1 COUNTING BY IDENTITY: A REPLY TO LIEBESMAN Oliver R. Marshall David Liebesman argues that we never count by identity. He generalizes from an argument that we don’t do so with sentences indicating fractions, or with measurement sentences on their supposed count readings. In response, I argue that measurement sentences aren’t covered by the thesis that we count by identity, in part because they don’t have count readings. Then I use the data to which Liebesman appeals, in his argument that we don’t count by identity using measurement sentences, in order to rebut his argument that we don’t count by identity using sentences indicating fractions. Key words: counting, sortals, measuring, quantities, fractions, contextualism 1. Introduction Counting the F’s by identity requires distinguishing them, before placing them in one-to-one correspondence with an initial segment of the numbers from 1 through m in their canonical order, and giving ‘there are m F’s’ as the answer to ‘how many F’s?’. Anyone, such as Cantor [1885: 346] or Frege [1894: 80], who purports to explain the application of numbers to collections via the establishment of a one-to-one correspondence between the former and members of the latter, presupposes that we count by identity. David Liebesman [2015] argues that we never count by identity. First he argues that we don’t do so with sentences like (1): (1) Two and a half oranges are on the table. Then he argues that sentences like (2) have count readings (henceforth ‘individuative readings’), as well as measure readings, and that we don’t count by identity when we use such sentences with their individuative readings: (2) Two litres of water are in the jug.