Darrell P. Rowbottom

In a recent contribution to Learning for Democracy, Richard Bailey argues that Thomas Kuhn advocated an indoctrinatory model of science education, which is fundamentally authority-based. While agreeing with Bailey’s conclusion, this article suggests that Kuhn was attempting to solve an important problem which Bailey only touches on – how to ensure that science students do not become hypercritical. It continues by offering a critical rationalist solution to this problem, arguing that paradigms qua exemplars should be historical problem-solving episodes, rather than model solutions to puzzles.

This article explores the practical significance of the notion of ‘World 3’ – a domain of abstract entities – for inquiry and education. First, it explains how ‘objectifying’ our thoughts and statements, viz. treating them as if they are objective, can help in inquiry to: promote impartiality towards ideas on the basis of their source and the manner in which they are presented; enable more effective communication; and encourage wider participation in debates. Second, the article examines how ‘objectification’ can be useful in group learning scenarios, insofar as these involve group inquiry.

Kuhn’s view of science is as follows. Science involves two key phases: normal and extraordinary. In normal science, disciplinary matrices (DMs) are large and pervasive. DMs involve “beliefs, values, techniques, and so on shared by the members of a given community” (Kuhn 1996, 175). “And so on” is regrettably vague, but Kuhn (1977, 1996) mentions three other key elements: symbolic generalizations (such as F=dp/dt), models (such as Bohr’s atomic model), and exemplars. These components of DMs overlap somewhat. For instance, symbolic generalizations may feature in techniques and beliefs, and models may exhibit values. To be a (genuine) scientist, in the normal science phase, is to puzzle solve within the boundaries of the DM. It is to buy into the ruling dogma (Kuhn 1963) and to accept that “failure to achieve a solution discredits only the scientist ... ‘It is a poor carpenter who blames his tools’” (Kuhn 1996, 80). Puzzle solving involves a wide variety of activities, including

Hájek has recently presented the following paradox. You are certain that a cable guy will visit you tomorrow between 8 a.m. and 4 p.m. but you have no further information about when. And you agree to a bet on whether he will come in the morning interval (8, 12] or in the afternoon interval (12, 4). At first, you have no reason to prefer one possibility rather than the other. But you soon realise that there will definitely be a future time at which you will (rationally) assign higher probability to an afternoon arrival than a morning one, due to time elapsing. You are also sure there may not be a future time at which you will (rationally) assign a higher probability to a morning arrival than an afternoon one. It would therefore appear that you ought to bet on an afternoon arrival. The paradox is based on the apparent incompatibility of the principle of expected utility and principles of diachronic rationality which are prima facie plausible. Hájek concludes that the latter are false, but doesn't provide a clear diagnosis as to why. We endeavour to further our understanding of the paradox by providing such a diagnosis.

When do we agree? The answer might once have seemed simple and obvious; we agree that p when we each believe that p. But from a formal epistemological perspective, where degrees of belief are more fundamental than beliefs, this answer is unsatisfactory. On the one hand, there is reason to suppose that it is false; degrees of belief about p might differ when beliefs simpliciter on p do not. On the other hand, even if it is true, it is too vague; for what it is to believe simpliciter ought to be explained in terms of degrees of belief. This paper presents several possible notions of agreement, and corresponding notions of disagreement. It indicates how the findings are fruitful for the epistemology of disagreement, with special reference to the notion of epistemic peerhood.

This paper compares and contrasts the concept of a stance with that of a paradigm qua disciplinary matrix, in an attempt to illuminate both notions. First, it considers to what extent it is appropriate to draw an analogy between stances and disciplinary matrices. It suggests that despite first appearances, a disciplinary matrix is not simply a stance writ large. Second, it examines how we might reinterpret disciplinary matrices in terms of stances, and shows how doing so can provide us with a better insight into non-revolutionary science. Finally, it identifies two directions for future research: “Can the rationality of scientific revolutions be understood in terms of the dynamic between stances and paradigms?” and “Do stances help us to understand incommensurability between disciplinary matrices?”

In Making Sense of Life , Keller emphasizes several differences between biology and physics. Her analysis focuses on significant ways in which modelling practices in some areas of biology, especially developmental biology, differ from those of the physical sciences. She suggests that natural models and modelling by homology play a central role in the former but not the latter. In this paper, I focus instead on those practices that are importantly similar, from the point of view of epistemology and cognitive science. I argue that concrete and abstract models are significant in both disciplines, that there are shared selection criteria for models in physics and biology, e.g. familiarity, and that modelling often occurs in a similar fashion.

