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The Metaphysics Research Lab

Philosophy Department
Nora Suppes Hall 107
Stanford University
Stanford, CA 94305

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Welcome to the web pages of the Metaphysics Research Lab. Whereasphysics is the attempt to discover the laws that govern fundamentalconcrete objects, metaphysics is the attempt to discover the laws thatsystematize the fundamental abstract objectspresupposed byphysical science, such as mathematical objects and relations, possiblestates and events, types (as opposed to tokens), possible and futureobjects, complex properties, etc. Abstract objects are even needed tounderstand what may turn out to be scientific fictions (e.g.,causality, models) as well as clearcut cases of scientific fictions(e.g., absolute simultaneity, the aether, and phlogiston). The goal ofmetaphysics, therefore, is to develop a formal ontology, i.e., aformally precise systematization of these abstract objects. Such atheory will be compatible with the world view of natural science ifthe abstract objects postulated by the theory are conceived aspatterns of the natural world.

In our research lab, we have developed such a theory: the axiomatictheory of abstract objects and relations. In many ways, this theoryis like a machine for detecting abstract objects (hence the name‘research lab’), for among the recursively enumerabletheorems, there are statements which assert the existence of theabstract objects mentioned above. Moreover, the properties of theseabstracta can be formally derived as consequences of the axioms. Thetheory systematizes ideas of philosophers such as Plato, Leibniz,Frege, Meinong, and Mally. Our results are collated in the documentPrincipia Logico-Metaphysica, which is authored by Edward N.Zalta (Ph.D./Philosophy), a Senior Research Scholar in the PhilosophyDepartment. An online version ofPrincipiaLogico-Metaphysica can be found by following the linktoThe Theory of Abstract Objects (see below). Inpublished work, the theory has been applied to problems in thephilosophy of language, intensional logic, the philosophy ofmathematics, and the history of philosophy.

Media Presentations

• Welcome Message (272K sound file) (.snd,.au, or.wav)
        (Recorded December 1, 1994)
• The Theory of Abstract Objects(Summary and Tutorial)
       ∃x(A!x & ∀F(xF≡ φ))
        (A!x &A!y) →(x=y ≡ □∀F(xF≡yF))
• Computational Metaphysics Web Pages (by Branden Fitelson, Paul E. Oppenheimer, and Edward N. Zalta)
• Streaming Video Lecture: Towards Leibniz's Goal of a Computational Metaphysics, presented by Edward N. Zalta at the Munich Center for Mathematical Philosophy Workshop, June 11, 2011 (Slides For the Lecture, in PDF)
• Streaming Video: Possible Worlds, the Lewis Principle and the Myth of a Large Ontology, joint work with Christopher Menzel, presented by Edward N. Zalta at the Munich Center for Mathematical Philosophy Workshop, June 4, 2011 (Slides For the Lecture, in PDF)
• Streaming Audio Lecture: A Logically Coherent AnteRem Structuralism, joint work with Uri Nodelman, presented byEdward N. Zalta at the Ontological Dependence Workshop, University ofBristol, February 2011(Slides for the talk) [This talk was developed intoa paper, retitled “Foundations for MathematicalStructuralism,” and published in the journalMind in2014. Here is apreprint.]
• Streaming Video Lecture: Steps Toward a Computational Metaphysics, joint work with Branden Fitelson, presented by both co-authors attheComputing and Philosophy Conference, OregonState University, August 8, 2003 (Slides For the Lecture, in PDF)

