Reference to Abstract Objects

Welcome to the home page of Reference to Abstract Objects (2009 -2012) which is a research project in the discipline of theoretical philosophy conducted in the Department of Philosophy, History, Culture and Art Studies at the University of Helsinki.

Participants:

• Gabriel Sandu, Professor, project leader
• Andrea Strollo, postdoc researcher (01.01.2012-31.12.2012)

Former members of the project:

• Anssi Korhonen, PhD (2009)
• Elina K Nurmi, MA, doctoral student (Cornell University) (2009-2011)
• K. Severi Hämäri, MA, doctoral student (2010)
• Markus Pantsar, Postdoc (2010-2011)

The project is funded by the Academy of Finland (decision: 127088, 09/26/2008).

Project description

The role and status of abstract objects is one of the most debated topics in contemporary analytic philosophy. On one side of the debate, there are the so-called Platonists. A Platonist holds that abstract objects such as numbers, sets, and propositions exist: there are various regions of discourse of the kind where true sentences, valid arguments and good explanations are being put forth which require the reality of abstract objects. Those who deny this are called anti-Platonists. According to them, the sentences, arguments and explanations alluded to by the Platonist can be either replaced or otherwise accounted for in ways that make no appeal to abstract objects.

During the last couple of decades or so, an impressive array of arguments has been put forth variously targeted at exhibiting Platonism as lacking any respectable philosophical motivation, or as being fundamentally detached from any plausible account of knowledge and reference. It is fair to say that, among contemporary analytic philosophers, anti-Platonism about abstract objects has come to be accepted as something of a default position. One of the most popular forms of anti-Platonism today is fictionalism, i.e., a view according to which sentences involving abstract-object terms are literally false; yet, they serve a certain purpose as "useful fictions".

This project has both a historical and a systematic goal. From a historical point of view, we will conduct a careful investigation of the problem of abstract objects as it appears in Frege and Russell so as to retrace the tensions that underlie the current philosophical debate(s) surrounding the notion of an abstract object. The results of this investigation will include, among other things, a novel account of propositions and propositional unity in Frege. From a systematic point of view, some of our broader goals will be to

• Undermine fictionalism as a credible research strategy
• Critically assess the logical and philosophical merits of one of its most important contemporary rivals in the field of philosophy of mathematics and logic: neo-Fregeanism (or neo-logicism)
• Develop an account of reference involving abstract-object terms that does not have the shortcomings of either fictionalism or the traditional forms of Platonism
• Show how this account fares in solving certain traditional puzzles (that at least seemingly involve reference to abstract objects) in philosophical semantics and in philosophy of logic and mathematics

Need help in using these pages?

Picture: Veikko Somerpuro