criticism of the Renaissance: * see Endnote 17
The term “Renaissance” was coined by the French historian Michelet in the 1850s & gained popularity with its use by Burckhardt in The Civilization of the Renaissance in Italy (1860).  He characterised the Renaissance as a great “renewal” of Western culture, where artists & thinkers broke free of the backward medieval world, established a new civilization based on the the Greek and Roman past.  Spengler, along with many other historians, is sceptical of this interpretation. 

 

Indians...number: see Endnote 18

Indian mathematics emerged from 1200 BC, however our knowledge of Indian number dates only from the period after 400 AD.  The decimal number system was first recorded in Indian mathematics.  A second significant discovery was the development of the concept of zero as a number.  In addition they knew & used negative numbers & made significant advances in arithmetic, algebra & trigonometry.

 

Brahmanic soul: * see Endnote 19

This is Spengler’s term for the Culture which emerged from Vedic India.  Brahma is a creator god in Hinduism; his consort is the goddess Saraswati; he is the father of Prajapatis.  Depicted with 4 faces, also known as Svayambhu (self-born) and Vāgīśa (Lord of speech & creator of the 4 Vedas, 1 from each of his mouths).  The Vedas are a body of Sanskrit texts from India & considered to be impersonal, authorless, not of a man but of a superhuman; they are among the oldest known sacred texts. The Samhitas (mantras and benedictions) date from 1700–1100 BC.  The Vedic period, Spengler’s Brahmanic Culture/Civilisation, spans from the mid-2nd to mid-1st millennium BC.

 

Brahman Nirvana:
In Indian religions, nirvana is synonymous with moksha and mukti.  All Indian religions assert it to be a state of perfect quietude, freedom, highest happiness along with it being the liberation from the repeating cycle of birth, life & death (or samsara).

 

zero:
The oldest evidence of zero is an ancient Indian scroll called the Bhakshali manuscript, from the 3rd or 4th century AD.  The notation it used was a placeholder dot symbol.  The concept of zero first appeared in India in 458 AD with the Sanskrit word for zero, śūnya.  It is a Buddhist concept which has multiple meanings depending on its context.  In English it can mean emptiness and sometimes voidness.  In 628 AD, Brahmagupta an astronomer-mathematician refers to zero in his text & provides a mathematical treatment.  He defined zero as the result of subtracting a number from itself.  He used the earlier notation style (a dot underneath a number).  He does not claim to have invented zero so it must have pre-dated him.  Philosophical & cultural factors unique to India were important to the development of zero as a mathematical concept & explain why other civilizations failed to develop the idea.  It is linked to the contemporary philosophy of emptiness or Shunyata found in Buddhism.  From this philosophy, a numeral to use in mathematical equations developed, a bridge between Indian philosophy and mathematics.

Alfarabi:
(872- 950 AD) renowned Persian philosopher & jurist who wrote in the fields of political philosophy, metaphysics, ethics and logic.  He spent significant time in Baghdad with Christian scholars.  He later spent time in Damascus, Syria and Egypt before returning to Damascus where he died.  In Arabic philosophical tradition, he is called "the Second Teacher", Aristotle being "the First Teacher".  He is credited with preserving the original Greek texts during the Middle Ages because of his commentaries and treatises, and influencing many prominent philosophers, like Avicenna and Maimonides.  His works became well-known in the East as well as the West.

 

Alkabi:

(aka Al-Kindi, this is either a mistranslation or Spengler’s spelling is wrong, a common mistake with Islamic style names) (801–873 AD) Muslim philosopher & mathematician, considered father of Arab philosophy; a Persian, educated in Baghdad, prominent figure in the House of Wisdom; appointed by Abbasid Caliphs to oversee the translation of Greek scientific & philosophical texts.  His main contribution to Islamic philosophy were efforts to make Greek thought accessible & acceptable to Muslims. The standard Arabic philosophical vocabulary originated with him & without him the work of philosophers like Al-Farabi & others would not have been possible.  One of his central concerns was to demonstrate compatibility between philosophy and natural theology on the one hand, and revealed theology.  He successfully incorporated Aristotelian & Neo-Platonist thought into an Islamic framework, vital in the introduction & popularization of Greek philosophy for Muslim philosophers.

 

ontology of Aristotle:

a branch of philosophy known as metaphysics, it is the study of the nature of being & the basic categories of being; it asks questions like: what entities exist, how are they grouped, similarities & differences.  For Plato the world (or actual things) imitate existing forms.  His epistemology (the study of the origin, nature, methods of knowledge) begins with universal abstracts (Forms) & moves onto knowledge of particular imitations of these forms.  He relies on deduction from a priori principles.  Likewise Aristotle aimed at establishing universals but argues reality is based on particular substances of physical things, not on universal abstracts (Forms).  His epistemology begins with the study of things that exist & happen in the world.  From these particulars he deduces the universal.  He accepted "form", what phenomena are based on, but saw it as "instantiated" in a particular substance.  He uses induction from examples alongside deduction.