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In Order. for Us to Discuss on Popper's Notion of Verisimilitude in Some On Popper's Notion of Verisimilitude Keiichiro KAMINO Osaka City University 1. Popper's Notion of Verisimilitude 2. Criticism on Popper's Theory of Verisimilitude 3. Suggested Ways of Defining the Notion 4. Popper's Rejoinders 5. Concluding Remarks The purpose of this essay is in the first place to make a survey of the problem situation in which the notion of verisimilitude is now found, and then try to clarify what Popper intends to do with the notion. Therefore, I shall sketch Popper's general epistemological position in so far as it is relevant to the present discussion, and also mention Popper's original proposal for the definition of the notion. Secondly, in order to make the situation clear, I shall introduce some of the criticisms raised against Popper's original proposal and also show what I think is the general trend in the recent attempts to define the notion. Finally, I shall examine Popper's reaction against those criticisms and new proposals which were produced by Tichy , Miller, and others, to try to see Popper's real intention concerning the notion of verisimiltude, and to find out a way which hopefully will lead to a better problem situation agreeable from Popper's point of view, which is based on critical rationalism. 1. Popper's Notion of Verisimilitude 1.1 Popper's epistemological point of view In order.for us to discuss on Popper's notion of verisimilitudein some detail, it would be necessary to characterise his general philosophical position so that all arguments will not drift astray. On the one hand Popper is surely sceptical with regard to the possibility of our attaining scientific truths. For according to Popper, scientifictheories are not the digest of observations; they are inventions, or conjectures boldly put forward for trial to be eliminated if they clash with observations. And he contends even that we can never have sufficiently good arguments in the empirical sciensesfor claiming that we have actually reached the truth. All theories are hypothetical, and all may be overthrown. Indeed, any attempt logically to justify a scientific statement as ture, would lead to an infinite regress. We can never have sufficient reasons for holding any scientific -1- 2 K. KAMINO Vol. 6 statement to be true, even if the statement be in fact true. Popper's rejection of the quest for justification has some affinity to the sceptical claim, which is very pessimistic with respect to the possibility of knowledge. In fact, he calls his own position dynamic scepticism, although he identifies this with 'critical inquiry'. On the other hand, however, he admits the possibility of the growth of know- ledge. He is always optimistic with the possibility of knowledge. Indeed, he is still optimistic, even when his theory of verisimilitude is exposedto severe attacks. With his theory of knowledge,however, one thing should be kept in our mind. The traditional view on knowledge claims that scientia is knowledgeof universal truths which are true of neccesity, and that knowledge can only be obtained by demon stration (though not necessarily logical demonstration). In the long history of Western thought since Plato and Aristotle, knowledge has been contrasted with belief or opinion, whose attribute is not 'true' but 'probable'. Knowledgeought to be true and to have certainty; opinion is more or less probable and subjective. In view of this, I contend that Popper stands on a very unique position. Certainly he claims that all scientifictheories are hypothetical, and strips off their garments of certainty. This naturally sounds as if he takes a kind of probabilism. It is clear, however,that he stands firmly on the traditional view that scientiais demonstrative, when he tries to demarcate scientia against pseudo-sciences. Because in trying to do so, he relies upon the power of logic, i.e., modustollens. I shall call Popper's position 'optimisticscepticism. This nice expressionI borrowed from P. Tichy. 1.2 Why Popper needs the notion of verisimilitude Popper's optimistic scepticism, however, does not claim that the truth itself is just an illusion. Some such description would indeed be a misleading one to express the nature of Popper's theory of knowledge. Popper maintains that even if there is no general criterion of truth for scientific theories, the notion of truth is logically legitimate. This, as he himself says, is very opposite to the positivistic position as was propounded by Wittgenstein that a concept is vacuous if there is no criterion for its application. The positivistic conceptionis as is known refuted by the modern development of logic, and especially by Tarski's theory of truth, which contains the theorem: for sufficientlyrich languages there can be no criterion of truth. (Popper, O.K., p. 321.) What