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Funtest kubus pooh minimarket in Bhusawal. Laplace then took it up, and managed to solve it by reducing it to operations with the standard apparatus of the game theorist, that is, an urn filled with very large numbers of black balls and white balls. Let the black balls stand for the existing population, the white balls for the average number of births.

The records returned by the intendants gave the. Imagine now a new play at the urn, giving b t white balls and an unknown number t of black balls. The answer depends on the size of the multiplier k. To be on the safe side, Laplace recommended taking samples of a million or more. When this was done just after the turn of the century, k came out to be The introduction of annual reporting of births and deaths to the central administration around marked an epoch in French statistics—the advance from occasional, imperfect, one-time, static surveys to continuous data collection and useful time series.

The first national statistical bureau, appropriately called the "department of tables" Tabellverket , came into existence in Sweden in ; it owed its precocity to the availability of a corps of inexpensive and experienced workers, the parish pastors, who had been keeping registers of their parishioners for fifty years or more. Johannisson sets forth in chapter 12 the Swedish case and its connection with English political arithmetic.

Norway and Denmark took their first national censuses in and set up their own bureaus of tables in The central German states, Mecklenburg, Hesse-Darmstadt, and Bavaria, and also Austria, counted themselves in and In , a colonel of militia mobilized the clergy of Scotland by threatening to quarter his troops. Back in France, the spirit of the Revolution puffed new vigor into the statisticians, who had it decreed, in , that every administrative unit should furnish each year, during November and December, the name, age, birthplace, residence, profession, and other means of subsistence of all citizens living in its territory.

Three out of 36, communes replied. No one succeeded in enforcing the decree until , when a number was obtained about a million less than Laplace had calculated. Another count, in , came out almost , larger than he had allowed. Napoleon liked these readings of the thermometer of public prosperity, but did not care to try again, lest the results reveal a decline in population and an argument for critics of his stewardship.

The census of was followed by that of Meanwhile the British faithfully fulfilled the requirement of a decennial census, which they took upon themselves for the first time in The land is easier to measure than the people. Our quantifying spirit came to ground in the late 18th century not only in exact cartography and geography as in the cases of the Ordnance and metric surveys but also in the exploitation of old forests and virgin lands.

Two examples are worth our attention, one from the Old World, where the quantifying landscaper faced constraints imposed by centuries of unregulated growth, and one from the New World, where the United States felt itself free to cut up the unsettled western territories as it pleased. The European mathematical landscapers made their greatest conquests in the princely forests of Germany. The products of these forests provided an essential element in the budgets of German states and principalities and an equally important item in the well-being of its inhabitants. By the end of the Seven Years' War in , enlightened princelings had recognized the need for prudent management of the remaining forest lands.

The following is derived from H. Lowood's account in chapter Forstwissenschaft required an inventory of the number and sorts of trees in the prince's domain, a plan for harvesting and reforestation so as to maximize yield while guaranteeing constant productivity, and a method for estimating the value of the cut timber.

Foresters developed methods of calculating wood mass from estimates of tree height; the more daring among them had recourse to the integral calculus to handle the irregular shapes of standing trees; others idealized the shapes to truncated cones; and all recognized the utility of the fiction of a Normalbaum , or standard tree, to which the natural specimens could be assimilated.

Two aspects of this management are relevant to the quantifying spirit. One is the amount of quantitative dog work Forstwissenschaft demanded. The manuals set out exemplary tables—paradigms in the true sense—to be filled in with details about the location, type, and yield of every commercial species grown in the forest. It has space for numbers; and it is only one of many tables in the manual.

The second aspect of interest is the compulsion to remake the forest to place the different species where they grew best so as to maximize not only the harvestable wood mass but also its quality and hence its value. Nature and custom prevented the full realization of this plan, but its design suggests what the mathematical landscaper might do when given a free hand.

That happened in the newly liberated British colonies in America. The several states had to honor the grants of land they had made to the officers and men of the Revolutionary army and the debts they owed to foreign governments. By most of the states had ceded most of their claims to western territories to the federal government.

That year Congress passed its first ordinance directing the method. The ordinance represented a great victory for the quantifiers, led by Thomas Jefferson, who insisted that the lands be surveyed into equal spans before being offered, and subdivided into parts affordable by small farmers; their opponents, primarily southern aristocrats and plantation owners, favored large grants to companies or wealthy individuals who would undertake to divide it up into such shapes and by such boundaries as suited their interests.

