page 349 note 1 I should like to thank Dr. Agassi here.
page 349 note 2 I infer from this that he no longer considers satisfactory the “trans-latability-criterion of cognitive meaning” which he advanced in his article, “Problems and Changes in the Empiricist Criterion of Meaning”, reprinted in Semantics and the Philosophy of Language, ed. L. Linsky, 1952.
page 349 note 3 “Between Analytic and Empirical”, PHILOSOPHY, April 1957, p. 115.
page 350 note 1 Thus Hempel is wrong when he remarks in a footnote that I “never explicitly” face the question whether it is all or only some “all-and-some” statements which are unfalsifiable. I wrote: “ ‘All-and-some’ statements may, as I have said, constitute falsifiable hypotheses. ‘All-and-some’ statements are empirical if they give rise to circumscribed existential statements of a falsifiable kind; otherwise not” (p. 127). Had Hempel borne this in mind he would hardly have claimed in section 5 that my contention that science does not employ the unfalsifiable kind of “all-and-some” statement is rebutted by the existence of the scientific hypothesis that for every elementary particle there exists an anti-particle. For I understand that this hypothesis, in conjunction with a description of an experimental set-up, gave rise a short time ago to the circumscribed existential statement that certain exciting phenomena would be recorded in the cyclotron at Berkeley about once every hour.
page 350 note 2 I was referring to Popper's thorough examination of the question of unfalsifiable, purely existential hypotheses hi science. See section 5 below.
page 350 note 3 Logical Foundations of Probability, Chicago, 1950, p. 479.
page 351 note 1 See section 2 above. Hempel rather suggests that I did simply adopt Popper's falsifiability-criterion at the outset; but on p. 117 I explained why I was deliberately refraining from doing so.
page 351 note 2 “A Purely Syntactical Definition of Confirmation”, The Journal of Symbolic Logic, 8, 1943, and “Studies in the Logic of Confirmation”, Mind, 54. 1945.
page 352 note 1 Hempel shows that I went astray in saying that two contradictory observation-reports could confirm the same non-analytic hypothesis, but this does not affect my argument from the equal confirmatory value of flatly conflicting reports. Moreover, it is the case that his theory allows an analytic hypothesis to be confirmed by contradictory observation-statements. This may seem a technical quibble, but it illustrates a serious difference between his and Popper's views of confirmation. Hempel's view is inductive in the sense that it involves a logical inference upwards from the evidence to the credibility of the hypothesis. And since a tautology is entailed by any synthetic statement, it follows that a tautological hypothesis will be empirically “confirmed” by any observation-statements, including contradictory ones. Popper's view is deductive and hypothetical: the only upward inference it allows is from counter-evidence to the falsity of the hypothesis. And since a hypothesis must be testable to be confirmable, this view has the satisfactory consequence that tautological statements cannot be empirically confirmed at all.
In the same footnote Professor Hempel says that I am “simply mistaken” in asserting that the “all-and-some” statement “Every substance has a solvent” is confirmable but not disconfirmable in his sense: his theory just does not allow any asymmetry between confirmability and disconfirmability. He does not mention my argument to the contrary and without his help I have been unable to detect any flaw in it. The predicates “soluble” and “insoluble” are asymmetrical in that one observation of a substance dissolving entails that that substance is soluble whereas no number of observations of a substance failing to dissolve can ever entail that it is insoluble. Hence, while observation can confirm (in Hempel's sense, which relies on the idea of an observation-report entailing the “development” of the hypothesis) “Every substance has a solvent”, no amount of observation can confirm “An insoluble substance exists”—or, consequently, disconfirm “Every substance has a solvent”.
page 353 note 1 See Popper, K. R., “Degree of Confirmation”, The British Journal for the Philosophy of Science, 18, 1954.
page 354 note 1 (i) “a is white”, (ii) “a is not white”, (iii) “a is a raven”, (iv) “a is no raven”, (v) “a is white and a raven”, (vi) “a is not white and a raven”, (vii) “a is white and no raven”, (viii) “a is not white and no raven”.
page 355 note 1 Hempel touches on the imprecision of several of my expressions and refers in passing to the precision of his own definition of confirmation. No doubt the comparison is just; yet I sometimes wonder whether too high a price may not be paid for the precision gained by employing a restricted artificial language. Professor Hempel mentions again that the languages for which he constructed his definition of confirmation are those with first-order functional calculi without identity. But since even simple arithmetical statements cannot be expressed in such languages, it seems doubtful whether his admittedly precise definition of confirmation could have much application to the theories of physics.