I offer an alternative account of the relationship of Hobbesian geometry to natural philosophy by arguing that mixed mathematics provided Hobbes with a model for thinking about it. In mixed mathematics, one may borrow causal principles from one science and use them in another science without there being a deductive relationship between those two sciences. Natural philosophy for Hobbes is mixed because an explanation may combine observations from experience (the ‘that’) with causal principles from geometry (the ‘why’). My argument shows (...) that Hobbesian natural philosophy relies upon suppositions that bodies plausibly behave according to these borrowed causal principles from geometry, acknowledging that bodies in the world may not actually behave this way. First, I consider Hobbes's relation to Aristotelian mixed mathematics and to Isaac Barrow's broadening of mixed mathematics in Mathematical Lectures (1683). I show that for Hobbes maker's knowledge from geometry provides the ‘why’ in mixed-mathematical explanations. Next, I examine two explanations from De corpore Part IV: (1) the explanation of sense in De corpore 25.1-2; and (2) the explanation of the swelling of parts of the body when they become warm in De corpore 27.3. In both explanations, I show Hobbes borrowing and citing geometrical principles and mixing these principles with appeals to experience. (shrink)

Many critics, Descartes himself included, have seen Hobbes as uncharitable or even incoherent in his Objections to the Meditations on First Philosophy. I argue that when understood within the wider context of his views of the late 1630s and early 1640s, Hobbes's Objections are coherent and reflect his goal of providing an epistemology consistent with a mechanical philosophy. I demonstrate the importance of this epistemology for understanding his Fourth Objection concerning the nature of the wax and contend that Hobbes's brief (...) claims in that Objection are best understood as a summary of the mechanism for scientific knowledge found in his broader work. Far from displaying his confusion, Hobbes's Fourth Objection in fact pinpoints a key weakness of Descartes's faculty psychology: its unintelligibility within a mechanical philosophy. (shrink)

Reason and Ethics in Hobbes's Leviathan JOHN DEIGH HOBBES'S ETHICS teaches the ways of self-preservation. Its lessons are arranged in a system of rules that Hobbes understood to be the laws of nature. These two themes, self-preservation and natural law, have inspired opposing inter- pretations of Hobbes's text. The historically dominant and still prevailing interpretation, which develops the former theme, is that Hobbes's ethics is a form of egoism. A later and less popular interpretation, which develops the latter theme, is (...) that his ethics is a system of absolutes, "a strict deontology. ''1 These two interpretations represent a dispute between what I will call ortho- doxy and dissent in Hobbes scholarship. The dispute chiefly turns on two questions: What is the basis of Hobbes's ethics? and How stringent are the rules it comprises?' Orthodoxy takes Hobbes's ethics to be based on his moral psychology, specifically, his theory of motivation. That theory, on the orthodox reading, is thoroughly egocentric. It holds that all voluntary action springs from self- interest.3 Hence, on this reading, one can attribute to Hobbes the view that a I am grateful to Ed Curley, Bernard Gert, Richard Kraut, Connie Rosati, and Ira Singer for their helpful comments on an earlier draft of this essay. ' A. E. Taylor, "The Ethical Doctrine of Hobbes," Philosophy a 3 : 406-24, esp. 408. ' One can find the orthodox interpretation in Henry Sidgwick's Outline of the History.. (shrink)

This chapter argues that the standard conception of Spinoza as a fellow-travelling mechanical philosopher and proto-scientific naturalist is misleading. It argues, first, that Spinoza’s account of the proper method for the study of nature presented in the Theological-Political Treatise (TTP) points away from the one commonly associated with the mechanical philosophy. Moreover, throughout his works Spinoza’s views on the very possibility of knowledge of nature are decidedly sceptical (as specified below). Third, in the seventeenth-century debates over proper methods in the (...) sciences, Spinoza sided with those that criticized the aspirations of those (the physico-mathematicians, Galileo, Huygens, Wallis, Wren, etc) who thought the application of mathematics to nature was the way to make progress. In particular, he offers grounds for doubting their confidence in the significance of measurement as well as their piece-meal methodology (see section 2). Along the way, this chapter offers a new interpretation of common notions in the context of treating Spinoza’s account of motion (see section 3). (shrink)

The sense in which Hobbes produced a science of politics is often misunderstood. It was not a science because it was derived somehow from scientific psychology or mechanics. It was not a science in the sense that he broke down states into their component systems and their properties. Instead, it is a normative doctrine. It states precepts for citizens to escape the condition of total war, and it states precepts for sovereigns to legislate well (frame "good laws" in the sense (...) of Leviathan, ch. 30.) The normativity of Hobbes's science is often missed. It contributes to what I call the "autonomy" of Hobbes politics within his system. (shrink)

This paper argues that Spinoza does not take extension in space to be a fundamental property of physical things. This means that when Spinoza calls either substance or a mode “an Extended thing”, he does not mean that it is a thing extended in three dimensions. The argument proceeds by showing, first, that Spinoza does not associate extension in space with substance, and second, that finite bodies, or physical things, are not understood through the intellect when they are conceived as (...) extended in space. I conclude by articulating some suggestions about where we should go from here in trying to understand Spinoza’s account of the attribute of extension and of the physical world. (shrink)

He has an astonishing range, and in this book he expands it still further. More than a mere introduction, Made with Words offers a coherent and well-argued picture of most of the main components of Hobbes's wide-ranging philosophy.