Historical Foundations

• Ernst Mally
• Plato and Meinong
• Gottlob Frege
• Gottfried Wilhelm Leibniz

Metaphysics Research Lab Personnel and Collaborators

• Edward N. Zalta, Senior Research Scholar, Philosophy Department, Stanford University.
  Upcoming Presentations:
  • Lecture (via Zoom), Sign-Language-Reality (SLR) Seminar, UniwersytetWarszawski, November 06, 2025.
  • Blockseminar, AI Systems Engineering, Universität Bamberg, Germany, November 28–December 3, 2025.
  • Lecture, International Workshop on Computational Ontology and Metaphysics, AI Systems Engineering, Universität Bamberg, Germany, December 4, 2025.
  • Participant, Kurt-Gödel-Prize 2025 Winners’ Symposium (Kurt-Gödel-Freundeskreis), Universität Bamberg, Dec 5, 2025.
• Jesse Alama, Assistant Editor, Stanford Encyclopedia of Philosophy, Stanford University.
• Colin Allen, Professor, History and Philosophy of Science, University of Pittsburgh
• Christoph Benzmüller, Lehrstuhl für AI Systems Engineering, Universität Bamberg.
• Otávio Bueno, Professor, University of Miami.
• Mark Colyvan, Professor, Philosophy, University of Sydney, Australia
• Branden Fitelson, Professor, Philosophy Department, Northeastern University.
• Daniel Kirchner, Research Fellow, AISE (Artificial Intelligence System Engineering) = The Research Group of the Department of Applied Computer Sciences at Otto-Friedrich-Universität Bamberg.
• Hannes Leitgeb, Chair and Head, Munich Center for Mathematical Philosophy, Ludwig-Maximilians Universität München.
• Bernard Linsky, Professor, Philosophy Department, U. of Alberta, Canada.
• Christopher Menzel, Professor, Philosophy Department, Texas A&M University.
• Michael Nelson, Associate Professor, Philosophy Department, University of California/Riverside.
• Uri Nodelman, Senior Research Engineer, Philosophy Department, Stanford University
• Paul E. Oppenheimer, Visiting Lecturer, University of Adelaide.
• Francis Jeffry Pelletier, Professor, Philosophy Department, University of Alberta, Canada
• Merel Semeijn, Theoretical Philosophy, University of Groningen and Leiden University.
• Daniel West, Doctoral Student, Philosophy Department, City University of New York Graduate Center.

(Former) Visitors to the Lab (reverse chronological order)

• Tadeusz Ciecierski, Assistant Professor, Institute of Philosophy, University of Warsaw, Poland
• Johannes Brandl, Associate Professor, Universität Salzburg
• Ondrej Tomala, Ph.D. Candidate, Charles University, Prague (The Czech Republic).
• Gabriel Sandu, Professor, Theoretical Philosophy, University of Helsinki, Finland
• Ju Shier, Professor, Zhongshan University; Director, Institute for Logic and Cognition, Zhongshan University, Guangzhou, China
• Nie Wenlong, Assistant Professor, Institute for Logic and Cognition, Zhongshan (Sun Yat-Sen) University, Guangzhou, China
• Kristë Shtufi, Forschungsassistent, University of Graz, Austria, and Lecturer at University of Prishtina, Kosovo.
• Sun-Joo Shin (Professor, Philosophy, Yale University)
• Paavo Pylkkanen, Associate Professor,Consciousness Studies Program, Skövde University, Sweden
• Anna Bjurman Pautz, Doctoral Student, Department of Philosophy, University of Lund, Sweden
• Keith Stenning, Professor, Division of Informatics (Human Communication ResearchCentre), University of Edinburgh, United Kingdom
• Daniel Nolan, Lecturer, Philosophy Department, University of Nottingham
• Greg Restall, Senior Lecturer, Philosophy Department, University of Melbourne, Melbourne, Australia
• Wolfgang Malzkorn, formerly of the Seminar für Logik und Grundlagenforschung, Universität Bonn, Germany
• Steven Horst, Associate Professor, Philosophy Department, Wesleyan University
• Godehard Link, Professor, Institut für Philosophie, Logik, undWissenschaftstheorie, Universität München, Germany
• Edwin Mares, Senior Lecturer, Philosophy Department, Victoria University ofWellington, New Zealand
• Karl-Georg Niebergall, Professor, Humboldt-Universität zu Berlin, Germany
• Peter Menzies, Associate Professor, Philosophy Department, Macquarie University, Australia
• John Bacon, Associate Professor, School of Philosophy, University of Sydney, Australia
• David Chalmers, Professor, New York University
• Andrew Irvine, Professor, Philosophy Department, University of British Columbia,Canada
• Christopher Gauker, Professor, Universität Salzburg
• Mark Textor, Lecturer, Kings College/London, United Kingdom
• Kees van Deemter, Informatics, University of Utrecht, The Netherlands

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