 The need to posit ‘intermediates’ can be seen as arising from the fact that one cannot perform arithmetical operations on these ‘Idea numbers’, as Cook Wilson called them, while one would need entities that are ‘in between’ (τά μεταξύ) sensible things and Idea numbers to account for arithmetical truths as elementary as ‘two and two make four’. Cook Wilson nevertheless argued against commitment to ‘intermediates’ (OPD, §4), his view being that arithmetical operations are always on particulars and if the ‘monadic numbers’ of arithmetic are plurality of units, Idea numbers are properties of these numbers. That Plato had reached this view of Idea numbers as ἀσύμβλητοι ἀριθμοί at the time he wrote the Republic or later on would be yet another issue.