Online research in philosophy

In this paper it is argued that qualitative theories (Q-theories) can be used to describe the statistical structure of cross classified populations and that the notion of verisimilitude provides an appropriate tool for measuring the statistical adequacy of Q-theories. First of all, a short outline of the post-Popperian approaches to verisimilitude and of the related verisimilitudinarian non-falsificationist methodologies (VNF-methodologies) is given. Secondly, the notion of Q-theory is explicated, and the qualitative verisimilitude of Q-theories is defined. Afterwards, appropriate measures for the statistical verisimilitude of Q-theories are introduced, so to obtain a clear formulation of the intuitive idea that the statistical truth about cross classified populations can be approached by falsified Q-theories. Finally, it is argued that some basic intuitions underlying VNF-methodologies are shared by the so-called prediction logic, developed by the statisticians and social scientists David K. Hildebrand, James D. Laing and Howard Rosenthal.

The expansion or revision of false theories by true evidence does not always increase their verisimilitude. After a comparison of different notions of verisimilitude the relation between verisimilitude and belief expansion or revision is investigated within the framework of the relevant element account. We are able to find certain interesting conditions under which both the expansion and the revision of theories by true evidence is guaranteed to increase their verisimilitude.

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.

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.

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.

This paper describes a theory of accuracy or approximate truth and applies it to problems in the realist interpretation of scientific theories. It argues not only that realism requires approximate truth, but that an adequate theory of approximation also presupposes some elements of a realist interpretation of theories. The paper distinguishes approximate truth from vagueness, probability and verisimilitude, and applies it to problems of confirmation and deduction from inaccurate premises. Basic results are cited, but details appear elsewhere. Objections are surveyed, including arguments by Miller, Laymon, and Laudan. Comparison is made with Niiniluoto's theory of verisimilitude, and the utility of his theory for realism assessed.

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.

Whitehead, in two basic books, considers two different approaches to point-free geometry: the inclusion-based approach , whose primitive notions are regions and inclusion relation between regions, and the connection-based approach , where the connection relation is considered instead of the inclusion. We show that the latter cannot be reduced to the first one, although this can be done in the framework of multivalued logics.