analysis: The Legacy of Elias M. Stein

This chapter seeks to establish the existence of pluricomplex Green's functions with singularities at certain multi poles, given by arbitrary local analytic functions. The Green's function plays a ... More

This chapter seeks to establish the existence of pluricomplex Green's functions with singularities at certain multi poles, given by arbitrary local analytic functions. The Green's function plays a central role in the study of functions of one complex variable or of two real variables. This chapter also attempts to develop a geometric/analytic approach to Monge-Ampère equations with measures on the right-hand side, where the singularities of the solution arise from blow-up constructions. Since blow-ups typically lead to degenerate Kähler forms, an essential tool in this chapter's approach is the recent existence theorems for the Dirichlet problem for complex Monge-Ampère equations with degenerate background form.Less