from Interlude - The Greek Mathematical Tradition as Background to Kant
Published online by Cambridge University Press: 21 October 2021
The previous chapters established the centrality and importance of Kant’s theory of magnitudes. Before investigating Kant’s views more deeply, Chapter 6 provides critical background concerning the theory of magnitude, which is rooted in Euclid’s Elements. It describes the organization and deductive structure of the Elements to explain tensions between Euclid’s account of number and continuous spatial magnitude that persisted into the eighteenth century. It then explains the theory of proportions, in particular, the crucial definition of sameness of ratio. It also describes the mathematical nature of the continuous spatial magnitudes implicitly defined by that theory, including their homogeneity. Euclid also covers number and arithmetic and he regards numbers as collections of units. Much of the theory of proportions covers numbers as well as continuous spatial magnitudes, although Euclid gives numbers a separate treatment. This commonality inspired the search for a universal mathematics that covered continuous magnitudes more generally as well as number. The chapter traces the history and development of these themes in the Euclidean mathematical tradition, and describes its influence on three of Kant’s immediate predecessors: Wolff, Kästner, and Euler. It explains why these philosophers and mathematicians regarded mathematics as a science of magnitudes and their measurement.
To save this book to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.
Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.
Find out more about the Kindle Personal Document Service.
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.