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::: center home >> events >> lunchtime >> 2003-04 >> abstracts

Tuesday, 2 March 2004
Ontology without Tears: A Solution to the Problem of Abstract Objects
(That Even a Naturalist Could Love)

Edward Zalta
Stanford University
12:05 pm, 817R Cathedral of Learning

Abstract: Natural science seems to be both formally and informally committed to abstract objects: (1) The mathematics language used in our best scientific theories is most naturally interpreted in terms of abstract, "mathematical objects".
(2) Probability spaces are defined over "possible events" and inductive logic measures the inductive strength with which certain "propositions" imply other propositions. (3) Natural laws, under one interpretation, involve "relations" among "properties" in the natural world. (4) And scientists often informally conceive and make claims like "There might be a planet perturbing the orbit of Uranus and it might have a period of x years", which are naturally interpreted as about possible objects and their possible properties. In this talk, I propose a way to naturalize these abstract entities, by developing formal principles that axiomatize them and re-interpreting those formal principles in a new way. These formal principles are comprehension principles which appear to assert the existence of abstract objects corresponding to certain expressible conditions in a formal language. However, if we reinterpret these principles in a certain way (for example, as precisely describing certain patterns or dispositions concerning linguistic behavior, or patterns of properties in the natural world), then a path opens up to naturalizing abstract objects. The resulting view might be thought of as something in between realism and fictionalism. The most interesting consequence is that the informal Wittgensteinian/Sellarsian theory of meaning becomes wedded to some precise machinery. (And when the patterns involve the inferential roles of the terms involved, there are connections to Brandom's work.) The present suggestion helps to make the informal theories of meaning more precise and make the formal machinery of abstract objects more acceptable to the naturalist.

Revised 3/11/08 - Copyright 2006