Bradley’s theory that relational judgments that appear to refer to a number of identifiable and discriminable individuals actually presuppose a single underlying reality gets confirmation from his logical analysis of a kind of judgment in which this reality is introduced directly.
Bradley’s definition of judgment introduces “ideal content.” What is “ideal content” and how is it acquired? Bradley was completely sure that the psychological particulars with which empiricists furnished the mind could not begin to explain judgment, knowledge, and cognition. If such things existed, they certainly could not function as predicates in judgment, since they could not be moved from their place in the mind.
The standard classification of judgments distinguished categorical, hypothetical, and disjunctive. Bradley reduces the universal form of the categorical judgment to a hypothetical form.
Bradley identifies a second kind of analytic judgments of sense that do have a grammatical subject.
The discussion of proper names allows Bradley to move to a second category of singular judgment-synthetic judgments of sense.
Bradley believes that not only are all universal judgments hypothetical, but also that all hypothetical judgments are universal.
Bradley is assuming that the truth of a hypothetical statement must depend on some (possibly) latent feature of reality. Singular judgments, however, appear to connect us more directly with solid fact. The synthetic judgment of sense has its special status as categorical because of its connection with a reality actually given. It therefore depends on the analytic judgment of sense which assigns an ideal content to that given. Bradley has already argued that all universal statements are hypothetical. This is now widely accepted.
Negative judgments, he believes, are more complicated than affirmative, since they must begin with a suggestion that is rejected in the judgment. Moreover, this rejection must depend on the assumption of a positive ground of exclusion, even if what this is may not be known. Negative existential judgments are of particular interest.
Bradley understands disjunction as providing a list of two or more mutually exclusive alternatives.