From Parts to Wholes (1850-1899)

"The world of ideas which it [mathematics] discloses or illuminates, the contemplation of divine beauty and order which it induces, the harmonious connection of its parts, the infinite hierarchy and absolute evidence of the truths with which mathematical science is concerned, these, and such like, are the surest groimds of its title of human regard, and would remain unimpaired were the plan of the universe unrolled like a map at our feet, and the mind of man qualified to take in the whole scheme of creation at a glance.” (James J Sylvester, "A Plea for the Mathematician", Nature 1, 1870)

"Nature creates unity even in the parts of a whole." (Eugène Delacroix, 1857)

"Analysis and synthesis, though commonly treated as two different methods, are, if properly understood, only the two necessary parts of the same method. Each is the relative and correlative of the other. Analysis, without a subsequent synthesis, is incomplete; it is a mean cut of from its end. Synthesis, without a previous analysis, is baseless; for synthesis receives from analysis the elements which it recomposes." (Sir William Hamilton, "Lectures on Metaphysics and Logic: 6th Lecture on Metaphysics", 1858)

"[…] the besetting danger is not so much of embracing falsehood for truth, as of mistaking a part of the truth for the whole." (John S Mill, "Dissertations and Discussions: Political, Philosophical, and Historical”, 1859)

"We have repeatedly observed that while any whole is evolving, there is always going on an evolution of the parts into which it divides itself; but we have not observed that this equally holds of the totality of things, which is made up of parts within parts from the greatest down to the smallest." (Herbert Spencer, "First Principles", 1862)

"The adaptation observed in men, animals and plants [...] one part of this adaptation is explained from a thought-process in the interior of these bodies [...] another part, however, the adaptation of the organism, by a thought-process in a greater whole." (Bernhard Riemann, Gesammelte Mathematische Werke, 1876)

"All things, man included, are parts of one great whole." (Richard M Bucke, "Man's Moral Nature", 1879)

"The old and oft-repeated proposition ‘Totum est majus sua parte’ [the whole is larger than the part] may be applied without proof only in the case of entities that are based upon whole and part; then and only then is it an undeniable consequence of the concepts ‘totum’ and ‘pars’. Unfortunately, however, this ‘axiom’ is used innumerably often without any basis and in neglect of the necessary distinction between ‘reality’ and ‘quantity’, on the one hand, and ‘nnumbe’ and ‘set’, on the other, precisely in the sense in which it is generally false." (Georg Cantor, "Über unendliche, lineare Punktmannigfaltigkeiten", Mathematische Annalen 20, 1882)

"The part always has a tendency to reunite with its whole in order to escape from its imperfection." (Leonardo Da Vinci, "The Notebooks of Leonardo da Vinci", 1888)