In chapter 9 of his ‘Problems of Philosophy’, Bertrand Russell tackles the nature of universals and their role in our acquisition of knowledge. He first observes that contrary to proper names, like John or London, they are represented in substantives or nouns, adjectives, prepositions and verbs. No sentence can be construed without the necessary presence of at least one word denoting a universal, which explains why ‘all truths involve universals, and all knowledge of truths involves acquaintance with universals.’

Philosophers have recognised the importance of adjectives and substantives but they have somehow neglected the nature and function of prepositions and verbs which, for Russell, ‘tend to express relations between two or more things.’ In this respect, the theories of Spinoza and Leibniz would attest a misguided interpretation of universals, namely ‘God’ in Spinoza and ‘monads’ in Leibniz. In both cases, the essential quality of Spinoza’s ‘God’ and Leibniz’s ‘monad’ prevents any kind of interaction or relation with any other entity or substance.

Taking the example of ‘whiteness’, Russell refutes Hume’s contention that there exists such a quality as ‘whiteness’ while ignoring the importance of universals in our apprehension of such a quality. Hume thinks that every time we recognise ‘white’, we see a resemblance with another white, experienced on a previous occasion. It can be argued that such an interpretation is fundamentally flawed as it fails to account for our very first encounter with the colour ‘white’. The latter is certainly not created ex nihilo. As far as Russell is concerned, the universal of ‘whiteness’ lies exclusively in this very relation of resemblance and not in a purely abstract idea of ‘whiteness’ or in my hanging one resemblance of ‘whiteness’ onto a previous one – in which case the resemblance required would have to enjoy the status of the universal ‘whiteness’ and so ad infinitum.

So, for Russell, opposed to any form of Idealism, it is ‘the relation of resemblance’ which constitutes ‘a true universal’. There is no pure idea of ‘whiteness’ in my mind since, if it were a simple act of thought, it should be theoretically identical to the very one capable of being produced by any other mind. However, because it is impossible for two people to produce an absolutely identical act of thought, the suggestion that ‘whiteness’ is a thought has, for Russell, to be rejected in favour of the seemingly more plausible explanation that ’what many different thoughts of whiteness have in common is their object and this object is different from all of them. Thus universals are not thoughts, though when known they are objects of thought.’ In other words, ‘it is not whiteness that is in our mind, but the act of thinking of whiteness.’

The presence of universals in propositions is therefore indisputable although their being is not mental as most philosophers are prepared to claim. Then, what sort of being is a universal? When we consider such a proposition as ‘Edinburgh is north of London’, we are not referring to an entity existing in the mind. The reality of the proposition is independent of our being aware of its existence. After all, there are millions of geographical locations which exist unknown to us and which we would simply be unable to describe in any proposition. In the present one: ‘Edinburgh is north of London’, ‘north of’ is neither in space nor in time, neither material nor mental; yet it is something … we must admit that the relation, like the term it relates, is not dependent upon thought, but belongs to the independent world which thought apprehends but does not create.’

Russell thus draws a radical distinction between things which can be pinpointed in quantifiable time, such as thoughts, feelings, minds and physical objects and, on the other hand, universals, which ‘subsist or have being, where ‘being’ is opposed to ‘existence’ as being timeless.’ Russell is referring here to the ‘unchangeable, rigid and exact’ world of the mathematician, logician, and metaphysician.