The "Pythagorean" Theory of the Derivation of Magnitudes
Bibliographic Data
| ID | 3938467 |
|---|---|
| Authors | J A Philip (corresponding author) |
| Year | 1966 |
| Volume | 20 |
| Issue | 1 |
| Pages | 32 |
| Publication date | 1966-01-01 |
| Peer Reviewed | Yes |
| Open Access | No |
| Type | ARTICLE |
| Venue | Phoenix (JOURNAL) |
| Journal identifiers | ISSN: 0031-8299 • E-ISSN: 1929-4883 |
| Publisher | JSTOR (PUBLISHER) |
| DOI | 10.2307/1086314 |
| OpenAlex | W2325961695 |
| Language | EN |
| Citations received | 4 |
MANY OF THE GREAT DEBATES in the history of thought have had their origin in, or turned on, what to later times seem minor problems-whether the earth moves, whether transubstantiation in fact occurs, whether we are descended from apes. Early in the fourth century B.c. we begin to hear echoes of what appears to have been such a debate. References then first occur to point, line, plane surface, solid, as the constituent elements in ideal and physical magnitudes. These elements play a major role in the mathematical and metamathematical theories of Plato and the Early Academy, and against such theories Aristotle directs much of the polemic of the Metaphysics. Plato, Speusippus, and Xenocrates, each in differing ways, derive magnitudes from the sequence point, line, surface, solid, and their speculations gave rise to a lively controversy concerning indivisible lines-a controversy that influenced Aristotle's notions of space, indivisibility, continuum. At the end of the fourth century we find Euclid defining the four terms as basic concepts in his Elements. Our earlier tradition is silent on the origin of these theories of derivation. I propose to discuss here the time when we may reasonably suppose that they arose, and the milieu in which their origin is most probable. The nature of the several theories, and their mutual relations, will be discussed only incidentally, in so far as is relevant to the theme.' It will be suggested that
Epistemology · Geometry · Ideal (ethics) · Metaphysics · Physics · Pythagorean theorem · Space (punctuation) · Theme (computing) · Theoretical physics · Classical Philosophy and Thought · History and Theory of Mathematics · Mathematics · Philosophy
| Unique citing works | 4 |
|---|---|
| Citations per year | 0,5 |
| Citation span | 2018 - 2022 (5) |
| Citation velocity | historical |
| Highly cited | No |
| Citation types | Neutral: 4 |