"In spite of their relations, science and religion remain, and must remain, distinct. If there were no other way of establishing a rational order between things than that of reducing the many to the one, either by assimilation or by elimination, the destiny of religion would appear doubtful." (Émile Boutroux, "Science and Religion in Contemporary Philosophy", 1908)
"There can be nothing clearer or more convenient for the purpose of setting one's ideas in order and for conducting an abstract discussion, than precise definitions and inviolable lines of demarcation." (Émile Boutroux, "Science and Religion in Contemporary Philosophy", 1908)
"The senses afford a primary conception of the world, which they show to be a mass of facts, endless in their variety. Man may observe, analyse, and describe them with ever-increasing exactness: this very description constitutes science." (Émile Boutroux, "The Contingency of the Laws of Nature", 1911)
"Science is reduction. Mathematics is its ideal, its form par excellence, for it is in mathematics that assimilation, identification, is most perfectly realized. The universe, scientifically explained, would be a certain formula, one and eternal, regarded as the equivalent of the entire diversity and movement of things." (Émile Boutroux, "Natural law in Science and Philosophy", 1914)
"The mathematical laws presuppose a very complex elaboration. They are not known exclusively either a priori or a posteriori, but are a creation of the mind; and this creation is not an arbitrary one, but, owing to the mind’s resources, takes place with reference to experience and in view of it. Sometimes the mind starts with intuitions which it freely creates; sometimes, by a process of elimination, it gathers up the axioms it regards as most suitable for producing a harmonious development, one that is both simple and fertile. The mathematics is a voluntary and intelligent adaptation of thought to things, it represents the forms that will allow of qualitative diversity being surmounted, the moulds into which reality must enter in order to become as intelligible as possible." (Émile Boutroux, "Natural Law in Science and Philosophy", 1914)
"The philosopher asks himself whether natural law as assumed by science, wholly coincides with law as really existing in nature; whether science and reality are so alike that science may be regarded as exhausting everything intelligible and true that the real contains." (Émile Boutroux, "Natural Law in Science and Philosophy", 1914)
"The world is an endless variety of facts, linked together by necessary and immutable bonds." (Émile Boutroux, "Natural law in Science and Philosophy", 1914)
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