Computational Metaphysics

“If we had it [a characteristica universalis], we should be able to reason in metaphysics and morals in much the same way as in geometry and analysis.” “If controversies were to arise, there would be no more need of disputation between two philosophers than between two accountants (Computistas). For it would suffice to take their pencils in their hands, to sit down to their slates (abacos), and to say to each other … : Let us calculate (Calculemus).” Gottfried Wilhelm Leibniz

The Basic Project

Computational metaphysics, as we practice it, is the implementation and investigation of formal, axiomatic metaphysics (i.e., the study of metaphysics using formally represented axioms and premises to derive conclusions) in an automated reasoning environment.

In one of the major strands of our research, we've worked within the axiomatic theory of abstract objects developed at the Metaphysics Research Lab at Stanford University. We have represented some of the axioms and definitions of abstract object theory in the syntax of various automated reasoning systems. With such representations, claims expressible in the formal language of object theory can often be proved or shown to be independent of the basic axioms and definitions. In some projects, we have used PROVER9 (and its accompanying model-finding program, MACE4 ), as our automated reasoning system. In other projects, we used a more generic framework, namely, TPTP syntax, which can be parsed by all current theorem provers and model-finders. But the latest developments in the computational implementation of the theory of abstract objects has been developed by Daniel Kirchner, using Isabelle/HOL.

Research Products in Computational Metaphysics

The list of completed works so far includes:

Links to the Computational Projects

Project Participants

Acknowledgments: Zalta and Oppenheimer would like to thank Chris Menzel, discussions with whom have helped us to see how to improve our results.