The Metaphysics Research Lab

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

Search These Pages

Welcome to the web pages of the Metaphysics Research Lab. Whereas physics is the attempt to discover the laws that govern fundamental concrete objects, metaphysics is the attempt to discover the laws that systematize the fundamental abstract objects presupposed by physical science, such as mathematical objects and relations, possible states and events, types (as opposed to tokens), possible and future objects, complex properties, etc. Abstract objects are even needed to understand 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 of metaphysics, therefore, is to develop a formal ontology, i.e., a formally precise systematization of these abstract objects. Such a theory will be compatible with the world view of natural science if the abstract objects postulated by the theory are conceived as patterns of the natural world.

In our research lab, we have developed such a theory: the axiomatic theory of abstract objects and relations. In many ways, this theory is like a machine for detecting abstract objects (hence the name ‘research lab’), for among the recursively enumerable theorems, there are statements which assert the existence of the abstract objects mentioned above. Moreover, the properties of these abstracta can be formally derived as consequences of the axioms. The theory systematizes ideas of philosophers such as Plato, Leibniz, Frege, Meinong, and Mally. Our results are collated in the document Principia Logico-Metaphysica, which is authored by Edward N. Zalta (Ph.D./Philosophy), a Senior Research Scholar in the Philosophy Department. An online version of Principia Logico-Metaphysica can be found by following the link to The Theory of Abstract Objects (see below). In published work, the theory has been applied to problems in the philosophy of language, intensional logic, the philosophy of mathematics, 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 Ante Rem Structuralism, joint work with Uri Nodelman, presented by Edward N. Zalta at the Ontological Dependence Workshop, University of Bristol, February 2011 (Slides for the talk) [This talk was developed into a paper, retitled “Foundations for Mathematical Structuralism,” and published in the journal Mind in 2014. Here is a preprint.]
• Streaming Video Lecture: Steps Toward a Computational Metaphysics, joint work with Branden Fitelson, presented by both co-authors at the Computing and Philosophy Conference, Oregon State 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, Uniwersytet Warszawski, 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 Research Centre), 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, und Wissenschaftstheorie, Universität München, Germany
• Edwin Mares, Senior Lecturer, Philosophy Department, Victoria University of Wellington, 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

Tools and Procedures Used To Create This Web Site in 1994