Realizing Reason pursues three interrelated themes. First, it traces the essential moments in the historical unfoldingfrom the ancient Greeks, through Descartes, Kant, and developments in the nineteenth century, to the presentthat culminates in the realization of pure reason as a power of knowing. Second, it provides a cogent account of mathematical practice as a mode of inquiry into objective truth. And finally, it develops and defends a new conception of our being in the world, one that builds on and transforms the now standard conception according to which our experience of reality arises out of brain activity due, in part, to merely causal impacts on our sense organs. Danielle Macbeth shows that to achieve an adequate understanding of the striving for truth in the exact sciences we must overcome this standard conception and that the way to do that is through a more adequate understanding of the nature of mathematical practice and the profound transformations it has undergone over the course of its history, the history through which reason is first realized as a power of knowing. Because we can understand mathematical practice only if we attend to the systems of written signs within which to do mathematics, Macbeth provides an account of the nature and role of written notations, specifically, of the principal systems that have been developed within which to reason in mathematics: Euclidean diagrams, the symbolic language of arithmetic and algebra, and Frege's concept-script, Begriffsschrift.
|Publisher:||Oxford University Press|
|Edition description:||New Edition|
|Product dimensions:||6.10(w) x 9.30(h) x 1.20(d)|
About the Author
Danielle Macbeth is T. Wistar Brown Professor of Philosophy at Haverford College in Pennsylvania and the author of Frege's Logic (Harvard University Press, 2005). She has also published on a variety of issues in the history and philosophy of mathematics, philosophy of language, philosophy of mind, pragmatism, and other topics. She was a Fellow at the Center for Advanced Study in the Behavioral Sciences in 2002-3, and has been the recipient of both an ACLS Burkhardt Fellowship and a Fellowship from the National Endowment for the Humanities.
Table of Contents
1. Where We Begin
2. Ancient Greek Diagrammatic Practice
3. A New World Order
4. Kant's Critical Turn
5. Mathematics Transformed, Again
6. Mathematics and Language
7. Reasoning in Frege's Begriffsschrift
8. Truth and Knowledge in Mathematics
9. The View from Here