Representations of Initial Sorts

Abstract

In this chapter I shall begin to work out the ideas contained in Chapter III in a rigorous manner, using the material of Chapter V to do so. The aim is to construct, for as many Sorts as possible, a Biparitous Representation (hereafter often abbreviated as Bip. Rep.) satisfying the conditions stated in (3.2). As I have already explained, any Sort which lacks such a representation can have no epistemological status in the empirical world; and as most Sorts fall into this class, those which have representations must be expected to have some recognisable reflection in the world we observe. In searching for representations, I confine attention to prime Sorts, as defined in (5.19.1); derived Sorts (such as pair-Sorts, power-Sorts), being constructed from prime Sorts, are evidently representable if and only if their prime ‘factors’ are so. But among prime Sorts, there is a further distinction to be made.