The Varieties of Practical Knowledge Chapter 2: Knowledge of Geometry and the Maker’s Knowledge Principle I. Introduction Recent developments in epistemology have seen a renewed appreciation of the theme of practical knowledge and its distinctive attributes in contrast with theoretical knowledge. By concentrating on theoretical propositional knowledge (knowledge that) to the exclusion of other forms of knowledge, such as knowledge-how and practical capacities and skills--- great swathes of knowledge—perhaps irreducible to propositional knowledge—escape the epistemologist’s notice. Furthermore, some contemporary epistemologists have put in a plea for epistemology to stop focusing exclusively on ‘knowledge’ and its components and to take into account other epistemic achievements and virtues such as understanding (Zagzebski 2001, cf. Kvanvig 2003). Such epistemic virtues are typically neglected in the sceptical tradition in epistemology that prizes epistemic certainty and the guarantee of knowledge above all else, above the quality of knowledge and its character, and allied epistemic virtues. Understanding is also neglected as an epistemic goal in discussions that employ purely externalist and reliabilist theories of knowledge. But understanding is making a comeback after being neglected for a few decades. Understanding pertains to bodies of knowledge and in examining the concept of understanding it is useful to consider particular fields or bodies of knowledge. Philosophy of mathematics has become a specialized field in its own right to the detriment of mainstream epistemology. The lack of attention to mathematical knowledge is particularly glaring in contemporary epistemology given the heavy emphasis in ancient and modern epistemology on mathematical knowledge—especially, knowledge of geometry—as the philosopher’s very paradigm of knowledge. Doubtless it would be a mistake to over- generalize and try to claim that all kinds of knowledge are like knowledge of geometry. But geometrical knowledge struck great philosophers like Plato and Kant as the paradigm of knowledge for a good reason: it seemed particularly secure, rigorous, necessarily true, certain, and even a priori. What is the explanation for the high epistemic status of mathematical knowledge? What is it about the mathematical method—the method in say, Euclid’s Elements—that is so impressive? How might attention to mathematical method and knowledge provide a way of enriching our view as epistemologists of the multi-faceted nature of knowledge? Some attention to the history of philosophy allows us to retrieve some promising leads in answering this question. Traditionally, one explanation for the success and special quality of mathematical knowledge stemed from the “maker’s knowledge” tradition. This tradition in the history of ideas has been discussed in Anthony Perez-Ramo’s study of Francis Bacon’s epistemology (Perez Ramos 1988) and also by Jaako Hintikka’s several classic articles on Kant’s