Akita University The Paradox of Corroboration Kiichi TACHIBANA Akita University I. Corroborationists Interpretation of Corroboration This short paper is not criticism of Popper s methodology of science but that of a certain interpretation of it. In his paper,'truth, Rationality and Growth of Scientific Knowledge, 1 Popper introduces third requirement and argues that corroboration is indispensable for growth of scientific knowledge and falsification is not enough. According to two different interpretations of third requirement which requires necessity of corroboration. Popperian school can be divided into two groups: falsificationists and corroborationists. J. Agassi and W. W. Bartley are representatives of former and!.lakatos and J.Worral are those of latter. 2 In this paper I limit my concern to criticism of corroborationism and do not argue for falsificationism. 3 In scientific research corroborations of hyposes occur. 4 The problem is how to evaluate role of corroboration or what is status of corroborated hyposis. The corroborationists' interpretations of corroboration are not monolithic. There is a wide spectrum of interpretations from a whiff of inductivism to full-blooded one. s However. y agree that corroboration can be used as criterion of rationality of ory-acceptance. More concretely speaking, a hyposis is empirically supported by corroboration. that is, -4-
failure of an attempted falsification, refore. it is rational to accept corroborated hyposis and it is irrational not to accept it. I maintain that this idea of empirical support produces similar paradox as well-known Hempel's paradox of confirmation. IT. Hempel's Paradox of Confirmation Hempel's paradox is as follows: CI) A hyposis: All ravens are black. ( (X) CRx- Bx) ) CII)Anoter hyposis: All non-black things are non-ravens. (X) C -Bx- -Rx) ) If Ra&Ba confirms CI), n -Bb&-Rb confirms CII). From law of contraposition C!) and CII) are logically equivalent. Therefore. -Bb&-Rb confirms CD. In short. a non-black non-raven, for example. a white rabbit confirms "All ravens are black." This is paradoxical. As Agassi says, Hempel's paradox is not a logical paradox. 6 To some it is paradoxical and to ors it is not paradoxical. The views on this paradox can be divided as follows: Cl) The paradox is genuine and insoluble. Popper: Hempel's paradox is refutation of "positive", verificationist or inductivist approach. 7 Neir a black raven nor a non-black non-raven confirms "All ravens are black." On or hand, paradox does not occur in case of falsification. For a non-black raven falsifies both "All ravens are black" and "All non-black things are non-ravens." (2) The paradox is only apparently paradoxical and solvable. -5-
Hempel: confirm Both "All a black raven and a non-black non-raven ravens are black." even though it is counter-intuitive. 8 Quine: The naturalness of classification, based on Darwinian natural selection. cannot be preserved by logical equivalence. "Black" apd "raven" are natural kinds. But "non-black" and "non-raven" are not natural. Therefore. "All ravens are black" is confirmed by a black raven. but not by a non-black non-raven. 9 Comments: According to Hempel. every object \'lhich is compatible with hyposis confirms it. According to Quine, every black raven confirms hyposis. Thus it is too easy to confirm hyposis as far as it is not falsified. However. degree of confirmation to hyposis is equal to o. even though confirming instances are numerous. For hyposis makes assertions about an infinite numbers of instances, while number of observed instances can only be finite. From anor point of view. Agassi says that any hyposes. excepting falsified ones, have an high degree of confirmation ---indeed near 1. for reason as follows: For example, "All ravens are black' can be reformulated to "No spatio-temporal region contains any non-black raven", which is logically equivalent to former. Almost all spatio-temporal regions are empty, so y do not contain non-black ravens. Therefore, degree of confirmation to hyposis is near to 1. 10 The above two assertions on degree of confirmation are summarized like this: If you try to confirm "All ravens are black" by numerous black ravens. you will accept that degree of confirmation is -6-
equal to 0. And if you try to confirm "There does not exist a non-black raven", you \'li 11 accept that degree of confirmation is equal to 1. "All ravens are black" and "There does not exist a non-black raven" are logically same. This is paradoxical. Agassi concludes." As long as our intuition hankers after popular doctrine of confirmation by satisfaction or instantiation, ---,we wi 11 not escape sense of paradox." 11 On or hand. Popper emphasizes tests of a hyposis. Instances which are irrelevant to tests are excluded. Then relevant instances are selected and 1 imi ted. So Popper uses term "corroboration" to distinguish from "confirmation." And Popper emphasizes that a hyposis cannnot be corroborated by instantiation which is irrelevant to tests and that corroboration is not a probability in sense of probability calculus. Therefore. corroboration is not paradoxical in above sense. ill. The Paradox of Corroboration In my opinion. re is anor sense of paradox. It has something to do with empirical character of a ory and vli th raional i ty of ory-acceptance. Concerning former. idea that corroboration empirically supports a hyposis produces paradox. And this paradox hits both confirmation and corroboration in so far as confirmation or corroboration of a hyposis is regarded as an empirical evidence for its rational acceptance. Corroboration is a falsification of potential falsifier of a hyposis. The falsifications of Ra&-Ba -7-
