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This is the first major study in any language on J.G. Fichte's philosophy of mathematics and theory of geometry. It investigates both the external formal and internal cognitive parallels between the axioms, intuitions and constructions of geometry and the scientific methodology of the Fichtean system of philosophy. In contrast to "ordinary" Euclidean geometry, in his "Erlanger Logik "of 1805 Fichte posits a model of an "ursprungliche" or original geometry - that is to say, a synthetic and constructivistic conception grounded in ideal archetypal elements that are grasped through geometrical or intelligible intuition. Accordingly, this study classifies Fichte's philosophy of mathematics as a whole as a species of mathematical Platonism or neo-Platonism, and concludes that the "Wissenschaftslehre "itself may be read as an attempt at a new philosophical mathesis, or "mathesis of the mind." "This work testifies to the author's exact and extensive knowledge of the Fichtean texts, as well as of the philosophical, scientific and historical contexts. Wood has opened up completely new paths for Fichte research, and examines with clarity and precision a domain that up to now has hardly been researched." Professor Dr. Marco Ivaldo (University of Naples) "This study, written in a language distinguished by its limpidity and precision, and constantly supported by a close reading of the Fichtean texts and secondary literature, furnishes highly detailed and convincing demonstrations. In directly confronting the difficult historical relationship between the "Wissenschaftslehre "and mathematics, the author has broken new ground that is at once stimulating, decidedly innovative, and elegantly audacious." Professor Dr. Emmanuel Cattin (Universite Blaise-Pascal, Clermont-Ferrand)
Daniel Breazeale presents a critical study of the early philosophy of J.G. Fichte, and the version of the Wissenschaftslehre or 'doctrine of science' that Fichte developed in Jena between 1794 and 1799. The book is intended to assist serious readers in their efforts to understand Fichte's philosophy within the context of its own era and to orient them in the ongoing scholarly debates concerning the character and significance of the Wissenschaftslehre. Breazeale focuses on explaining what Fichte was (and was not) trying to accomplish and precisely how he proposed to accomplish this, as well as upon the difficulties implicit in his project and his often novel strategies for overcoming them. To this end, the volume addresses a variety of specific themes, issues, and problems that will be familiar to any student of Fichte's early writings and which continue to be fiercely debated by his interpreters. These include: the relationship of the finite human self to the purely self-positing I, transcendental philosophy as a 'pragmatic history of the mind', Fichte's 'synthetic' method of philosophizing, the standpoint of life vs. the standpoint of speculation, the extra-philosophical presuppositions and implications of the Wissenschaftslehre, the different senses of 'intellectual intuition' in Fichte's early writings, the controversial doctrine of the 'check' (Anstoß) upon the free actions of the I, the various theoretical and practical tasks of philosophy, the refutation of dogmatism and the 'choice' of a philosophical standpoint, the relationship of transcendental idealism to skepticism, the interests of reason, and the problematic 'primacy of the practical' in Fichte's thought.
Descartes's concept of the mind, as distinct from the body with which it forms a union, set the agenda for much of Western philosophy's subsequent reflection on human nature and thought. This is the first book to give an analysis of Descartes's pivotal concept that deals with all the functions of the mind, cognitive as well as volitional, theoretical as well as practical and moral. Focusing on Descartes's view of the mind as intimately united to and intermingled with the body, and exploring its implications for his philosophy of mind and moral psychology, Lilli Alanen argues that the epistemological and methodological consequences of this view have been largely misconstrued in the modern debate. Informed by both the French tradition of Descartes scholarship and recent Anglo-American research, Alanen's book combines historical-contextual analysis with a philosophical problem-oriented approach. It seeks to relate Descartes's views on mind and intentionality both to contemporary debates and to the problems Descartes confronted in their historical context. By drawing out the historical antecedents and the intellectual evolution of Descartes's thinking about the mind, the book shows how his emphasis on the embodiment of the mind has implications far more complex and interesting than the usual dualist account suggests.
