Numbers versus nominalists
One who sincerely utters the latter, it is argued, is thereby committed, whereas one who utters the former is not, to there being besides the moons of Mars such a thing as their number. Therefore, by embracing (1E) while disowning (2E) the nominalist can consistently deny that there are numbers while accepting the sober pronouncements of mature science.1 The tactic is immediately suspect. The observational sentence (1E) logically entails a sentence that straightforwardly expresses that there is some number or other of a certain sort: