Relationalism is the view that a quantity (i.e., space or mass) consists only of a network of concrete objects that stand in determinate relations (spatial relations or mass-relations). At its very core, the theory claims that an object possesses a determinate quantity fundamentally by standing in determinate relations in that quantity to other objects. For instance, my laptop’s mass consists fundamentally in the fact that it is k times more or less massive than other objects (my neighbor’s car, the Earth, the International Prototype of the Kilogram). The view is nominalistic insofar as, according to it, facts about quantities are fundamental facts about particulars (that they are so and so related) and not about their attributes (like quantitative universals or positions in abstract state spaces). I offer here an argument against this theory, which I call “ultimate” (borrowing Bird’s (2005) term) because it shows that the very core of this theory fails to account for what it is supposed to account for: the fact that objects possess determinate quantities. I show that by merely situating objects in relation to each other, it fails to situate them anywhere really, that is, to endow them with well-determined quantities.
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