Synthese

, Volume 88, Issue 2, pp 201–228 | Cite as

Mathematics, science and ontology

  • Thomas Tymoczko
Article

Abstract

According to quasi-empiricism, mathematics is very like a branch of natural science. But if mathematics is like a branch of science, and science studies real objects, then mathematics should study real objects. Thus a quasi-empirical account of mathematics must answer the old epistemological question: How is knowledge of abstract objects possible? This paper attempts to show how it is possible.

The second section examines the problem as it was posed by Benacerraf in ‘Mathematical Truth’ and the next section presents a way of looking at abstract objects that purports to demythologize them. In particular, it shows how we can have empirical knowledge of various abstract objects and even how we might causally interact with them.

Finally, I argue that all objects are abstract objects. Abstract objects should be viewed as the most general class of objects. The arguments derive from Quine. If all objects are abstract, and if we can have knowledge of any objects, then we can have knowledge of abstract objects and the question of mathematical knowledge is solved. A strict adherence to Quine's philosophy leads to a curious combination of the Platonism of Frege with the empiricism of Mill.

Keywords

Natural Science General Class Science Study Abstract Object Mathematical Knowledge 

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Copyright information

© Kluwer Academic Publishers 1991

Authors and Affiliations

  • Thomas Tymoczko
    • 1
  1. 1.Dept. of Philosophy Wright HallSmith CollegeNorthamptonUSA

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