Technology and Mathematics by Unknown

Author:Unknown
Language: eng
Format: epub
ISBN: 9783319937793
Publisher: Springer International Publishing

In his correspondence with Damaris Masham (1659–1708), Leibniz even speculated on machines that could “imitate reason” (Jones 2014, pp. 194–195; cf. Widmaier 1986). However, not even Leibniz, one of the most prolific and inventive scholars of his times, managed to produce anything like the universal language that would be necessary for anyone – human or machine – to perform the calculations that would replace ordinary reasoning and argumentation.

In a much more modest form, these ideas were revived by the English logician George Boole (1815–1864). In his The Laws of Thought (1854) he developed an algebraic analysis of properties. For instance, if w denotes white things, and s denotes sheep, then ws denotes those objects that are both white and sheep, w + s those objects that are either white or sheep, w − s those that are white but not sheep, etc. 1 denotes “everything”, and thus 1 − w denotes everything that is not white. Boole proposed “laws of thought” such as: xy = yx

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