"Mathesis of the mind" : a study of Fichte's Wissenschaftslehre and geometry /
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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 "ursprüngliche" 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."
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Based on the author's thesis (Ph. D.)--Ludwig-Maximilians-Universität, Munich, 2009. :
1 online resource (iii, 304 pages) : illustrations. :
Includes bibliographical references. :
9789401207683 :
Available to subscribing member institutions only.
Essays in the philosophy and history of logic and mathematics /
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The book is a collection of the author's selected works in the philosophy and history of logic and mathematics. Papers in Part I include both general surveys of contemporary philosophy of mathematics as well as studies devoted to specialized topics, like Cantor's philosophy of set theory, the Church thesis and its epistemological status, the history of the philosophical background of the concept of number, the structuralist epistemology of mathematics and the phenomenological philosophy of mathematics. Part II contains essays in the history of logic and mathematics. They address such issues as the philosophical background of the development of symbolism in mathematical logic, Giuseppe Peano and his role in the creation of contemporary logical symbolism, Emil L. Post's works in mathematical logic and recursion theory, the formalist school in the foundations of mathematics and the algebra of logic in England in the 19th century. The history of mathematics and logic in Poland is also considered. This volume is of interest to historians and philosophers of science and mathematics as well as to logicians and mathematicians interested in the philosophy and history of their fields.
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A collection of previously published essays; those originally written in Polish have been translated into English for this publication. :
1 online resource (343 pages) :
Includes bibliographical references (p. 301-334) and index. :
9789042030916 :
0303-8157 ; :
Available to subscribing member institutions only.
Aristotle and mathematics : aporetic method in cosmology and metaphysics /
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John Cleary here explores the role which the mathematical sciences play in Aristotle's philosophical thought, especially in his cosmology, metaphysics, and epistemology. He also thematizes the aporetic method by means of which he deals with philosophical questions about the foundations of mathematics. The first two chapters consider Plato's mathematical cosmology in the light of Aristotle's critical distinction between physics and mathematics. Subsequent chapters examine three basic aporiae about mathematical objects which Aristotle himself develops in his science of first philosophy. What emerges from this dialectical inquiry is a different conception of substance and of order in the universe, which gives priority to physics over mathematics as the cosmological science. Within this different world-view, we can better understand what we now call Aristotle's philosophy of mathematics.
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1 online resource (xxxvi, 558 pages) :
Includes bibliographical references (p. 505-528) and indexes. :
9789004320901 :
0079-1687 ; :
Available to subscribing member institutions only.