Belief revision theory concerns methods for reformulating an agent's epistemic state when the agent's beliefs are refuted by new information. The usual guiding principle in the design of such methods is to preserve as much of the agent's epistemic state as possible when the state is revised. Learning theoretic research focuses, instead, on a learning method's reliability or ability to converge to true, informative beliefs over a wide range of possible environments. This paper bridges the two perspectives by assessing the (...) reliability of several proposed belief revision operators. Stringent conceptions of minimal change are shown to occasion a limitation called inductive amnesia: they can predict the future only if they cannot remember the past. Avoidance of inductive amnesia can therefore function as a plausible and hitherto unrecognized constraint on the design of belief revision operators. (shrink)

In recent years, the question of the reliability of Machine Learning (ML) methods has acquired significant importance, and the analysis of the associated uncertainties has motivated a growing amount of research. However, most of these studies have applied standard error analysis to ML models—and in particular Deep Neural Network (DNN) models—which represent a rather significant departure from standard scientific modelling. It is therefore necessary to integrate the standard error analysis with a deeper epistemological analysis of the possible differences between DNN (...) models and standard scientific modelling and the possible implications of these differences in the assessment of reliability. This article offers several contributions. First, it emphasises the ubiquitous role of model assumptions (both in ML and traditional science) against the illusion of theory-free science. Secondly, model assumptions are analysed from the point of view of their (epistemic) complexity, which is shown to be language-independent. It is argued that the high epistemic complexity of DNN models hinders the estimate of their reliability and also their prospect of long term progress. Some potential ways forward are suggested. Thirdly, this article identifies the close relation between a model’s epistemic complexity and its interpretability, as introduced in the context of responsible AI. This clarifies in which sense—and to what extent—the lack of understanding of a model (black-box problem) impacts its interpretability in a way that is independent of individual skills. It also clarifies how interpretability is a precondition for a plausible assessment of the reliability of any model, which cannot be based on statistical analysis alone. This article focuses on the comparison between traditional scientific models and DNN models. However, Random Forest (RF) and Logistic Regression (LR) models are also briefly considered. (shrink)

The aim of this contribution is to provide a rather general answer to Hume’s problem. To this end, induction is treated within a straightforward formal paradigm, i.e., several connected levels of abstraction. Within this setting, many concrete models are discussed. On the one hand, models from mathematics, statistics and information science demonstrate how induction might succeed. On the other hand, standard examples from philosophy highlight fundamental difficulties. Thus it transpires that the difference between unbounded and bounded inductive steps is crucial: (...) while unbounded leaps of faith are never justified, there may well be reasonable bounded inductive steps. In this endeavour, the twin concepts of information and probability prove to be indispensable, pinning down the crucial arguments, and, at times, reducing them to calculations. Essentially, a precise study of boundedness settles Goodman’s challenge. Hume’s more profound claim of seemingly inevitable circularity is answered by obviously non-circular hierarchical structures. (shrink)

I review and challenge the views on simplicity and its role in linguistics put forward by Ludlow. In particular, I criticize the claim that simplicity—in the sense pertinent to science—is nothing more than ease of use or “user-friendliness”, motivated by economy of labor. I argue that Ludlow’s discussion fails to do justice to the diversity of factors that are relevant to simplicity considerations. This, in turn, leads to the neglect of crucial cases in which the rationale for simplification is unmistakably (...) epistemic, as well as instances where simplicity is part of the content of substantive, empirical hypotheses. I illustrate these points with examples from the history of generative linguistics, such as: the shaping influence exerted by simplicity, via its involvement in the notion of “linguistically significant generalization”, its methodological and substantive contribution to the goal of explanatory adequacy, and its central role in the Minimalist Program’s search “beyond explanatory adequacy”. (shrink)

The twin goals of this essay are: to investigate a family of cases in which the goal of guaranteed convergence to the truth is beyond our reach; and to argue that each of three strands prominent in contemporary epistemological thought has undesirable consequences when confronted with the existence of such problems. Approaches that follow Reichenbach in taking guaranteed convergence to the truth to be the characteristic virtue of good methods face a vicious closure problem. Approaches on which there is a (...) unique rational doxastic response to any given body of evidence can avoid incoherence only by rendering epistemology a curiously limited enterprise. Bayesian approaches rule out humility about one’s prospects of success in certain situations in which failure is typical. (shrink)

Almost all commentators acknowledge that among the grounds on which scientists perform theory-choices are criteria of simplicity. In general, simplicity is regarded either as only a logico-empirical quality of a theory, diagnostic of the theory's future predictive success, or as a purely aesthetic or otherwise extra-empirical property of it. This paper attempts to demonstrate that the simplicity-criteria applied in scientific practice include both a logico-empirical and a quasi-aesthetic criterion: to conflate these in an account of scientists' theory-choice is to court (...) confusion. (shrink)

The aim of this contribution is to provide a rather general answer to Hume's problem, the well-known problem of induction. To this end, it is very useful to apply his differentiation between ``relations of ideas'' and ``matters of fact'', and to reconsider earlier approaches. In so doing, we consider the problem formally, as well as empirically. Next, received attempts to solve the problem are discussed. The basic structure of inductive problems is exposed in chap. 6. Our final conclusions are to (...) the positive, i.e., Hume's problem can be dealt with - solved - in a constructive way. More specifically, bounded generalisations can be justified, and the key to the solution is the concept of information. (shrink)

Scientific knowledge develops in an increasingly fragmentary way.A multitude of scientific disciplines branch out. Curiosity for thisdevelopment leads into quests for a unifying understanding. To a certain extent, foundational studies provide such unification. There is a tendency, however, also of a fragmentary growth of foundational studies, like in a multitude of disciplinaryfoundations. We suggest to look at the foundational problem, not primarily as a search for foundations for one discipline in another, as in some reductionist approach, but as a steady (...) revelation ofpresuppositions for individual scientific theories – which are boundto meet, sooner or later, in a common language. A decisive point hereis our holistic conception of language, as a whole of description-interpretation processes which are entangled(complementary) in the language itself. For every language there is alinguistic complementarity. We suggest this unique form ofentanglement as a unifying presupposition, ultimately foundational forall communicable knowledge. Involved is a linguistic realism, in terms ofwhich we critically examine ``language-world'' problems, as exposed byWittgenstein, and Russell, about a foundational interdependence of language andreality (world). Throughout, we attach to the developmentof foundational studies of mathematics, logics, and the naturalsciences. In particular, we study the interpretation problem foraxioms of infinity in some detail. We emphasize that the holistic concept of language contradicts Carnap's semiotic fragmentation thesis (thus, no clean cutbetween syntax, semantics, pragmatics). (shrink)

The fact that simplicity has been linked with induction by many philosophers of science, some of whom have proposed or supported criteria of “inductive simplicity,” means that the problem must be given some serious attention. I take “inductive simplicity” as a title, however, only by way of concession to these historical treatments, since it is precisely the burden of my paper to show that there is no such thing. So much for the conclusion. I shall spend the remainder of my (...) time arguing for it. (shrink)

Ockham’s razor is the idea that simpler hypotheses are to be preferred over more complex ones. In the context of medical diagnosis, this is taken to mean that when a patient has multiple symptoms, a single diagnosis should be sought that accounts for all the clinical features, rather than attributing a different diagnosis to each. This paper examines whether diagnostic parsimony can be justified by reference to probability theory. I argue that while attempts to offer universal justifications of diagnostic parsimony (...) fail, a more constrained use of this diagnostic principle can be supported. (shrink)