: Marin Mersenne was central to the new mathematical approach to nature in Paris in the 1630s and 1640s. Intellectually, he was one of the most enthusiastic practitioners of that program, and published a number of influential books in those important decades. But Mersenne started his career in a rather different way. In the early 1620s, Mersenne was known in Paris primarily as a writer on religious topics, and a staunch defender of Aristotle against attacks by those who would replace (...) him by a new philosophy. In this essay, I would like to examine Mersenne's changing attitude toward Galileo. In the early 1620s, Mersenne lists Galileo among the innovators in natural philosophy whose views should be rejected. However, by the early 1630s, less than a decade later, Mersenne has become one of Galileo's most ardent supporters. How, then, did Mersenne learn to love Galileo? (shrink)

early modern philosophers commonly appeal to a mathematical method to demonstrate their philosophical claims. Since such claims are not always followed by what we would recognize as mathematical proofs, they are often dismissed as mere rhetoric. René Descartes, Thomas Hobbes, and Benedict de Spinoza are perhaps the most well-known early modern philosophers who fall into this category. It is a matter of dispute whether the ordo geometricus amounts to more than a method of presentation in Spinoza’s philosophy. Descartes and Hobbes (...) clearly appeal to a method of discovery modeled after geometry, but neither employs it to develop a heavily quantitative physics. Whereas Descartes’s version of the geometrical method .. (shrink)

Applies a philosophical analysis of the natural sciences to the social sciences.

Hobbes' philosophy of geometry was eccentric to contemporary movements and worsted in specific controversy. But he laid down stipulations defining geometry and its method which might provide a significant and workable alternative "meta-geometry". Some of these are isolated and reinterpreted here, especially those concerned with describing magnitudes, motions and quantities, and with his use of proportions. Rather than refutation of commentaries and historical rehash, the effort here is to isolate definitive texts and to offer a reinterpretation of their arguments in (...) succinct form showing their coherence and their interdependence with his other philosophic principles. (shrink)

Descartes was disappointed with most of the Objections collected to accompany the Meditations in 1641, but he took a particularly dim view of the Third Set. ‘I am surprised that I have found not one valid argument in these objections,’ he wrote, close to the end of a series of curt and dismissive replies. The author of the objections was Thomas Hobbes. There was one other unfriendly exchange between Descartes and Hobbes in 1641. Descartes received through Mersenne some letters criticizing (...) theses in the Dioptrics, one of the Essays published with the Discourse on Method in 1637. Mersenne did not name Hobbes as the writer of the letters, attributing them to an unspecified Englishman, and it seems that Descartes never connected the critic of his optics with the author of the objections to his metaphysics. Nevertheless, Descartes responded with some hostility to the letters, angrily rebutting some points about refraction and charging that others had been appropriated from his own writings. Insinuating that the English correspondent was dishonest, Descartes decided to have no more to do with him. A meeting between the two men did take place in 1648 at a dinner given by the Marquis of Newcastle, but even on this occasion they did not see eye to eye, getting into an argument about the nature of hardness. (shrink)

The relations between different areas of knowledge have been a subject of interest to philosophers as well as to scientists and mathematicians from antiquity. While recent work in this direction has been largely concerned with the question whether one branch of knowledge can be reduced to another , the questions which exercised the Greek philosophers on these matters have a different starting point. Taking for granted that there are a number of distinct areas of knowledge, they proceeded to consider a (...) variety of relations which they observed to hold among the sciences as they knew them; the question of the priority of one science to another is a recurrent theme. In fact, three sorts of orderings were noticed, and the associated conceptions of priority are interesting. Only one of them is the concern of the present paper, though, and I shall briefly describe the remaining two only for purposes of contrast. (shrink)

Analyses the sense in which Hobbes conceived of his political theory as enjoying the status of a ‘science’. It examines the two different concepts of scientific knowledge developed by Hobbes at different times and in different connections, and describes how Hobbes became convinced—mistakenly—that he had found a way of combining the two.

The sixteenth-century philosopher Jacopo Zabarella stands near the end of the long Aristotelian dominance of western academic philosophy. Yet, despite the fact that Aristotelianism was soon to be overwhelmed by other currents of thought, Zabarella’s influence on western thought would continue into at least the nineteenth century, and he still provides useful discussions relevant to today’s Aristotle scholars. In what follows, I discuss the existence and essence of matter, and show how Zabarella argues for his claims. What is especially notable (...) about the existence and essence of matter as a topic is that matter is clearly at the center of his well-known interest concerning the nature of scientific methodology. (shrink)

Presents an interpretation of the famous engraved title page of Hobbes's Leviathan, in which the ‘person’ of the state is depicted as a colossal figure composed of smaller individual figures. It argues that the origins of this design can be found in an optical device developed by the French scientist Jean François Niceron, which used a specially cut lens to create a single composite figure out of separate smaller figures; and it explores the significance of this for Hobbes's theory of (...) ‘representation’. (shrink)

This volume contains more than twenty essays in the history of modern philosophy and history of religion by R.H. Popkin.