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Hermann von Helmholtz’s distinction between “pure intuitive” and “physical” geometry must be counted as the most influential of his many contributions to the philosophy of science. In a series of papers from the 1860s and 70s, Helmholtz argued against Kant’s claim that our knowledge of Euclidean geometry was an a priori condition for empirical knowledge. He claimed that geometrical propositions could be meaningful only if they were taken to concern the behaviors of physical bodies used in measurement, from which it followed that it was posterior to our acquaintance with this behavior. This paper argues that Helmholtz’s understanding of geometry was fundamentally shaped by his work in sense-physiology, above all on the continuum of colors. For in the course of that research, Helmholtz was forced to realize that the color-space had no inherent metrical structure. The latter was a product of axiomatic definitions of color-addition and the empirical results of such additions. Helmholtz’s development of these views is explained with detailed reference to the competing work of the mathematician Hermann Grassmann and that of the young James Clerk Maxwell. It is this separation between 1) essential properties of a continuum, 2) supplementary axioms concerning distance-measurement, and 3) the behaviors of the physical apparatus used to realize the axioms, which is definitive of Helmholtz’s arguments concerning geometry.
KNOWLEDGE OF SCIENCE AND NATURAL PHILOSOPHY IN THE early Roman Empire was largely an inheritance from the ancient Greeks. Christian beliefs and ideas about the world that emerged during the first few centuries after Christ interacted with the dominant pagan view and helped shape a new outlook and a new worldview. If the wisdom of the world had previously been embedded in pagan learning, the triumph of Christianity in the late fourth century changed all that. The new wisdom emanated from Sacred Scripture, the Bible, and in the fundamental belief that an omniscient and omnipotent God had created our world from nothing, a conception that would have been utterly incomprehensible and unintelligible to traditional Greek philosophers. An important part of our story concerns the interrelationship between pagan and Christian learning. The eventual explicit and self-conscious use of reason as a force in medieval intellectual life emerged from this interrelationship, with results that were profound for the late Middle Ages and for the future of Western society.
CHRISTIANITY AND LATE ANTIQUITY
To understand what happened in the twelfth century, it is necessary to begin with the early Middle Ages, with its roots in the late Roman Empire. During that period in Western Europe, intellectual life was shaped by concerns about the Christian religion and its theology, and by a modest amount of secular learning that was largely an inheritance from pagan Greek sources, such as Plato, Aristotle, Cicero, and the Stoics.
WHAT MADE IT POSSIBLE FOR WESTERN CIVILIZATION TO develop science and the social sciences in a way that no other civilization had ever done before? The answer, I am convinced, lies in a pervasive and deep-seated spirit of inquiry that was a natural consequence of the emphasis on reason that began in the Middle Ages. With the exception of revealed truths, reason was enthroned in medieval universities as the ultimate arbiter for most intellectual arguments and controversies. It was quite natural for scholars immersed in a university environment to employ reason to probe into subject areas that had not been explored before, as well as to discuss possibilities that had not previously been seriously entertained.
Reason and the spirit of inquiry appear to be natural companions. This spirit of inquiry can be aptly described as the spirit of “poking around,” a spirit that manifests itself through an urge to apply reason to almost every kind of question and problem that confronts scholars of any particular period. Indeed, a vital aspect of “poking around” involves an irresistible urge to raise new questions, which eventually give rise to even more questions. I regard the spirit of poking around as nothing less than the spirit of scientific inquiry.
When scholars in the eleventh and twelfth centuries began the process of opposing reason to authority, they also began what may be appropriately called “the culture of poking around,” or the irrepressible urge to probe into many things.
THE EMPHASIS ON REASON – ITS DEVELOPMENT AND APPLICATION – that was so characteristic of medieval Western Europe, and which we have described, must now briefly be viewed in the broader context of subsequent history. It is essential to do this because I have claimed that the Age of Reason began in the Middle Ages. If it did, what connection does the latter have with the former? To make the connection, we must first arrive at some sense of what the phrase “Age of Reason” signifies.
