It would be better not to believe in abstract objects if we could get away with it
In their book A Subject without an Object: Strategies for the Nominalistic Interpretation of Mathematics (the main topic of the book is well conveyed by its subtitle), John Burgess and Gideon Rosen suggest that – in fact, they argue at some length for the conclusion that – the motivation for undertaking nominalistic reconstructions of mathematics has not been clearly and persuasively formulated. This seems to me to be wrong. At any rate, it seems to me that it is not hard to formulate the motivation (or a sufficient motivation) for this project clearly and persuasively. Suppose one could show this: it would be better not to believe in abstract objects if one could get away with it. Or this, if it is not the same: it would be philosophically desirable to accept only philosophical positions that do not require their adherents to affirm the existence of abstract objects. I will take it that it is evident why someone who accepted this conclusion (or either of them, if they are different) would have a strong motivation for wishing that a nominalistic reconstruction or interpretation of mathematics were available.
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