Table Of ContentMECHANICAL EPISTEMOLOGY AND MIXED MATHEMATICS:
Descartes’s Problems and Hobbes’s Unity
by
Marcus P. Adams
B.A., Lee University, 2003
M.Div., Ashland Theological Seminary, 2006
M.A., Western Michigan University, 2008
Submitted to the Graduate Faculty of
The Kenneth P. Dietrich School of Arts and Sciences in partial fulfillment
of the requirements for the degree of
Doctor of Philosophy
University of Pittsburgh
2014
UMI Number: 3583999
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This dissertation was presented
by
Marcus P. Adams
It was defended on
April 8, 2014
and approved by
Stephen Engstrom, Professor of Philosophy, University of Pittsburgh
Daniel Garber, Stuart Professor of Philosophy, Princeton University
Douglas Jesseph, Professor of Philosophy, University of South Florida
Paolo Palmieri, Associate Professor History & Philosophy of Science, University of Pittsburgh
Nicholas Rescher, Distinguished University Professor of Philosophy, University of Pittsburgh
Dissertation Advisor:
Peter Machamer, Professor of History & Philosophy of Science, University of Pittsburgh
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Copyright © by Marcus P. Adams
2014
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MECHANICAL EPISTEMOLOGY AND MIXED MATHEMATICS:
Descartes’s Problems and Hobbes’s Unity
Marcus P. Adams, Ph.D.
University of Pittsburgh, 2014
My dissertation answers what appears to be a simple question: How is Hobbes’s politics related
to his physics and metaphysics? However, answering this question has proved more difficult for
scholars than it appears at first glance, and there has there has been no consensus in the literature
over the past fifty years. Two well-represented extremes dominate the literature: the first view
claims that Hobbes’s politics is deduced from his physics and ultimately his metaphysics; and the
second view claims that the politics arose independently of Hobbes’s other work. My dissertation
argues that Hobbes does in fact provide a unified systematic philosophy, and I contrast this unity
with problems in Descartes's epistemology and optics. To make this argument, I carve a middle
way between the two extremes in the literature by situating Hobbes within mechanical
philosophy and 17th century mathematics.
I use three concepts to clarify Hobbes’s project: mechanical explanation, maker’s
knowledge, and mixed mathematical science. First, I show that for Hobbes a mechanical
explanation involves tracing the motions of bodies at various levels of complexity, from simple
points in geometry to human bodies in the state of nature and to commonwealth bodies. This
view provides Hobbes with resources for a naturalized epistemology, which I show is the point at
issue in Hobbes’s Objections to Descartes's Meditations. Second, Hobbes says that we have
“maker's knowledge” in geometry and politics. I show that “maker’s knowledge” is Hobbes's
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empiricist answer to (1) how we have causal knowledge in politics and mathematics by
constructing and (2) how mathematics is applicable to the world. Finally, I show that the mixed
mathematical sciences, e.g., optics, were Hobbes's inspiration for a unified philosophical system.
I argue that the physics in De corpore, the optics in De homine, and the politics in Leviathan are
treated by Hobbes as mixed mathematical sciences, which provides a new way to see Hobbes as
a consistent and non-reductive naturalist. Viewed in this light, the Leviathan turns out to have
more methodological similarities to optics than to geometry.
