page 343 note 1 The points here briefly stated have been discussed extensively in the literature on the subject of verification, falsification, and confirmation. Some sections in Professor Popper's Logik der Forschung (Wien, Springer Verlag, 1935) bear on the verifiability and falsifiability of quantified statements (see, for example, section 66), detailed and explicit general discussions may be found, for example, in part III of Carnap, R., “Testability and Meaning,” Philosophy of Science, Vol. 3 (1936), pp. 419–71, and Vol. 4 (1937), pp. 1–40; and in Hempel, C. G., “Problems and Changes in the Empiricist Criterion of Meaning,” Revue Internationale de Philosophie, No. II (1950), pp. 41–63.
The restriction, in the text above, of non–falsifiability to “most” non–analytic mixed generalizations is to indicate that there are exceptions. And as Mr. Watkins never explicitly faces this question, it might be appropriate to emphasize and illustrate this point. For example, then, the sentence “. ” contradicts the observation statement “Pa. ~Qa” and thus is strictly falsifiable; again, the “all–and–some” statement (x) (Ey) (Px ~ Qy)” is falsifiable in the wider sense since, in conjunction with the universal hypothesis “(y)~Qy,” it implies the universal hypothesis “(x) Px.”
page 344 note 1 See K. Popper, op. cit., section 4, esp. p. 10.
page 344 note 2 Carnap, R., Logical Foundations of Probability (University of Chicago Press, 1950), sections 1, 2, 3.
page 344 note 3 For a somewhat more liberal and considerably more explicit statement of the requirements an explication should meet if it is to afford an adequate philosophical analysis, see chapter I of Goodman, N., The Structure of Appearance (Harvard University Press, 1951).
page 344 note 4 See Hempel, C. G., “Studies in the Logic of Confirmation,” Mind, vol. 54 (1945), pp. 1–26, 97–121; especially pp. 13 ff. A fuller formal development of the conception of confirmation proposed in this essay is given in my article, “A Purely Syntactical Definition of Confirmation,” The Journal of Symbolic Logic, Vol. 8 (1943), pp. 122–43.
page 344 note 5 Professor Goodman has given a particularly concise and lucid presentation and appraisal of the paradoxes of confirmation in his book, Fact, Fiction, and Forecast(Harvard University Press, 1955), pp.68–73. A much fuller analysis, and a detailed confrontation of my concept of confirmation with central concepts in the theory of inductive probability, has been provided by Professor Carnap, op. cit., sections 87 and 88.
page 345 note 1 Mr. Watkins's impression to the contrary arises quite clearly from his improper construal of the observation statements in question. For example, the observation statements which he phrases as “This swan is white” and “ This swan is not white,” and which he considers as contradictories of each other, have the confirmatory import he attributes to them (op. cit., p. 119) only if they are taken to be equivalent to “This is a swan and this is white” and “This is a swan and this is not white,” respectively; and plainly, these two sentences are not contradictories of each other.—Similarly, Mr. Watkins is simply mistaken in asserting, on p. 127 of his article, that “on Hempel's instantiation–theory of confirmation, “Every substance has a solvent” turns out to be confirmable but not disconfirmable;” on the contrary, it is a theorem of that theory that any confirmable sentence is disconfirmable, namely, by the evidence sentences confirming its negation (see, f. ex., p. 110 of my article in Mind).
page 346 note 1 It is understood, of course, that here as in Mr. Watkins's discussion, expressions such as “mass of evidence,” “set of observation statements,” etc., refer to potential evidence, as represented by a set of observation statements which must be logically consistent, but need not be true.
page 348 note 1 Cf., for example, my articles “The Concept of Cognitive Significance: A Reconsideration”, Proc. Amer. Acad. of Arts and Sciences, Vol. 80, No. I (1951), pp. 61–77; and “The Theoretician's Dilemma,” forthcoming in Feigl, H., Scriven, M., and Maxwell, G. (eds.), Minnesota Studies in the Philosophy of Science, Vol. II (Minneapolis, University of Minnesota Press, 1957). As is made clear in these articles, my views on the analytic–synthetic dichotomy are strongly influenced by those of Goodman, Quine, and White. A new and highly ingenious criterion of cognitive significance has recently been suggested by Carnap, in his essay “The Methodological Character of Theoretical Concepts,” in Feigl, H. and Scriven, M. (eds.), Minnesota Studies in the Philosophy of Science, Vol. I (Minneapolis, University of Minnesota Press, 1956), pp. 38–76.—Finally, I should like to call attention here to an incisive critical and constructive study of the basic tenets of empiricism: Scheffler, I., “Prospects of a Modest Empiricism,” The Review of Metaphysics, Vol. 10, pp. 383–400, 602–625(1957).