Eames discusses this issue in Bertrand Russell's Theory of Knowledge, pp.151-154. The targets are Dewey's theory of warranted assertibility and Reichenbach's theory of verifiability, which both tie truth to what is or can be known. Russell's main objections are that truth must provide a goal for knowledge, and therefore must be conceived as wider than knowledge. What Russell calls "paradoxes" are the consequences that the law of excluded middle would have to be abandoned for a number of claims if one identifies truth with knowable truth. His example is "It snowed on Manhattan island in the year 1 AD" being either true or false regardless of the fact that no evidence may ever be found one way or the other. Even the proposition "Caesar conquered Gaul", which we can verify based on historical documents, is not true in lieu of such documents but in lieu of the event that occurred in the past. To this Russell adds a moral criticism of pragmatists and positivists that by restricting truth they removed it as a goal from beyond inquiry towards which the search for knowledge is directed.
Russell was of course aware that the law of excluded middle was rejected by intuitionists, hence his oblique admission that the "paradoxes" can be accepted. Their rejection was, however, largely restricted to mathematics, and logical positivists, at least, did not abandon classical logic overtly. But even Carnap, a positivist logicist, did not accept Frege-Russell's universalism about logic (no object/meta language separation), so they could accept it as a law of the object language while admitting existence of undecidable statements. An extension of intuitionism to philosophy of science was later developed by Dummett under the name of anti-realism. Dummett calls the kinds of truths Russell was talking about "verification-transcendent truths", and those who accept them metaphysical realists. Since metaphysical realism has well known problems with explaining meaningfulness of verification-transcendent claims (not yet prominent in Russell's time) Dummett replays some of Russellian arguments, but now as arguments against the law of excluded middle.