Olav Benjamin Vassend proposes two solutions to the “interpretive problem” of assigning nonzero probabilities to hypotheses that are known to be false. He argues that the verisimilitude interpretation (probability expresses the degree of belief that the hypothesis is closest to the truth) and the counterfactual interpretation (probability is conditional on a false supposition) are equivalent. While Vassend’s intuition about these two solutions is basically correct, the technical details of his treatment need elaboration and correction. Appropriate tools for combining verisimilitude and Bayesian probabilities can be found in my Truthlikeness.

Charles S. Peirce argued that, besides deduction and induction, there is a third mode of inference which he called “hypothesis” or “abduction.” He characterized abduction as reasoning “from effect to cause,” and as “the operation of adopting an explanatory hypothesis.” Peirce's ideas about abduction, which are related also to historically earlier accounts of heuristic reasoning (the method of analysis), have been seen as providing a logic of scientific discovery. Alternatively, abduction is interpreted as giving reasons for pursuing a hypothesis. Inference to the best explanation (IBE) has also been regarded as an important mode of justification, both in everyday life, detective stories, and science. In particular, scientific realism has been defended by an abductive nomiracle argument (Smart, Putnam, Boyd), while the critics of realism have attempted to show that this appeal to abduction is question-begging, circular, or incoherent (Fine, Laudan, van Fraassen). This paper approaches these issues by distinguishing weaker and stronger forms of abduction, and by showing how these types of inferences can be given Peircean and Bayesian probabilistic reconstructions.

A holistic account of the meaning of theoretical terms leads scientific realism into serious troubles. Alternative methods of reference fixing are needed by a realist who wishes to show how reference invariance is possible in spite of meaning variance. This paper argues that the similarity theory of truthlikeness and approximate truth, developed by logicians since the mid 1970s, helps to make precise the idea of charitable theoretical reference. Comparisons to the recent proposals by Kitcher and Psillos are given. This argument helps to undermine the scepticist meta-induction about theories, and thereby to reevaluate Laudan's alleged confutation of scientific realism.

In a recent article, Goldstick and O'Neill propose a definition for the comparative “truer than” relation between rival propositions. This definition is studied here in a context where the concept of “convexity” is well defined for propositions. It turns out that the Goldstick-O'Neill definition gives a reasonable but very restricted sufficient condition for the “truer than” relation, but fails as a necessary condition.

While most philosophers of science agree that science is, perhaps in many ways, a highly successful enterprise, there is no consensus about the best way of defining and measuring this success. Philosophers are also divided in their views about two further issues: What does the success of a scientific theory indicate? What is the best way of explaining this success?

After some remarks about institutional and pragmatic measures of success, this paper concentrates on rival ways of defining cognitive success. Four realist measures of epistemic credit are discussed: probability, confirmation (corroboration), expected verisimilitude, and probable verisimilitude. Laudan’s non-realist concept of the problem-solving effectiveness of a theory is compared to Hempel’s notion of systematic power. I argue that such truth-independent concepts alone are insufficient to characterize scientific advance. But if they are used as truth-dependent epistemic utilities, they serve as fallible indicators of the truth or truthlikeness of a theory.

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.

In A History of the Mathematical Theory of Probability (1865), I. Todhunter tells that among the “learned conversations” of the Florentine gentlemen the following question was once proposed: “A horse is really worth a hundred crowns, one person estimated it at ten crowns and another at a thousand; which of the two made the more extravagant estimate?” When consulted on this matter, Galileo pronounced the two estimates to be equally extravagant, “because the ratio of a thousand to a hundred is the same as the ratio of a hundred to ten”. A priest named Nozzolini thought that the higher estimate is more mistaken, since “the excess of a thousand above a hundred is greater than that of a hundred above ten.” (p. 5).

Todhunter's comment on this issue is interesting: it does not appear to him that “the discussion is of any scientific interest or value”.

In a recent article [4], Fred I. Dretske has proposed a new analysis of natural laws. Dretske rejects the more or less standard view which says that laws are universal truths with a special function or status in science. As an alternative account, he suggests that laws are expressed by singular statements describing the relationship between universal properties and magnitudes: the statement

(1) It is a law that F's are G's3.

is to be analysed as

(2) F-ness ↦ G-ness.

I shall argue, however, that Dretske's reasons for rejecting the standard account are not conclusive. Moreover, his own proposal seems to be either inadequate or reducible to that version of the standard account which takes laws to be nomically necessary generalizations.

Inductive logic studies the structural properties of epistemic probabilities. Its basic task is to determine how various factors may influence rational degrees of belief in the truth of hypotheses on the basis of some evidence. Its distinctive feature in comparison with other approaches to epistemic probabilities is the attention paid to the idea - not in vogue during the 1940's when Carnap started his program, but very influential in much of the contemporary work within the history and the philosophy of science - that our knowledge claims, or our rational beliefs about the reality, are significantly influenced or preconditioned. by language. While dependence on (formal) language is one of the “logical” aspects of inductive probabilities, the role of other relevant, possibly extra-logical, determinants of rational degrees of belief is expressed, within the systems of inductive logic, by means of at most a finite number of parameters.