New York: Harper & Brothers, 1851. First edition in English. Translated from the first edition, published in French in 1835. Some foxing and marginal toning. Light pencil marginalia on a couple pages. A very good copy. Rebound in twentieth century polished calf over marbled boards. Gilt spine. Octavo. 260, [12, ads] pp. Item #17496
Comte begins with a definition of mathematics, as follows: “We are now able to define mathematical science with precision, by assigning to it as its object the indirect measurement of magnitudes, and by saying it constantly proposes to determine certain magnitudes from others by means of the precise relations existing between them. This enunciation, instead of giving an idea of only an art…characterizes immediately a true science, and shows it at once to be composed of an immense chain of intellectual operations, which may evidently become very complicated, because of the series of intermediate links which it will be necessary to establish between the unknown quantities and those which admit of a direct measurement…” (p. 25).
Auguste Comte (1798 – 1857) was a philosopher, mathematician, and writer who developed the concept of positivism in the wake of the French Revolution. He was also an innovator in the field of sociology, even coining the term in the early 1850s. Comte’s work influenced John Stuart Mill, Harriet Martineau, Herbert Spencer, and eventually the sociological theories of Émile Durkheim. He also developed innovative theories on religion, humanism, and altruism (a term he may have coined) and contributed to utopian literature and thought. Comte is considered the first philosopher of science in the modern sense of the term, and the present work represents his exploration of philosophical principles in the field of mathematics.