The Ordinance of stipulated that a Geographer's Line be run due west beginning at the intersection of the Ohio River with the western boundary of Pennsylvania, and that every 6 miles lines be run due south until they met the Ohio. These north-south strips, known as ranges, were to be cut into squares 6 miles on a side by parallels to the Geographer's Line. The squares, known as townships, might be further divided into 36 lots of one square mile each, later called sections. In each such township the federal government reserved for parks or other purposes four lots symmetrically placed, and, for a school to be run by the settlers, an additional lot at the center.

It is not possible to make the boundaries of the townships parallels of latitude and meridians of longitude and also to have all townships 6 miles square irrespective of their distance north or south of any east-west baseline. Surveyors adjusted to this impertinence of the earth's curvature by incorporating correction lines parallel to the baseline at mile intervals. The middle townships are slightly larger, the northerly ones slightly smaller. At the correction line, the shorter-than-average sides terminating the townships below were expanded into the longer-than-average sides terminating the townships above.

Albert White, A history of the rectangular survey system Washington, D. The earth still exacts a penalty for the presumption of those who would cut it into equal pieces. Motorists in the Great Plains, who can speed from east to west along roads that go straight as an arrow forever, must stop every 24 miles where north-south boundary roads jog suddenly at the correction lines.

Jefferson's original proposal would have divided the western territories into what he called "hundreds"—squares with sides of 10 nautical miles—rather than the townships of 36 square statute miles Congress eventually authorized. Each hundred was to contain 1, Jeffersonian acres and so on, for Jefferson, who invented the American system of pennies, dimes, and dollars, championed decimal division almost as strongly as democracy.

He and the professor of mathematics who helped him work out his system of rigid squares recommended it for its order and clarity, and as an obstacle to cheating. They argued that irregular lots inspired fraud, and could point to the experience of Massachusetts, which discovered that holdings in the country typically held 10 percent more land, and often percent more land, than had been granted.

Friendly surveyors set the boundaries where their clients wished. The square grid made the practice much more difficult and allowed purchasers to get more or less what they paid for. Industry did not escape attempts at rationalization induced by the quantifying spirit. The first volumes of both sets came into print in the early s, obedient to our periodization and consequent to a rush to secure priority.

The grandest vision in this direction was possessed by a. French general, Jean-Baptiste de Gribeauval, who beginning around plumped for standardized armaments with standardized parts. His notion of uniformity or interchangeability came to the United States via its champion of numeracy, Thomas Jefferson. The enlightened French general saw truly if distantly: the exactness that his quantifying and military spirit knew to be achievable was indeed accomplished by force of arms, by gun-makers to the U.

Even in the rudimentary, gross industry of the 18th century a program to rationalize through experiment and measurement may be discerned. The interrelations of physics, chemistry, mathematics, self-help, nonconforming education, and invention in industrializing Britain, especially the Midlands, during the later part of the 18th century have been examined at length. Clock-makers, the very model of the exact machinist, made the textile industry tick; instrument-makers created the precision tools that made possible the realization of Watt's engines.

This approach contrasted with that of French engineers, like Coulomb or Charles Borda, who liked to work from the principles of analytic mechanics. Watt perhaps occupies an intermediate position. Musson and Eric Robinson, Science and technology in the industrial revolution Manchester: Manchester University Press, , 28, —8, —6, —30, —40; A. Hall, "Engineering and the scientific revolution," Technology and culture, 2 , —41, on —8.

Cardwell, "Science, technology and industry," in G. Rousseau and Roy Porter, eds. Studies in the historiography of eighteenth-century science Cambridge: Cambridge University Press, , —83, on —72, and From Watt to Clausius Ithaca: Cornell University Press, , 46, 72— One did not need to proceed from the axioms of the Principia to a new machine, or wish to do so, to share a primary trait of the men of science of the late 18th century: an instrumentalist use of mathematics.

In chapter 10, S. Lindqvist schematizes the advance of the quantifying-instrumentalist approach to technological improvement by examining episodes in Swedish experience. To dramatize the difference between academic science and engineering imperative, the episodes take place in "labs in the woods"—or, anyway, on location, where facilities for large-scale experiment existed. In the case of water power, the very considerable advance in effective quantification between the early 18th and the early 19th centuries is made clear by a comparison between the 25, disjointed, inaccurate, useless experiments undertaken by Christopher Polhem on his own initiative and the sustained, precise, theoretically motivated and mathematically analyzed measurements made under the direction of Pehr Lagerhjelm on a commission from the Swedish Ironmasters' Association.

