Distinguishing the specific from the recognitional and the canonical, and the nature of ratios

Abstract

There are three independent properties of a mode of presentation (m.p.) of a number: being specific; being recognitional; and being canonical. A perceptual m.p. of the form that many Fs is specific although it is neither recognitional nor canonical. The literature has not distinguished noncanonical from nonspecific m.p.s of numbers. Ratios are fundamentally ratios of magnitudes.