Koyré's exaltation of the "Platonic and Pythagorean" elements of the Scientific Revolution... was based on a demonstrably false understanding of how Galileo reached his conclusions. Koyré asserted that Galileo merely used experiments as a check on the theories he devised by mathematical reasoning. But later research has definitively established that Galileo's experiments preceded his attempts to give a mathematical account of their results.
Galileo GalileiRelated topics
account false later platonic pythagorean research revolution understanding galileoRelated quotes
Philosophical questions are not by their nature insoluble. They are, indeed, radically different from scientific questions, because they concern the implications and other interrelations of ideas, not the order of physical events; their answers are interpretations instead of factual reports, and their function is to increase not our knowledge of nature, but our understanding of what we know.
Susanne Langer
Von Neumann languages do not have useful properties for reasoning about programs. Axiomatic and denotational semantics are precise tools for describing and understanding conventional programs, but they only talk about them and cannot alter their ungainly properties. Unlike von Neumann languages, the language of ordinary algebra is suitable both for stating its laws and for transforming an equation into its solution, all within the "language."
John Backus
But Hermotimus, the Colophonian, rendered more abundant what was formerly published by Eudoxus and Theætetus, and invented a multitude of elements, and wrote concerning some geometrical places. But Philippus the Mendæan, a disciple of Plato, and by him inflamed in the mathematical disciplines, both composed questions, according to the institutions of Plato, and proposed as the object of his enquiry whatever he thought conduced to the Platonic philosophy.
Proclus
I know that most men - not only those considered clever, but even those who are very clever and capable of understanding most difficult scientific, mathematical, or philosophic, problems - can seldom discern even the simplest and most obvious truth if it be such as obliges them to admit the falsity of conclusions they have formed, perhaps with much difficulty - conclusions of which they are proud, which they have taught to others, and on which they have built their lives.
Leo Tolstoy
The really deep divergence between the humanistic and scientific sensibilities is one of temporality. Very nearly by definition, the scientist knows that tomorrow will be in advance of today. A twentieth-century schoolboy can manipulate mathematical and experimental concepts inaccessible to a Galileo or a Gauss. For a scientist the curve of the future is positive. Inevitably, the humanist looks back.
George Steiner