Theodorus Kuipers

Naive and refined truth approximation

The naive structuralist definition of truthlikeness is an idealization in the sense that it assumes that all mistaken models of a theory are equally bad. The natural concretization is a refined definition based on an underlying notion of structurelikeness.In Section 1 the naive definition of truthlikeness of theories is presented, using a new conceptual justification, in terms of instantial and explanatory mistakes.In Section 2 general constraints are formulated for the notions of structurelikeness and truthlikeness of structures.In Section 3 a refined definition of truthlikeness of theories is presented, based on the notion of structurelikeness, using a sophisticated version of the conceptual justification for the naive definition.In Section 4 it is shown that ‘idealization and concretization’ is a special kind of potentially refined truth approximation.

Verisimilitude and belief change for nomic conjunctive theories

In this paper, we address the problem of truth approximation through theory change, asking whether revising our theories by newly acquired data leads us closer to the truth about a given domain. More particularly, we focus on “nomic conjunctive theories”, i.e., theories expressed as conjunctions of logically independent statements concerning the physical or, more generally, nomic possibilities and impossibilities of the domain under inquiry. We define both a comparative and a quantitative notion of the verisimilitude of such theories, and identify suitable conditions concerning the (partial) correctness of acquired data, under which revising our theories by data leads us closer to “the nomic truth”, construed as the target of scientific inquiry. We conclude by indicating some further developments, generalizations, and open issues arising from our results.

On the generalization of the continuum of inductive methods to universal hypotheses

Carnaps continuum of inductive methods (Carnap, 1952) has been considered, by himself and others, as a proof for the claim that the intuitive concept of rational degree of belief can be explicated, at least with respect to simple situations, in a satisfactory way. At the same time it has been considered as new evidence for the intuitive feeling that such an explication would only be possible for singular (or, individual) hypotheses but not for universal hypotheses. In particular, it was felt that it would not be possible to generalize Carn~Lps continuum in an acceptable way so that Carnaps continuum appears as an extreme special case. In this paper it will be shown that this particular conjecture is false and that, consequently, the general conjecture is also false. The requirements for an acceptable generalization will be stated precisely and, in view of the literature on tiffs subject, we have the strong conviction that these requirements will generally be admitted to be necessary and sufficient from the finitary (inductive) point of view. The generalized continuum is not new, however. It is essentially contained in Hintikkas (1966) a-X-system and it is essentially equivalent to the class of systems which have recently been introduced by I-Iintikka and Niiniluoto (1976). The main technical result of this article is the proof that the latter class of system,; is equivalent to a particular subsystem of Hintikkas combined system. Hintikka and Niiniluoto could already conclude that it was possible to treat universal hypotheses in a fundamentally acceptable way. The equivalence theorem enables us to specify precisely why and in what sense we are justified to talk about the generalization of Carnaps continuum. Moreover it shows that this generalization is axiomatically as well as technically as simple as ever could be expected.

The Dual Foundation of Qualitative Truth Approximation

The main formal notion involved in qualitative truth approximation by the HD-method, viz. ‘more truthlike’, is shown to not only have, by its definition, an intuitively appealing ‘model foundation’, but also, at least partially, a conceptually plausible ‘consequence foundation’. Moreover, combining the relevant parts of both leads to a very appealing ‘dual foundation’, the more so since the relevant methodological notions, viz. ‘more successful’ and its ingredients provided by the HD-method, can be given a similar dual foundation.According to the resulting dual foundation of ‘naive truth approximation’, the HD-method provides successes (established true consequences) and counterexamples (established wrongly missing models) of theories. Such HD-results may support the tentative conclusion that one theory seems to remain more successful than another in the naive sense of having more successes and fewer counterexamples. If so, this provides good reasons for believing that the more successful theory is also more truthlike in the naive sense of having more correct models and more true consequences.In the dual foundation of ‘refined truth approximation’, HD-results remain of the same two kinds, but ‘more successful’ is taken in the refined sense of accommodating counterexamples while saving relevant successes, in which case ‘more truthlike’ can be taken in the refined sense of improving relevant models while saving relevant consequences. In this way one gets a realistic dual account of qualitative truth approximation by the HD-method.The model foundation can also be extended to the methodological notions, but not in a very plausible way. The consequence foundation only seems specifiable for naive truth approximation, in which case it is plausible. In sum, the dual foundation is superior to both.

Models, postulates, and generalized nomic truth approximation

The qualitative theory of nomic truth approximation, presented in Kuipers in his (from instrumentalism to constructive realism, 2000), in which ‘the truth’ concerns the distinction between nomic, e.g. physical, possibilities and impossibilities, rests on a very restrictive assumption, viz. that theories always claim to characterize the boundary between nomic possibilities and impossibilities. Fully recognizing two different functions of theories, viz. excluding and representing, this paper drops this assumption by conceiving theories in development as tuples of postulates and models, where the postulates claim to exclude nomic impossibilities and the (not-excluded) models claim to represent nomic possibilities. Revising theories becomes then a matter of adding or revising models and/or postulates in the light of increasing evidence, captured by a special kind of theories, viz. ‘data-theories’. Under the assumption that the data-theory is true, achieving empirical progress in this way provides good reasons for the abductive conclusion that truth approximation has been achieved as well. Here, the notions of truth approximation and empirical progress are formally direct generalizations of the earlier ones. However, truth approximation is now explicitly defined in terms of increasing truth-content and decreasing falsity-content of theories, whereas empirical progress is defined in terms of lasting increased accepted and decreased rejected content in the light of increasing evidence. These definitions are strongly inspired by a paper of Gustavo Cevolani, Vincenzo Crupi and Roberto Festa, viz., “Verisimilitude and belief change for conjunctive theories” (Cevolani et al. in Erkenntnis 75(2):183–222, 2011).

Philosophy of design research

The paper investigates the conceptual possibility of a threefold distinction in design research that parallels the threefold distinction of laws, theories and research programs in nomic research, viz. design laws, design theories, and design research programs. In view of a rather different picture of design or, more broadly, applied theories of Ilkka Niiniluoto, the paper leaves the challenge to start comparative case studies to evaluate the two conceptions.

A realist partner for Linda: confirming a theoretical hypothesis more than its observational sub-hypothesis

It is argued that the conjunction effect has a disjunctive analog of strong interest for the realism–antirealism debate. It is possible that a proper theory is more confirmed than its (more probable) observational sub-theory and hence than the latter’s disjunctive equivalent, i.e., the disjunction of all proper theories that are empirically equivalent to the given one. This is illustrated by a toy model.

Introduction to ‘Logic and philosophy of science: in the footsteps of E.W. Beth’

Evert Willem Beth (Almelo, July 7, 1908—Amsterdam, April 12, 1964) was the main founder of logic and formal philosophy in The Netherlands. His remarkable research career produced ground-breaking insights in the foundations of mathematics and philosophy, and his teaching inspired a generation of gifted students. Moreover, Beth’s organizational talents were instrumental in creating the Amsterdam Institute for Logic and Foundations of the Exact Sciences, the first true philosophy department in The Netherlands, and the international Division of Logic, Methodology and Philosophy of Science. This issue of Synthese pays tribute to the lasting influence of this remarkable person.