David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Synthese 88 (2):201 - 228 (1991)
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 BETA
Peter Aczel (1988). Non-Well-Founded Sets. Csli Lecture Notes.
Alice Ambrose (1966). Essays in Analysis. New York, Humanities P..
Paul Benacerraf (1973). Mathematical Truth. Journal of Philosophy 70 (19):661-679.
Charles S. Chihara (1973). Ontology and the Vicious-Circle Principle. Ithaca [N.Y.]Cornell University Press.
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