Aristotle, The Pythagoreans, and Structural Realism

Abstract

Aristotle’s main objection to Pythagorean number ontology is that it posits as a basic subject what can exist only as inherent in a subject. I then show how contemporary structural realists posit an ontology much like that of Aristotle’s Pythagoreans. Both take the objects of knowledge to be structure, not the subject of structure. I discuss both how pancomputationalists such as Edward Fredkin approach the Pythagorean account insofar as on their account all reality can in principle be expressed as one (very big) number, made up of discrete units, and even more moderate varieties of structural realism, like that of Floridi, share with pancomputationalism the aspect of “Pythagorean” ontology that Aristotle finds so objectionable: positing structure or form with no substrate. I conclude by arguing that Aristotle himself is drawn to something close or (identical) to a structural realist ontology in Metaphysics 7.3