The Bloomsbury Companion to Bertrand Russell by Russell Wahl

Author:Russell Wahl
Language: eng
Format: epub
ISBN: 9781474278065
Publisher: Bloomsbury UK

The upshot is that we can break up any group of four in different ways into two groups each containing exactly two. More formally it says: For all properties θ!, there are exa ctly four entities that exemplify θ! if and only if there are properties φ! and ψ! such that there are exactly two entities that exemplify φ! and exactly two other entities that exemplify ψ!, and the entities that are θ! are in one-to-one correspondence with entities that either exemplify φ! or exemplify ψ!. It is a mouthful to say. Can we directly perceive it? No. But we can perceive an instance of it. We have only to notice pictorial representation (below fig. 1) to see one way to break a group of four into two independent groups of two. It should be noted that cp-logic is required for this to hold since, for any θ! exemplified by exactly four entities, it is comprehension that assures that there are universals φ! and ψ! each exemplified by exactly two entities and such that no φ!’s are ψ!’s. Without the comprehension of universals afforded by cp-logic, “two plus two are four” would not be a relation between universals.

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