Socratic irony can be understood independently of the immortal heroics of Plato’s Socrates. We need a systematic account and criticism of it both as a debate-winning strategy of argumentation and teaching method. The Speaker introduces an issue pretending to be at a lower intellectual level than her co-debaters, or Participants. An Audience looks over and evaluates the results. How is it possible that the Speaker like Socrates is, consistently, in the winning position? The situation is ironic because the Participants fight (...) from a losing position but realize it too late. Socratic irony compares with divine irony: divine irony is a subtype of Socratic irony since you lose when you challenge gods. Socratic irony is also, prima facie, a subtype of dramatic irony when the Audience knows more than the Participants on the stage. We must distinguish between the ideal and realistic elements of Socratic Irony. The very idea of Socratic irony looks idealized, or it is an ideal case, which explains the Speaker’s consistently winning position. In real life, the debate must be rigged, or the Dutch Book argument applies to the Participants, if the Speaker is so successful. (shrink)

The notion of indivisibles and atoms arose in ancient Greece. The continuum—that is, the collection of points in a straight line segment, appeared to have paradoxical properties, arising from the ‘indivisibles’ that remain after a process of division has been carried out throughout the continuum. In the seventeenth century, Italian mathematicians were using new methods involving the notion of indivisibles, and the paradoxes of the continuum appeared in a new context. This cast doubt on the validity of the methods and (...) the reliability of mathematical knowledge which had been regarded as established by the axiomatic method in geometry expounded by Aristotle’s younger contemporary Euclid. The teaching of indivisibles was banned within the Society of Jesus, the Jesuits. In England, indivisibles were used by the mathematician John Wallis, and there was an acrimonious and extended feud between Wallis and the philosopher Thomas Hobbes over legitimate methods of argument in mathematics. Notions of the infinitesimal were used by Isaac Newton and Gottfried Leibniz, and were attacked by Bishop Berkeley for the vagueness of the concept and the illegitimate reasoning applied to it. This article discusses aspects of these events with reference to the book Infinitesimal by Amir Alexander and to other sources. Also discussed are wider issues arising from Alexander’s book including: the changes in cultural sensibility associated with the growth of new mathematical and scientific knowledge in the seventeenth century, the changes in language concomitant with these changes, what constitutes valid methods of enquiry in various contexts, and the question of authoritarianism in knowledge. More general aims of this article are to widen the immediate mathematical and historical contexts in Alexander’s book, to bridge a gap in conversations between mathematics and the humanities, and to relate mathematical ideas to wider human and contemporary issues. (shrink)

This paper aims both to tackle the technical issue of deciphering Hobbes’s derivation of the sine law of refraction and to throw some light to the broader issue of Hobbes’s mechanical philosophy. I start by recapitulating the polemics between Hobbes and Descartes concerning Descartes’ optics. I argue that, first, Hobbes’s criticisms do expose certain shortcomings of Descartes’ optics which presupposes a twofold distinction between real motion and inclination to motion, and between motion itself and determination of motion; second, Hobbes’s optical (...) theory presented in Tractatus Opticus I constitutes a more economical alternative, which eliminates the twofold distinction and only admits actual local motion, and Hobbes’s derivation of the sine law presented therein, which I call “the early model” and which was retained in Tractatus Opticus II and First Draught, is mathematically consistent and physically meaningful. These two points give Hobbes’s early optics some theoretical advantage over that of Descartes. However, an issue that has baffled commentators is that, in De Corpore Hobbes’s derivation of the sine law seems to be completely different from that presented in his earlier works, furthermore, it does not make any intuitive sense. I argue that the derivation of the sine law in De Corpore does make sense mathematically if we read it as a simplification of the early model, and Hobbes has already hinted toward it in the last proposition of Tractatus Opticus I. But now the question becomes, why does Hobbes take himself to be entitled to present this simplified, seemingly question-begging form without having presented all the previous results? My conjecture is that the switch from the early model to the late model is symptomatic of Hobbes’s changing views on the relation between physics and mathematics. (shrink)

This paper examines Hobbes’s criticisms of Robert Boyle’s air-pump experiments in light of Hobbes’s account in _De Corpore_ and _De Homine_ of the relationship of natural philosophy to geometry. I argue that Hobbes’s criticisms rely upon his understanding of what counts as “true physics.” Instead of seeing Hobbes as defending natural philosophy as “a causal enterprise … [that] as such, secured total and irrevocable assent,” 1 I argue that, in his disagreement with Boyle, Hobbes relied upon his understanding of natural (...) philosophy as a mixed mathematical science. In a mixed mathematical science one can mix facts from experience with causal principles borrowed from geometry. Hobbes’s harsh criticisms of Boyle’s philosophy, especially in the _Dialogus Physicus, sive De natura aeris_, should thus be understood as Hobbes advancing his view of the proper relationship of natural philosophy to geometry in terms of mixing principles from geometry with facts from experience. Understood in this light, Hobbes need not be taken to reject or diminish the importance of experiment/experience; nor should Hobbes’s criticisms in _Dialogus Physicus_ be understood as rejecting experimenting as ignoble and not befitting a philosopher. Instead, Hobbes’s viewpoint is that experiment/experience must be understood within its proper place – it establishes the ‘that’ for a mixed mathematical science explanation. (shrink)

