This volume contains thirteen papers that were presented at the 2017 Annual Meeting of the Canadian Society for History and Philosophy of Mathematics/Société canadienne d’histoire et de philosophie des mathématiques, which was held at Ryerson University in Toronto. It showcases rigorously reviewed modern scholarship on an interesting variety of topics in the history and philosophy of mathematics from Ancient Greece to the twentieth century. A series of chapters all set in the eighteenth century consider topics such as John Marsh’s techniques (...) for the computation of decimal fractions, Euler’s efforts to compute the surface area of scalene cones, a little-known work by John Playfair on the practical aspects of mathematics, and Monge’s use of descriptive geometry. After a brief stop in the nineteenth century to consider the culture of research mathematics in 1860s Prussia, the book moves into the twentieth century with an examination of the historical context within which the Axiom of Choice was developed and a paper discussing Anatoly Vlasov’s adaptation of the Boltzmann equation to ionized gases. The remaining chapters deal with the philosophy of twentieth-century mathematics through topics such as an historically informed discussion of finitism and its limits; a reexamination of Mary Leng’s defenses of mathematical fictionalism through an alternative, anti-realist approach to mathematics; and a look at the reasons that mathematicians select specific problems to pursue. Written by leading scholars in the field, these papers are accessible to not only mathematicians and students of the history and philosophy of mathematics, but also anyone with a general interest in mathematics. (shrink)

Efforts to develop democratic schools have moved along particular rules and standards of ‘reasoning’ even when expressed through different ideological and paradigmatic lines. From attempts to make a democratic education to critical pedagogy, different approaches overlap in their historical construction of the reason of schooling: designing society by designing the child. These approaches to democracy make inequality into the premise of equality, assuming a consensual partition of the world and the need for specific agents to monitor partitioned boundaries, thus reinserting (...) differences as the basis of practice. Democracy, however, according to Jacques Rancière, only becomes visible when its partitioning is challenged under the opinion of equality. Yet, undoing the epistemological dogma of planning embodied in the notions of ‘critical’ and deliberative democracy might also involve confronting the comparative style of thought which provides the epistemological ‘rules’ that insert inequality as equality. Deleuze and Guattari's rhizome and Derrida's justice help extend Rancière's democracy and equality into unfamiliar terrain. What implications might this have for thinking about educational policy and curriculum? The argument, ironically, maintains Enlightenment attitudes about reason and rationality, but while ‘trying’ different epistemological rules and recognizing how the epistemological and ontological fold into one another it provides an alternative understanding of education and democracy. (shrink)

This Handbook is a combination of authoritative exposition, comprehensive survey, and fundamental research exploring the underlying unifying themes in the various areas. The intended audience is graduate students and researchers in the areas of computing and logic, as well as other people interested in the subject. We assume as background some mathematical sophistication. Much of the material will also be of interest to logicians and mathematicians.

This paper examines some of the metaphysical assumptions behind Aquinas’s denials that a human rational soul unites with matter at conception and that a human rational soul is capable of developing and arranging the organic parts of an embryo. The paper argues that Buridan does not share these assumptions and holds that a soul is capable of developing and arranging organic parts. It argues that, given hylomorphism about the nature of organisms, including human beings, Buridan’s view is philosophically superior to (...) Aquinas’s in several respects. Finally, the paper poses an apparent inconsistency between several of Buridan’s texts on this topic and attempts to show that the inconsistency is merely apparent. (shrink)

This note uses an analysis of Broussais's objection to medical ontology to suggest why Broussais's neologism o o is derived not from o but from a conflation of o and the plural of o o. For Broussais medical ontology, in contrast to philosophical ontology, always refers to abstract entities alleged to explain sensible symptoms, o o, in the sense of indivisible particles in the writings of Lucretius and Epicurus, are such particles; o are not. Keywords: Broussais, disease, medical ontology CiteULike (...) Connotea Del.icio.us What's this? (shrink)

In his new work on the Kyoto School David Williams presents the first “reading” in English of the complete text of the three Chūō Kōron symposia held by members of the second generation in the early 1940s. In addition, he provides an extensive commentary that explores the inability of “liberal history” to account for the political realities of wartime Japan and the “moral worldview” of the four symposists. Adopting the empirical methodology of earlier works, Williams proposes an alternative thesis of (...) “Confucian Revolution” that takes into account the “logic and conventions” of Japan as a Confucian society. His focus on the influence of Confucianism brings to the fore a neglected aspect of modern Japanese political philosophy that yields important insight into the nature of the Kyoto School's wartime thought and their struggle against the Tōjō regime. (shrink)

This study considers three aspects of “The Christian Mysteries,” one of Newman’s early Anglican sermons: 1) the use of Scripture in the exposition of the Mysteries of Faith; 2) the definition of Mystery; and 3) the moral effect of Mystery.