I have given some thought to the issue of Popper’s faith in realism and the relation of that faith to his attack on positivism and verificationist theories of truth. It seems to me that the two are closely tied. What exactly was all the fuss about falsification versus verification? Do they amount to the same thing in the end? Well, no.
Popper held with verisimilitude for science. Science moves along by stumbling into theories to make sense of data and works to prove the theory wrong. He held that there was no truth in science, only approach to the truth. Alongside this recognition of uncertainty in matters of the empirical world, Popper was a dogmatic realist in his philosophy and a dogmatic defender of bivalence in logic. There could be no question in his mind about whether the world outside his head existed independently of his perception of it. Knowledge doesn’t touch or affect reality in his view. The world is there in any case, true or false.
This leads, it seems to me, to his need for a demarcation theory. He needed to find a place for his dogmatic realism in a world of uncertain facts. One way is science; uncertain, fumbling along in trial and error; and the other way metaphysics, the world where certain truths and bi-valence hold. Ironically, in spite of Popper’s total aversion to Plato’s theories of politics, he was very much a Platonist and follower of Plato’s guide, Parmenides, in his separation of these two ways: the way of doxa and the way of truth. The positivists dismissed the “way of truth” (metaphysics) as dogmatic illusion. Popper couldn’t give up his metaphysical commitment to realism. The positivists had their demarcation theory: what could be verified was meaningful, and the rest was rubbish (metaphysics). Popper’s version saved metaphysics from the positivist’s rubbish heap. Did Popper’s visceral opposition to the positivists rest in this need to maintain his realist metaphysics?
I should give a little explanation of my use of the term “dogmatic”. As I read him, Popper uses it to refer to those with whose metaphysics he disagrees. I try to use it in the sense of Sextus Empiricus, as referring to those who “have claimed to discover the truth.” The difference in my mind is that the latter use tries to identify an attitude that has closed off the search for truth. The former declares that a victory has been won.
Was Popper a dogmatic believer in bi-valence? There is a section on Brouwer in Epistemology Without a Knowing Subject. Popper explains in a footnote that this paper was an address before a logic conference that occurred shortly after Brouwer’s death and it definitely has a respectful tone, apparently as a result. But he concludes “I regard Brouwer’s subjectivist epistemology, and the philosophical justification of his intuitionist mathematics, as mistaken.” The Law of the Excluded Middle (LEM) is definitely part of Popper’s logic and this implies bi-valence. In many locations Popper argues that throwing out the Law of Non-contradiction (LNC) would be the end of logic. In What is Dialectic he repeats Lewis’s “proof” that from a contradiction any proposition can be derived, without addressing the truly problematic element of this argument, namely its use of disjunctive syllogism.
So I don’t think there is any doubt that Popper thought that bi-valence was true in Sextus’s sense. He closed off criticism of the two bookends that support bi-valence, LEM and LNC. I am not saying that Popper was not a champion of criticism. He was a heroic champion of argument. It is just that I think he thought that battle was over. I am not so sure.