Shapiro (1996) says, “Accordingly, numerals are not genuine singular terms, but are disguised bound variables.” A reference to the number 3 really means: in the model of Dedekind arithmetic at hand, the successor of the successor of the successor of zero. One difference between structuralism in practice and eliminative structuralism, however, is that the structuralist-in-practice drops the elimination claim, the nominalist ontological claim that abstract structural objects do not exist; rather, the structuralist-in-practice simply follows the structuralist imperative to pursue
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