Francesco Patrizi da Cherso's concept of space and its later influence

This study considers the contribution of Francesco Patrizi da Cherso (1529–1597) to the development of the concepts of void space and an infinite universe. Patrizi plays a greater role in the development of these concepts than any other single figure in the sixteenth century, and yet his work has been almost totally overlooked. I have outlined his views on space in terms of two major aspects of his philosophical attitude: on the one hand, he was a devoted Platonist and sought always to establish Platonism, albeit his own version of it, as the only currect philosophy; and on the other hand, he was more determinedly anti-Aristotelian than any other philosopher at that time. Patrizi's concept of space has its beginnings in Platonic notions, but is extended and refined in the light of a vigorous critique of Aristotle's position. Finally, I consider the influence of Patrizi's ideas in the seventeenth century, when various thinkers are seeking to overthrow the Aristotelian concept of place and the equivalence of dimensionality with corporeality. Pierre Gassendi (1592–1652), for example, needed a coherent concept of void space in which his atoms could move, while Henry More (1614–1687) sought to demonstrate the reality of incorporeal entities by reference to an incorporeal space. Both men could find the arguments they needed in Patrizi's comprehensive treatment of the subject.     

Jewish theologies of space in the scientific revolution: Henry More,Joseph Raphson,Isaac Newton and their predecessors

Theological speculations on God's relation to place and space were introduced into the Jewish tradition by the early rabbis, initially in response to the previous appearance of words like māqôm (place) in Biblical literature. In the Middle Ages, Jewish philosophers modified these rabbinical ideas in the context of Aristotelian, Neoplatonic, and anti-Aristotelian currents within Jewish thought. One development in medieval Jewish thought of special interest for the development of ideas of space was the rise of Cabala, which Christian thinkers of the Renaissance and early modern periods saw as a sacred and primeval deposit of wisdom akin to prisca theologia. Both Henry More and, under More's influence, Joseph Raphson made use of Cabalist ideas in developing their own theologies of space. Isaac Newton was aware of these Jewish ideas but for the most part repudiated them, while making some use of māqôm as an expression of God's omnipresence.     

Kant and Newton on the a priori necessity of geometry

In the Transcendental Aesthetic, Kant explicitly rejects Newton’s absolutist position that space is an actually existing thing; however, Kant also concedes that the absolutist successfully preserves the a priori necessity that characterizes our geometrical knowledge of space. My goal in this paper is to explore why the absolutist can explain the a priori necessity of geometry by turning to Newton’s De Gravitatione, an unpublished text in which Newton addresses the essential features associated with our representation of space and the relationship between our geometrical investigation of space and our knowledge of the form of space that is a part of the natural order. Attention to Newton’s account of space in De Gravitatione offers insight into the sense in which absolutist space is a priori and reveals why, in the Aesthetic, Kant could concede a priori geometrical knowledge to his absolutist opponent. What I highlight in particular is that, by Kant’s standards, Newton employs the very constructive method of mathematics that secures the a priori necessity of geometry, even though, as an absolutist, and as emphasized in the arguments of the Aesthetic, Newton fails to provide a metaphysics of space that explains the success of his mathematical method.     

Towards a science of the individual: the Aristotelian search for scientific knowledge of individual entities

This article seeks to take a step towards recognizing that science can deal with the concrete and individual as well as the universal. I shall concentrate on some of Aristotle’s texts, as there is a long tradition going back to Aristotle, according to which science deals only with the universal, although his work also contains texts of a very different tenor. He tries to improve the process of definition as an attempt to bring science closer to the concrete, but ends up realizing that there are some unreachable limits. There is, however, a second Aristotelian approach to the problem in Metaphysica M 10, a passage which takes scientific rapprochement to the individual further by introducing a distinction between science in potential and science in act. The former is universal, but the latter deals with individual substances and processes. Aristotle himself acknowledges here that in one sense science is universal and in another it is not, a position that raises important ontological and epistemological problems. Some suggestions are also offered concerning the kind of truth applicable to science in act, that is, practical truth.     

Radical mathematical Thomism: beings of reason and divine decrees in Torricelli’s philosophy of mathematics

Evangelista Torricelli (1608-1647) is perhaps best known for being the most gifted of Galileo’s pupils, and for his works based on indivisibles, especially his stunning cubature of an infinite hyperboloid. Scattered among Torricelli’s writings, we find numerous traces of the philosophy of mathematics underlying his mathematical practice. Though virtually neglected by historians and philosophers alike, these traces reveal that Torricelli’s mathematical practice was informed by an original philosophy of mathematics. The latter was dashed with strains of Thomistic metaphysics and theology. Torricelli’s philosophy of mathematics emphasized mathematical constructs as human-made beings of reason, yet mathematical truths as divine decrees, which upon being discovered by the mathematician ‘appropriate eternity’. In this paper, I reconstruct Torricelli’s philosophy of mathematics—which I label radical mathematical Thomism—placing it in the context of Thomistic patterns of thought.     