THE MEDIEVAL AND EARLY MODERN “AGES OF REASON”
Many rightly regard the seventeenth century as a century of momentous change because it produced a “Scientific Revolution,” an expression that is commonly used to characterize the science of that century. The designation is appropriate because of the contributions of a series of extraordinary figures – Galileo Galilei, Johannes Kepler, René Descartes, Christiaan Huyghens, Robert Boyle, Isaac Newton, and many others – who produced scientific theories, experiments, and treatises that reflected a new approach to nature that radically transformed the way science had been done within the earlier context of medieval Aristotelian natural philosophy. Galileo captured a fundamental aspect of the dramatic change when he declared:
Philosophy is written in this grand book, the universe, which stands continually open to our gaze. But the book cannot be understood unless one first learns to comprehend the language and read the letters in which it is composed.
THE FACULTY OF ARTS OF ANY MEDIEVAL UNIVERSITY HAD MORE students and more teaching masters than any of the three other higher faculties: theology, medicine, and law. This was necessarily true because the bachelor of arts and master of arts degrees were prerequisites for entry into the higher faculties. Therefore, all students began their careers in the arts faculty. By virtue of the subjects taught, the faculty of arts was the primary repository of reason in any medieval university. This is evident from the range of courses taught: astronomy, mathematics, optics, logic, and natural philosophy. All were inherently analytical subjects except natural philosophy, which was nevertheless taught as if it were analytical.
THE OLD AND NEW LOGIC
Although logic was a basic subject, it was always regarded as an instrument for the critical study of all other areas of learning. We have already seen the role it played in the twelfth century. In the thirteenth century, Peter of Spain reiterated the central role that logic was accorded in the twelfth century when he declared that “[l]ogic is the art which provides the route to the principles of all methods, and hence logic ought to come first in the acquisition of the sciences.” With the translations of Aristotle's previously unknown logical works, which were added to the old logic, logic was given a substantial foundational role in the curriculum of the medieval university.
MOST WHO STUDY THE POLITICAL, SOCIAL, INSTITUTIONAL, AND intellectual developments in Western Europe during the Middle Ages find it easy to believe that “Western civilization was created in medieval Europe.” George Holmes, the author of that sweeping statement, argues further that
[t]he forms of thought and action which we take for granted in modern Europe and America, which we have exported to other substantial portions of the globe, and from which indeed, we cannot escape, were implanted in the mentalities of our ancestors in the struggles of the medieval centuries.
Just what was implanted in the peoples of the Middle Ages between approximately 1050 to 1500? Nothing less than a capacity for establishing the foundations of the nation state, parliaments, democracy, commerce, banking, higher education, and various literary forms, such as novels and history. By the late Middle Ages, Europe had also produced numerous laborsaving technological innovations. The profound problems involved in reconciling church and state, and natural philosophy and Scripture were first seriously encountered in this same period. Indeed, it was during the Middle Ages that canon and civil law were reorganized and revitalized. Not only did these newly fashioned disciplines lay the foundations of Western legal systems, but from the canon law also came the concept of a corporation, which enabled various institutions in the West – commercial, educational, and religious – to organize and govern themselves in a manner that had never been done before.
NATURAL PHILOSOPHY, OR NATURAL SCIENCE AS IT WAS SOMETIMES called, was the most widely taught discipline at the medieval university. For more than four centuries, virtually all students who obtained the master of arts degree had studied natural philosophy, and most undergraduates were exposed to significant aspects of it. What was natural philosophy for university students in the late Middle Ages?
WHAT IS NATURAL PHILOSOPHY?
In the broadest sense, natural philosophy was the study of change and motion in the physical world. In Chapter 3, we saw that it was one of Aristotle's three subdivisions of theoretical knowledge, or knowledge for its own sake. Natural philosophy was concerned with physical bodies that existed independently and were capable of motion, and therefore subject to change. In truth, Aristotle's natural philosophy was also concerned with bodies in motion that were themselves unchanging, as was assumed for all celestial bodies. In general, Aristotle's natural philosophy was concerned with separately existing animate and inanimate bodies that undergo change and possess an innate source of movement and rest.
