 The contemporary debate about platonism developed in earnest when Quine argued (1948) that mathematical objects exist, having changed his mind about the nominalist approach he had defended earlier (Goodman &amp; Quine 1947). Quine’s 1948 argument involves three key premises, all of which exerted significant influence on the subsequent debate: (i) mathematics is indispensable for empirical science; (ii) we should be ontologically committed to the entities required for the truth of our best empirical theories (all of which should be expressible in a first-order language); and (iii) the entities required for the truth on an empirical theory are those in the range of the variables bounded by its first-order quantifiers (i.e., the entities in the domain of the existential quantifier ‘\(\exists x\)’ and the universal quantifier ‘\(\forall x\)’). He concluded that in addition to the concrete entities contemplated by our best empirical science, we must accept the existence of mathematical entities, even if they are abstract (see also Quine 1960, 1969, 1976).