Accounts of the problem of abstract objects generally focus on three questions: the ontological status of abstract objects, how knowledge of such objects is possible and the ground of the distinction between abstract and concrete entities. When the problem of abstract objects is stated with this generality, it could arguably be regarded as a long-standing philosophical concern, just as much present in Plato’s theory of forms and scholastic debates over nominalism as in contemporary debates. What is there to prevent us, for example, from characterizing Locke’s doctrine of abstract ideas as giving an account of the ontological, epistemological and metaphysical status of entities such as numbers and geometrical shapes? Insofar as philosophers have long speculated over the status of such entities, the problem of abstract objects appears to be one with a long history. The term ‘abstract object’ is nonetheless a recent addition to the philosophical lexicon concomitant with the application of new methods of logical analysis to traditional metaphysical problems. This suggests that contemporary debates about abstract entities reflect a significant conceptual shift rather than a superficial change in terminology.
KeywordsAbstract Object Singular Term Ontological Status Abstract Entity Mathematical Entity
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