Version: v1, Published online: 1998
Retrieved January 23, 2019, from https://www.rep.routledge.com/articles/thematic/abstract-objects/v-1
The central philosophical question about abstract objects is: Are there any? An affirmative answer – given by Platonists or Realists – draws support from the fact that while much of our talk and thought concerns concrete (roughly, spatiotemporally extended) objects, significant parts of it appear to be about objects which lie outside space and time, and are therefore incapable of figuring in causal relationships. The suggestion that there really are such further non-spatial, atemporal and acausal objects as numbers and sets often strikes Nominalist opponents as contrary to common sense. But precisely because our apparent talk and thought of abstracta encompasses much – including virtually the whole of mathematics – that seems indispensable to our best attempts to make scientific sense of the world, it cannot be simply dismissed as confused gibberish. For this reason Nominalists have commonly adopted a programme of reductive paraphrase, aimed at eliminating all apparent reference to and quantification over abstract objects. In spite of impressively ingenious efforts, the programme appears to run into insuperable obstacles.
The simplicity of our initial question is deceptive. Understanding and progress are unlikely without further clarification of the relations between ontological questions and questions about the logical analysis of language, and of the key distinction between abstract and concrete objects. There are both affinities and, more importantly, contrasts between traditional approaches to ontological questions and more recent discussions shaped by ground-breaking work in the philosophy of language initiated by Frege. The importance of Frege’s work lies principally in two insights: first, that questions about what kinds of entity there are cannot sensibly be tackled independently of the logical analysis of language; and second, that the question whether or not certain expressions should be taken to have reference cannot properly be separated from the question whether complete sentences in which those expressions occur are true or false.
Hale, Bob. Abstract objects, 1998, doi:10.4324/9780415249126-N080-1. Routledge Encyclopedia of Philosophy, Taylor and Francis, https://www.rep.routledge.com/articles/thematic/abstract-objects/v-1.
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