The intelligibility of motion and construction: Descartes’ early mathematics and metaphysics, 1619-1637

I argue for an interpretation of the connection between Descartes’ early mathematics and metaphysics that centers on the standard of geometrical intelligibility that characterizes Descartes’ mathematical work during the period 1619 to 1637. This approach remains sensitive to the innovations of Descartes’ system of geometry and, I claim, sheds important light on the relationship between his landmark Geometry (1637) and his first metaphysics of nature, which is presented in Le monde (1633). In particular, I argue that the same standard of clear and distinct motions for construction that allows Descartes to distinguish ‘geometric’ from ‘imaginary’ curves in the domain of mathematics is adopted in Le monde as Descartes details God’s construction of nature. I also show how, on this interpretation, the metaphysics of Le monde can fruitfully be brought to bear on Descartes’ attempted solution to the Pappus problem, which he presents in Book I of the Geometry. My general goal is to show that attention to the standard of intelligibility Descartes invokes in these different areas of inquiry grants us a richer view of the connection between his early mathematics and philosophy than an approach that assumes a common method is what binds his work in these domains together.     

‘One common matter’ in Descartes' physics: the Cartesian concepts of matter quantities,weight and gravity

ABSTRACT

It is common to assume that Descartes did not have a conception of an object's matter density independently of its size, but this is a rather incomplete assessment of the early modern natural philosopher's theory. Key to our understanding of Descartes's physics is a consideration of the ratios between the quantities of the different types of matter in which an object consists. As these ratios determine the degree of an object's porosity and elasticity, they also affect in Descartes's theory the phenomena of gravity and weight.     

Carl du Prel (1839–1899): explorer of dreams, the soul, and the cosmos

Nineteenth-century spiritism was a blend of religious elements, the philosophy of mind, science and popular science and contacts with extraterrestrials were a commonplace phenomenon during spiritistic séances. Using the example of Carl du Prel (1839–1899) I show how his comprehensive mystic philosophy originated in a theory of extraterrestrial life. Carl du Prel used a Darwinian and monistic framework, theories of the unconscious and a Neo-Kantian epistemology to formulate a philosophy of astronomy and extraterrestrial life. He claimed that the mechanism of Darwinian selection is responsible for the distribution of stars and the orbits of the planets. In his speculations on the nature of extraterrestrial life he used the concept of organ projection to argue that technical solutions on earth will be realized organically on other planets and claimed that superior extraterrestrials have quantitatively and qualitatively different senses and thus different forms of intuition. A comparison with Camille Flammarion, spiritist and populariser of astronomy, demonstrates the contextual complexities of spiritism. In contrast to du Prel’s sober Neo-Kantian philosophical speculations, Flammarion was a late proponent of a French esoteric tradition that was rooted in romantic socialism, painted grand cosmological vistas and emphasized reincarnation. I put forward the hypothesis that current discourses on extraterrestrial life are affected by the spiritist tradition mainly through the ‘Golden Age’ science fiction literature of the 1940s and 50s and its successors. However, neither Carl du Prel nor Camille Flammarion contributed significantly to this tradition, which is mainly shaped by the psychical research of J. B. Rhine.     

Sources of error in forecasts and expectations: U.K. economic models, 1984–8

This paper presents a comparative analysis of the sources of error in forecasts for the UK economy published over a recent four-year period by four independent groups. This analysis rests on the archiving at the ESRC Macroeconomic Modelling Bureau of the original forecasts together with all their accompanying assumptions and adjustments. A method of decomposing observed forecast errors so as to distinguish the contributions of forecaster and model is set out; the impact of future expectations treated in a ‘model-consistent’ or ‘rational’ manner is specifically considered. The results show that the forecaster's adjustments make a substantial contribution to forecast performance, a good part of which comes from adjustments that bring the model on track at the start of the forecast period. The published ex-ante forecasts are usually superior to pure model-based ex-post forecasts, whose performance indicates some misspecification of the underlying models.     

Francesco Patrizi’s two books on space: geometry, mathematics, and dialectic beyond Aristotelian science

Francesco Patrizi was a competent Greek scholar, a mathematician, and a Neoplatonic thinker, well known for his sharp critique of Aristotle and the Aristotelian tradition. In this article I shall present, in the first part, the importance of the concept of a three-dimensional space which is regarded as a body, as opposed to the Aristotelian two-dimensional space or interval, in Patrizi’s discussion of physical space. This point, I shall argue, is an essential part of Patrizi’s overall critique of Aristotelian science, in which Epicurean, Stoic, and mainly Neoplatonic elements were brought together, in what seems like an original theory of space and a radical revision of Aristotelian physics. Moreover, I shall try to show Patrizi’s dialectical method of definition, his geometrical argumentation, and trace some of the ideas and terms used by him back to Proclus’ Commentary on Euclid. This text of Proclus, as will be shown in the second part of the article, was also important for Patrizi’s discussion of mathematical space, where Patrizi deals with the status of mathematics and redefines some mathematical concepts such as the point and the line according to his new theory of space.