DOI 10.1515/sem-2013-0019 Semiotica 2013; 194: 3 – 20 Søren Harnow Klausen Approaching the abstract: Building blocks for an epistemology of abstract objects Abstract: Abstract objects are widely held to pose a formidable epistemological challenge. It has seemed mysterious to many how we can have access to such strange and intangible entities. The article considers ive inluential ways to meet the challenge: Transcendental arguments, the indispensability argument, insist- ing that we just are able to grasp abstract objects and that no further explanation is needed, abstractionist accounts, and ontological reduction. None of these ap- proaches is by itself suicient or completely convincing, but together they make out a strong cumulative case for the accessibility of abstract objects. Keywords: abstract objects; epistemology; ontology; transcendental arguments; indispensability argument; mental modeling Søren Harnow Klausen: University of Southern Denmark. E-mail: harnow@ifpr.sdu.dk 1 Introduction Abstract objects play a rather ambivalent role in philosophy and science. They are oten posited for epistemological reasons. Philosophers from Plato and Aris- totle to the present day have argued that the possibility of knowledge, especially of a scientiic kind, depends on the existence of abstract forms or patterns in a world that would otherwise be too fragmented and unstable to support our at- tempt to construct theories and concepts with general signiicance. But abstract objects have just as oten been put into doubt and subjected to reduction or elim- ination for epistemological reasons, as philosophers with empiricist leanings have questioned how we could ever have knowledge of such queer entities. This dilemma has been given both classic and contemporary expressions. In one of his most profound and enigmatic dialogues, Plato let Parmenides carry out an almost complete demolition of his own theory of the forms, only to conclude that it would nevertheless be irrational to deny their existence, since this would leave our thought without any object and destroy the possibility of communica- tion (Parmenides 134E). And Paul Benacerraf has argued that taking mathematics – and its scientiic use – seriously commits us to a thoroughgoing realism about mathematical objects, which unfortunately engenders seemingly intractable Brought to you by | University Library of Southern Denmark - Syddansk Universitetsbib Authenticated | 130.226.87.174 Download Date | 4/10/13 5:19 PM