Some Logical Mensuration

Abstract

Science grows frighteningly fast. True enough. (Perhaps, too true.) Does it occasionally make progress too? Although most realists like to think that it does, even if they are unsure when it does, there are a couple of sceptical misgivings that invite consideration before an affirmative answer is returned (unfortunately, they often don't get it). One is the suggestion that scientific hypotheses succeeding one another in a field of inquiry are habitually couched in languages so disparate as to be beyond compare; this, the incommensurability thesis, appears in muted form in Kuhn's The Structure of Scientific Revolutions, more noisily in the writings of Feyerabend. The second problem grants commensurability and demands to be given a clear sense in which 'successive theories grow ever closer to, or approximate more and more closely to, the truth' (to quote Kuhn); this, the problem of verisimilitude, was formulated as a problem of logic by Popper in Conjectures and Refutations and aggravated by the proofs of Tichy and the reviewer that Popper's own answer didn't work. Between these two quite proper sceptical scruples we can locate a third (no longer reputable) question, whether scientific theories can partake of theory-independent truth and falsehood (that their meanings be at least partly theory-independent is necessary if they are to be commensurable); this, the problem of objective truth, is solved without remainder, most realists maintain, by Tarski's theory of truth. There is of course yet a further opportunity for captious scepticism here: we may dispute the fact of progress