Online research in philosophy

I aim to clarify the argument for space that Newton presents in De Gravitatione (composed prior to 1687) by putting Newton's remarks into conversation with the account of geometrical knowledge found in Proclus's Commentary on the First Book of Euclid's Elements (ca. 450). What I highlight is that both Newton and Proclus adopt an epistemic progression (or “order of knowing”) according to which geometrical knowledge necessarily precedes our knowledge of metaphysical truths concerning the ontological state of affairs. As I argue, (...) Newton's commitment to this order of knowing clarifies the interplay of the imagination and understanding in geometrical inquiry and illuminates how geometrical knowledge of space can lead to knowledge that space depends on and is related to God. In general, appreciating the Proclean elements of Newton's argument brings added light to the significance of geometrical inquiry for his general natural philosophical program and grants us insight into the philosophical grounding for the notion of absolute space that is presented in the Principia mathematica (1687). (shrink)

My goal in this paper is to develop our understanding of the role the imagination plays in Kant’s Critical account of geometry, and I do so by attending to how the imagination factors into the method of reasoning Kant assigns the geometer in the First Critique. Such an approach is not unto itself novel. Recent commentators, such as Friedman (1992) and Young (1992), have taken a careful look at the constructions of the productive imagination in pure intuition and highlighted the (...) importance of the imagination’s activity for securing the universality of geometry knowledge. Specifically, as their respective examinations bring to light, it is only with due attention to the imagination that we can make sense of how a .. (shrink)

Commentators attempting to understand the empirical method that Isaac Newton applies in his Mathematical Principles of Natural Philosophy (1687) are forced to grapple with the thorny issue of how to reconcile Newton's rejection of hypotheses with his appeal to absolute space. On the one hand, Newton claims that his experimental philosophy does not rely on claims that are assumed without empirical evidence, and on the other hand, Newton appeals to an absolute space that, by his own characterization, does not make (...) any impressions on our senses. Howard Stein (1967, 2002) has offered an insightful strategy for reconciling this apparent contradiction and suggested a way to enhance our understanding of Newton's 'empiricism' such that absolute space can be preserved as a legitimate part of Newton's experimental project. Recently, Andrew Janiak (2008) has posed a worthy challenge to Stein's empirical reading of Newton and directed our attention to the metaphysical commitments that underlie the experimental philosophy of Newton's Principia . Although Stein and Janiak disagree on the degree to which Newton's empiricism influences his natural philosophy, both agree and clearly show that an adequate treatment of Newton's empiricism cannot be divorced from consideration of Newton's views on God and God's relationship to nature. (shrink)

Building on the work of Henk Bos and John Schuster, I will examine how the story of Descartes-the-philosopher and Descartes-the-mathematician proceeds in the years immediately following 1628. Specifically, I will focus on the 1633 Le Monde and the 1637 Geometry and hope to show that Descartes is still trying in this period to integrate his distinctively Cartesian version of math with his distinctively Cartesian version of philosophy. Being even more specific, I will look at the creation story presented in Le (...) Monde in conjunction with Descartes’ solution to the Pappus problem, which was published in the Geometry. On the reading I’ll offer, we find both a mathematical influence on the early metaphysics in Le Monde as well as (and this is the heart of my account) a metaphysical grounding for one very important part of the mathematical program that Descartes presents in the Geometry. (shrink)

In the preface to the Principia (1687) Newton famously states that “geometry is founded on mechanical practice.” Several commentators have taken this and similar remarks as an indication that Newton was firmly situated in the constructivist tradition of geometry that was prevalent in the seventeenth century. By drawing on a selection of Newton's unpublished texts, I hope to show the faults of such an interpretation. In these texts, Newton not only rejects the constructivism that took its birth in Descartes's Géométrie (...) (1637); he also presents the science of geometry as being more powerful than his Principia remarks may lead us to believe. (shrink)