This is a very important book. It has already become required reading for researchers on the relation between the exact sciences and Kant’s philosophy. The main theme is that Kant’s continuing program to find a metaphysics that could provide a foundation for the science of his day is of crucial importance to understanding the development of his philosophical thought from its earliest precritical beginnings in the thesis of 1747, right through the highwater years of the critical philosophy, to his last (...) unpublished writings in the Opus postumum. In the course of articulating this theme, Friedman has made extensive use of detailed historical information about their scientific and mathematical background to illuminate Kant’s texts. Over and over again, such information is used to suggest interesting and quite subtle interpretations for texts that may have seemed puzzling or just wrong-headed. (shrink)

Kant famously declares that “although all our cognition commences with experience, … it does not on that account all arise from experience”. This marks Kant’s disagreement with empiricism, and his contention that human knowledge and experience require both sensation and the use of certain a priori concepts, the Categories. However, this is only the surface of Kant’s much deeper, though neglected view about the nature of reason and judgment. Kant holds that even our a priori concepts are acquired, not from (...) sensation, but “originally,” because our mind has a fundamental capacity to judge that, upon sensory stimulation, generates the Categories through its basic logical functions of judgment. This “epigenesis” of reason and our fundamental capacity to judge that drives it is the topic of Longuenesse’s fascinating book, and the source of her title. (shrink)

"Kant and the Capacity to Judge" will prove to be an important and influential event in Kant studies and in philosophy.

My goal here is to explore the relationship between pure and applied mathematics and then, eventually, to draw a few morals for both. In particular, I hope to show that this relationship has not been static, that the historical rise of pure mathematics has coincided with a gradual shift in our understanding of how mathematics works in application to the world. In some circles today, it is held that historical developments of this sort simply represent changes in fashion, or in (...) social arrangements, governments, power structures, or some such thing, but I resist the full force of this way of thinking, clinging to the old school notion that we have gradually learned more about the world over time, that our opinions on these matters have improved, and that seeing how we reached the point we now occupy may help us avoid falling back into old philosophies that are now no longer viable. In that spirit, it seems to me that once we focus on the general question of how mathematics relates to science, one observation is immediate: the march of the centuries has produced an amusing reversal of philosophical fortunes. Let me begin there. In the beginning, that is, in Plato, mathematical knowledge was sharply distinguished from ordinary perceptual belief about the world. According to Plato’s metaphysics, mathematics is the study of eternal and unchanging abstract Forms,1 while science is uncertain and changeable opinion about the world of mere becoming. Indeed, in Plato’s lights, of the two, only mathematics deserves to be called ‘knowledge’ at all! Of course if sense perception cannot give us knowledge, if mathematics is not about perceivable things, then Plato owes us an account of how we ordinary humans achieve this wonderful insight into the properties of the abstract world of Forms. Plato’s answer is that we do not actually acquire mathematical knowledge at all; rather, we recollect it from a time before birth, when our souls, unencumbered by physical bodies, were free to commune with the Forms, and not just the mathematical ones, either – also Truth, Beauty, Justice, the Good, and so on.2 Whatever appeal this position may have held for the ancient Greeks, it will not begin to satisfy a contemporary, scientifically minded philosopher.. (shrink)

My topic here is metaphilosophy, the question of how philosophy is properly done. For some years now, I've been developing a particularly austere, roughly naturalistic approach to philosophical questions that I call 'second philosophy'. It has seemed to me that one effective way to convey the spirit of second philosophy is to compare and contrast it with other more familiar methods, like transcendental or therapeutic philosophy. Here I hope to pursue this sort of engagement with two other venerable schools of (...) thought: Hume's 'science of man' and Reid's 'philosophy of common sense'. Hume presents a fitting starting point for any discussion of naturalism -- even more so when Reid is on the agenda -- so my first pass at a portrait of the second philosopher traces her relations to the 'scientist of man'. Of course, Hume's cheerfully industrious inquirer eventually lands on the barren rock of skepticism, so we'll also take a second-philosophical look at the kinds of considerations that led poor Hume to his shipwreck. This sets the stage for Reid. (shrink)

This chapter presents and illustrates fundamental principles of the intuitionistic mathematics devised by L.E.J. Brouwer and then describes in largely nontechnical terms metamathematical results that shed light on the logical character of that mathematics. The fundamental principles, such as Uniformity and Brouwer’s Theorem, are drawn from the intuitionistic studies of logic and topology. The metamathematical results include Gödel’s negative and modal translations and Kleene’s realizability interpretation. The chapter closes with an assessment of anti-realism as a philosophy of intuitionism.