Akita University which is a potential falsifier eir Ra&Ba. or support CI). -Ra&Ba By of a hyposis -Ra&-Ba. fictitious The above CD are instances example paradox may be evident. There has been a hyposis that all ravens are black. A scientist receives an observational report that a white raven was discovered. The crisis of a falsification of hyposis occurs. Some scientists go to see white raven and inspect it carefully. As a result white raven turns out to be a black raven which is painted white. falsifying instance is falsified. raven supports swallow \ rhich CD. Simil::irly The A whitely-painted black a \-rhitely-painted wears a raven costume supports CD. black Or a whitely-painted yello\-r canary \olhich \ rears a raven costume supports CI). Can se instances empirically support hyposis? According to Popper. empirical content of a ory is determined observational by Cand equal statements. contradict ory, statements \orhich statements which or basic class of statements. those which not class of all observational follow do to) not from contradict empirical character of it. ory. Thus 1 2 ory have any no The results of failure of attempted falsification are that y do not contradict ory. empirical Therefore. character y of have ory. supported empirically by m? corroborated ory. empirically? This which is nothing to Then do is with ory Is it rational to accept is only paradoxical. apparently For a supported corroborated hyposis is mistakenly regarded as empirically supported. -8-
Akita University though in fact it is not. On or hand, by successful falsification we find that results contradict ory. As Popper says, "Once a ory is refuted. its emp i rica 1 character is secure. " 1 3 Theories are emp i rica 11 y falsified. but not supported. 14 Next let us turn to latter. that is, rationality of ory-acceptance. In order to make scientific knowledge grow. overthrow of an accepted ory is indispensable. Agassi says as follows: "The whole importance of refutation of received opinion, or of best scientific opinion or idea or proposal. is just this: refutation opens road to innovation. Nothing is a more potent heuristic than refutation. Nothing is more conducive to progress than criticism of current situation. nothing more likely to herald new than discontent with old. Criticism is liberation. The positive power of negative thinking." 15 GenerallY speaking, it is not irrational to critisize a corroborated hyposis. for criticism may lead to progress. On or hand. I do not think that it is rational to accept corroborated hyposis for two reasons. First it is illusional to think that a hyposis is empirically supported by corroboration. as I mentioned above. Secondly re is a paradox in idea that in order to accept a hyposis rationally, it must be corroborated in first test. Suppose a hyposis which has two new predictions: one is doomed to be refuted and or to be corroborated. When you test latter first. it is rational to accept hyposis because it is corroborated. To contrary, \ rhen you test former -9-
Akita University first. it is not rational to accept it because it is refuted. Therefore. I cannot assign any positive role on corroboration. According to Agassi. corroboration is nothing but a failed refutation. " outcome of attempts that look promising but misfire." 16 Agassi considers that corroboration is not "positive" but "negative" or at least "neutral." From his idea of corroboration paradox does not occur. Notes 1. K. R. Popper. Truth. Rationality and Growth of Scientific Knowledge, in Conjectures and Refutations. Routledge and Kegan Paul. London. 1963. pp.215-250. 2. J.Agassi. Science in Flux. Reidel. Dordrecht, 1975.passim. W.W.Bartley, Critical Study The Philosophy of Karl Popper Part III. Rationality, Criticism. and Logic. in Philosophia. 11. 1982. pp.204-206. I.Lakatos. Popper on Demarcation and Induction. in P.A.Scilpp(ed.) The Philosophy of Karl Popper. Open Court. La Salle. Illinois. 1974. pp.241-274. J.Worral. The Ways in Which Methodology of Scientific Research Programmes Improve on Popper's Methodology, in G. Radni tzky and G. Andersson Ceds.) Progress and Rationality in Science. Reidel. Dordrecht. 1978.pp.45-70. 3.As for a comparison between corroborationism and falsificationism, see my paper. Falsificationism versus Corroborationism. in Miscellanea Philosophica. University of Tsukuba Philosophical Association. no. 1.1982. pp.67-78. 4. For example, discovery of Neptune corroborates Newtonian ory or Eddington's eclipse -10-
experiment of 1919 corroborates Einstein's general ory of relativity. 5. D.Miller, Conjectural Knowledge: Popper's Solution of Problem of Induction. in P. Levinson Ced.) In Pursuit of Truth. Humanities Press, New Jersey, 1982, pp.17-49. And among critics of Popper re are some who interpret Popper as a corroborationist and ors who interpret Popper as a falsificationist. 6. Agassi. Corroboration Versus Induction, in British Journal for Philosophy of Science, 9, 1959, p.311. This paper is owing to Agassi' s suggestion that I should make clear meanings of "paradoxical", commenting on my ear 1 i er draft. 7. Popper. Quine on My Avoidance of "Paradox of Confirmation", in P. A. Scilpp(ed.) The Philosophy of Karl Popper. p.989. M.Fisch. who tries to solve Hempel's paradox, insists that paradoxes however are not a fallacy of verificationism qua verificationism. but rar a fallacy of formalism as such because seeking refutation disobeys Equivalence Principle. However, I am afraid that re is an error in his argument. For seeking refutation obeys Equivalence Principle. For example, in order to test both "All with no wings do not fly" and "All that fly have wings", one should search for someting that flies \orithout \'lings. M. Fisch. Hempel's Ravens. The Natural Classification of Hyposes and Growth of Knowledge, in Erkenntnis, Vol. 21. No. 1. 1984, p. 53. 8. C.G.Hempel. Studies in Logic of Confirmation, in Mind, 54, 1945, pp. 18-21. 9. W. V. Quine, On Popper's Negative Methodology, in The -11-
Philosophy of Karl Popper. p.219. 10. Agassi. The Gentle Art of Philosophical Polemics. Open Court. La Salle. Illinois. 1988. PP. 41-42. Agassi says that this idea is a powerful generalization of Hempel's result and is originated in Popper's Logik der Forschung, \ Ihich preceded Hempel's \ rork. The Popper's paradox is.. clearly stated in his Realism and Aim of Science. Hutchison. London. 1983.pp.256-7. 11. Agassi' s work. in note 10. p. 42. 12. Popper. Conjectures and Refutations. Routledge, London. 1963. p.385. 13. Ibid., p. 240. 14. Popper says that a hyposis may be supported by a failed refutation. that is. corroboration. I have to confess that I do not understand meanings of "may" and "support" in this context. See Popper's work. in note 10. p. 235. 15. 16. Agassi's work. in note 10. pp.497-498. Agassi. in his private letter. April 28. 1991. -12-