Clarification Quotes (7 quotes)
As our researches have made clear, an animal high in the organic scale only reaches this rank by passing through all the intermediate states which separate it from the animals placed below it. Man only becomes man after traversing transitional organisatory states which assimilate him first to fish, then to reptiles, then to birds and mammals.
Annales des Sciences Naturelles (1834), 2 (ii), 248. Trans. in E. S. Russell, Form and Function (1916), 82.
Cellular pathology is not an end if one cannot see any alteration in the cell. Chemistry brings the clarification of living processes nearer than does anatomy. Each anatomical change must have been preceded by a chemical one.
Attributed in H. Coper and H. Herken, Deutsche Medizini Wochenschrift (18 Oct 1963), 88, No. 42, 2035, in the original German, “Nach der Überlieferung durch His soll Virchow geäußert haben: ‘Die Zellular-pathologie ist nicht am Ende, wenn man an einer Zelle keine Veränderungen mehr sehen kann. Die Chemie steht der Erklärung der Lebensvorgänge näher als die Anatomie. Jede anatomische Verände-rung setzt notwendig eine chemische voraus.’” As translated in Angel Pentschew,'Morphology and morphogenesis of lead encephalopathy', Acta Neuropathologica (Sep 1965) 5, No. 2, 133-160, as cited in I. Arthur Michaelson and Mitchell W. Sauerhoff, 'Animal Models of Human Disease: Severe and Mild Lead Encephalopathy in the Neonatal Rat', Environmental Health Perspectives (May 1974), 7, 204 & 223 footnote. Note: Although given in quotation marks in the original German text, the subject quote is almost definitely NOT verbatim, but only a paraphrase of Virchow’s teachings. The German text introduces the subject quote with, “Nach der Überlieferung durch His soll Virchow geäußert haben:…” which means, “According to tradition Virchow is said to have expressed:…” (using Google translate). However, it is useful as a succinct statement to the effect of what Virchow might say to summarize his doctrine.
From time immemorial, the infinite has stirred men's emotions more than any other question. Hardly any other idea has stimulated the mind so fruitfully. Yet, no other concept needs clarification more than it does.
In address (4 Jun 1925), at a congress of the Westphalian Mathematical Society in Munster, in honor of Karl Weierstrass. First published in Mathematische Annalen (1926), 95, 161-190. Translated by Erna Putnam and Gerald J. Massey as 'On the Infinite', collected in Paul Benacerraf (ed.) Philosophy of Mathematics: Selected Readings (1983), 185. Compare another translation elsewhere on this page, beginning, “The Infinite!…”.
I see with much pleasure that you are working on a large work on the integral Calculus [ ... ] The reconciliation of the methods which you are planning to make, serves to clarify them mutually, and what they have in common contains very often their true metaphysics; this is why that metaphysics is almost the last thing that one discovers. The spirit arrives at the results as if by instinct; it is only on reflecting upon the route that it and others have followed that it succeeds in generalising the methods and in discovering its metaphysics.
Letter to S. F. Lacroix, 1792. Quoted in S. F. Lacroix, Traité du calcul differentiel et du calcul integral (1797), Vol. 1, xxiv, trans. Ivor Grattan-Guinness.
I would clarify that by ‘animal’ I understand a being that has feeling and that is capable of exercising life functions through a principle called soul; that the soul uses the body's organs, which are true machines, by virtue of its being the principal cause of the action of each of the machine's parts; and that although the placement that these parts have with respect to one another does scarcely anything else through the soul's mediation than what it does in pure machines, the entire machine nonetheless needs to be activated and guided by the soul in the same way as an organ, which, although capable of rendering different sounds through the placement of the parts of which it is composed, nonetheless never does so except through the guidance of the organist.
'La Mechanique des Animaux', in Oeuvres Diverses de Physique et de Mechanique (1721), Vol. 1, 329. Quoted in Jacques Roger, Keith R. Benson (ed.), Robert Ellrich (trans.), The Life Sciences in Eighteenth-Century French Thought, (1997), 273-4.
Logic issues in tautologies, mathematics in identities, philosophy in definitions; all trivial, but all part of the vital work of clarifying and organising our thought.
'Last Papers: Philosophy' (1929), in The Foundations of Mathematics and Other Logical Essays (1931), 264.
The infinite! No other question has ever moved so profoundly the spirit of man; no other idea has so fruitfully stimulated his intellect; yet no other concept stands in greater need of clarification than that of the infinite.
Address in memory of Karl Weierstrass. As quoted in Journal of the University of Bombay (1933), 2, 201. Also in Tobias Dantzig, Number: The Language of Science (1937), 237. Also partially quoted as epigraph in in James Roy Newman, The World of Mathematics (1956), Vol. 3, 1593. which dates the address as 1921. Another translation for perhaps the same address ('On the Infinite'), in honor of Weierstrass, dates it as 4 Jun 1925, in Paul Benacerraf (ed.) Philosophy of Mathematics (1983), 183. See this alternate version elsewhere on this page, beginning, “From time immemorial…”.