Einstein is widely understood as regarding “principle theories” (such as the theory of relativity) as explanatorily powerless. This brief paper shows that Einstein's remarks admit of another interpretation, according to which principle theories possess explanatory power. This interpretation is motivated primarily by showing that James Jeans made remarks very similar to Einstein's at nearly the same time, but Jeans reconciled those remarks with holding principle theories to be explanatory. Einstein's remarks could well be getting at the same point as Jeans's. This view of principle and constructive theories is independently valuable. It undermines Salmon's “friendly physicist” example as an argument for the view that there are facts that can be explained by both principle and constructive theories.

The article discusses agent-based simulation as a tool of sociological understanding. Based on an inferential account of understanding, it argues that computer simulations increase our explanatory understanding both by expanding our ability to make what-if inferences about social processes and by making these inferences more reliable. However, our ability to understand simulations limits our ability to understand real world phenomena through them. Thomas Schelling's checkerboard model of ethnic segregation is used to demonstrate the important role played by abstract how-possibly models in the process of building a mechanistic understanding of social phenomena.

The history of thought experiments is now gaining a great deal of attention, and this is due to the renewed interest of philosophers on the subject. This paper inquires into the history of the philosophy of thought experiments. We name the period to be examined in this paper the “forerun.” Its main stakeholders are Georg C. Lichtenberg, Novalis, and Immanuel Kant. We will present and discuss the work of each of them in order to characterize the period, and then reveal parallels and lessons that apply to more recently proposed accounts of thought experiments.

Hilbert first mentioned ideal elements in his 1898–99 lectures on geometry. He described them as important, fruitful, and of frequent occurrence in mathematics, pointing to the examples of negative, irrational, imaginary, ideal and transfinite numbers. In geometry, he had in mind the examples of points, lines, and planes at infinity, whose introduction gives geometry a certain completeness, by making theorems such as those of Pappus and Desargues universally valid. In this article I will discuss how Hilbert transformed our view of the Pappus and Desargues theorems by showing that they express the underlying algebraic structure of projective geometry. I will compare this result with another of Hilbert's great contributions, his calculus of ends. By studying the ideal elements of the hyperbolic plane, Hilbert similarly extracted algebraic structure from the axioms of hyperbolic geometry. Hilbert's treatments of projective and hyperbolic geometry have another important common element: construction of real numbers. To achieve this, Hilbert has to add an axiom of continuity to the geometry axioms, but he evidently wants to show that the real numbers can be put on a geometric foundation.

Although it is now widely accepted that in science, non-cognitive values play a role, it is still debated whether this has implications for its objectivity. It seems that the task of philosophers here is twofold: to flesh out what kinds of non-cognitive values play what kinds of roles, and to evaluate the implications for objectivity. I attempt to contribute to both tasks by introducing the value of egalitarianism, and showing how this non-cognitive value shapes three alternative explanations of the Movius Line. It is argued that although these explanations are motivated by egalitarianism, they are nevertheless objective.

This paper presents the reactions to Descartes' account of the heartbeat expressed by the Leuven professors Fortunatus Plempius and Libertus Fromondus, reactions that also involved the Utrecht professor Henricus Regius. I show that the letters exchanged between Descartes and the two Leuven professors in 1637–1638 stirred a continuous debate, followed through a series of publications, up to the condemnations of Cartesianism in 1662–1663. I investigate the extent to which the reception of Descartes' account of the heartbeat contributed to the initial rejection of Cartesianism in Leuven and how physiological arguments were motivated by theological concerns throughout these exchanges.

We discuss Kochan's recent criticism of the work of Joseph Rouse (Kochan 2011). We argue that Kochan fails to show that both Rouse's own work and his Heidegger interpretation are plagued by insurmountable problems. We also try to locate the deeper, meta-philosophical reasons that are responsible for what we take to be Kochan's misreading of Rouse's work. This allows us to throw some light on the standoff that so often seems to characterize debates on scientific realism.

We analyze some of the main approaches in the literature to the method of ‘adequality’ with which Fermat approached the problems of the calculus, as well as its source in the παρισότης of Diophantus, and propose a novel reading thereof. Adequality is a crucial step in Fermat's method of finding maxima, minima, tangents, and solving other problems that a modern mathematician would solve using infinitesimal calculus. The method is presented in a series of short articles in Fermat's collected works (62, pp. 133–172). We show that at least some of the manifestations of adequality amount to variational techniques exploiting a small, or infinitesimal, variation e. Fermat's treatment of geometric and physical applications suggests that an aspect of approximation is inherent in adequality, as well as an aspect of smallness on the part of e. We question the relevance to understanding Fermat of 19th century dictionary definitions of παρισότης and adaequare, cited by Breger, and take issue with his interpretation of adequality, including his novel reading of Diophantus, and his hypothesis concerning alleged tampering with Fermat's texts by Carcavy. We argue that Fermat relied on Bachet's reading of Diophantus. Diophantus coined the term παρισότης for mathematical purposes and used it to refer to the way in which 1321/711 is approximately equal to 11/6. Bachet performed a semantic calque in passing from parisoo to adaequo. We note the similar role of, respectively, adequality and the Transcendental Law of Homogeneity in the work of, respectively, Fermat (1896) and Leibniz (1858) on the problem of maxima and minima.

The study of scientific models has become an active and important focus in history and philosophy of science, and to a lesser extent in sociology of science. Such attention acknowledges that models are central to scientific practice and that they are distinct from both theory and data, but there is a growing realization that modeling practices differ between and within disciplines. This special issue uses this realization to extend the discussion on models into new areas and different uses in the human and social sciences.