17th/18th Century Logic

In this chapter, I consider the largely overlooked influence of E. W. von Tschirnhaus' treatise on method, the Medicina mentis, on Wolff's early philosophical project (in both its conception and execution). As I argue, part of Tschirnhaus' importance for Wolff lies in the use he makes of principles gained from experience as a foundation for the scientific enterprise in the context of his broader philosophical rationalism. I will show that this lesson from Tschirnhaus runs through Wolff's earliest philosophical discussions, and (...) indeed continues to inform his major texts in logic and mathematics just before the publication of the German Metaphysics. In the end, my discussion has the effect of revealing Tschirnhaus to be an exceptionally important influence on Wolff's development, perhaps even as important (or so I suggest) as Leibniz. (shrink)

In the chapter of the Critique of Pure Reason entitled ‘The Discipline of Pure Reason in Dogmatic Use’, Kant contrasts mathematical and philosophical knowledge in order to show that pure reason does not (and, indeed, cannot) pursue philosophical truth according to the same method that it uses to pursue and attain the apodictically certain truths of mathematics. In the process of this comparison, Kant gives the most explicit statement of his critical philosophy of mathematics; accordingly, scholars have typically focused their (...) interpretations and criticisms of Kant’s conception of mathematics on this small section of the Critique. (shrink)

This paper considers Kant’s conception of force and causality in his early pre-Critical writings, arguing that this conception is best understood by way of contrast with his immediate predecessors, such as Christian Wolff, Alexander Baumgarten, Georg Friedrich Meier, Martin Knutzen, and Christian August Crusius, and in terms of the scientific context of natural philosophy at the time. Accordingly, in the True estimation Kant conceives of force in terms of activity rather than in terms of specific effects, such as motion. Kant’s (...) explicit arguments in the Nova dilucidatio for physical influx are directed primarily against the conception of grounds and existence held by Wolff, Baumgarten, and Meier, and only secondarily against Leibniz. Finally, Kant’s reconciliation of the infinite divisibility of space and the unity of monads in the Physical monadology is designed to respond to objections that could be raised naturally by Wolff and Baumgarten.Author Keywords: Kant; Pre-Critical; Force, Causality; Wolff; Leibniz. (shrink)

his paper explores the relationship between Kant’s views on the metaphysical foundations of Newtonian mathematical physics and his more general transcendental philosophy articulated in the Critique of pure reason. I argue that the relationship between the two positions is very close indeed and, in particular, that taking this relationship seriously can shed new light on the structure of the transcendental deduction of the categories as expounded in the second edition of the Critique.Author Keywords: Kant; Mathematical physics; Transcendental deduction.

Aesthetics in philosophy of mathematics is too narrowly construed. Beauty is not the only feature in mathematics that is arguably aesthetic. While not the highest aesthetic value, being interesting is a sine qua non for publishability. Of the many ways to be interesting, being explanatory has recently been discussed. The motivational power of what is interesting is important for both directing research and stimulating education. The scientific satisfaction of curiosity and the artistic desire for beautiful results are complementary but both (...) aesthetic. (shrink)

This work provides some interesting new results on the notion of the topos and the theory of hypothetical syllogisms in Aristotle based on an incisive interpretation of Aristotle's _Topics_ and certain passages of the _Analytics_.

The article is concerned with the account of Aristotle's theory of disputation given by Robert Kilwardby in his commentary, composed in Paris during the 1240s, on Aristotle's Prior Analytics. Specifically, I show that Kilwardby covers demonstrative as well as dialectical disputations, and gives an elementary account of the rules governing such disputations, in their adversarial forms as well as in an idealized form where the interlocutors engage in a cooperative activity. I describe the resemblances and the differences between disputations as (...) theorized by Kilwardby and the game of obligationes as understood by some of his contemporaries. (shrink)