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Cover
Descartes’s Method: The Formation of the Subject of Science
Copyright
Dedication
Epigraph
Contents
Acknowledgments
Preface
Abbreviations
English translations
Introduction: Descartes’s Method: Universality without Uniformity
PART ITHE HABITUAL UNITYOF SCIENCEAquinas to Descartes
1: The Habitual Unity of Individual Sciences: Aquinas to Suárez
1.1 Hexis/Habitus
1.2 Aristotle’s Ban on Genus-Crossing (μετάβασις) in Posterior Analytics I.7
1.3 Aquinas’s Habitual Interpretation of the Unity of Science
1.4 The Ontology of Scientific Habitus: Simple Quality or Complex Order?
1.4.1 Aquinas’s Gradient Ontology of Scientific Habitus
1.4.2 Scotus’s Virtual Containment Ontology of Scientific Habitus
1.4.3 Ockham’s Aggregate Ontology of Scientific Habitus
1.4.4 Suárez’s Pluralist Ontology of Scientific Habitus
1.5 Genus-Crossing and Subalternation
2: The Habitual Unity of Science: Descartes
2.1 The Cartesian Scientific Habitus: Basic Properties
2.2 The Subject, Acquisition, and Ontology of the Cartesian Scientific Habitus
2.3 Suspending Aristotle’s Ban on Genus-Crossing
2.4 Supertranscendental Extrinsic Denomination: The Simple Natures
2.5 The Unity of Science in Rules
2.6 Rule 1 in the Cambridge Manuscript
PART II: THE OPERATIONS AND CULTURE OF THE METHOD
3: The Operations of the Method: Intuition, Deduction, and Enumeration
3.1 The Principle of Proportionality
3.2 Facie ad faciem: Intuition
3.2.1 Descartes’s Interlocutors in the Definition of Intuition in Rule 3
3.3 Illatio: Deduction
3.4 Enumeratio, sive inductio: Enumeration
3.4.1 Enumeration₁: Reduction and Order
3.4.1.1 Clarity and Distinctness in Problems: Relevant and Irrelevant Conditions
3.4.2 Enumeration₂: Irreducibly Complex Linear and Non-Linear Inference and the Expansion of Intuition
3.4.3 Sufficient, Complete, and Distinct Enumeration₃: Inference and Class Construction
3.5 Problems: Definition and Taxonomy
3.6 Perspicacity and Sagacity: Two Intellectual Virtues or Habitus
3.7 The Order of Operations
4: The Culture of the Method: The Methodological Function of Mathesis Universalis
4.1 Mathesis Universalis: The Second Degree of the Cartesian Scientific Habitus
4.2 The Science of Order and Measure
4.3 First Lesson: The Theory of Order in Rule 6
4.4 Second Lesson: Direct and Indirect Deductions
4.5 From Recreational Mathematics to Mathesis Universalis
4.6 Mathesis Universalis and the Unity of Mathematics in Rules 13–21
4.7 Mathesis Universalis, Cartesian Mathematics, and Method
4.7.1 Mathesis Universalis and the Cambridge Manuscript
4.8 From Mathesis Universalis to the Problem of the Limits of Knowledge
PART III: THE FIRST PROBLEM OF THE METHOD: The “Noblest Example”
5: Defining the Problem of the Limits of Knowledge in Rules
5.1 The Noblest Example: Three Problems
5.2 The “Method of Enumeration”
5.3 Sufficient Enumeration₂, Supposition, and Truth in Rule 12
5.4 Two Concepts of Epistemic Limit in Rule 8
6: Descartes’s Theory of the Faculties in Rules
6.1 Mechanism, Habitus, and the Limits of Knowledge in Rules
6.2 Sensation and Figure
6.3 From Figure to Representation: The Common Sense, the Phantasy, and the Passivity of Vis Cognoscens
6.4 The Activity of Vis Cognoscens and Descartes’s Habitual Theory of the Faculties in Rules
7: Descartes’s Theory of the Objects of Knowledge in Rules
7.1 The Simple Natures
7.2 The Enumerative Criteria: Cognitive Indivisibility, Self-Evidence, and Univocity
7.3 The Intellectual Simple Natures and the Use of the Pure Intellect
7.4 The Material Simple Natures and the Use of the Intellect and the Imagination
7.5 Epistemic Transcendentals: The Common Simple Natures
7.6 Negations, Privations, and the Compositionality of Thought
7.7 The Theory of Conjunction: Descartes’s First Theory of Distinctions
7.8 Complexity and Confusion: Permissible and Impermissible Varieties
7.9 Intuition and Judgment
7.10 Judgment, Composition, and Error
7.11 Descartes’s Conclusions
7.12 The Theory of Simple Natures: Neither Realism Nor Idealism
8: The Origins of Cartesian Dualism in Rule 12
8.1 New Evidence, Old Problem
8.2 Descartes’s Dualism in RulesAT
8.3 Dualism in RulesCM
PART IV: APPLICATIONS: Perfectly and Imperfectly Understood Problems
9: Perfectly Understood Problems: Method and Mathematics in Rules 13-21
9.1 The Cartesian Scientific Habitus in Mathematics
9.2 The Unity of Discrete and Continuous Magnitude in the Imagination
9.3 Abstracting Problems from Particular Subject-Matters
9.4 The Unit
9.5 Symbolic Intuition? Algebraic Notation in Rules
9.6 The Geometrical Calculus
9.7 The Problem of Root Extraction
9.8 The Collapse of Descartes’s Methodological Enterprise in Rules
10: Imperfectly Understood Problems: Descartes’s Deduction of the Law of Refraction and the Shape of the Anaclastic Lens in Rule 8
10.1 Neither “Mixed Mathematics” nor “Physico-Mathematics”
10.2 Problems in Previous Reconstructions
10.3 From Imperfectly Understood Problems to Perfectly Understood Problems: Enumeration₁
10.4 What is a Natural Power (Potentia Naturalis)? Descartes’s Pre-Metaphysical Physics
10.5 The Action of Light
10.6 How Light Passes through Transparent Media
10.7 Deducing the Law of Refraction
10.8 Deducing the Anaclastic
10.9 Order of Research and Order of Exposition
PART V: BEYOND RULES
11: Descartes’s Method after Rules
11.1 Method or Methods?
11.2 From Rules to Discourse
11.3 The Turn to Metaphysics
11.4 Method and System after Rules
11.5 Simple Natures and Simple/Primitive Notions after Rules
11.6 Simple Natures and Descartes’s Ontology of Substance, Attribute, and Mode
Conclusion: Reassessing the Meaning of Method in Descartes
APPENDIX: Descartes’s Rules: Manuscripts, Dates, and Title(s)
Bibliography
Index