This dissertation discusses the work of Thomas Hobbes, and has two main themes. The first is Hobbes's materialism, and the second is Hobbes's relationships to other philosophers, in particular his place in the mechanist movement that is said to have replaced Aristotelianism as the dominant philosophy in the seventeenth century. -/- I argue that Hobbes does not, for most of his career, believe the general materialist view that bodies are the only substances. He believes, rather, that ideas, which are our (...) main mechanism for thinking about the world, allow us to understand many bodies, but not to understand every thing we recognize to exist. The incomprehensible things include God---and, early in Hobbes's career, the human mind. Discussing materialism and our knowledge of God leads me to engage with the debate over Hobbes's alleged atheism. I argue that the evidence for Hobbes's atheism is weak at best. Hobbes is a sincere theist, though his view is sometimes unusual. -/- My discussion of Hobbes's relationships to other philosophers has three parts. In chapter five I argue that Hobbes's views about method are in important ways similar to Zabarella's. In chapter six I look at Hobbes's rejection of the view, held by some scholastic Aristotelians, that accidents can sometimes exist without inhering in substances. Thus we see two sides of Hobbes's interaction with the Aristotelian tradition. Sometimes that interaction is just rejection, but at other times Hobbes takes over views from that tradition. Then in chapter seven I consider whether, and in what sense, Hobbes is a mechanist. I argue that the narrative of mechanism and Aristotelianism is a less powerful explanation than it has seemed to some to be, because it is hard to see what mechanists have in common. (shrink)

Thomas Hobbes was, rather famously, a nominalist. The core of that nominalism is the belief that the only universal things are universal names: there are no universal objects, or universal ideas. This paper looks at what Hobbes's views about universal names were, how they evolved over time, and how Hobbes argued for them. The remainder of the paper considers two objections to Hobbes's view: a criticism made by several of Hobbes's contemporaries, that Hobbes's view could not account for people saying (...) the same thing in different languages; and a more recently popular criticism of Hobbes, that his nominalism's reliance on similarity implicitly (and inconsistently) involves reliance on a universal. (shrink)

Thomas Hobbes (1588-1679), whose current reputation rests largely on his political philosophy, was a thinker with wide ranging interests. In philosophy, he defended a range of materialist, nominalist, and empiricist views against Cartesian and Aristotelian alternatives. In physics, his work was influential on Leibniz, and lead him into disputes with Boyle and the experimentalists of the early Royal Society. In history, he translated Thucydides's History of the Peloponnesian War into English, and later wrote his own history of the Long Parliament. (...) In mathematics he was less successful, and is best remembered for his repeated unsuccessful attempts to square the circle. But despite that, Hobbes was a serious and prominent participant in the intellectual life of his time. (shrink)

Within the paradigm of political liberalism, Hobbes’s legal philosophy has the peculiarity that individual property rights are treated as conditional and derived from the State’s absolute property rights, and thus common, State and individual property are explicitly recognised as three different juridical realities. Through determining the place that Hobbes’s few references to common property hold within his legal philosophy, it is possible to turn the thought of this classic author into a very useful theoretical tool for thinking the possibilities and (...) limits of a political strategy betting for common property against State property. (shrink)

Newton characterizes the reasoning of Principia Mathematica as geometrical. He emulates classical geometry by displaying, in diagrams, the objects of his reasoning and comparisons between them. Examination of Newton’s unpublished texts shows that Newton conceives geometry as the science of measurement. On this view, all measurement ultimately involves the literal juxtaposition—the putting-together in space—of the item to be measured with a measure, whose dimensions serve as the standard of reference, so that all quantity is ultimately related to spatial extension. I (...) use this conception of Newton’s project to explain the organization and proofs of the first theorems of mechanics to appear in the Principia. The placementof Kepler’s rule of areas as the first proposition, and the manner in which Newton proves it, appear natural on the supposition that Newton seeks a measure, in the sense of a moveable spatial quantity, of time. I argue that Newton proceeds in this way so that his reasoning can have the ostensive certainty of geometry. (shrink)

The late 19th-century Ignorabimus controversy over the limits of scientific knowledge has often been characterized as proclaiming the end of intellectual progress, and by implication, as plunging Germany into a crisis of pessimism from which Liberalism never recovered. My research supports the opposite interpretation. The initiator of the Ignorabimus controversy, Emil du Bois-Reymond, was a physiologist who worked his whole life against the forces of obscurantism, whether they came from the Catholic and Conservative Right or the scientistic and millenarian Left. (...) Du Bois-Reymond’s doubt that scientists would ever elucidate consciousness must therefore be seen as an endorsement, and not a rejection, of his faith in reason. (shrink)