then are we doing, when we say that we are seeking for truth We say, for instance, that we have come nearer to the truth, or that some theory Tl is superseded by some new theory T2, because T2 is more like the truth than T1. These are somehow intuitive assertions, of course. Can we, however, give good reasons for these propositions at least in some cases. If the notion of truth is dubious, so will be the notion of a better approach to the truth, or of a nearness to the truth or of a greater verisimilitude. Fortunately, however, the legitimacy of the notion of -2- No. 1 On Popper's Notion of Verisimilitude 3 truth has been established by Tarski. Can we then hope that we may say the notion of verisimilitudeis also legitimate? I hope the answer is in the affirmative. In advocating the notion of verisimilitiude,what does Popper take to be its advant ages or utilities? First let us see how it explicates our notion of scientificinvestiga tion. The task of scienceis, in a sense, to cover by hits as much as possibleof the true statements, by the method of proposing theories or conjectures which seems to us promising, and as little as possible of the false conjectures. It is therefore very important that we conjecture true theories; but truth is not the only important properties of our conjectural theories. We are not particularly interested in pro- posing trivialities or tautologies; as "all tables are table" will not be a scientific truth. On the contrary, we know for instance that Newtonian physics is false. We know that few of scientifictheories we discover are true, or perhaps none is. Even so, we think that it is a much better 'approximation' to the truth, because it contains a number of interesting and informative true consequencses; the truth content of Newtonian physics is very great indeed. The fact is that we are not simply looking for truth, but are looking for interest- ing and enlightening truth. The introduction of the concept of versimilitude, there- fore, brings us a considerable advantage over the simple formulation that the aim of science is truth. The notion of verisimilitude will free scientific theories from the search of trivial truths, and at the same time, will explain why we are interested in some fales theories such as Newtonian physics or Einstein's relativity theories which have a great truth content. We admit false theories or statements if they are not ' too false' (if they have not too large falsity content) and contain a great truth content. Popper also adds that the search for verisimilitude is a clearer and a more realistic aim than the search for truth, and that we can have strong and reasonably good arguments for claiming that we may have made progress towards the truth. Moreover, he claims, we can explain the method of science, and much of the history of science, as the rational procedure for getting nearer to truth. (cf. ibid., pp. 57-8) 1.3 Popper's definition of verisimilitude Popper's theory of verisimilitude was first presented in Popper (1962) and (1963). It has since been expanded in Popper (1972). Popper's logical notion of verisimili- tude is a combination of two notions, both of which were originally introduced by Tarski; one is the notion of truth and the other is the notion of the logical con- tent of a statement, i.e., its consequence class. Now the content or the strength of a deductive theory can be determined by the size of its consequence class. The greater the consequence class of a theory is, the stronger it is. In other words, the comparability of theory will be reduced to set-theoretical inclusion relation. The size of the consequence class, however, -3- 4 K. KAMINO Vol 6 does not establish the superiority of theory, or so Popper thought in the sixties. In assessing scientific theories, we are interested in the increase of true con- sequences, of course. Thus Popper first tried to define both the truth content and the falsity content of theory. Thus Popper said: the set A of all true statements following from any given statement a is called the truth content of a. It is a deductive system., in symbols: A=Cn(A)=Cn(a), and vice versa, (to every statement say a there corresponds a finitely axiomatizable system say A) therefore, A=A•¿T=Cn(a•Ét). To define the falsity content of A, he drew upon the idea of the relative content A, given B, or A, B. A,B=Cn(A,B)=Cn(A•¾B)-Cn(B)=Cn(a&b)-Cn(b) The falsity content, then, AF=A,AT=Cn(A+AT)-Cn(AT)=Cn(A)-Cn(AT). Thus, for the notion of verisimilitude, he said: a theory T, has less versimilitude than a theory TQ if and only if (a) their truth contents and falsity conetents (or their measure) are comparable, and either (b) the truth content but not the falsity content of Tl is smaller than that of T2, or (c) the truth content of Tl is not greater than that of T2, but its falsity content is greater.
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