Axel Gelfert

The present paper examines the role of exact results in the theory of many‐body physics, and specifically the example of the Mermin‐Wagner theorem, a rigorous result concerning the absence of phase transitions in low‐dimensional systems. While the theorem has been shown to hold for a wide range of many‐body models, it is frequently ‘violated’ by results derived from the same models using numerical techniques. This raises the question of how scientists regulate their theoretical commitments in such cases, given that the models, too, are often described as approximations to the underlying ‘full’ many‐body problem.

Hume concludes Book II of his Treatise of Human Nature with a section on the passion of curiosity, ‘that love of truth, which was the first source of all our enquiries’. At first sight, this characterisation of curiosity – as the motivating factor in that specifically human activity that is the pursuit of knowledge – may seem unoriginal. However, when Hume speaks of the ‘source of all our enquiries’, he is referring both to the universal human pursuit of knowledge and to his own philosophical project. Seen in this light, his discussion of curiosity takes on a new significance, as it weaves together elements of his systematic account of human nature – notably, his theory of cognition and motivation – with observations about the pursuit of philosophy as well as the progress of the arts and sciences. In the present paper, I offer a reconstruction of Hume’s view on curiosity and its role in cognition and inquiry.

This paper argues that a successful philosophical analysis of models and simulations must accommodate an account of mathematically rigorous results. Such rigorous results may be thought of as genuinely model-specific contributions, which can neither be deduced from fundamental theory nor inferred from empirical data. Rigorous results provide new indirect ways of assessing the success of models and simulations and are crucial to understanding the connections between different models. This is most obvious in cases where rigorous results map different models on to one another. Not only does this put constraints on the extent to which performance in specific empirical contexts may be regarded as the main touchstone of success in scientific modelling, it also allows for the transfer of warrant across different models. Mathematically rigorous results can thus come to be seen as not only strengthening the cohesion between scientific strategies of modelling and simulation, but also as offering new ways of indirect confirmation

Immanuel Kant is often regarded as an exponent of the ‘individualist’ tradition in epistemology, according to which testimony is not a fundamental source of knowledge. The present paper argues that this view is far from accurate. Kant devotes ample space to discussions of testimony and, in his lectures on logic, arrives at a distinct and stable philosophical position regarding testimony. Important elements of this position consist in (a) acknowledging the ineliminability of testimony; (b) realizing that testimony can establish empirical knowledge with certainty; (c) establishing a presumptive principle regarding the acceptance of testimony; (d) arguing for a symmetry between knowledge based on experience and knowledge based on testimony. Rejecting testimony as a fundamental source of knowledge merely on the basis that no theoretically necessary ground for its truth can be given, would, as Kant puts it, indicate ‘a lack of moral interest’. Such ‘incredulity’ would be a form of ‘logical egoism’: it demonstrates an unwillingness or inability to think oneself in the place of others, yet this we must do if we are to trust our own judgements. While Kant strongly endorses testimony as a source of empirical knowledge, he does, however, make one important restriction: ‘Propositions of reason’ (Vernunftwahrheiten), such as universal moral principles, may not be adopted on the basis of testimony. I argue that this distinction, between testimonial knowledge of empirical matters of fact and individual knowledge of propositions of reason, is an important element of Kant’s epistemology of testimony, as it explains how his strong endorsement of testimony as a source of knowledge can be squared with his equally strong demand for intellectual autonomy. Finally, I comment on the overall implications of this account for Kant’s discussion, elsewhere in his work, of the public nature of communication.

In his previous books, The Theory of Epistemic Rationality (1987) and Working Without a Net (1993), Richard Foley presented a highly influential account of what it means for one’s beliefs and belief-forming practices to be rational. Developing a positive new account of epistemic rationality, however, has never been Foley’s sole concern. His project is metaepistemological in character as much as it is epistemological. Put crudely, questions such as ‘What makes some beliefs knowledge?’ are of equal importance to Foley as such questions as ‘How is scepticism possible?’. Indeed, given the way in which philosophical debates tend to be shaped, it may be the more fruitful way of tackling a philosophical problem to start from questions of the latter type and work one’s way backward to the fundamental questions that gave rise to the debate in the first place. Such an approach need not be strictly historical; rather, it will be meta-epistemological in that it probes deeply into the possibility of an epistemological theory, its prospective subject matter as well as its limitations. Given the difficulty of constructing a coherent epistemological theory and defending it against the various objections that are standardly run against such theories, it should often prove more viable to illustrate the general meta-epistemological ‘lessons’ by way of referring to previous epistemological theories and the long-standing debates that surround them. Hence, a metaepistemological approach naturally gives rise to an historically informed outlook.

Edgar Allan Poe’s standing as a literary figure, who drew on (and sometimes dabbled in) the scientific debates of his time, makes him an intriguing character for any exploration of the historical interrelationship between science, literature and philosophy. His sprawling ‘prose-poem’ Eureka (1848), in particular, has sometimes been scrutinized for anticipations of later scientific developments. By contrast, the present paper argues that it should be understood as a contribution to the raging debates about scientific methodology at the time. This methodological interest, which is echoed in Poe’s ‘tales of ratiocination’, gives rise to a proposed new mode of—broadly abductive—inference, which Poe attributes to the hybrid figure of the ‘poet-mathematician’. Without creative imagination and intuition, Science would necessarily remain incomplete, evenby its own standards. This concern with imaginative (abductive) inference ties in nicely with his coherentism, which grants pride of place to the twin virtues of Simplicity and Consistency, which must constrain imagination lest it degenerate into mere fancy.