04 February 2021

On Symbols (1850-1859)

"To deduce the laws of the symbols of Logic from a consideration of those operations of the mind which are implied in the strict use of language as an instrument of reasoning." (George Boole, "An Investigation of the Laws of Thought", 1854)

"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."(William J M Rankine, "On the Harmony of Theory and Practice in Mechanics", 1856)

"[...] the symbols of algebra, when employed in abstruse and complex theoretical investigations, constitute a sort of thought-saving machine, by whose aid a person skilled in its use can solve problems respecting quantities, and dispense with the mental labour of thinking of the quantities denoted by the symbols, except at the beginning and the end of the operation." (William J M Rankine, "On the Harmony of Theory and Practice in Mechanics", 1856)

"Nature is a temple, where, from living pillars, confused words are sometimes allowed to escape; here man passes, through forests of symbols, which watch him with looks of recognition." (Charles Baudelaire, "Les fleurs du mal", 1857)

"As you are aware, no perceptions obtained by the senses are merely sensations impressed on our nervous systems. A peculiar intellectual activity is required to pass from a nervous sensation to the conception of an external object, which the sensation has aroused. The sensations of our nerves of sense are mere symbols indicating certain external objects, and it is usually only after considerable practice that we acquire the power of drawing correct conclusions from our sensations respecting the corresponding objects." (Hermann von Helmholtz, "On the Physiological Causes of Harmony", 1857)

"The most accomplished in the use of symbols must sometimes throw aside his abstractions and resort to homelier methods for trial and verification - not doubting, in so doing, the truth which lies at the bottom of his symbolism, but distrusting his own powers." (George Boole, "A Treatise on Differential Equations", 1859)

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