Newton on action at a distance and the cause of gravity

In this discussion paper, I seek to challenge Hylarie Kochiras’ recent claims on Newton’s attitude towards action at a distance, which will be presented in Section 1. In doing so, I shall include the positions of Andrew Janiak and John Henry in my discussion and present my own tackle on the matter (Section 2). Additionally, I seek to strengthen Kochiras’ argument that Newton sought to explain the cause of gravity in terms of secondary causation (Section 3). I also provide some specification on what Kochiras calls ‘Newton’s substance counting problem’ (Section 4). In conclusion, I suggest a historical correction (Section 5).     

‘Good Sense’ in context: A response to Kidd

In his response to my (2010), Ian Kidd claims that my argument against Stump’s interpretation of Duhem’s concept of ‘good sense’ is unsound because it ignores an important distinction within virtue epistemology. In light of the distinction between reliabilist and responsibilist virtue epistemology, Kidd argues that Duhem can be seen as supporting the latter, which he further illustrates with a discussion of Duhem’s argument against ‘perfect theory’. I argue that no substantive argument is offered to show that the distinction is relevant and can establish that Duhem’s ‘good sense’ can be understood within responsibilist virtue epistemology. I furthermore demonstrate that Kidd’s attempt to support his contention relies on a crucial misreading of Duhem’s general philosophy of science, and in doing so highlight the importance of understanding ‘good sense’ in its original context, that of theory choice.     

Cartesian analysis and synthesis

This paper aims to provide an explication of the meaning of ‘analysis’ and ‘synthesis’ in Descartes’ writings. In the first part I claim that Descartes’ method is entirely captured by the term ‘analysis’, and that it is a method of theory elaboration that fuses the modern methods of discovery and confirmation in one enterprise. I discuss Descartes’ methodological writings, assess their continuity and coherence, and I address the major shortcoming of previous interpretations of Cartesian methodology. I also discuss the Cartesian method in the context of other conceptions of scientific method of that era and argue that Descartes’ method significantly transforms these conceptions. In the second part I argue that mathematical and natural-philosophical writings exhibit this kind of analysis. To that effect I examine in Descartes’ writings on the method as used in mathematics, and Descartes’ account of the discovery of the nature of the rainbow in the Meteors. Finally, I briefly assess Descartes’ claim regarding the universality of his method.     

Reflections on Kant’s concept (and intuition) of space

In this paper, I investigate an important aspect of Kant’s theory of pure sensible intuition. I argue that, according to Kant, a pure concept of space warrants and constrains intuitions of finite regions of space. That is, an a priori conceptual representation of space provides a governing principle for all spatial construction, which is necessary for mathematical demonstration as Kant understood it.     

Intensions, belief and science: Kuhn’s early philosophical outlook (1940-1945)

Between 1940 and 1945, while still a student of theoretical physics and without any contact with the history of science, Thomas S. Kuhn developed a general outline of a theory of the role of belief in science. This theory was well rooted in the philosophical tradition of Emerson Hall, Harvard, and particularly in H. M. Sheffer’s and C. I. Lewis’s logico-philosophical works—Kuhn was, actually, a graduate student of the former in 1945. In this paper I reconstruct the development of that general outline after Kuhn’s first years at Harvard. I examine his works on moral and aesthetic issues—where he displayed an already ‘anti-Whig’ stance concerning historiography—as well as his first ‘Humean’ approach to science and realism, where his earliest concern with belief is evident. Then I scrutinise his graduate work to show how his first account of the role of belief was developed. The main aim of this paper is to show that the history of science illustrated for Kuhn the epistemic role and effects of belief he had already been theorising about since around 1941.     

The Passions of the soul and Descartes’s machine psychology

Descartes developed an elaborate theory of animal physiology that he used to explain functionally organized, situationally adapted behavior in both human and nonhuman animals. Although he restricted true mentality to the human soul, I argue that he developed a purely mechanistic (or material) ‘psychology’ of sensory, motor, and low-level cognitive functions. In effect, he sought to mechanize the offices of the Aristotelian sensitive soul. He described the basic mechanisms in the Treatise on man, which he summarized in the Discourse. However, the Passions of the soul contains his most ambitious claims for purely material brain processes. These claims arise in abstract discussions of the functions of the passions and in illustrations of those functions. Accordingly, after providing an intellectual context for Descartes’s theory of the passions, especially by comparison with that of Thomas Aquinas, I examine its ‘machine psychology’, including the role of habituation and association. I contend that Descartes put forth what may reasonably be called a ‘psychology’ of the unensouled animal body and, correspondingly, of the human body when the soul does not intervene. He thus conceptually distinguished a mechanistically explicable sensory and motor psychology, common to nonhuman and human animals, from true mentality involving higher cognition and volition and requiring (in his view) an immaterial mind.     

