unending decimal (without reoccurrence or periodicity):

this is a description of an irrational number: a decimal number in which the decimal expansion does not terminate, nor end with a repeating sequence.  Examples are the decimal representation of π

 

Democritus's atoms: * see EndNote<A>

There is a strong element of randomness in the Classic atomic theory.  It lacks a first cause, one of Aristotle’s chief criticisms.

and see pages 38, 3865 above

 

Protagoras (man as the measure, not creator of things):

(490-420 BC) pre-Socratic Greek philosopher & first Sophist.  Often considered the first relativist.  He begins his lost work, Truth with this statement:

“Of all things the measure is man: of those that are, that they are; and of those that are not, that they are not”.

It is intentionally ambiguous.  Plato, Aristotle & Sextus Empiricus (are main sources) understand the phrase “man” as referring to each individual.  Each person is the measure of their own sensations, a proposition supporting the empiricist theory (all knowledge is based on sensory data).  Plato suggests that Protagoras’ phrase had a broader meaning, framing all opinions & judgements.  Likewise Aristotle and Sextus Empiricus promote a broader interpretation: his idea encompasses sensations but more generally all opinions & judgements, especially value judgements.    Thus each individual is the ultimate arbiter of all their own judgements

and see Chapter IX page 311 Chapter X page 365

 

causality-principle:

all real events necessarily have a cause; the principle indicates the existence of a logical relationship between 2 events, the cause and the effect, and an order between them: the cause always precedes the effect.  An important property of the principle is that it entails predictability.  In classical physics an effect cannot occur before its cause.  Another principle is that cause and effect is mediated across space & time.  A basic foundation of scientific research is the belief in the casual inevitability of natural phenomenon.  The scientist’s job is to identify the causes of such phenomenon & if possible discover the interrelationships between cause and effect.

 

scientia experimentalis:

Latin, meaning empiric; term used by Roger Bacon to describe his method.  In his Opus Majus he asserts that “theories supplied by reason should be verified by sensory data, aided by instruments, and corroborated by trustworthy witnesses”

 

Roger Bacon:

(1219-1292) an English philosopher who has been credited as one of the earliest European advocates of the modern scientific method.  He applied the empirical method of Ibn al-Haytham (Alhazen) to observations in texts attributed to Aristotle.  He discovered the importance of empirical testing when the results he obtained were different than those that would have been predicted by Aristotle.

and see Chapter III page 99, Chapter X pages 362, 365

 

a priori:

Latin, meaning from the earlier; often used in philosophy to distinguish types of knowledge by its reliance on empirical evidence.  A priori knowledge is that which is independent from experience. Kant's Critique of Pure Reason employs the term primarily used as modifiers to the noun "knowledge".  He lists space, time & causality as a priori intuitions thru which reality is mediated, and by which we experience living.

 

The Classical mode of regarding Nature:

Spengler here is referring to Apollonian science, and especially the Summer and Autumnal periods

 

Democritus:

(460-370 BC) Greek pre-Socratic philosopher famous for his formulation of an atomic theory of the universe.

 

Anaxagoras:

(500-428 BC) Greek pre-Socratic philosopher, brought philosophy & the spirit of scientific inquiry from Ionia to Athens.  His observations on celestial bodies & the fall of meteorites led him to form new theories on the universe, and to prediction of the impact of meteorites.  He gave a number of novel scientific accounts of natural phenomena.  He deduced a correct explanation for eclipses & described the Sun as a fiery mass larger than the Peloponnese, as well as attempting to explain rainbows.

 

Aristotle: * see EndNote <B>

(384–322 BC) Aristotle wrote across many subjects embracing the arts & science.  His writing covered most of the sciences including biology, botany, chemistry, philosophy of science, physics, psychology & zoology.  He pioneered the study of zoology, both observational & theoretical.

and see Chapter I pages 9, 27, Chapter V page 178 Chapter VIII pages 259, 284 Chapter IX pages 304, 318, 321, 323 Chapter X pages 351, 352, 361, 366 and above page 386

 

ἀλλοίωσις:

Greek, alteration (from Aristotle, Physics)

 

ἀνάγκη:

Greek, necessity in the philosophical sense ( Aristotle, Posterior Analytics) also logical necessity , laws of nature

 

ἐντελέχεια:

Greek, full complete reality, actuality