Bradley, Francis Herbert (1846–1924)

4. Logic

The Principles of Logic looks strange to anyone whose conception of logic has been shaped by the formalism of Frege and Russell. Devoid of mathematically inspired methods, of axioms and rules of inference, it proves no theorems and employs no calculi. Often the text seems contaminated with discussion of psychological matters. Familiar terms, such as ‘identity of indiscernibles’, are used in ways unfamiliar enough to make one unsure whether they have much to do with what other people mean by them, and the terminology is often bewilderingly loose. Nevertheless, and despite its idealist vocabulary and florid metaphor, its title is apposite, for the book is devoted to issues fundamental to logic. It brought the notion of meaning, for instance, to the centre of the philosophical stage; and the absence of calculi is at least partly the result of a principled opposition to formal logic and the mathematicization of reasoning on the grounds that inference was thereby detached from the practice of science and the acquisition of knowledge. Some of its doctrines have been greatly influential, often via their impact on Russell, such as the suggestion that the logical form of universal sentences is hypothetical (a prototypical instance of the distinction between logical and grammatical form). It is a transitional work, expressing in the vocabulary of ideas and judgments views which were to usher in the era of meanings, sentences and propositions.

Much of the book is polemical, and, as in Ethical Studies, Bradley develops his own views gradually through criticism of others. It is divided into three, the first dealing with judgment and the remainder with inference. He begins by arguing that atomists such as Hume, who thought of judgments in terms of ideas, failed to distinguish the sense of ‘idea’ in which ideas are important to logic: they are not datable occurrences like mental images but abstract universals. He is thus often portrayed as rejecting psychologism in logic, but this is an exaggeration, for he thinks of logic’s subject matter as mental acts, not as sentences, or propositions in the sense of Russell or of Moore. He then rejects some standard accounts of judgment. He complains that a subject–predicate account cannot do justice to relational judgments, and that thinking of judgment as the coupling of two ideas makes it impossible to see how judgment can be about anything real, since all the ingredients of judgments are universal and belong to the realm of idea, whereas reality is stubbornly particular and actual. As Bradley also argued that there could be no unique designation of individuals, even grammatical names and demonstratives being disguised general terms, he may have planted the seed of Russell’s elimination of grammatically proper names by application of the Theory of Definite Descriptions (see Russell, B.A.W.). Bradley’s own account of judgment is ‘the act which refers an ideal content … to a reality beyond the act’. (By ‘ideal content’ he means a universal abstracted from a mental image; later he realized that this overestimates the role of mental imagery in judgment.)

When Bradley turns to inference, his targets remain the same. He complains that the mathematical logics of his time cannot represent valid relational inferences. He rejects Hume’s account of inference in terms of the association of ideas on the grounds that Hume’s ideas, as datable particulars, are fleeting entities which cannot be revived by association (see Hume, D. §2). Association is possible between ideas only if they are universals. (He calls this process ‘redintegration’.) He rejects both syllogistic and Mill’s methods of induction for failing to recognize that reasoning can proceed only on the basis of the generality implicit in the universals essential to inference (see Inductive inference). His own account of inference is that it is ‘ideal experiment’: ideal in that it belongs to thought, experiment in that its results are not guaranteed in advance by a complete set of logical laws which infallibly determine their own application.

Underlying much of Bradley’s criticism of previous accounts of judgment and inference is hostility to psychological atomism, whose particulars he regarded not as concrete universals, realities in their own right, but as abstractions from the continuous whole which is psychological life. But likewise he regarded judgments themselves as infected with abstraction, since their subject matter is necessarily selected from a background and accordingly falsifies reality. Thus the objections which destroy misleading accounts of logic start to threaten logic itself, and, consistently, the book ends by suggesting that no inference is ever really valid and no judgment ever really true. Here it spills over into the metaphysics it had ostensibly tried to avoid. Bradley’s view is that logic presupposes a ‘copy’ (correspondence) theory of truth, but it is clear that he thinks this theory metaphysically inadequate, a view he develops in Essays on Truth and Reality, where he argues for ‘the identity of truth knowledge and reality’. Thus the claim that Bradley held a coherence theory of truth (endlessly repeated in textbooks) is mistaken. (Because he held reality to be a unified whole, he thought the test of truth to be ‘system’, which includes what is commonly meant by coherence (see Truth, coherence theory of §1).) This identity theory of truth, that for a thought to be true is for it to be identical with the logical subject of which it is predicated – reality itself – has led to his being unfairly accused of confusing predication with identity. His relation to the correspondence theory exemplifies a constant difficulty in trying to understand Bradley: he adopts various theories and suggestions temporarily only to abandon them as ultimately unsatisfactory, so that it can be hard to work out his commitments.