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
reinterpreting 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.
