Platonists and nominalists will likely disagree whether Goodman and Quine successfully argue their case in their joint paper. Goodman and Quine will be able to account for any actual mathematical proof and any theorem actually proven, since there are at any stage only finitely many of them, each of which is small enough to fit in our universe comfortably. Thus, arguably, they reach their goal of explaining the agreement in mathematical practice without presupposing mathematical platonism. Due to its finitistic nature, however, the account radically falls short of giving explications that are extensionally equivalent to the platonists’ conceptions (see Rossberg and Cohnitz 2009 for discussion and a landscape of possible solutions). Goodman later (1956) explains that nominalism is not incompatible with the rejection of finitism; it is