Epistemological Reflections on the Idea of a Metaphysical System

Abstract Book 1 of Spinoza’s Ethics and David Lewis’s On the Plurality of Worlds are considered as representative works of systematic metaphysics. The former is presented in axiomatic-deductive form (at least in intention), the latter is not. It is contended that Plurality could, in principle, have been presented in axiomatic-deductive form, and that any metaphysical system could in principle be so presented. It is further contended that, once a given metaphysical system has been presented in axiomatic-deductive form, questions about its epistemic status are essentially questions about the epistemic status of its axioms. The axioms of certain mathematical theories (Zermelo-Fraenkel set theory, Peano Arithmetic, the axioms of the real line) are held by many to have a property that various philosophers at various times have called ‘being evident even to the meanest capacity’ (Hobbes); ‘being self-evident’, ‘being perceived clearly and distinctly to be true’ (Descartes); ‘being intuitively obvious’, and ‘forcing themselves upon us as true’ (Gödel). It is argued that the history of metaphysics amply demonstrates that metaphysics cannot pretend to have available to it a set of axioms that have this feature, and that there therefore cannot be a metaphysic ‘that will be able to present itself as a science’.