Charles de Bovelles's treatise on the regular polyhedra (Paris, 1511)

The mathematical works of the French philosopher Charles de Bovelles (c. 1479–1566) have received little attention from historians of scientific thought. At the University of Paris, Bovelles studied under Jacques Lefèvre d'Étaples, sharing with him a high regard for the Christian Neoplatonic philosophy of Nicholas of Cusa. One aspect of Cusanus's philosophy (described in his major work, On Learned Ignorance) was particularly favoured by Lefèvre and Bovelles: the use of geometrical symbolism to provide mathematical guidance to the divine. While Lefèvre was preparing an edition of Cusanus's works (Paris, 1514), Bovelles wrote a treatise of his own, in which the geometry of the five polyhedra was used to provide an approach to the mystery of the Trinity. Seen in the context of Renaissance syncretism of Platonism and Christianity, Bovelles's treatise adds a theological layer of interpretation to the literal meaning of the polyhedral physics described by Plato in the Timaeus. In so doing, it contributes to the discussion of a problem that was later to concern several Renaissance philosophers and cosmologists, including, at the end of the century, Johannes Kepler.     

Science,self improvement and the first industrial revolution

This study considers Newton's views on space and time with respect to some important ontologies of substance in his period. Specifically, it deals in a philosophico-historical manner with his conception of substance, attribute, existence, to actuality and necessity. I show how Newton links these “features” of things to his conception of God's existence with respect of infinite space and time. Moreover, I argue that his ontology of space and time cannot be understood without fully appreciating how it relates to the nature of Divine existence. In order to establish this, the ontology embodied in Newton's theory of predication is analysed, and shown to be different from the presuppositions of the ontological argument. From the historical point of view Gassendi's influence is stressed, via the mediation of Walter Charleton. Furthermore, Newton's thought on these matters is contrasted with Descartes's and Spinoza's. In point of fact, in his earliest notebook Newton recorded observations on Descartes's version of the ontological argument. Soon, however, he was to oppose the Cartesian conception of the actuality of Divine existence by means of arguments similar to those of Gassendi. Lastly, I suggest that the nature and extent of Henry More's influence on Newton's conception of how God relates to absolute space and time bears further examination.     

Interpreting Aristotle on mixture: problems about elemental composition from Philoponus to Cooper

Aristotle’s On generation and corruption raises a vital question: how is mixture, or what we would now call chemical combination, possible? It also offers an outline of a solution to the problem and a set of criteria that a successful solution must meet. Understanding Aristotle’s solution and developing a viable peripatetic theory of chemical combination has been a source of controversy over the last two millennia. We describe seven criteria a peripatetic theory of mixture must satisfy: uniformity, recoverability, potentiality, equilibrium, alteration, incompleteness, and the ability to distinguish mixture from generation, corruption, juxtaposition, augmentation, and alteration. After surveying the theories of Philoponus (d. 574), Avicenna (d. 1037), Averroes (d. 1198), and John M. Cooper (fl. circa 2000), we argue for the merits of Richard Rufus of Cornwall’s theory. Rufus (fl. 1231-1256) was a little known scholastic philosopher who became a Franciscan theologian in 1238, after teaching Aristotelian natural philosophy as a secular master in Paris. Lecturing on Aristotle’s De generatione et corruptione, around the year 1235, he offered his students a solution to the problem of mixture that we believe satisfies Aristotle’s seven criteria.     

The Whewell-Mill debate on predictions,from Mill's point of view

John Stuart Mill, in his debate with William Whewell on the nature and logic of induction, is regarded as being the first to dismiss the supposed value of successful predictions as merely psychological. I shall argue that this view of the Whewell-Mill debate on predictions misconstrues Mill’s position and argument. From Mill’s point of view, the controversial point was not the question whether predictions ‘count more’ than ex-post explanations but the alleged assertion by Whewell that the successful predictions of the wave theory of light prove the existence of the ether. Mill argued that, on the one hand, the predictions of the wave theory of light do not and cannot provide evidence for the existence of the ether; as evidence for the laws of the theory, on the other hand, the predictions are superfluous, the laws being already well-confirmed. Mill actually endorsed a requirement of independent support closely resembling Whewell’s requirements for hypotheses; the controversy on the value of predictions is a product of the 20th century.     

Poincaréan intuition revisited: what can we learn from Kant and Parsons?

This paper provides a comprehensive critique of Poincaré’s usage of the term intuition in his defence of the foundations of pure mathematics and science. Kant’s notions of sensibility and a priori form and Parsons’s theory of quasi-concrete objects are used to impute rigour into Poincaré’s interpretation of intuition. In turn, Poincaré’s portrayal of sensible intuition as a special kind of intuition that tolerates the senses and imagination is rejected. In its place, a more harmonized account of how we perceive concrete objects is offered whereby intuitive knowledge is consistently a priori whatever the domain of application.     

Quantitative realizations of philosophy of science: William Whewell and statistical methods

In this paper, I examine William Whewell’s (1794–1866) ‘Discoverer’s Induction’, and argue that it supplies a strikingly accurate characterization of the logic behind many statistical methods, exploratory data analysis (EDA) in particular. Such methods are additionally well-suited as a point of evaluation of Whewell’s philosophy since the central techniques of EDA were not invented until after Whewell’s death, and so couldn’t have influenced his views. The fact that the quantitative details of some very general methods designed to suggest hypotheses would so closely resemble Whewell’s views of how theories are formed is, I suggest, a strongly positive comment on his views.     

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.