The Metaphysics Research Lab

The Metaphysics Research Lab consists of a group of researchers located around the world collaborating with Edward N. Zalta on the axiomatic theory of abstract objects.  This theory consists of principles that govern the abstract objects presupposed in the natural sciences, such as mathematical objects and relations, possible states, possible and future objects, etc. The two main principles of the theory are existence and identity conditions for abstract objects: ∃x(A!x & ∀x(xF ≡ φ)) and A!x & A!y → (∀F(xF ≡yF) → x=y).

Currently, Zalta and Uri Nodelman are working on a paper in which they define the technical notion of a ‘possibility’ (as used in the work of Humberstone, van Benthem, Holliday, and others) and derive the main principles that these researchers use to characterize these entities. The slides for a recent talk on this topic can be found here.

Recently, Zalta collaborated with Hannes Leitgeb and Nodelman on a paper that shows how object theory offers a logicist account of mathematics. This paper, “A Defense of Logicism” is forthcoming in the Bulletin of Symbolic Logic. Zalta and Nodelman also recently collaborated on a paper that defines the primitive notions, and derives the axioms, of second-order Peano Arithmetic. This paper, “Number Theory and Infinity Without Mathematics” is forthcoming at the Journal of Philosophical Logic. And Zalta's paper “The Metaphysics of Routley Star” is forthcoming at the Australasian Journal of Logic.

Other recent papers include:

• “Mathematical Pluralism”, Noûs 2024 (published online open access)
• “Foundations for Mathematical Structuralism” (with U. Nodelman) (Mind, 2014)
• “Steps Towards a Computational Metaphysics” (with Branden Fitelson) (J. Philosophical Logic, 2007)

Links: 

The Metaphysics Research Lab home page

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