Online research in philosophy

A metric approach to Popper’s verisimilitude question is proposed which is related to point-free geometry. Indeed, we define the theory of approximate metric spaces whose primitive notions are regions, inclusion relation, minimum distance, and maximum distance between regions. Then, we show that the class of possible scientific theories has the structure of an approximate metric space. So, we can define the verisimilitude of a theory as a function of its (approximate) distance from the truth. This avoids some of the difficulties arising from the known definitions 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.

In this paper I assess the obstacles to a transfer of Lakatos's methodology of scientific research programmes to mathematics. I argue that, if we are to use something akin to this methodology to discuss modern mathematics with its interweaving theoretical development, we shall require a more intricate construction and we shall have to move still further away from seeing mathematical knowledge as a collection of statements. I also examine the notion of rivalry within mathematics and claim that this appears to be significant only at a high level. In addition, ideas of ‘progress’ in mathematics are outlined.

In this paper, an attempt is made to solve various problems posed to current theories of verisimilitude: (1) the (Miller's) problem of linguistic variance; (2) the problem of which are the best scientific methods for getting the most verisimilar theories; and (3) the question of the ontological commitment in scientific theories. As a result of my solution ot these problems, and with the help of other considerations of epistemological character, I conclude that the notion of Tarskian truth is dispensable in a rational (and realist) interpretation of the scientific enterprise. As a logical result, however, falsificationism will be vindicated. ... and in brief, a speaker must always aim at verisimilitude, and send the truth packing.

Summary For Imre Lakatos hismethodology of scientific research programmes was not only a philosophical theory of science and scientific change but also the conceptual foundation of empirical and historical studies of science. At least terminologically this view is today widely accepted: The concept of aresearch programme is used in all sorts of literature on science. In the present paper I argue that this concept can lead to serious distortions of empirical and historical studies of science if it is not detached from the Lakatosian philosophical framework. Themethodology of scientific research programmes has three main pitfalls, which may lead to disorientations of empirical and historical studies of science: (1) Contrary to what the term research programme may suggest, it offers no perspective on scientific research as an object of analysissui generis; (2) its concept of science is too narrow and covers only minor parts of what counts as science in the real world; (3) it reduces history of science to a mere sequence of research programmes and thereby eliminates the fact that there is an evolution of the structure of research programmes, too.

Research Programme and Development of Science. For Imre Lakatos his methodology of scientific research programmes was not only a philosophical theory of science and scientific change but also the conceptual foundation of empirical and historical studies of science. At least terminologically this view is today widely accepted: The concept of a research programme is used in all sorts of literature on science. In the present paper I argue that this concept can lead to serious distortions of empirical and historical studies of science if it is not detached from the Lakatosian philosophical framework. The methodology of scientific research programmes has three main pitfalls, which may lead to disorientations of empirical and historical studies of science: (1) Contrary to what the term "research programme" may suggest, it offers no perspective on scientific research as an object of analysis sui generis; (2) its concept of science is too narrow and covers only minor parts of what counts as science in the real world; (3) it reduces history of science to a mere sequence of research programmes and thereby eliminates the fact that there is an evolution of the structure of research programmes, too.

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.

An epistemic notion of verisimilitude (as the degree in which a theory seems closer to the full truth to a scientific community) is defined in several ways. Application to the structuralist description of theories is carried out by introducing a notion of empirical regularity in structuralist terms. It is argued that these definitions of verisimilitude can be used to give formal reconstructions of scientific methodologies such as falsificationism, conventionalism and normal science.

Some peculiarities of the evaluation of theories within scientific research programmes (SRPs) and of the assessing of rival SRPs are described assuming that scientists try to maximise an 'epistemic utility function' under economic and institutional constraints. Special attention is given to Lakatos' concepts of 'empirical progress' and 'theoretical progress'. A notion of 'empirical verisimilitude' is defended as an appropriate utility function. The neologism 'methodonomics' is applied to this kind of studies.