The Logical Foundations of Bradley's Metaphysics: Judgment, Inference, and Truth (review)

As the subtitle suggests, the book is organized around the themes of judgment, inference and truth. Material for the first two topics is largely taken from the second edition of Bradley's Principles of Logic. The discussion of his conception of truth relies on essays written in reply to various authors. In general, the book is to be welcomed by students of Bradley for its remarkably clear and unpretentious exposition of central themes in these difficult topics.

Much of the book is taken up with discussion of the views of Bradley's precursors and contemporaries in British and German idealism, material that is important for understanding Bradley's own views. Hegel scholars may cringe, however, at the oft-repeated claim, stated without qualification, that Hegel regarded thought and reality as identical. Allard argues that Hegel must maintain this because his view of deductive inference required that objects be self-determining, and self-determining objects require the identity of thought and being (139). The argument is particularly puzzling in the light of the fact that Bradley's view of inference also requires the self-development of its objects (164), although he denied that thought and reality are identical. Bradley may have read Hegel this way, but Allard does not establish this or give an adequate argument of his own that Hegel claimed that thought and reality are identical.

Beginning with the section on judgment, Allard often finds Bradley's reasoning ambiguous, laconic, or simply incorrect. He does not draw this conclusion, however, about Bradley's notorious argument that relations among mental contents are mere "fictions of the mind." Bradley claimed that if A and B were related by C, then C must also have relations to A and to B, which must then be related to C, and so on "for ever." Allard gives an eleven-step reconstruction of this infinite regress argument, and he apparently believes that he has validated Bradley's reasoning, appealing at one point to mathematical induction. Allard's discussion does not acknowledge, however, what it would take to produce a valid infinite regress argument. Generally speaking, one must show first that the set of elements related by some relation must be infinite, and second, that the existence of such an infinity of elements is impossible. Bradley describes the first few steps of an iterative process which, he says, must continue indefinitely and result in infinitely many relations and related entities. To make this into a valid argument, one would have to show that each new iteration always results in a new entity, without cycles or duplications. That is, it must be shown that the relation between successive stages in the iteration is well-founded. If the relation is not well-founded, mathematical induction is not possible. Even if well-foundedness could be shown, it would still be necessary to argue that the resulting infinity is unacceptable. That is, if it could be shown that if there is even one relation then there must be infinitely many of them, it must be argued that there cannot be infinitely many relations, or at least that the mind could not contain infinitely many. Perhaps Bradley's failure to address either the issue of well-foundedness or the impossibility of infinitude should not be held against him, but when the contemporary relevance of Bradley's philosophy is assessed, use ought to be made of contemporary logical tools and standards.

The leading idea of Allard's discussion of Bradley's theory of inference is his attempt to avoid Mill's puzzle that if a syllogism is valid, it must beg the question, since what the conclusion asserts is already asserted in the premises. It is difficult to see, however, just what it is in Bradley's theory that avoids this problem. Allard identifies the key element as Bradley's interpretation of universal judgments as conditionals, and conditionals as abbreviated inferences. He believes that this avoids understanding the premise "All...