Reading on: The revival and revision of Greek learning

Randall, John H. Jr. The Making of the Modern Mind Fiftieth Anniversary Edition, Columbia University Press, New York 1976 [excerpts — 950 words]

The more fully the record of late medieval and Renaissance thought is studied, the clearer it becomes that the most daring departures from Aristotelian science were carried on within the Aristotelian framework, and by means of a critical reflection on the Aristotelian doctrines.

The chief of these newly-discovered ideas were the methods of the Greek mathematicians. Indeed, the one contribution the Humanists can fairly claim to have made to the rise of modem science was to send men to the study of the ancient sources of Alexandrian science...

Several practical questions of technology combined to support this interest in a mathematical treatment of natural problems. The extended navigation of the preceding century had called for more exact tables of the stars; the measurement involved turned men to the mathematical astronomy of Ptolemy and finally drove out the Aristotelian non-quantitative treatment. And the new problems of fortification and artillery led to the demand for a practical science of mechanics…

The stimulus of Archimedes in particular sent men to work upon “practical geometries” and useful “new sciences. What they sought and found in the ancients were primarily effective techniques and fruitful ways of procedure and discovery…

The natural science of early modern times was thus hardly a complete break with the past, but rather a continuous development from the most critical teachings of the later Middle Ages, stimulated by technical demands and inspired by fresh contact with the achievements of Alexandrian thought…

THE DIRECT APPEAL TO NATURE
In the Renaissance, as always, men turned to the careful observation of nature only after every other idea and authority had failed. What the revival of ancient learning did for science was to bring a wealth of conflicting suggestions into men’s ken, and force them to appeal to reason to decide…

In the most practical fields this recourse to nature occurred first. The great artist engineers, Leonardo and Michelangelo and Raphael and Dbrer, were forced to study anatomy, mathematical perspective, and mechanics to paint and build aright…

Nor must we overlook the stimulus that came from the use of increasingly accurate tools and instruments in the more complex economic life of trade and manufactures. When Europeans borrowed from the East the compass and the sextant, so necessary to developing commerce, and began to use astronomical tables to find their way at sea; when gunpowder demanded improved fortifications and new devices, and when the craftsman came to adopt more and more mechanical aids, there grew up a new body of experience and knowledge about nature quite independent of the traditional lore. Above all, men learned the necessity of exact measurement and refined calculations, and acquired mechanical habits of thought that proved their utility in daily life.

THE NEW METHOD
For those who forsook the authority of the ancients, the chief problem seemed to be an authoritative and infallible method. Science today can rest on its achievements without too great a concern about its methods or their theoretical certainty. It was not so when science meant a break with everything that men had reverenced as true. The search for a method that would give certain knowledge was the paramount scientific problem of the sixteenth century.

Ironically enough, the very discovery of Copernicus that the earth moved increased the distrust of the senses and experience, and sent men to mathematics as the only unshakable knowledge. If men’s eyes lied here, where could they be trusted? This helps to explain why the mathematical method had already worked itself out to completeness in Newton when experimental science had hardly been born…

Every scientific innovator attacked the problem of method; most of them have left detached precepts that betray where the new interest lies. The Spanish scientific and social reformer Vives called experiment the only road to truth; but it was not by mere blind experiment that the new knowledge was to come. Leonardo knew far better when he said, “Whoever appeals to authority applies not his intellect but his memory” and “They say that that knowledge is mechanical which issues from experience, and that is scientific which is born and ends in the mind. But, as it seems to me, those sciences are vain and full of errors which are not born of experience, mother of all certitude… And this is the true rule to be followed by the investigators of natural phenomena… begin from experience and with that discover the causes.”

But though knowledge must begin and end in experience, its method must be rigidly mathematical. “No human investigation can call itself true science unless it proceeds through mathematical demonstrations... He who scorns the certainty of mathematics will not be able to silence sophistical theories which end only in a war of words”

Here are almost all the elements for the new method. But not till Galileo were they seriously and convincingly applied…

Select a single instance, like that of the ball rolling down the incline, analyze it completely to find the simple mathematical principle exemplified in it —the law of acceleration — deduce the consequences mathematically, and test by further experiment. Completed scientific knowledge will thus have passed both the test of accord with facts and of deduction from fundamental mathematical laws of nature. This has, indeed, been the method of physics to the present day, and to Galileo primarily belongs the honor of its formulation.

But in Galileo it was buried in the midst of the record of his discoveries and his quick-tempered polemical broadsides. At the same time Francis Bacon writing in England his Novum Organum, the new logic or tool, was sketching his version of the new method.