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TABLE OF CONTENTS
PREFACE .................................................................................................................................... XI
1.0 INTRODUCTION ........................................................................................................ 1
1.1 HOBBES AND THE UNITY OF THE SCIENCES ......................................... 1
1.2 UNIFIED VERSUS DISJOINT SCIENCES ..................................................... 4
2.0 THE WAX AND THE MECHANICAL MIND: REEXAMINING HOBBES’S
OBJECTIONS TO DESCARTES’S MEDITATIONS ............................................................... 9
2.1 INTRODUCTION ............................................................................................... 9
2.2 THE WAX IN THE SECOND MEDITATION AND HOBBES’S
OBJECTION ....................................................................................................................... 12
2.2.1 “Tak[ing] off the clothes, as it were”: Descartes’s Method and the Wax. 12
2.2.2 Hobbes’s Objection: Conceiving versus Perceiving and Reasoning as the
“Linking of Names” ................................................................................................... 15
2.3 A MECHANICAL EPISTEMOLOGY FOR MECHANICAL MINDS ...... 17
2.3.1 Hobbes’s Philosophical Psychology: Stages 1 and 2 of the Mechanism ... 17
2.3.2 From the Mechanical Mind to Mechanical Epistemology: Stages 3 and 5
of the Mechanism ....................................................................................................... 22
2.3.2.1 Conceptions and Language ................................................................ 22
2.3.2.2 The Activity of Philosophizing ........................................................... 26
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2.3.2.3 Questioning an Epistemology of Simplest Conceptions ................... 30
2.4 REVISITING HOBBES’S FOURTH OBJECTION TO THE
MEDITATIONS .................................................................................................................. 34
2.5 CONCLUSION .................................................................................................. 37
3.0 MECHANICAL EPISTEMOLOGY, MAKER’S KNOWLEDGE, AND
SCIENTIA .................................................................................................................................... 38
3.1 INTRODUCTION ............................................................................................. 38
3.2 CAUSAL KNOWLEDGE IN A WORLD OF UNDERDETERMINED
APPEARANCES ................................................................................................................ 41
3.3 GEOMETRIC CONSTRUCTION AND CAUSAL KNOWLEDGE ........... 45
3.3.1 Knowledge of Particular Causes in Geometry ............................................ 48
3.3.2 Knowledge of Universal Causes in Geometry through Definition ............ 52
3.4 FIRST PHILOSOPHY AS COMPUTATION AND CONSTRUCTION ..... 64
3.5 CONCLUSION: BUT IS CAUSAL KNOWLEDGE REALLY AVAILABLE
IN NATURAL PHILOSOPHY? ....................................................................................... 73
4.0 HOBBES, ARISTOTLE, AND MIXED MATHEMATICS .................................. 76
4.1 INTRODUCTION ............................................................................................. 76
4.2 GEOMETRY AND HOBBESIAN OPTICS ................................................... 79
4.2.1 A Case study from Hobbes’s Optics in De homine 2 .................................. 79
4.2.2 Hobbes’s Geometry in De corpore Part III ................................................. 83
4.2.3 De homine Case Study Revisited .................................................................. 88
4.2.4 Hobbes’s Optics and the Deductivist Account ............................................ 92
4.3 ARISTOTLE AND HOBBES ON MIXED MATHEMATICS ..................... 94
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4.3.1 Aristotle on Mixed Mathematics .................................................................. 95
4.3.2 Hobbes and the Aristotelian Mixed Mathematics Tradition ..................... 97
4.4 CONCLUSION ................................................................................................ 101
5.0 HOBBES, BOYLE, AND NATURAL PHILOSOPHY AS “TRUE PHYSICS” 105
5.1 INTRODUCTION ........................................................................................... 105
5.2 DE CORPORE PART IV AS MIXED-MATHEMATICAL “TRUE
PHYSICS” ......................................................................................................................... 108
5.2.1 The Explanation of Sensation in De corpore 25.1-2 .................................. 108
5.2.2 The Explanation of Swelling of the Parts of the Body when Warm in De
corpore 27.3 ............................................................................................................... 115
5.2.3 De corpore Part IV Reconsidered ............................................................... 124
5.3 MIXED MATHEMATICS AND LEVIATHAN AND THE AIRPUMP ...... 125
5.4 CONCLUSION ................................................................................................ 132
6.0 HUMAN SCIENCE AND POLITICS .................................................................... 134
6.1 INTRODUCTION ........................................................................................... 134
6.2 HUMANS CONSIDERED AS NATURAL BODIES ................................... 136
6.2.1 Leviathan Part I versus Hobbes’s Other Works ....................................... 137
6.2.2 A Complete Account of the Passions.......................................................... 139
6.2.2.1 Elements of Law ................................................................................. 139
6.2.2.2 Complete Account of the Passions: De homine and Leviathan ..... 141
6.2.3 Making an “Inference from the Passions” to the State of Nature........... 145
6.2.3.1 Driving Passions and Humans outside of Society .......................... 148
6.2.3.2 How the Driving Passions are Related to One Another ................ 153
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6.2.4 Reason and Persons ..................................................................................... 156
6.3 HUMANS AS CITIZENS ............................................................................... 160
6.3.1 Final Causes in the Commonwealth and Not in Geometry ..................... 161
6.3.2 The Maker(s) of the Commonwealth versus The Maker in Geometry .. 164
6.3.2.1 Maker’s Knowledge for Those Who enter the Covenant? ............ 164
6.3.2.2 The Sovereign as Maker and Politics as Mixed Mathematics ...... 171
BIBLIOGRAPHY ..................................................................................................................... 179
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