Online research in philosophy

Zwart and Franssen’s impossibility theorem reveals a conflict between the possible-world-based content-definition and the possible-world-based likeness-definition of verisimilitude. In Sect. 2 we show that the possible-world-based content-definition violates four basic intuitions of Popper’s consequence-based content-account to verisimilitude, and therefore cannot be said to be in the spirit of Popper’s account, although this is the opinion of some prominent authors. In Sect. 3 we argue that in consequence-accounts , content-aspects and likeness-aspects of verisimilitude are not in conflict with each other, but in agreement . We explain this fact by pointing towards the deep difference between possible-world- and the consequence-accounts, which does not lie in the difference between syntactic (object-language) versus semantic (meta-language) formulations, but in the difference between ‘disjunction-of-possible-worlds’ versus ‘conjunction-of-parts’ representations of theories. Drawing on earlier work, we explain in Sect. 4 how the shortcomings of Popper’s original definition can be repaired by what we call the relevant element approach. We propose a quantitative likeness-definition of verisimilitude based on relevant elements which provably agrees with the qualitative relevant content-definition of verisimilitude on all pairs of comparable theories. We conclude the paper with a plea for consequence-accounts and a brief analysis of the problem of language-dependence (Sect. 6).

I. A. Kieseppä's criticism of the methodological use of the theory of verisimilitude, and D. B. Resnik's arguments against the explanation of scientific method by appeal to scientific aims are critically considered. Since the notion of verisimilitude was introduced as an attempt to show that science can be seen as a rational enterprise in the pursuit of truth, defenders of the verisimilitude programme need to show that scientific norms can be interpreted (at least in principle) as rules that try to increase the degree of truthlikeness of scientific theories. This possibility is explored for several approaches to the problem of verisimilitude.

I. A. Kieseppä''s criticism of the methodological use of the theory of verisimilitude, and D. B. Resnik''s arguments against the explanation of scientific method by appeal to scientific aims are critically considered. Since the notion of verisimilitude was introduced as an attempt to show that science can be seen as a rational enterprise in the pursuit of truth, defenders of the verisimilitude programme need to show that scientific norms can be interpreted (at least in principle) as rules that try to increase the degree of truthlikeness of scientific theories. This possibility is explored for several approaches to the problem of verisimilitude.

Popper distinguishes the problems of theoretical and pragmatic preference between rival theories, but he claims that there is a common non-inductive solution to both of them, viz. the "best-tested theory", or the theory with the highest degree of corroboration. He further suggests that the degrees of corroboration serve as indicators of verisimilitude. One may therefore raise the question whether the recent theory of verisimilitude gives a general non-inductive solution to the problem of theoretical preference. This paper argues that this is not the case: the theory of verisimilitude is applicable to this problem if and only if there is an independent solution to the problem of induction. Moreover, the solutions to the theoretical and pragmatic problems of preference coincide only in some special cases.

Popper’s original definition of verisimilitude in terms of comparisons of truth content and falsity content has known counter-examples. More complicated approaches have met with mixed success. This paper uses a new account of logical content to develop a definition of verisimilitude that is close to Popper’s original account. It is claimed that Popper’s mistake was to couch his account of truth and falsity content in terms of true and false consequences. Comparison to a similar approach by Schurz and Wiengartner show certain advantages of this new approach.

ACCORDING TO POPPER, SCIENTIFIC THEORIES ARE TO BE ACCEPTED IN SO FAR AS THEY ARE FALSIFIABLE AND IN SO FAR AS THEY HAVE BEEN CORROBORATED. THE CONCEPTS OF FALSIFIABILITY AND CORROBORATION ARE SUBMITTED TO DETAILED ANALYSIS. THE POINT OF ACCEPTING THEORIES, ACCORDING TO POPPER, IS TO OBTAIN THEORIES OF HIGH VERISIMILITUDE. HOWEVER THE BEST WE CAN DO IS TO OBTAIN THEORIES OF HIGH PROBABLE VERISIMILITUDE. POPPER’S CRITERIA FOR ACCEPTING THEORIES WILL ONLY LEAD TO THEORIES OF HIGH PROBABLE VERISIMILITUDE ON NON-POPPERIAN ASSUMPTIONS ABOUT INDUCTION.

Karl Popper introduced the idea of verisimilitude to explicate the intuitive idea that a theory T2, even though it is strictly speaking false, may be closer to the truth than a competitor T1. However, as is now well known, the results of Pavel Tichý, John Harris and David Miller establish that on Popper’s qualitative theory of verisimilitude, a theory T2 could be closer to the truth than another theory T1 only if T2 contains no false sentences. This result has been taken universally to show the inadequacy of Popper’s original account of verisimilitude, since the Miller-Tichý-Harris Theorem conflicts with the very basic intuition which first led Popper to formulate his theory.In this paper I shall first review the Miller-Tichý-Harris Theorem and examine a number of attempts to salvage the concept of verisimilitude. It will be argued that none of these attempts is successful. Finally an alternative, simple and intuitively satisfactory account of verisimilitude will be offered. This account will be along the lines first suggested by Popper, but it is not subject to any known limitation theorem. Further, the account is capable of giving verisimilitude orderings between not only scientific theories, but philosophical theories as well. This will be achieved without the use of the excessive formalism which dominates the contemporary verisimilitude research programs.

2 Popper's Logical Definition of Verisimilitude. 3 Popper's Probabilistic Definition of Verisimilitude. 4 Conclusion.

JOSEPH AGASSI 1. Sir Karl Popper has offered two different theories of scientific progress, his theory of conjectures and refutations and corroboration, as well as his theory of verisimilitude increase. The former was attacked by some old-fashioned inductivists, yet is triumphant; the latter has been refuted by Tichy and by Miller to Popper’s own satisfaction. Oddly, however, the theory of verisimilitude was developed because of some deficiency in the theory of corroboration, and though in its present precise formulation it was refuted, Popper still holds it in general terms, and I think he still hopes to find a better precise formulation of it. My aims in the present note are to pin-point the deficiency of Popper’s theory of corroboration and to use this for a precise formulation of verisimilitude increase acceptable to him. For my part, however, I see the situation in a different way, as will be indicated at the end of this note.

1. Sir Karl Popper has offered two different theories of scientific progress, his theory of conjectures and refutations and corroboration, as well as his theory of verisimilitude increase. The former was attacked by some old-fashioned inductivists, yet is triumphant; the latter has been refuted by Tichy and by Miller to Popper’s own satisfaction. Oddly, however, the theory of verisimilitude was developed because of some deficiency in the theory of corroboration, and though in its present precise formulation it was refuted, Popper still holds it in general terms, and I think he still hopes to find a better precise formulation of it. My aims in the present note are to pin-point the deficiency of Popper’s theory of corroboration and to use this for a precise formulation of verisimilitude increase acceptable to him. For my part, however, I see the situation in a different way, as will be indicated at the end of this note.