 Surprisingly for those who subscribe to the common view, first broadcast by Russell in 1900 in A Critical Exposition of the Philosophy of Leibniz and much repeated thereafter, that Bradley thought all judgments to be of subject/predicate form and accordingly failed to recognize relational judgments as a distinct kind, Bradley’s treatment of inference includes the complaint that the mathematical logics of his time cannot represent valid relational inferences. His own initial account of inference is that it is ‘ideal experiment’: ‘ideal’ in that these are thought-experiments which remain in the realm of idea, but nevertheless experiments in that their results are not guaranteed in advance by a complete set of logical laws which infallibly determine their own application (a view reminiscent of Wittgenstein). But later, after a long and tangled consideration of the question of how it is possible for a deductive inference to be reflected in reality, he comes up with a revised account: ‘Every inference is the ideal self-development of an object taken as real’ (Principles, Terminal Essay I, p. 598). Bradley seems here to be following the Humean idea that there are no logical relations between distinct existences: the reason that valid inference can be reflected in reality is that it can never take one beyond the original subject matter.