II.
Outline of the Doctrine of Knowledge (1810)
“Once the first principles are disposed of, the body of doctrine contained in the recent textbooks of elementary geometry does not, and from the nature of the case cannot, show any substantial differences from that set forth in the Elements.”
Introduction, p. v
The Thirteen Books of Euclid's Elements (1908)
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Thomas Little Heath 46
British civil servant and academic 1861–1940Related quotes
Duke of Leeds v. New Radnor (1788), 2 Brown's Rep. (by Belt), 339.
Source: The Moral Judgment of the Child (1932), Ch. 2 : Adult Constraint and Moral Realism <!-- p. 183 -->
Context: As Bovet has demonstrated in the field of morals, rules do not appear in the mind of the child as innate facts, but as facts that are transmitted to him by his seniors, and to which from his tenderest years he has to conform by means of a sui generis form of adaptation. This, of course, does not prevent some rules from containing more than others an element of rationality, thus corresponding to the deepest fundamental constants of human nature. But whether they be rational or simply a matter of usage and consensus of opinion, rules imposed on the childish mind by adult constraint do begin by presenting a more or less uniform character of exteriority and sheer authority. So that instead of passing smoothly from an early individualism (the "social" element of the first months is only biologically social, so to speak, inside the individual, and therefore individualistic) to a state of progressive cooperation, the child is from his first year onwards in the grip of coercive education which goes straight on and ends by producing what Claprède has so happily called a veritable "short circuit."
"Mathematics without foundations"
Source: Philosophical Papers Volume 1: Mathematics, Matter, and Method (1975, 1979)
Context: (If we identify sets with the points that represent them in the various possible concrete structures, we might say: it is not possible for all possible sets to exist in any one world!) Yet set theory does not become impossible. Rather, set theory becomes the study of what must hold in, e.g. any standard model for Zermelo set theory.
Source: Italian Fascism and Developmental Dictatorship, (1979), p. 119
"Nothing in Biology Makes Sense Except in the Light of Evolution" (1973)