Curriculum Vitae
Cathay Ming Lih Liu Education
University of North Carolina at Chapel Hill Ph.D. in Philosophy (expected May 2012)
Dissertation: Committee:
Descartes’ Unity of Method, Mathematics and Metaphysics Alan Nelson (chair)
My main focus is on Descartes' influential treatment of the interrelationships among geometry, algebra, and physics. Contrary to the dominant view, I argue that Descartes’ early Rules for the Direction of Our Native Intelligence articulates the philosophical Method that he followed throughout his career. This Method allows him to determine both the metaphysical and the epistemic relations between objects by decomposing the conceptual dependencies contained in our ideas of them. In my view, recognizing this fact has significant consequences for understanding his mathematics, physics and broader philosophical system. I argue that Descartes was able to bring algebraic methods to bear on geometrical problems because both share an identical subject matter: extension. Thus, when Descartes claims physics is nothing but mathematics, my Method-based interpretation of his claim argues for a strong, metaphysical unification of physics and mathematics. Mathematics is unified with physics because they share an identical subject matter, viz. extension. The entities of both physics and mathematics depend ontologically and conceptually on extension. M.A. in Philosophy
Thesis:
May 2008
Descartes’ Philosophical Grounds for Algebra and Geometry
University of California, Irvine M.A. in Philosophy
Thesis:
B.A. in Philosophy
Research & Teaching Interests
August 2006
Descartes’ Philosophy of Science and Explanation June 2004
Areas of Specialization
Early Modern Philosophy, History & Philosophy of Science Areas of Competence
Logic (through Non-Axiomatic Set Theory and Completeness), Metaphysics & Epistemology Additional Teaching Competence
Chinese Philosophy, Ethics, Applied Ethics
Awards & Honors
Graham Kenan Fellowship Medieval Early Modern Studies Ryan-Headley Dissertation Grant Henry Horace Williams Dissertation Fellowship Mid-Atlantic Seminar in Early Modern Philosophy, Graduate Student Award Future Faculty Fellowship Program Bertha Colton Williams Fellowship Mary Taylor Williams Fellowship
www.cathayliu.com ●
[email protected] ● 949.891.1362
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2012 2011-2012 2010 2010 2009 2007-2008 2006-2007
Department of Philosophy ● UNC, CB#3125 ● Chapel Hill, NC 27599
Cathay M. Liu C.V. page 2
Presentations
Scientia Workshop: University of California, Irvine “Unification and Priority in Descartes’ Algebra and Geometry” — October 2011 Atlantic Canada Seminar in Early Modern Philosophy: Dalhousie University (Canada) “Cartesian Counting? Go Figure.” — July 2011 Kings College of London/UNC Conference on Early Modern Philosophy: UNC–Chapel Hill “A Count of Cartesian Universals” — May 2011 North Carolina Philosophical Society: Appalachian State University “Unification and Priority in Descartes’ Algebra and Geometry” — February 2011 Mid-Atlantic Seminar in Early Modern Philosophy: Johns Hopkins University “Descartes’ Priority of Geometry over Algebra” — April 2010 South Central Seminar in Early Modern Philosophy: University of Texas—San Antonio “Descartes’ Priority of Geometry over Algebra” — October 2009 North Carolina Philosophical Society: High Point University “Certainty and Explanation in Descartes” — February 2007 Mini-Conference in Early Modern Philosophy: UNC–Chapel Hill Comments on Kurt Smith’s “Debunking the Direct Realist Reading of Descartes” — April 2008
Teaching Experience
As Principal Instructor at UNC-Chapel Hill
Introduction to Asian Philosophy
Scheduled for Summer 2012
Great Works:
Spring 2011
Experience and Reality:
Spring 2010
Introduction to Mathematical Logic:
Fall 2009 Summer 2010 Summer 2011
Introduction to Bioethics:
Summer 2009
Introduction to Ethics:
Summer 2008
As Teaching Assistant at UNC-Chapel Hill
Philosophy of Science (Marc Lange): Spring 2009 Making Sense of Ourselves (CDC Reeve): 2008 As Teaching Assistant at UCI
Introduction to Modern Philosophy (Alan Nelson): 2006 Introduction to Philosophy (Gerasimos Santas): 2006 Contemporary Moral Problems (Miren Bohem): 2005 Introduction to Moral Philosophy (Gerasimos Santas): 2005 Introduction to Philosophy of Law (Jason Ford): 2005 Languages
Native: English and Chinese (Mandarin) Research: Latin and French
Professional Service
Organizer of Kings College London/UNC Conference on Early Modern Philosophy UNC Philosophy Department Hiring/Search Committee 44th Chapel Hill Colloquium in Philosophy Committee Chapel Hill Philosophy Speaker’s Committee Coordinator of Chapel Hill Philosophy Outreach Program Presented Lecture Series for Philosophy Club at Cary Academy (Cary, NC) Presented Philosophy of Science Lecture Series at New Century High School (Saxapahaw, NC)
Citizenship
U.S.A. & Taiwan, Republic of China
www.cathayliu.com ●
[email protected] ● 949.891.1362
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2010-2011 2010-2011 2009-2010 2007-2008 2007-2008 2007-2008 2006-2007
Department of Philosophy ● UNC, CB#3125 ● Chapel Hill, NC 27599
Cathay M. Liu C.V. page 3
Graduate Seminars Taken
Logic and Philosophy of Science
Mathematical Logic (Keith Simmons) Philosophy of Scientific Explanation (Kyle Stanford) Set Theory (Penelope Maddy) Metalogic (Kent Johnson) Incompleteness/Recursion Theory (Ben Escoto) Philosophy of Logic I (Penelope Maddy) Philosophy of Logic II (Penelope Maddy) Philosophy of Physics: Space and Time (John Roberts) Fine-Tuning Arguments (John Roberts) Philosophy of Psychology (Joshua Knobe) Metaphysics and Epistemology
Philosophy of Mind (William Bristow) Word/World Connections* (Penelope Maddy) How to Refer (Michelle Montague) Metaphysics of Modality (William Lycan) Philosophy of Existence* (Robert Merrihew Adams) Internal Time Consciousness (Martin Schwab) Wittgenstein* (Alan Nelson) History of Philosophy