Studies of charcoal-burning show the same pattern: some rough, qualitative assessments around and a thorough, careful, quantitative investigation by the Ironmasters around The Ironmasters were by no means the first in Sweden to explore productivity carefully and quantitatively. Lindqvist gives as the earliest example an effort to apply brain to brawn: a detailed study of the efficiency of human muscle power, carried out in the naval yards at Karlskrona in the early s. We touch upon quantification in technology in two additional contexts.

Lundgren chapter 8 points to the increased use of the balance in mineralogy and pharmacy after the middle of the 18th century and its more frequent presence in chemical laboratories. Here an instrument applied primarily to improve technique entered an environment where it was to effect—or to help effect—a revolution in physical principles. Rider's example chapter 4 goes the other way.

She moves from the elevated reaches of the theory of universal. The signaling codes, which found employment during the Napoleonic wars, disclose evidence of the operation of the quantifying spirit. And, as G. Broberg demonstrates beyond peradventure in chapter 2, these summae were made possible only by suppressing most of what was known. Take the notorious case of insects. John Ray, writing in the s, guessed that there might be as many as 20, species of them.

Fifty years later, Pieter van Musschenbrock made it ,; another forty years, and it had reached , The total number of species of plants, animals, polyps, and microscopical creatures evidently exceeded the number of insects. How survey it all? Encyclopedists and lexicographers had an easy and obvious method: they could list their information alphabetically and leave synthesis to the reader. The chemists, perplexed with some hundreds of mixed salts and the prospect of many more, found their salvation in the new gases, the composition of water, and the linguistics of Condillac.

Their nomenclature of and its purely instrumentalist definition of "element" were so well constructed that they survived the discovery that their most controversial ingredient, oxygen, is not, as its carefully chosen name implied, the acidic principle. Crosland, Historical studies in the language of chemistry London: Heinemann, , —92, —2. His way was not only arithmetical but also geometrical. The placement of species identified by arithmetical criteria under genera and higher orders permitted a two-dimensional layout of God's plan.

It fit perfectly the instrumentalist character of the quantifying spirit. The physicist Biot made it the first great achievement of 18th-century science, "a universal systematic method," capable of arraying a vast amount of information "down to the smallest detail. The binomial approach to knowledge was as characteristic of the Age of Reason as silk stockings.

Natural species did not exhaust the species of nature. With human help, plants and animals disinclined to breed in the wild could be made to father and mother hybrids. In chapter 9, in our closest approach to sex, J. Larson describes J. Koelreuter's crossing of two species of tobacco plant and analyses of the resulting bastards. More interesting for our purposes than Koelreuter's deductions about the transformability of plants was his quantitative method. His compulsion to measure equaled that of his contemporary Ezra Stiles, president of Yale University, who took the temperature of the weather twice a day for thirty years, weighed his children regularly before breakfast, and counted houses, warehouses, 16 stills, 77 oxen, 35 cows, and 1, sheep on supernumerary walks in Rhode Island one autumn.

It is scarcely a challenge to discover in the cultural and political history of the 18th century developments that created or strengthened this support. The more obvious include the rise of the benevolent despots of central Europe, with their cameralist bureaucracies and programs of economic rationalization; the multiplication in France of enlightened philosophers and their fellow travelers, intent on transforming the arts, sciences, education, and government; the acceleration of industrial innovation in Britain owing to a happy conjunction of capital, skilled labor, natural resources, and expanding markets; and, throughout the Atlantic countries, that insistence on guiding society by the lamp of human reason, however dim it might be, rather than by the light of revelation or the radiance of sun kings, that marked the "age of democratic revolutions.

The tempo of these developments picked up around the middle of the 18th century. The exemplary despots of Prussia and Austria then established their positions. The precise origins of great social revolutions do not lend themselves to exact dating. Nonetheless, the quantitative instrument of the historian, the time scale, demands the effort. The balance of contemporary learned opinion seems to incline toward the same date for the quickening of the industrial revolution in Britain that Arnold Toynbee proposed a century ago: Links between these wider movements and ours may be made at several levels.

