I was reading Russell's An Inquiry into Meaning and Truth (1940) and I noted the following passage in the Introduction,

Finally, there is the question of the relation between truth and knowledge. Attempts have been made to define “truth” in terms of “knowledge”, or of concepts, such as “verifiability”, which involve “knowledge”. Such attempts, if carried out logically, lead to paradoxes which there is no reason to accept. I conclude that “truth” is the fundamental concept, and that “ knowledge” must be defined in terms of “truth”, not vice versa. T his entails the consequence that a proposition may be true although we can see no way of obtaining evidence either for or against it. It involves also a partial abandonment of the complete metaphysical agnosticism that is favoured by the logical positivists.

My Question

Does anyone know which paradoxes Russell is referring to here? If so, can some references be cited?

  • $\begingroup$ See, for example, The Liar's Paradox, which was formalised by Gödel as "this sentence is not provable" to prove his incompleteness result, thus demonstrating a true statement whose truth is not formally knowable. $\endgroup$ – Nick R Oct 14 '17 at 19:50
  • $\begingroup$ @NickR: The Liar's Paradox is not an epistemological paradox and more specifically it arises due to self-reference. The most well known paradox concerning "knowability" (defined in terms of "verifiability") and "truth" is Fitch's Paradox of Knowability but I doubt whether it was known to Russell at that time. $\endgroup$ – user 170039 Oct 15 '17 at 3:43
  • $\begingroup$ Very curious: Fitch's paradox, at least as reported in the wp link, seems to be yet another one involving directly or indirectly either a self-reference or something very close to it. $\endgroup$ – terry-s Oct 15 '17 at 17:45

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.

  • $\begingroup$ Actually I thought that Russell was talking about something like Fitch's Paradox or Moore's Paradox. Do you know whether any one of them was known to Russell (especially Moor's paradox)? $\endgroup$ – user 170039 Oct 16 '17 at 11:48
  • $\begingroup$ @user170039 Certainly not in 1940. Moore came up with his original sentence in 1942, and presented a version of it in a 1944 Cambridge lecture as "It is raining but I don’t believe that it is", where Wittgenstein heard it. Church developed it into an argument only in 1945 in a referee report to Fitch's unpublished paper, see SEP. Wittgenstein called it "Moore's paradox" in Philosophical Investigations, which is how it got famous, see McGinn. $\endgroup$ – Conifold Oct 16 '17 at 18:19

There was a lot of use of the "Verification Principle" back then, which went something like: A sentence has meaning iff it can be verified. This was accepted for a while, but stock in the Verification Principle went down when it came to light that the Verification Principle itself could not be verified. Thing is, though, I think it was Wittgenstein (rather than Russell) who actually pointed this out.


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