Online research in philosophy

Hempel's qualitative criteria of converse consequence and special consequence for confirmation are examined, and the resulting paradoxes traced to the general intransitivity of confirmation. Adopting a probabilistic measure of confirmation, a limiting form of transitivity of confirmation from evidence to predictions is derived, and it is shown to what extent its application depends on prior probability judgments. In arguments involving this kind of transitivity therefore there is no necessary "convergence of opinion" in the sense claimed by some personalists. The conditions of application of the limiting transitivity theorem are most perspicuously described in terms of De Finetti's notion of exchangeability, which leads to a suggested revaluation of the function of theories in relation to confirmation and explanation.

Contemporary Bayesian confirmation theorists measure degree of (incremental) confirmation using a variety of non-equivalent relevance measures. As a result, a great many of the arguments surrounding quantitative Bayesian confirmation theory are implicitly sensitive to choice of measure of confirmation. Such arguments are enthymematic, since they tacitly presuppose that certain relevance measures should be used (for various purposes) rather than other relevance measures that have been proposed and defended in the philosophical literature. I present a survey of this pervasive class of Bayesian confirmation-theoretic enthymemes, and a brief analysis of some recent attempts to resolve the problem of measure sensitivity.

Confirmation theory is the study of the logic by which scientific hypotheses may be confirmed or disconfirmed, or even refuted by evidence. A specific theory of confirmation is a proposal for such a logic. Presumably the epistemic evaluation of scientific hypotheses should largely depend on their empirical content – on what they say the evidentially accessible parts of the world are like, and on the extent to which they turn out to be right about that. Thus, all theories of confirmation rely on measures of how well various alternative hypotheses account for the evidence.1 Most contemporary confirmation theories employ probability functions to provide such a measure. They measure how well the evidence fits what the hypothesis says about the world in terms of how likely it is that the evidence should occur were the hypothesis true. Such hypothesis-based probabilities of evidence claims are called likelihoods. Clearly, when the evidence is more likely according to one hypothesis than according to an alternative, that should redound to the credit of the former hypothesis and the discredit of the later. But various theories of confirmation diverge on precisely how this credit is to be measured?

Glymour's account of confirmation is seen to have paradoxical consequences when applied to the confirmation of theories containing theoretical functions. An alternative conception of instances derived from Sneed's reconstruction of physical theories is conjoined with the instance view of confirmation to produce an account of confirmation that avoids these problems. The topic of selective confirmation is discussed, and it is argued that theories containing theoretical functions are not selectively confirmable.

The problem addressed in this paper is “the main epistemic problem concerning science”, viz. “the explication of how we compare and evaluate theories [...] in the light of the available evidence” (van Fraassen, BC, 1983, Theory comparison and relevant Evidence. In J. Earman (Ed.), Testing scientific theories (pp. 27–42). Minneapolis: University of Minnesota Press). Sections 1– 3 contain the general plausibility-informativeness theory of theory assessment. In a nutshell, the message is (1) that there are two values a theory should exhibit: truth and informativeness—measured respectively by a truth indicator and a strength indicator; (2) that these two values are conflicting in the sense that the former is a decreasing and the latter an increasing function of the logical strength of the theory to be assessed; and (3) that in assessing a given theory by the available data one should weigh between these two conflicting aspects in such a way that any surplus in informativeness succeeds, if the shortfall in plausibility is small enough. Particular accounts of this general theory arise by inserting particular strength indicators and truth indicators. In Section 4 the theory is spelt out for the Bayesian paradigm of subjective probabilities. It is then compared to incremental Bayesian confirmation theory. Section 4 closes by asking whether it is likely to be lovely. Section 5 discusses a few problems of confirmation theory in the light of the present approach. In particular, it is briefly indicated how the present account gives rise to a new analysis of Hempel’s conditions of adequacy for any relation of confirmation (Hempel, CG, 1945, Studies in the logic of comfirmation. Mind, 54, 1–26, 97–121.), differing from the one Carnap gave in § 87 of his Logical foundations of probability (1962, Chicago: University of Chicago Press). Section 6 adresses the question of justification any theory of theory assessment has to face: why should one stick to theories given high assessment values rather than to any other theories? The answer given by the Bayesian version of the account presented in section 4 is that one should accept theories given high assessment values, because, in the medium run, theory assessment almost surely takes one to the most informative among all true theories when presented separating data. The concluding section 7 continues the comparison between the present account and incremental Bayesian confirmation theory.

A formalism for the incremental confirmation of one hypothesis relative to another hypothesis and the requirement for adding a hypothesis to a belief system is presented as a sufficient explication of confirmation. The formalism is contrasted with the explications of confirmation offered by Ian Hacking and Karl Popper. It is shown to solve some of the problems which are most often put forth as foils of similar approaches to confirmation theory. Finally, the method is indicated by which the formalism avoids all other standard problems.

Confirmation of a hypothesis by evidence can be measured by one of the so far known incremental measures of confirmation. As we show, incremental measures can be formally defined as the measures of confirmation satisfying a certain small set of basic conditions. Moreover, several kinds of incremental measure may be characterized on the basis of appropriate structural properties. In particular, we focus on the so-called Matthew properties: we introduce a family of six Matthew properties including the reverse Matthew effect; we further prove that incremental measures endowed with reverse Matthew effect are possible; finally, we shortly consider the problem of the plausibility of Matthew properties.

This paper discusses an almost sixty year old problem in the philosophy of science -- that of a logic of confirmation. We present a new analysis of Carl G. Hempel's conditions of adequacy (Hempel 1945), differing from the one Carnap gave in §87 of his Logical Foundations of Probability (1962). Hempel, it is argued, felt the need for two concepts of confirmation: one aiming at true theories and another aiming at informative theories. However, he also realized that these two concepts are conflicting, and he gave up the concept of confirmation aiming at informative theories. We then show that one can have Hempel's cake and eat it, too: There is a (rank-theoretic and genuinely nonmonotonic) logic of confirmation -- or rather, theory assessment -- that takes into account both of these two conflicting aspects. According to this logic, a statement H is an acceptable theory for the data E if and only if H is both sufficiently plausible given E and sufficiently informative about E. Finally, the logic sheds new light on Carnap's analysis (and solves another problem of confirmation theory).

Recent work on the logical theory of confirmation has centered on accounts of the confirmation of hypotheses relative to auxiliary assumptions or background theory. Whether such relative confirmation actually increases the credibility of the (relatively) confirmed hypothesis will depend in various ways on the epistemic status of the auxiliaries involved. Most obviously, if the auxiliaries are not themselves credible, confirmation relative to them will not increase the credibility of the hypothesis thus confirmed. A complete theory of confirmation must thus combine an account of relative confirmation with an account of the route from relative confirmation to real confirmation. Some recent criticisms of hypothetico-deductive and bootstrapping accounts of relative confirmation are undermined by failure to appreciate the limitations of relative confirmation.

ON WHAT GROUNDS OUGHT WE TO CHOOSE BETWEEN COMPETING CONFIRMATION THEORIES? THE ARTICLE BEGINS BY DISTINGUISHING BETWEEN CONFIRMATION THEORIES AND OTHER THEORIES WHICH MIGHT BE CONFUSED WITH THEM, SUCH AS THEORIES OF ACCEPTABILITY. IT THEN ARGUES THAT A CONFIRMATION THEORY OUGHT TO ANALYSE RATHER THAN EXPLICATE OUR ORDINARY STANDARDS OF CONFIRMATION. IT WILL DO THIS IN SO FAR AS IT IS COHERENT AND DOES NOT YIELD COUNTERINTUITIVE JUDGMENTS.