6. Outline Russell's theory of universals and his defence of it in The Problems of Philosophy. That is, explain what he means by a universal, why he thinks universals are indispensable in knowledge, what he takes their ontological status to be and why.
For Russell relations (e.g., ‘in,’ ‘greater than,’ ‘north of,’ etc.) and qualities (e.g., ‘red,’ ‘tall,’ ‘ornate,’ etc.) are good examples of common types of universals. Though universals are often treated as ethereal and scholarly abstractions, Russell is quite correct to point out that they so thoroughly infiltrate our common speech that it may very well be impossible to formulate a sentence without employing one or more universals. For instance, when we ask what things are (what dogs are, or what justice is) we tend to answer by isolating qualities which all particular instances of ‘dog’ or ‘justice’ possess. We isolate or abstract those general qualities which are common to all the particular instances of the quality or thing in question. What we isolate in cases like this is, in Plato’s terms, the ‘form’ or ‘idea’ of which the particular instances partake. Or, in Russell’s terms (employed to avoid confusing associations with ‘ideas’) we abstract the ‘universal’ from the particular.
Qualities have, historically, been the privileged example of universals, much to Russell’s metaphysical chagrin. But, as mentioned above, Russell also takes relations to be universals, and perhaps more instructive examples thereof. For example, when we say things like “A is in B” we imply that two particulars (A and B) partake of a universal relation, a relation which is exhibited by but not limited to this particular instance. We can only make sense of the relation ‘in’ as something separate from any given instance of ‘in-ness’. The necessity to thus understand universals as logically separable from their particular instantiations requires what at first appears to be a rather strange ontological stance. Universals cannot be particular physical objects in the spatiotemporal world we inhabit because, unlike physical things, universals do not and cannot change. They are immutable. It is hard to understand what it would even mean for the relation ‘in’ to change. They are immutable, but also insensible: we cannot happen upon these relations themselves as items of sense data apart from their particular instantiations. We don’t see in-ness, we see, e.g., object A and object B.
A common ontological response to universals’ implacable non-physicality is to relegate them to the realm of the mental. This is a Kantian move which Russell similarly rejects. For him universals are not mental things either: they are not simply the way that human or, indeed, any other possible consciousness ‘structures’ or categorizes the experiential world. This is suggested by the following example.
Whether or not any mind has thought or could possibly think that Edinburgh is north of London, this relation still holds true. It would be true to say that Edinburgh is north of London even if no minds had ever or could ever exist. Now this shows that universals cannot be mental in character just insofar as the truth of this proposition—a proposition which contains the universal relation ‘north of’—does not rest on its being mentally apprehended or apprehendable.
Yet a universal is something, as we can see based on the fact that the truth of propositions like ‘Edinburgh is north of London’ relies on the phrase ‘north of’ having a determinate meaning. ‘A is north of B’ must refer to something more than ‘X thinks that A is north of B’ if the truth conditions of the sentence (which have nothing to do with minds apprehending the proposition) are to be duly respected. Thus, a universal must be something, though something neither mental nor physical. These somethings inhabit another, a ‘third’ ontological realm, a realm quite different from the physical and mental realms which are the daily bread of ontologists.
This third realm, which is at least as inspired by Frege as it is by Plato, is timeless, immutable, and insensible. Negative characterizations, all, but helpful nonetheless. Russell suggests that a further terminological subtlety which is, I think helpful for understanding how we can think of the being of universals. He suggests that while the objects of the more familiar realms of ontology may be characterized as ‘existing’ (i.e., as being through time and in space), we would be better off thinking of universals as ‘subsisting’ or ‘having being’.
Universals, as atemporal immutable objects, seem entirely divorced from the fray of mortal existence which is the concern of philosophers. But, as Russell endeavors to point out, they are of crucial importance when it comes to epistemology, and especially the epistemology of a priori knowledge which has long been the special province of philosophy.
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For Russell, a priori knowledge is any knowledge which does not require any sensory input as evidence (though it may—indeed it must—be prompted or elicited by some sensory input). His privileged examples of such knowledge are mathematics and logic.
At the outset of his explication of the epistemology of a priori knowledge Russell makes it clear that universals are to occupy a central role. He writes: “All a priori knowledge deals exclusively with the relations of universals” 59. A rather direct statement which in effect amounts to the claim that a priori knowledge is acquired through our acquaintance (via various processes of abstraction) with the universal relations that hold between universals.
Russell’s arithmetical example is helpful here. Take the proposition ‘2+2=4’. How do we know it to be true, a priori (as Russell suggests we do). Russell first asks what we mean or understand by this proposition. He argues that we understand ‘2+2=4’ to be a proposition about ‘twos,’ ‘fours,’ and ‘collections’ rather than as a proposition about particular twos, fours, and collections. The statement certainly implies things about such particulars but makes no direct claims about them. It does not tell us, e.g., that these two eggs and those two eggs add together to give us four eggs; it merely leads us via inference to this conclusion. ‘2+2=4’ is thus a statement about universals and the relations among them. Russell is concerned to show here the crucial difference between a priori knowledge, which is non-experiential, and the applications of a priori generalizations to particular cases.
The key difference to be highlighted, and a difference which revolves around the separation of universals from the mental and physical realms, is between the sorts of evidence enlisted to support a priori claims on the one hand and empirical claims on the other. Empirical claims must be supported by appropriate sensory inputs (e.g., There is at time t an x such that x possesses quality y. A priori claims, by contrast, are supported only by universals which make no existential or temporal claims. This has the interesting (and scientifically fortunate) result that we can know with certainty that an a priori proposition is true or false without ever having encountered (or without even being capable of encountering) any particular instantiation of what it states generally.
So, in summary, Russell believes that universals are exemplified best by relations and that they are ontologically distinct from mental and physical objects insofar as they inhabit a third, separate ontological realm whose objects are better characterized as ‘subsisting’ atemporally than as existing in space and time. They must inhabit such a realm in order to make it possible for us to differentiate (as we do) between something’s being true and it’s merely being taken to be true. Thus their ontological strangeness (immutable, insensible, atemporal) is wedded to their epistemological necessity. Their epistemological import is even more apparent in the special case of a priori knowledge, which relies completely upon universals for evidentiary support.