“[The mathematical character of Descartes' physics lies in its methodological nature, namely, the] axiomatic structure of the whole system, in the establishment of indubitable foundations and the deduction of the phenomena.”

—  Eduard Jan Dijksterhuis

Source: The mechanization of the world picture, 1961, p. 414; as cited in: ‎Marleen Rozemond (2009), Descartes's Dualism. p. 235

Adopted from Wikiquote. Last update June 3, 2021. History

Help us to complete the source, original and additional information

Do you have more details about the quote "[The mathematical character of Descartes' physics lies in its methodological nature, namely, the] axiomatic structure o…" by Eduard Jan Dijksterhuis?
Eduard Jan Dijksterhuis photo
Eduard Jan Dijksterhuis7
Dutch historian 1892–1965

Related quotes

“Another feature of Alexandrian algebra is the absence of any explicit deductive structure. The various types of numbers… were not defined. Nor was there any axiomatic basis on which a deductive structure could be erected. The work of Heron, Nichomachus, and Diophantus, and of Archimedes as far as his arithmetic is concerned, reads like the procedural texts of the Egyptians and Babylonians… The deductive, orderly proof of Euclid and Apollonius, and of Archimedes' geometry is gone. The problems are inductive in spirit, in that they show methods for concrete problems that presumably apply to general classes whose extent is not specified. In view of the fact that as a consequence of the work of the classical Greeks mathematical results were supposed to be derived deductively from an explicit axiomatic basis, the emergence of an independent arithmetic and algebra with no logical structure of its own raised what became one of the great problems of the history of mathematics. This approach to arithmetic and algebra is the clearest indication of the Egyptian and Babylonian influences… Though the Alexandrian Greek algebraists did not seem to be concerned about this deficiency… it did trouble deeply the European mathematicians.”

Morris Kline (1908–1992) American mathematician

Source: Mathematical Thought from Ancient to Modern Times (1972), p.144

Galileo Galilei photo

“This [experimentation] is the custom—and properly so—in those sciences where mathematical demonstrations are applied to natural phenomena, as is seen in the case of perspective, astronomy, mechanics, music, and others where the principles, once established by well-chosen experiments, become the foundations of the entire superstructure.”

Galileo Galilei (1564–1642) Italian mathematician, physicist, philosopher and astronomer

Salviati, Third Day. Change of Position
Dialogues and Mathematical Demonstrations Concerning Two New Sciences (1638)

Hans Freudenthal photo

“Our mathematical concepts, structures, ideas have been invented as tools to organise the phenomena of the physical, social and mental world. Phenomenology of a mathematical concept, structure, or idea means describing it in its relation to the phenomena for which it was created, and to which it has extended in the learning process of mankind, and, as far as this description is concerned with the learning process of the young generation, it is didactical phenomenology, a way to show the teacher the places where the learner might step into the learning process of mankind.”

Hans Freudenthal (1905–1990) Dutch mathematician

Source: The Concept and the Role of the Model in Mathematics and Natural and Social Sciences (1961), p. ix

David Hilbert photo

“The organic unity of mathematics is inherent in the nature of this science, for mathematics is the foundation of all exact knowledge of natural phenomena. That it may completely fulfil this high mission, may the new century bring it gifted masters and many zealous and enthusiastic disciples!”

David Hilbert Mathematical Problems

Mathematical Problems (1900)

Alain Badiou photo

“1. We are the contemporaries of a third epoch of science after the Greek and Galilean. The caesura which opens this third epoch is not (a with the Greek) an invention - that of demonstrative mathematics - nor is it (like the Galilean) a break - that which mathematized the discourse of physics. It is a split, through, which the very nature of the base of mathematical rationality reveals itself, as does the character of hte dision of thought which establishes it.”

Alain Badiou (1937) French writer and philosopher

Introduction
Being and Event (1988)

George Henry Lewes photo

“Whatever lies beyond the limits of experience, and claims another origin than that of induction and deduction from established data, is illegitimate.”

George Henry Lewes (1817–1878) British philosopher

Vol. 1, p. 17
The Foundations of a Creed (1874-5)

“# General system theory in the narrower sense (G. S. T.), trying to derive from a general definition of “system” as complex of interacting components, concepts characteristic of organized wholes such as interaction, sum, mechanization, centralization, competition, finality, etc., and to apply them to concrete phenomena.
While systems theory in the broad sense has the character of a basic science, it has its correlate in applied science, sometimes subsumed under the general name of Systems Science.”

Ludwig von Bertalanffy (1901–1972) austrian biologist and philosopher

Source: General System Theory (1968), 4. Advances in General Systems Theory, p. 90-91

Ervin László photo

“Systems philosophy first must find out the "nature of the beast" This is the question of what is meant by "system", and how systems are realized in reality in various levels of observation. In Laslo's terms, this is the methodology and theory of natural systems. Secondly, there is epistemology, i. e. the methodology and theory of cognitive systems.”

Ervin László (1932) Hungarian musician and philosopher

Source: Introduction to Systems Philosophy (1972), p. xix.

Albert Einstein photo

“Physics is essentially an intuitive and concrete science. Mathematics is only a means for expressing the laws that govern phenomena.”

Albert Einstein (1879–1955) German-born physicist and founder of the theory of relativity

From Lettre à Maurice Solvine, by A. Einstein (Gauthier-Villars: Paris 1956)
Attributed in posthumous publications, Albert Einstein: A guide for the perplexed (1979)

Jack Vance photo

“There can be no doubt as to the facts as I have stated them. Orthodoxy derives from this axiomatic foundation, and the two systems are mutually reinforcing: hence each is doubly validated.”

Jack Vance Dying Earth

Source: Dying Earth (1950-1984), The Eyes of the Overworld (1966), Chapter 4, "The Sorcerer Pharesm"

Related topics