The Principle of Sufficient Reason

Spinoza , the No Shared Attribute thesis , and the Principle of Sufficient Reason

1 Introduction According to Spinoza, 'In Nature there cannot be two or more substances of the same nature or attribute' (IP5). 1 Call this the 'No Shared Attribute' thesis, 2 hereafter NSA. It is widely recognised (indeed, virtually undeniable) that NSA plays a crucial role in Spinoza's argument in The Ethics for his version of substance monism—for the view that there exists only one substance,...

A Rehabilitation of the Principle of Insufficient Reason

The Cosmological Argument, Sufficient Reason, and Why-Questions

Sufficient Decrease Principle on Riemannian Manifolds

Tools from Riemannian geometry (suitable Riemannian metric, exponential map, search along geodesics, covariant differentiation, sectional curvature, etc) are now used in Mathematical Programming to obtain deeply theoretical results and practical algorithms [3]-[11]. §1 lists basic propositions appearing in the numerical finding of a critical point of a real function defined on a Riemannian mani...

Sufficient Stochastic Maximum Principle for Discounted Control Problem

In this article, the sufficient Pontryagin’s maximum principle for infinite horizon discounted stochastic control problem is established. The sufficiency is ensured by an additional assumption of concavity of the Hamiltonian function. Throughout the paper, it is assumed that the control domain U is a convex set and the control may enter the diffusion term of the state equation. The general resu...