rational element
121Algebraically closed field — In mathematics, a field F is said to be algebraically closed if every polynomial in one variable of degree at least 1, with coefficients in F , has a root in F . ExamplesAs an example, the field of real numbers is not algebraically closed,… …
122Naive set theory — This article is about the mathematical topic. For the book of the same name, see Naive Set Theory (book). Naive set theory is one of several theories of sets used in the discussion of the foundations of mathematics.[1] The informal content of… …
123arithmetic — arithmetically, adv. n. /euh rith meuh tik/; adj. /ar ith met ik/, n. 1. the method or process of computation with figures: the most elementary branch of mathematics. 2. Also called higher arithmetic, theoretical arithmetic. the theory of… …
124mysticism — /mis teuh siz euhm/, n. 1. the beliefs, ideas, or mode of thought of mystics. 2. a doctrine of an immediate spiritual intuition of truths believed to transcend ordinary understanding, or of a direct, intimate union of the soul with God through… …
125Greek arithmetic, geometry and harmonics: Thales to Plato — Ian Mueller INTRODUCTION: PROCLUS’ HISTORY OF GEOMETRY In a famous passage in Book VII of the Republic starting at Socrates proposes to inquire about the studies (mathēmata) needed to train the young people who will become leaders of the ideal… …
126John Scottus Eriugena and Anselm of Canterbury — Stephen Gersh INTRODUCTION by John Marenbon John Scottus Eriugena came from Ireland, as his name indicates (‘Scottus’ meant ‘Irishman’ in the Latin of this period, and ‘Eriugena’, a neologism invented by John himself, is a flowery way of saying… …
127Philosophy (The) of the Italian Renaissance — The philosophy of the Italian Renaissance Jill Kraye TWO CULTURES: SCHOLASTICISM AND HUMANISM IN THE EARLY RENAISSANCE Two movements exerted a profound influence on the philosophy of the Italian Renaissance: scholasticism and humanism, both of… …
128British moralists of the eighteenth century: Shaftesbury, Butler and Price — David McNaughton In this chapter I discuss the moral theories of three influential writers: Anthony Ashley Cooper, Third Earl of Shaftesbury (1671–1713); Joseph Butler (1692–1752) and Richard Price (1723–91). All three wrote extensively on issues …