It is a common view that the axioms of probability can be derived from the following assumptions: probabilities reflect degrees of belief, degrees of belief can be measured as betting quotients; and a rational agent must select betting quotients that are coherent. In this paper, I argue that a consideration of reasonable betting behaviour, with respect to the alleged derivation of the first axiom of probability, suggests that and are incorrect. In particular, I show how a rational agent might assign a ‘probability’ of zero to an event which she is sure will occur

When a doctor tells you there’s a one percent chance that an operation will result in your death, or a scientist claims that his theory is probably true, what exactly does that mean? Understanding probability is clearly very important, if we are to make good theoretical and practical choices. In this engaging and highly accessible introduction to the philosophy of probability, Darrell Rowbottom takes the reader on a journey through all the major interpretations of probability, with reference to real–world situations. In lucid prose, he explores the many fallacies of probabilistic reasoning, such as the ‘gambler’s fallacy’ and the ‘inverse fallacy’, and shows how we can avoid falling into these traps by using the interpretations presented. He also illustrates the relevance of the interpretation of probability across disciplinary boundaries, by examining which interpretations of probability are appropriate in diverse areas such as quantum mechanics, game theory, and genetics. Using entertaining dialogues to draw out the key issues at stake, this unique book will appeal to students and scholars across philosophy, the social sciences, and the natural sciences.

This paper shows that so-called ‘threshold concepts’ have been defined in a way that makes it impossible, even in principle, to empirically isolate them. It continues by proposing an alternative theoretical framework, and argues: (1) that concepts are not reducible to abilities; (2) that acquisition of a given concept can be necessary, but not sufficient, for the possession of an ability; and (3) that being ‘threshold’ is an extrinsic property, such that what is threshold for one person is not for another. It closes by outlining two resultant problems for related empirical research. First, how is it possible to test for concepts, rather than abilities? Second, how can we tell if there is more than one possible conceptual route to the same ability?

How should educational research be contracted? And is there anything wrong with the way that public funding of educational research is currently administered? We endeavour to answer these questions by appeal to the work of two of the most prominent philosophers of science of the twentieth century, namely Popper and Kuhn. Although their normative views of science are radically different, we show that they would nonetheless agree on a number of key rules concerning the extent to which scientific practice should be influenced ‘from the outside’. We then show that these rules are often broken in the way that research is publicly funded in the UK.

We argue that the inference from dispositional essentialism about a property (in the broadest sense) to the metaphysical necessity of laws involving it is invalid. Let strict dispositional essentialism be any view according to which any given property’s dispositional character is precisely the same across all possible worlds. Clearly, any version of strict dispositional essentialism rules out worlds with different laws involving that property. Permissive dispositional essentialism is committed to a property’s identity being tied to its dispositional profile or causal role, yet is compatible with moderate interworld variation in a property’s dispositional profile. We provide such a model of dispositional essentialism about a property and metaphysical contingency of the laws involving it.

This paper offers a novel ‘changing places’ account of identification in games, where the consequences of role swapping are crucial. First, it illustrates how such an account is consistent with the view, in classical game theory, that only outcomes (and not pathways) are significant. Second, it argues that this account is superior to the ‘pooled resources’ alternative when it comes to dealing with some situations in which many players identify. Third, it shows how such a ‘changing places’ account can be used in games where some of the players identify with one another, but others do not. Finally, it illustrates how the model can handle the notion that identification comes in degrees.

This paper presents a new 'discontinuous' view of Popper's theory of corroboration, where theories cease to have corroboration values when new severe tests are devised which have not yet been performed, on the basis of a passage from The Logic of Scientific Discovery. Through subsequent analysis and discussion, a novel problem for Popper's account of corroboration, which holds also for the standard view, emerges. This is the problem of the Big Test : that the severest test of any hypothesis is actually to perform all possible tests. But this means that Popper's demand for 'the severest tests' amounts simply to a demand for 'all possible tests'. The paper closes by considering how this bears on accommodation vs. prediction, with respect to corroboration

This paper, which is based on recent empirical research at the University of Leeds, the University of Edinburgh, and the University of Bristol, presents two difficulties which arise when condensed matter physicists interact with molecular biologists: (1) the former use models which appear to be too coarse-grained, approximate and/or idealized to serve a useful scientific purpose to the latter; and (2) the latter have a rather narrower view of what counts as an experiment, particularly when it comes to computer simulations, than the former. It argues that these findings are related; that computer simulations are considered to be undeserving of experimental status, by molecular biologists, precisely because of the idealizations and approximations that they involve. The complexity of biological systems is a key factor. The paper concludes by critically examining whether the new research programme of ‘systems biology’ offers a genuine alternative to the modelling strategies used by physicists. It argues that it does not.

How are we to understand the use of probability in corroboration functions? Popper says logically, but does not show we could have access to, or even calculate, probability values in a logical sense. This makes the logical interpretation untenable, as Ramsey and van Fraassen have argued. -/- If corroboration functions only make sense when the probabilities employed therein are subjective, however, then what counts as impressive evidence for a theory might be a matter of convention, or even whim. So isn’t so-called ‘corroboration’ just a matter of psychology? -/- In this paper, I argue that we can go some way towards addressing this objection by adopting an intersubjective interpretation, of the form advocated by Gillies, with respect to corroboration. I show why intersubjective probabilities are preferable to subjective ones when it comes to decision making in science: why group decisions are liable to be superior to individual ones, given a number of plausible conditions. I then argue that intersubjective corroboration is preferable to intersubjective confirmation of a Bayesian variety, because there is greater opportunity for principled agreement concerning the factors involved in the former.