Mathematics, science and ontology

Synthese 88 (2):201 - 228 (1991)
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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.



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References found in this work

Science Without Numbers: A Defence of Nominalism.Hartry H. Field - 1980 - Princeton, NJ, USA: Princeton University Press.
Truth and other enigmas.Michael Dummett - 1978 - Cambridge: Harvard University Press.
The foundations of arithmetic.Gottlob Frege - 1884/1950 - Evanston, Ill.,: Northwestern University Press.

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