This paper investigates a certain puzzling argument concerning number
expressions and their meanings, the Easy Argument for Numbers. After finding faults
with previous views, I offer a new take on what’s ultimately wrong with the Argument:
it equivocates. I develop a semantics for number expressions which relates various
of their uses, including those relevant to the Easy Argument, via type-shifting. By
marrying Romero’s (Linguist Philos 28(6):687–737, 2005) analysis of specificational
clauses with Scontras’ (The semantics of measurement, 2014) semantics for Degree
Nouns, I show how to extend Landman’s (Indefinites and the type of sets, Blackwell,
Oxford, 2004) Adjectival Theory to numerical specificational clauses. The resulting
semantics can explain various contrasts observed by Moltmann (Philos Stud 162:499–
536, 2013a), but only if Scontras’ contention that degrees and numbers are sortally
distinct is correct. At the same time, the Easy Argument can establish its intended
conclusion only if numbers and degrees are mistakenly assumed to be identical.

EB00000002707K

Available

• Numbers and Cardinalities: What’s Really Wrong with the Easy Argument for Numbers?