Mathematical philosophy, a study of fate and freedom; lectures for educated laymen, by Cassius J. Keyser.

THE GROUP CONCEPT 229 In his Philosophie der Griechen (Vol. III, 2nd edition) Zeller, speaking of the speculations of the Stoics, says: Out of the original substance the separate things are developed according to an inner law. For inasmuch as the first principle, according to its definition, is the creative and formative power, the whole universe must grow out of it with the same necessity as the animal or the plant from the seed. The original fire, according to the Stoics and Heraclitus, first changes to " air " or vapor, then to water; out of this a portion is precipitated as earth, another remains water, a third evaporates as atmospheric air, which again kindles the fire, and out of the changing mixture of these four elements there is formed,-from the earth as center,the world.... Through this separation of the elements there arises the contrast of the active and the passive principle: the soul of the world and its body.... But as this contrast came in time, so it is destined to cease; the original substance gradually consumes the matter, which is segregated out of itself as its body, till at the end of this world-period a universal world conflagration brings everything back to the primeval condition.... But when everything has thus returned to the original unity, and the great world-year has run out, the formation of a new world begins again, which is so exactly like the former one that in it all things, persons and phenomena, return exactly as before; and in this wise the history of the world and the deity... moves in an endless cycle through the same stages. A similar view of cosmic history is present in the speculations of Empedocles, for whom a cycle consists of four great periods: Predominant Love-a state of complete aggregation; decreasing Love and increasing Hate; predominant Strife-complete separation of the elements; decreasing Strife and increasing Love. At the end of this fourth period, the cycle is complete and is then repeated

/ 485
Pages

Actions

file_download Download Options Download this page PDF - Pages 222-241 Image - Page 222 Plain Text - Page 222

About this Item

Title
Mathematical philosophy, a study of fate and freedom; lectures for educated laymen, by Cassius J. Keyser.
Author
Keyser, Cassius Jackson, 1862-1947.
Canvas
Page 222
Publication
New York,: E. P. Dutton & company,
[1925]
Subject terms
Mathematics -- Philosophy

Technical Details

Link to this Item
https://name.umdl.umich.edu/aca0682.0001.001
Link to this scan
https://quod.lib.umich.edu/u/umhistmath/aca0682.0001.001/248

Rights and Permissions

The University of Michigan Library provides access to these materials for educational and research purposes. These materials are in the public domain in the United States. If you have questions about the collection, please contact Historical Mathematics Digital Collection Help at [email protected]. If you have concerns about the inclusion of an item in this collection, please contact Library Information Technology at [email protected].

DPLA Rights Statement: No Copyright - United States

Manifest
https://quod.lib.umich.edu/cgi/t/text/api/manifest/umhistmath:aca0682.0001.001

Cite this Item

Full citation
"Mathematical philosophy, a study of fate and freedom; lectures for educated laymen, by Cassius J. Keyser." In the digital collection University of Michigan Historical Math Collection. https://name.umdl.umich.edu/aca0682.0001.001. University of Michigan Library Digital Collections. Accessed May 3, 2025.
Do you have questions about this content? Need to report a problem? Please contact us.