The need of the increasingly bureaucratic state to organize itself and control its resources gave an impulse to the. Hartwell, "The causes of the industrial revolution: An essay in methodology," in R. Hartwell, ed. Palmer, The age of the democratic revolution. Industrial innovation encouraged quantitative experiment. The political philosophy of the Enlightenment and its application in revolution spread notions of reason and nature compatible with the rationalization realizable by numbers.

The interconnection of the themes of revolutionary rhetoric, numeracy, bureaucratic imperative, and precision measurement is evident in the course and nature of the reform of weights and measures effected during the French Revolution, which is the subject of chapter 7. The institutions of benevolent despotism and enlightened bureaucracy provided many niches for mathematicians.

One set of niches harbored salaried academicians. Their opportunities increased rapidly shortly after , when the rate of founding of academies doubled over what it had been in the previous half-century. This enlargement continued until the French Revolution and affected the quality as well as the quantity of academicians. The insistence upon expertise in a science as a condition for admission, although not always imposed, did create an environment more favorable than earlier more lenient times to the advancement of quantifying spirits. The upward mobility of the mathematically talented is nowhere better illustrated than in the career of Laplace, who has already appeared several times in these few pages, as a contributor to the Standard Model, to the theory of population statistics and tacitly to the metric reform.

We end our book with R. Hahn on Laplace's career as we began with T. We thus frame our accounts of the quantifying spirit with scientific biographies that, between them, encapsulate the transformation documented in the balance of the book. Crosland, ed. There are two distinct opinions regarding the status of science in the 18th century.

One dismisses the period as an uninteresting interval between the breakthroughs of the 17th century and the expanding industrialism of the 19th. The opposing view holds that the 18th century was the time when all the important work of the previous century bore fruit. The dismissers argue that nothing really new emerged in the 18th century.

In direct opposition to these nay-sayers, other historians have identified much of the intellectual life of the 18th century with the fostering of its heritage from the scientific revolution. The Enlightenment thus climaxes the development of early modern science. It marks the Enlightenment as a period of.

The ferment of knowledge: Studies in the historiography of eighteenth-century science Cambridge: Cambridge University Press, , introduction. New York: H. Holt and Co. In this volume we sidestep the difficulty by restricting our attention to the working out of a particular method, or, as it might better be called in many instances, of an appeal to a slogan.

That slogan, as Galileo formulated it, holds that "the book of nature is written in the language of mathematics. In the 18th century, this proposition inspired the work of the most productive mathematicians and underlay the program of the most ambitious philosophers, who proposed to extend it beyond the book of nature to the books of man—that is, to all exercises of human reason. We see two phases in the 18th-century elaboration of this proposition. Until about , "mathematics" was applied to the general exercise of reason as opposed to mathematics itself and the quantified parts of astronomy and physics more as a symbol and slogan than as a useful tool.

In this first phase the philosophy of Leibniz's epigone, Christian Wolff, is exemplary. In the last third of the century, however, the equation of reason with mathematics inspired instrumentalist and quantitative approaches to a wide range of problems in various sciences, arts, and technologies. We take the activities of this quantifying spirit to have been progressive, in the sense that under its inspiration the achievements of the scientific revolution were extended and reinterpreted in a way that made possible rapid advance in mathematics, physical sciences, and statistics conceived as the sciences of the state in the early 19th century.

In what follows, Wolff's method is seen as representative of the process by which reason was "naturalized" during the first half of the 18th century. The purpose is to provide both an introduction and a contrast to the applications of the quantifying spirit later in the century that form the subject matter of the other essays in this volume. Leibniz wanted not only to see the world as a machine with a "static structure of matter in geometrical and mechanical relation"; he also wanted to give exact mathematical expression to all the processes and changes that took place in the world.

Through the infinitesimal calculus he found a constant law that remained valid for an infinite number of processes and changes. The elements constituting the universe, nature, and human life were not particles of matter, but forces and motions. Each element or individual substance—Leibniz called them "monads"—was complete in itself, a microworld or a mirror of the universe, and yet intimately related to all other individuals in a system of pre-established harmony.

The mathematical system came by its harmony naturally. Given this structure of the world it was natural for Leibniz to take another step: to organize human knowledge in a mathematical pattern. Drawing both on the Lullian tradition that sought a universal language and on his own mathematical work, Leibniz wanted to create a mathesis universalis or ars characteristica , which would represent, combine, and produce all possible knowledge.