Because the domain of natural philosophy was the whole of nature, as the name suggests, it did not represent any single science, but could, and did, embrace bits and pieces of all sciences. In this sense, natural philosophy was “The Mother of All Sciences.”
FOR MOST OF THE TWELFTH CENTURY, LEARNING IN WESTERN Europe was based on treatises that had originated within a Latin tradition that was comprised largely of handbooks, compendia, and encyclopedic works. Much of this knowledge had roots in Greek treatises written during the Hellenistic period. Some of this encyclopedic knowledge reached Latin authors, who either knew enough Greek to understand it or had access to translations.
THE LATIN TRADITION OF LEARNING IN THE EARLY MIDDLE AGES PRIOR TO THE INFLUX OF NEW TRANSLATIONS
Two Roman authors of the first century A.D. made significant contributions. Seneca (d. A.D. 68) titled his most famous treatise Natural Questions and filled it with information about geographical and meteorological phenomena into which he interjected morals drawn from nature, a feature that made his book popular with Christians. Pliny the Elder (A.D. 23/24–79), Seneca's contemporary, wrote a massive encyclopedic treatise in 37 books titled Natural History. Almost anything was grist for Pliny's insatiable information mill. These two treatises and the numerous extant handbooks in Greek and Latin formed a basis for subsequent authors who wrote for a Latin-speaking audience. As we saw in Chapter 1, between the fourth and eighth centuries, such authors as Macrobius, Chalcidius, Martianus Capella, Boethius, Cassiodorus, Isidore of Seville, and Venerable Bede provided the means for understanding the cosmic structure and operation of the world.
In the thirteenth century, theology became a professional discipline taught in independent faculties of theology at the universities of Paris and Oxford, the most important schools of theology during the thirteenth and fourteenth centuries. The faculties of theology controlled the content of theological education and the granting of the master's degree in theology. From the early centuries of Christianity, theologians always regarded their discipline as superior to that of any secular subject. Secular learning was viewed traditionally as the handmaid of theology and, therefore, subordinate to it. After all, the objective of theology was to interpret and explicate the mysteries of the faith and the meaning of Sacred Scripture. But what theology lacked until the thirteenth century was knowledge of its place in the scheme of learning. How did it relate to other disciplines, especially logic and natural philosophy?
Is Theology a Science?
In the course of the thirteenth century, many theologians, beginning with Alexander of Hales and continuing on through St. Thomas Aquinas and many others, discussed the question of “whether theology is a science.” In posing this question, theologians were inquiring whether theology is a science in the Aristotelian sense of science, namely, science as demonstrative knowledge derived from premises that are “true, necessary, certain, immediate, and appropriate to the phenomenon to be explained.”
BY THE ELEVENTH AND TWELFTH CENTURIES, A NEW CIVILIZATION had emerged in Western Europe. That new civilization was largely a product of the peoples of northern Europe, who had been at the fringes of Roman civilization for many centuries. In the course of a lengthy period of upheaval and transformation, from around 400 to 1000, a new Europe was formed in the West, the product of a fusion of the new, largely Germanic, peoples with the inhabitants of the older Roman civilization.
CENTURIES OF DISSOLUTION: EUROPE AT ITS NADIR
The birth of the new Europe was a lengthy process because Germanic tribes – Ostrogoths, Visigoths, Burgundians, Lombards, Franks, and others – from the fourth to the seventh centuries were constantly at war in the northern part of continental Europe, or in process of migration, as imperial Rome weakened and gradually dissolved in Western Europe. Just when it seemed that the Franks under Charlemagne would bring a much greater degree of stability and peace than had hitherto been known in Europe, the death of Charlemagne in 814 brought further disintegration. The tendency toward central government ended, and the trend toward feudal states accelerated as noble families sought to retain whatever power and land they possessed, and to add whatever they could by fair means or foul.