This important collection of more than twenty original essays by prominent Kant scholars covers the multiple aspects of Kant’s teaching in relation to his published works. With the Academy edition’s continuing publication of Kant’s lectures, the role of his lecturing activity has been drawing more and more deserved attention. Several of Kant’s lectures on metaphysics, logic, ethics, anthropology, theology, and pedagogy have been translated into English, and important studies have appeared in many languages. But why study the lectures? When they are read in light of Kant’s published writings, the lectures offer a new perspective of Kant’s philosophical development, clarify points in the published texts, consider topics there unexamined, and depict the intellectual background in richer detail. And the lectures are often more accessible to readers than the published works. This book discusses all areas of Kant's lecturing activity. Some essays even analyze in detail the content of Kant's courses and the role of textbooks written by key authors such as Baumgarten, helping us understand Kant’s thought in its intellectual and historical contexts. Contributors: Huaping Lu-Adler; Henny Blomme ; Robert Clewis; Alix Cohen; Corey Dyck; Faustino Fabbianelli; Norbert Fischer; Courtney Fugate; Paul Guyer; Robert Louden; Antonio Moretto; Steve Naragon; Christian Onof; Stephen Palmquist; Riccardo Pozzo; Frederick Rauscher; Dennis Schulting; Oliver Sensen; Susan Shell; Werner Stark; John Zammito; Günter Zöller
In a fragment entitled Elementa Nova Matheseos Universalis (1683?) Leibniz writes “the mathesis [...] shall deliver the method through which things that are conceivable can be exactly determined”; in another fragment he takes the mathesis to be “the science of all things that are conceivable.” Leibniz considers all mathematical disciplines as branches of the mathesis and conceives the mathesis as a general science of forms applicable not only to magnitudes but to every object that exists in our imagination, i.e. that is possible at least in principle. As a general science of forms the mathesis investigates possible relations between “arbitrary objects” (“objets quelconques”). It is an abstract theory of combinations and relations among objects whatsoever. In 1810 the mathematician and philosopher Bernard Bolzano published a booklet entitled Contributions to a Better-Grounded Presentation of Mathematics. There is, according to him, a certain objective connection among the truths that are germane to a certain homogeneous field of objects: some truths are the “reasons” (“Gründe”) of others, and the latter are “consequences” (“Folgen”) of the former. The reason-consequence relation seems to be the counterpart of causality at the level of a relation between true propositions. Arigorous proof is characterized in this context as a proof that shows the reason of the proposition that is to be proven. Requirements imposed on rigorous proofs seem to anticipate normalization results in current proof theory. The contributors of Mathesis Universalis, Computability and Proof, leading experts in the fields of computer science, mathematics, logic and philosophy, show the evolution of these and related ideas exploring topics in proof theory, computability theory, intuitionistic logic, constructivism and reverse mathematics, delving deeply into a contextual examination of the relationship between mathematical rigor and demands for simplification.
Tarek Dika presents a systematic account of Descartes' method and its efficacy. He develops an ontological interpretation of Descartes's method as a dynamic and, within limits, differentiable problem-solving cognitive disposition or habitus, which can be actualized or applied to different problems in various ways, depending on the nature of the problem. Parts I-II of the book develop the foundations of such an habitual interpretation of Descartes's method, while Parts III-V demonstrate the fruits of such an interpretation in metaphysics, natural philosophy, and mathematics. This is the first book to draw on the recently-discovered Cambridge manuscript of Descartes's Rules for the Direction of the Mind (1620s): it gives a concrete demonstration of the efficacy of Descartes's method in the sciences and of the underlying unity of Descartes's method from Rules for the Direction of the Mind to Principles of Philosophy (1644).
Phenomenology and analytic philosophy have skirmished often, but seldom in ways conducive to dialectical progress. Generally, the skirmishes seem more "political" than philosophical, as when one side ridicules the methods of the other or criticizes the viability of the other's issues and assump tions. Analytic interest in third person objectivity is often spurned by Continental philosophers as being unduly abstract. Continental interest in first person subjectivity is often criticized by analysts as being muddled and imprecise. Logical analysis confronts the power of metaphor and judges it "too ambiguous" for rigorous philosophical activity. The language of metaphor confronts the power of logical analysis and deems it "too restric tive" for describing the nature and structures of authentic human exper ience. But are the two approaches really incompatible? Perhaps because each side of the "divide" has been working at problems largely uninteresting to the "opposition" it has been easy to ignore or underestimate the importance of this issue. But now each side is being led into a common field of problems associated with the nature of mind, and there is a new urgency to the need for examining carefully the question of conceptual compatibility and the potential for dialogue. Analytic thinkers are typically in the business of concept clarification and objective certi fication. Continental philosophers employ introspection in the interest of a project of description and classification that aims to be true to the full subtlety and complexity of the human condition.
Giordano Bruno and the Geometry of Language brings to the fore a sixteenth-century philosopher's role in early modern Europe as a bridge between science and literature, or more specifically, between the spatial paradigm of geometry and that of language. Arielle Saiber examines how, to invite what Bruno believed to be an infinite universe-its qualities and vicissitudes-into the world of language, Bruno forged a system of 'figurative' vocabularies: number, form, space, and word. This verbal and symbolic system in which geometric figures are seen to underlie rhetorical figures, is what Saiber calls 'geometric rhetoric.' Through analysis of Bruno's writings, Saiber shows how Bruno's writing necessitates a crafting of space, and is, in essence, a lexicon of spatial concepts. This study constitutes an original contribution both to scholarship on Bruno and to the fields of early modern scientific and literary studies. It also addresses the broader question of what role geometry has in the formation of any language and literature of any place and time.