The physicist who states a law of nature with the aid of a mathematical formula is abstracting a real feature of a real material world, even if he ha… - Hilary Putnam

It is evident that Feyerabend is misusing the term 'meaning.' He is not alone in such misuse: in the last thirty years, misusing the term 'meaning' has been one of the most common, if least successful, ways of 'establishing' philosophical propositions. But how did this distressing state of affairs come to be? The blame must be placed squarely upon the Logical Positivists. The 'Verifiability Theory of Meaning' ('the meaning of a sentence is its method of verification') was, from the first, nothing but a persuasive redefinition. If to call metaphysical propositions 'meaningless' were only to assert that these propositions are empirically untestable, it would be harmless (the metaphysicians always said that their assertions were neither empirically testable nor tautologies); but, of course, it is not harmless, because the Positivist hopes that we will accept his redefinition of the term 'meaning,' while retaining the pejorative connotations of being 'meaningless' in the customary {linguistic) sense, i.e. being literally without sense.

The techniques employed by philosophers of physics are usually the very ones being employed by philosophers of a less specialized kind (especially empiricist philosophers) at the time. Thus Mill's philosophy of science largely reflects Hume's associationism; Reichenbach's philosophy of science reflects Viennese positivism with its conventionalism, its tendency to identify (or confuse) meaning and evidence, and its sharp dichotomy between 'the empirical facts' and 'the rules of the language'; and (coming up to the present time) Toulmin's philosophy of science is an attempt to give an account of what scientists do which is consonant with the linguistic philosophy of Wittgenstein. For this reason, errors in general philosophy can have a far-reaching effect on the philosophy of science. The confusion of meaning with evidence is one such error whose effects are well known: it is the contention of the present paper that overworking of the analytic-synthetic distinction is another root of what is most distorted in the writings of conventional philosophers of science.

The real significance of the Russell paradox, from the standpoint of the modal-logic picture, is this: it shows that no concrete structure can be a standard model for the naive conception of the totality of all sets; for any concrete structure has a possible extension that contains more 'sets'. (If we identify sets with the points that represent them in the various possible concrete structures, we might say: it is not possible for all possible sets to exist in any one world!) Yet set theory does not become impossible. Rather, set theory becomes the study of what must hold in, e.g. any standard model for Zermelo set theory.