Plato (Gerasimos Santas) Aristotle (CDC Reeve) Plato, Aristotle, Wittgenstein (Nicholas White) Medieval Philosophy* (Marilyn McCord Adams) Medieval and Early Modern Causation* (Marilyn McCord Adams and Robert M. Adams) Newton and Leibniz (Andrew Janiak and Alan Nelson) History & Philosophy of the Scientific Revolution (Tad Schmaltz and Seymour Mauskopf) Rationalism (Alan Nelson) Descartes* (Tad Schmaltz) Descartes (Alan Nelson) Spinoza* (Alan Nelson) Empiricism (Alan Nelson) Hobbes (Nicholas Jolley) Locke* (Alan Nelson) Hume (Alan Nelson) Kant (Alan Nelson) Demonstration and Logic (Alan Nelson) Nietzsche* (Martin Schwab) Ethics and Value Theory
History of Moral Philosophy (Thomas Hill) Well Being (Susan Wolf and Richard Kraut) Empirical Moral Psychology (Jesse Prinz and Joshua Knobe) Adam Smith* (Geoffrey Sayre-McCord)
‘*’ Denotes Audit
www.cathayliu.com ●
[email protected] ● 949.891.1362
●
Department of Philosophy ● UNC, CB#3125 ● Chapel Hill, NC 27599
Cathay M. Liu C.V. page 4
References
Daniel Garber
Stuart Professor of Philosophy Princeton University
[email protected] 609.258.4307
Andrew Janiak
Creed C. Black Associate Professor of Philosophy Duke University
[email protected] 919.660.3057
Marc Lange
Bowman and Gordon Gray Professor UNC-Chapel Hill
[email protected] 919.962.3324
Alan Nelson
Professor of Philosophy UNC-Chapel Hill
[email protected] 919.780.4558
Tad Schmaltz
Professor of Philosophy University of Michigan
www.cathayliu.com ●
[email protected] ● 949.891.1362
[email protected] 734.764.6285
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Department of Philosophy ● UNC, CB#3125 ● Chapel Hill, NC 27599
Cathay M. Liu C.V. page 5
Dissertation Abstract
At least since Kant, philosophers have attempted to explain the relationship between mathematics and the empirical sciences. In the early modern period there were numerous attempts to address the fundamental philosophical issue of how mathematical idealizations and abstractions can be so strikingly useful for capturing the complexities of the physical world. This issue, I ague, did not haunt Descartes. Instead, he challenged the division between the concrete entities of physics and the abstract entities of mathematics. Descartes famously viewed all human knowledge, scientia, as a unified, interconnected whole: metaphysics at the roots, a trunk of physics, and medical, mechanical and ethical branches come together to form a tree of knowledge. But I argue that Descartes thinks there is an even stronger unification between mathematics and physics: a metaphysical unification. When Descartes claims physics is nothing but mathematics, he does not merely mean that his physics employs mathematical techniques and characterizations. He means the entities of physics are metaphysically identical to the entities of mathematics, thus ontologically collapsing any distinction between the two. My argument for this strong unification of physics and mathematics is a result of my systematic study of Descartes’ philosophy through the lens of his distinctive Method. Focusing on his Rules for the Direction of Our Native Intelligence, I reconstruct the heart of his Method. I vindicate Descartes’ claims to have employed this single Method throughout his career and intellectual pursuits. My interpretation contrasts strongly with the dominant view of the Rules as a youthful project that Descartes abandoned by the time he delved into metaphysics. Other interpretations mistakenly think the Method in the Rules applies merely to Descartes’ early mathematical work. Instead, I argue the Method allows him to determine metaphysical relations by tracing and decomposing the conceptual dependencies contained in our ideas. Ordering ideas in terms of dependence exposes both the metaphysical relations between objects in our thought, and their relative epistemic and conceptual priority. Using conceptual ordering, Descartes can reach intuitions of the simplest natures and principles from which the complex ideas were composed. My approach to Descartes’ philosophy has implications that range from the fundamental metaphysical and epistemological roots of his philosophy to the tangible scientific fruits that so interested him. Starting with his mathematical contributions, I analyze his idiosyncratic unification of algebra and geometry. Descartes was able to bring algebraic methods to bear on geometrical problems because both algebra and geometry had an identical subject matter: extension. But his emphasis on geometric magnitudes as opposed to numeric expressions is a result of the conceptual dependence of algebraic expressions on geometric objects. This conceptual dependence explains the sense in which Descartes thought geometry was epistemically prior. My interpretation of Descartes’ mathematics leads to a re-interpretation of his views on the ontological status of universals. Properly understood, his Method brings out a surprisingly thoroughgoing nominalism, rather than the Platonism commonly attributed to him. I support this reading by examining his account of counting and measuring. I argue that the deployment of numbers, e.g., an act of counting, is conceptually dependent on our ideas of extension: ideas of extension are prior to ideas of numbers. Mathematics is unified with physics because they share an identical subject matter, viz. extension. The entities of both physics and mathematics depend ontologically and conceptually on extension. For Descartes, there is no puzzle about the applicability of mathematics to physics.
www.cathayliu.com ●
[email protected] ● 949.891.1362
●
Department of Philosophy ● UNC, CB#3125 ● Chapel Hill, NC 27599