Spinoza’s Epistemology through a Geometrical Lens

Description

This book interrogates the ontology of mathematical entities in Spinoza as a basis for addressing a wide range of interpretive issues in Spinoza’s epistemology―from his antiskepticism and philosophy of science to the nature and scope of reason and intuitive knowledge and the intellectual love of God. Going against recent trends in Spinoza scholarship, and drawing on various sources, including Spinoza’s engagements with optical theory and physics, Matthew Homan argues for a realist interpretation of geometrical figures in Spinoza; illustrates their role in a Spinozan hypothetico-deductive scientific method; and develops Spinoza’s mathematical examples to better illuminate the three kinds of knowledge. The result is a portrait of Spinoza’s epistemology as sanguine and distinctive yet at home in the new Cartesian and Galilean scientific-philosophical paradigm. Acknowledgments Contents Abbreviations List of Figures Chapter 1: Introduction 1.1 The Question of Mathematization 1.2 Outline of Chapters 1.3 A Note on Texts References Chapter 2: Mathematics and Methodology: Spinoza Contra Skepticism 2.1 The Dogmatic Response 2.2 Mathematical Ideas qua Epistemic Exemplars: Problems for the Dogmatic Interpretation 2.3 Attaining the Idea of God: The Cartesian Response 2.3.1 Textual Evidence for the Cartesian Interpretation 2.4 The Cartesio-Dogmatic Response 2.5 Objections and Replies References Chapter 3: Realism and Antirealism About Mathematical Entities 3.1 Figures as Beings of Reason 3.1.1 Figures as (Imaginative) Universals 3.1.2 Figures as a Form of Measure 3.1.3 Figures as Non-beings 3.1.4 Genetically Conceived Figures 3.2 Reductio ad Acosmism: The Case Against Antirealism 3.3 Figure and Finite Bodies: The Case for Realism 3.3.1 Descartes and the Ontological Status of Figures 3.3.2 Spinoza’s Theory of Corporeal Individuals and Figure 3.3.3 What Are Figures in Spinoza? 3.4 True Ideas of Number? References Chapter 4: Reason and Imagination in Spinozan Science 4.1 Reason and Spinozan Science 4.1.1 Common Notions as Foundations of Reason and Laws of Nature 4.2 Imagination in Spinozan Science and Issues of Adequacy 4.2.1 From the Historia Naturae to Common Notions 4.2.2 Descending to Particulars 4.3 Peculiar Common Notions References Chapter 5: Geometry and Spinozan Science 5.1 Spinoza on the Geometry of Optical Lenses 5.2 Response to an(other) Objection from Letter 12 5.2.1 The Commensurability Response 5.3 Letters 80–83 and the Incompleteness of Spinozan Science References Chapter 6: Spinoza’s Notions of Essence 6.1 Common Essence, Species Essence, and Individual Essence 6.2 Formal Essence, Actual Essence, and Existence 6.2.1 Formal Essences and Existence 6.2.1.1 Essences and Definitions 6.2.2 Actual Essences and Existence 6.2.3 E2p8 Reconsidered References Chapter 7: Intuitive Knowledge: The Perfection of Reason 7.1 Preliminary Analysis of the Principal Texts 7.2 The Content of Intuitive Knowledge: The Common Essence Interpretation 7.3 Beyond the Common Essence Interpretation 7.3.1 A Geometrical Alternative to the Fourth Proportional Example: The Isoperimetric Problem 7.3.2 The Isoperimetric Example and Spinoza’s Definition of Intuitive Knowledge 7.4 The Difference Between Reason and Intuitive Knowledge: A Method Interpretation 7.4.1 Can Conatus Save the Content Interpretation? 7.5 Amor Dei Intellectualis and the Supremacy of Intuitive Knowledge 7.6 Intuitive Knowledge in Spinozan Science References Chapter 8: Conclusion 8.1 Spinoza’s Epistemic Outlook 8.2 Spinoza Vis-à-Vis Descartes (and Galileo) References References Index