Splitting atoms in natural language

The classic Fregean analysis of numerical statements runs into problems with
sentences containing non-integers such as John read 2.5 novels, since it takes such
statements to specify the cardinality of a set which by definition must be a natural
number. We propose a semantics for numeral phrases which allows us to count
mereological subparts of objects in such a way as to predict several robust
linguistic intuitions about these sentences. We also identify a number of open questions
which the proposal fails to address and hence must be left to future research.