
as translated by Arnold Dresden from: Brouwer, L. E. J. (1913). Intuitionism and formalism. Bulletin of the American Mathematical Society, 20(2), 81–96. (quote on p. 84)
Source: 1840s, The Mathematical Analysis of Logic, 1847, p. 5
as translated by Arnold Dresden from: Brouwer, L. E. J. (1913). Intuitionism and formalism. Bulletin of the American Mathematical Society, 20(2), 81–96. (quote on p. 84)
That these are the laws employed in the demonstration of the principal theorems in Algebra, a slight examination of the processes will easily shew ; but they are not confined to symbols of numbers ; they apply also to the symbol used to denote differentiation.
p. 237 http://books.google.com/books?id=8lQ7AQAAIAAJ&pg=PA237; Highlighted section cited in: George Boole " Mr Boole on a General Method in Analysis http://books.google.com/books?pg=PA225-IA15&id=aGwOAAAAIAAJ&hl," Philosophical Transactions, Vol. 134 (1844), p. 225; Other section (partly) cited in: James Gasser (2000) A Boole Anthology: Recent and Classical Studies in the Logic of George Boole,, p. 52
Examples of the processes of the differential and integral calculus, (1841)
Source: 1850s, An Investigation of the Laws of Thought (1854), p. 42
“All language is symbolic, so far as it is applied to mental and spiritual phenomena and action.”
Source: Morals and Dogma of the Ancient and Accepted Scottish Rite of Freemasonry (1871), Ch. III : The Master, p. 62
Context: All religious expression is symbolism; since we can describe only what we see, and the true objects of religion are The Seen. The earliest instruments of education were symbols; and they and all other religious forms differed and still differ according to external circumstances and imagery, and according to differences of knowledge and mental cultivation. All language is symbolic, so far as it is applied to mental and spiritual phenomena and action. All words have, primarily, a material sense, howsoever they may afterward get, for the ignorant, a spiritual non-sense. To "retract," for example, is to draw back, and when applied to a statement, is symbolic, as much so as a picture of an arm drawn back, to express the same thing, would he. The very word " spirit" means " breath," from the Latin verb spiro, breathe.
"On the Harmony of Theory and Practice in Mechanics" (Jan. 3, 1856)
Context: In treating of the practical application of scientific principles, an algebraical formula should only be employed when its shortness and simplicity are such as to render it a clearer expression of a proposition or rule than common language would be, and when there is no difficulty in keeping the thing represented by each symbol constantly before the mind.<!--p. 177
Source: 1850s, An Investigation of the Laws of Thought (1854), p. 37; Cited in: William Torrey Harris (1879) The Journal of Speculative Philosophy, p. 109
Source: Examples of the processes of the differential and integral calculus, (1841), p. 237; Lead paragraph of Ch. XV, On General Theorems in the Differential Calculus,; Cited in: James Gasser (2000) A Boole Anthology: Recent and Classical Studies in the Logic of George Boole,, p. 52
Source: 1850s, An Investigation of the Laws of Thought (1854), p. 165; As cited in: James Joseph Sylvester, James Whitbread Lee Glaisher (1910) The Quarterly Journal of Pure and Applied Mathematics. p. 350