Russell - A Very Short Indroduction by A. C. Grayling Read Free Book Online

things than one is to reject monism.
    Rejection of monism constitutes a rejection of idealism for Russell because it is crucial to idealism that the relation of experience to its objects should be internal; which is in effect to say that there is no such relation; which is again in effect to say that relations are unreal. But on Russell’s opposed view that relations are real, experience cannot be conflated with its objects; which is to say that those objects exist independently of being experienced. And this is central to what Russell and Moore meant by realism.
    It is disputable whether Russell is right in thinking that all the idealists (including Leibniz), and before them the Schoolmen with their metaphysics of substance and attribute, were committed to the view that all propositions are subject-predicate in form. But he certainly took himself to have discovered a highly important flaw in previous philosophy. With the rejection of idealism he went for a time to the other extreme, that of being a realist about everything. By his own account he was a ‘naïve realist’ in the sense of one who believes that all the perceived properties of material objects are genuine properties of them, a physical realist in believing that all the theoretical entities of physics are ‘actually existing entities’ ( MPD 48–9), and a Platonic realist in believing also in the existence, or at least in the ‘being’ (where this is a qualified and perhaps lesser kind of existence), of ‘numbers, the Homeric gods, relations, chimeras, and four-dimensional spaces’ ( The Principles of Mathematics ( PoM ) 449). Russell later trimmed this luxuriant universe by applying ‘Ockham’s razor’, the principle that entities should not be multiplied unnecessarily. For example, if physical objects can be exhaustively explained in terms of subatomic entities, then a basic inventory of the universe should not contain both trees and the quarks, leptons, and gauge particles of which trees are made. This, later, was how he applied the technique of analysis. But he still believed in an inclusive realism in PoM , to which he turned after encountering the work of Giuseppe Peano in Paris in 1900.
    The foundations of mathematics
    Leibniz had dreamed of a characteristica universalis , a universal and completely precise language, use of which will solve all philosophical problems. Russell recognized, in his book on Leibniz, that this was a desire for a symbolic logic, by which Russell then meant the ‘Boolean algebra’ developed by George Boole in the mid-nineteenth century. But at that juncture he did not think Leibniz was right to suppose that philosophical problems can be solved by employing the technicalities of a deductive logical system, for the reason that the truly important questions of philosophy are about matters that are ‘anterior to deduction’, namely, the concepts or facts referred to in the premisses from which inference starts. Whatever these are, Russell argued, they are not supplied to us by logic; logic can only help us in reasoning about them.
    But Russell changed his mind when he encountered Peano’s work. Peano’s advances in logical technique (they had been anticipated by Gottlob Frege, but neither Peano nor Russell then realized this) immediately suggested to Russell ways of stating the fundamental principles of logic, and of showing two centrally important things: first, how all the concepts of mathematics can be defined in terms of them, and secondly, how all mathematical truths can be proved from them. In short, it suggested to Russell how to show that logic and mathematics are identical. This is the aim of both PoM , and its more fully worked out version, Principia Mathematica ( PM ).
    The project of deriving mathematics from logic is known as ‘logicism’. In PoM Russell did not attempt a rigorous assault on this part of the programme, limiting himself instead to an informal sketch. The rigorous assault was left to PM .