This language would serve not only as a philosophical method but also as the key to a true encyclopedia. In the mathesis universalis , each human concept or idea corresponded to a different symbol or combination of symbols. By combining these symbols according to mathematically defined rules, Wolff's method could produce long lists of new truths and confirm old ones.

The new language became for Leibniz both a means of communication and a new kind of logic, a way to formulate statements and an instrument of reason. The most influential philosopher in the Leibnizian tradition was Christian Wolff. Wolff was not an original thinker. Instead, he took the foundation of his system from his teacher Leibniz, systematized it, and put it within the grasp of any educated person. Because of his. Alcan, , esp. Lewis and C. Mathematics held symbolic value as the driving force behind the progress of science, and also the progress of reason and free thought.

As Newton had given the universe a mathematical structure, so Wolff aimed to subsume human and society within a vast mathematical system. He pushed his mathematical method into every possible area: philosophy and science, theology and ethics, politics and public finance. Many historians of philosophy have described Wolff as one of the most influential philosophers of his time, without, however, paying much attention to his ideas.

Paul Hazard made Wolff "the intellectual leader of Germany" and a general-purpose sage admired by all nations. Lewis White Beck portrays Wolff as a rationalist in the Enlightenment spirit: "Wolff is the best German representative of a general movement of thought towards deism, utilitarianism and free thought that was sweeping over Europe as a whole. These characterizations of Wolff and his influence claim both too much and too little.

Too much, because terms like "rationalism" and "mathematics" did not necessarily imply Enlightenment, nor did Wolff's philosophy. It was the form of mathematics that interested him, its way of pursuing an argument to its proof. The characterizations claim too little because the association of Wolff's brand of rationalization with the Enlightenment neglects the vast effort at systematization of all knowledge inherited from Leibniz and the 17th century.

Wolff turned to the connection between mathematics and philosophy early in his career. He obtained his doctorate in with a dissertation on ethics based on mathematical foundations. He soon came into contact with Leibniz, who nominated him for election to the Academy of Sciences in Berlin. In Wolff became professor of mathematics at Halle and later assumed the chair of philosophy. In Wolff's work the one subject cannot be distinguished from the other. Wolff announced his own particular specialty—the application of mathematics to philosophy—in his Ratio praelectionum Wolfianarum in mathesin et philosophiam universam The book, usually known as his "German metaphysics," sets out Wolff's philosophy virtually in its entirety; it brought him wider renown and prefigured a whole literary genre during the 18th century.

Wolff's stature as a liberal theologian has also contributed to his reputation as a rationalist philosopher of the Enlightenment. In Halle, the dominant theology was the conservative strain of Pietism developed by August Hermann Francke, which sought renewal within the Church. Competition came from influential orthodox.

Meiner, , 31— Jahrhundert," — Wolff found himself at odds with this eclectic combination. In he delivered a formal address on the teaching of Confucius, Oratio de sinarum philosophia practica , which emphasized its strict morality. From this Wolff argued that morality could be comprehended by reason alone. Here he linked up with the deism that had been spreading steadily since the midth century and that often saw in Confucianism the confirmation of its ideas. Wolff's address contained nothing new or sensational, but under the circumstances it was taken as a challenge.

The Pietists retaliated by accusing Wolff of atheism; condemnatory sermons echoed in the churches and protests ascended to higher levels; the highly regarded theologian Johann Franz Buddeus, orthodox but favorably disposed to the Pietists, wrote an indictment of Wolff's views. Wolff retreated to Marburg, a little university town in the landgraviate of Hessen, an environment more conducive to his reputation. Within a few years he was being hailed as the greatest mathematician and philosopher of his age; students on their grand tours included a stop in Marburg to attend his lectures; scientific academies and universities throughout Europe wooed him.

He began to write in Latin, which permitted access to a wider international audience. The s saw the appearance of the great classical works, Philosophia prima sive ontologia , Cosmologia generalis , Psychologia empirica , Psychologia rationalis , Theologia naturalis 2 vols. Again, they contained little new, but developed and refined Wolff's ideas in different philosophical disciplines and generated popularity, renown, and followers for their author. Michael Albrecht Hamburg: Meiner, , with a page introduction. See also Beck, Early German philosophy , ff. Wolff's reputation as a rationalist and freethinker derived more from his banishment than from his writings.

His position was enhanced when Frederick the Great ascended the throne of Prussia and decreed that salvation was everyone's responsibility. One of Frederick's first acts was to recall Wolff to Halle and to shower him with honors. