Even bold and revolutionary thinkers bow to the judgment of science. Kropotkin wants to break up all existing institutions, but he does not touch science. Ibsen goes very far in his critique of bourgeois society, but he retains science as a measure of truth. Levi Strauss has made us realize that Western thought is not the lonely peak of human achievement it was once thought to be, but he and his followers exclude science from their relativization of ideologies. Marx and Engels were convinced that science would aid the workers in their quest for mental and social liberation.

In effect what Luther said in 1517 was that we may appeal to a demonstrable work of God, the Bible, to override any established authority. The Scientific Revolution begins when Nicolaus Copernicus implied the bolder proposition that there is another work of God to which we may appeal even beyond this: the great work of nature. No absolute statement is allowed to be out of reach of the test, that its consequence must conform to the facts of nature. The habit of testing and correcting the concept by its consequences in experience has been the spring within the movement of our civilization ever since. In science and in art and in self-knowledge we explore and move constantly by turning to the world of sense to ask, Is this so? This is the habit of truth, always minute yet always urgent, which for four hundred years has entered every action of ours; and has made our society and the value it sets on man.

The outlook before the Scientific Revolution was content with scholastic logic applied to a nature of hierarchies. The Scientific Revolution ended that: it linked the rational and the empirical, thought and fact, theory and practical experiment. And this has remained the content of science ever since.

If Spinoza had in fact tried to construct his philosophical system by the method that our contemporary positivism would have recommended to him, it is not difficult to imagine what he would have produced as a ‘system’. He would only have brought together the purely mechanical and religious, mystical ‘general ideas’ that were guiding all (or almost all) naturalists in his day. Spinoza understood very clearly that religious, theological mysticism was the inevitable complement of a purely mechanistic (geometrical, mathematical) world outlook, i.e. the point of view that considers the sole ‘objective’ properties of the real world to be only the spatial, geometrical forms and relations of bodies. His greatness was that he did not plod along behind contemporaneous natural science, i.e. behind the one-sided, mechanistic thinking of the coryphaei of the science of the day, but subjected this way of thinking to well substantiated criticism from the angle of the specific concepts of philosophy as a special science. This feature of Spinoza’s thinking was brought out clearly and explicitly by Friedrich Engels: ‘It is to the highest credit of the philosophy of the time that it did not let itself be led astray by the restricted state of contemporary natural knowledge, and that from Spinoza right to the great French materialists it insisted on explaining the world from the world itself and left the justification in detail to the natural science of the future.’ [Dialectics of Nature] That is why Spinoza has come down in the history of science as an equal contributor to its progress with Galileo and Newton, and not as their epigone, repeating after them the general ideas that could be drawn from their work. He investigated reality himself from the special, philosophical angle, and did not generalise the results and ready-made findings of other people’s investigation, did not bring together the general ideas of the science of his day and the methods of investigation characteristic of it, or the methodology and logic of his contemporary science. He understood that that way led philosophy up a blind alley, and condemned it to the role of the wagon train bringing up in the rear of the attacking army the latter’s own ‘general ideas and methods’, including all the illusions and prejudices incorporated in them. That is why he also developed ‘general ideas and methods of thought’ to which the natural science of the day had not yet risen, and armed future science with them, which recognised his greatness three centuries later through the pen of Albert Einstein, who wrote that he would have liked ‘old Spinoza’ as the umpire in his dispute with Niels Bohr on the fundamental problems of quantum mechanics rather than Carnap or Bertrand Russell, who were contending for the role of the ‘philosopher of modern science’ and spoke disdainfully of Spinoza’s philosophy as an ‘outmoded’ point of view ‘which neither science nor philosophy can nowadays accept’. Spinoza's understanding of thinking as the activity of that same nature to which extension also belonged is an axiom of the true modern philosophy of our century, to which true science is turning more and more confidently and consciously in our day (despite all the attempts to discredit it) as the point of view of true materialism.

More than any of his predecessors Plato appreciated the scientific possibilities of geometry. .. By his teaching he laid the foundations of the science, insisting upon accurate definitions, clear assumptions, and logical proof. His opposition to the materialists, who saw in geometry only what was immediately useful to the artisan and the mechanic is... clear. ...That Plato should hold the view... is not a cause for surprise. The world's thinkers have always held it. No man has ever created a mathematical theory for practical purposes alone. The applications of mathematics have generally been an afterthought.

We literally understand, then, a thorough study and assimilation of all the scientific works of primary importance on which the knowledge of Marxist theory rests. We might use a striking formula of Spinoza's to represent this objective: Spinoza said that a science solely of conclusions is not a science, that a true science is a science of premisses (principles) and conclusions in the integral movement of the demonstration of their necessity.

The second helpful notion mimics Galileo’s50 conclusion that scientific reality is often revealed only by math as if math was the language of God. Galileo’s attitude also works well in messy, practical life. Without numerical fluency, in the part of life most of us inhabit, you are like a one-legged man in an ass-kicking contest.

The Scientific Revolution revolution was a change from a world of things ordered according to their ideal nature, to a world of events running in a steady mechanism of before and after.

If Korzybski cannot be said to have established an empirical science, what then has he done? He has pointed a way toward the establishment of such a science. He was a precursor of an intellectual revolution which is just now beginning and which promises to match that of the Renaissance. If Korzybski is seen in this role, then the question of his originality or erudition is not important. He might have something of a dilettante in him. He might have pretended to have more specialized knowledge than he actually had. Great portions of his outlook might be found in the works of more modest and more meticulous workers, That is not important. He was a man of vision and an apostle. Such men are all too rare in our age of specialization.

The seventeenth century witnessed the birth of modern science as we know it today. The science was something new, based on a direct confrontation of nature by experiment and observation. But there was another feature of the new science—a dependence on numbers, on real numbers of actual experience.
...The ancients knew a few numerical laws... But prior to the Scientific Revolution, the goal of science (or the study of nature) was not to seek laws of nature expressed in terms of numbers or number relations. ...the new science ...not only found laws based on numbers but they were also willing to express these laws in terms of higher powers of numbers—squares and cubes.

[T]radition links us with the revolutionary science of the Renaissance... we can distinguish... four major periods of advance. [C]entred in Italy... the renewal of mechanics, anatomy, and astronomy with Leonardo, Vesalius, and Copernicus, destroying the authority of the Ancients in their central doctrines of man and the world. [S]preading to the Low Countries, France, and Britain, beginning with Bacon, Galileo, and Descartes, and ending in Newton, hammered out a new mathematical mechanical model of the world. [C]entred in industrial Britain and revolutionary Paris, opened... areas of experience... as... electricity... It was then that science could help... with power, machinery, and chemicals, to transform production and transport. [T]he scientific revolution of our own time. ...[T]he beginning of a world science, transforming old and creating new industries, permeating every aspect of human life. ...[N]ow... we find science directly involved in the violent and terrible drama of wars and social revolution.

The goal of deriving all the phenomena of nature from a few basic physical laws and the axioms of mathematics had been set by Galileo...
In studying curvilinear motions on the earth Galileo had found the parabola to be the basic curve. In the heavens... Kepler... had found the ellipse to be the basic curve. Why this difference? ...since parabola and ellipse are both conic sections there was the provocative suggestion that perhaps some physical law unified these related paths of motion. ...
It has often happened in the history of mathematics and science that major problems remained outstanding... great minds... succeeded only in revealing the true difficulties... and in generating an atmosphere of dispair... Then a genius appeared... with ideas that seemed remarkably simple once propounded, clarified the entire situation, dispelled the confusion, restored order, and produced a new synthesis that embraced far more even than the phenomena under consideration. The genius who... picked up the torch of science dropped by Galileo, was Isaac Newton.

The philosopher Comte has made the statement that chemistry is a non-mathematical science. He also told us that astronomy had reached a stage when further progress was impossible. These remarks, coming after Dalton's atomic theory, and just before Guldberg and Waage were to lay the foundations of chemical dynamics, Kirchhoff to discover the reversal of lines in the solar spectrum, serve but to emphasize the folly of having "recourse to farfetched and abstracted Ratiocination," and should teach us to be "very far from the litigious humour of loving to wrangle about words or terms or notions as empty".

the idea that mathematics expresses the essential reality of nature was first put explicitly, in modern times, by scientists, such as Sir James Jeans and Werner Heisenberg, but within a few decades, these ideas were being transmitted almost subliminally. As a result, after passing through graduate school, most physicists have come to regard this attitude toward mathematics as being perfectly natural. However, in earlier generations such views would have been regarded as strange and perhaps even a little crazy — at all events irrelevant to a proper scientific view of reality.