The present work is substantially a dissertation presented to the Faculty of the Graduate School of the University of Toronto. While aware of the numerous imperfections of the work I have decided, on the urging of many colleagues, to publish it at this time because of the current relevance of the subject-matter and especially of the collection of texts. I am happy to acknowledge my indebtedness to the faculty of the Pontifical Mediaeval Institute of Toronto and especially to the Reverend (...) Ignatius Eschmann, O.P., who first suggested the idea of this study and whose encouragement and assistance brought it to completion. My thanks are due also to the Reverend George Klubertanz, S.J., and Mr. Paul Mathews, both of the Department of Philosophy of Saint Louis University, and" for invaluable secretarial assistance, to Mrs. Savina Tonella and Miss Agnes Kutz. R. J. HENLE, S.j. Saint Louis December, 1954 TABLE OF CONTENTS GENERAL INTRODUCTION... (shrink)

THE MAIN THESIS OF THIS STUDY may be summarized as follows: In Schopenhauer's earliest work, The Fourfold Root of the Principle of Sufficient Reason, two different lines of philosophical thought can be identified, each arising from a different source. The first of these is the a priori Kantianism and idealism heavily emphasizing the function of the a priori principle of causality, and the forms of time and space. This line comes from Schopenhauer's study of Kantianism. The second line of thought (...) consists of an implicitly realistic analysis of perception which seems to arise from Schopenhauer's personal reflection on perceptual experience. This experiential analysis seems to be partially due to his medical studies, as his use of medical rather than philosophical authorities indicates. This realistically oriented element can be extricated from the totality of Schopenhauer's philosophy with the result that it can furnish new insights valuable for the understanding and confirmation of philosophical direct realism. (shrink)

Forcing with [κ] κ over a model of set theory with a strong partition cardinal, M. Spector produced a generic ultrafilter G on κ such that κ κ /G is not well-founded. Theorem. Let G be Spector-generic over a model M of $ZF + DC + \kappa \rightarrow (\kappa)^\kappa_\alpha, \kappa > \omega$ , for all $\alpha . 1) Every cardinal (well-ordered or not) of M is a cardinal of M[ G]. 2) If A ∈ M[ G] is a well-ordered subset (...) of M, then A ∈ M. Let Φ = κ κ /G. 3) There is an ultrafilter U on Φ such that every member of U has a subset of type Φ, and the intersection of any well-ordered subset of U is in U. 4) Φ satisfies Φ → (Φ) α β for all $\alpha and all ordinals β. 5) There is a linear order Φ' with property 3) above which is not "weakly compact", i.e., $\Phi' \nrightarrow (\Phi')^2$. (shrink)

Following [3], we build higher-order models of analysis resembling the frameworks of nonstandard analysis. The models are entirely canonical, constructed without Choice. Weak transfer principles are developed and the models are applied to topology, graph theory, and measure theory. A Loeb-like measure is constructed.

Following [3], we build higher-order models of analysis resembling the frameworks of nonstandard analysis. The models are entirely canonical, constructed without Choice. Weak transfer principles are developed and the models are applied to topology, graph theory, and measure theory. A Loeb-like measure is constructed.

INTRODUCTION An effort has been made to collect and list in this Part One every text from the works of Saint Thomas in which the terms 'Plato' or..

The paper "Partitions of Products" [DiPH] investigated the polarized partition relation $\begin{pmatrix}\omega\\\omega\\\omega\\\vdots\end{pmatrix} \rightarrow \begin{pmatrix}\alpha_1\\\alpha_1\\\alpha_2\\\vdots \end{pmatrix}$ The relation is consistent relative to an inaccessible cardinal if every α i is finite, but inconsistent if two are infinite. We show here that it consistent (relative to an inaccessible) for one to be infinite. Along the way, we prove an interesting proposition from ZFC concerning partitions of the finite subsets of ω.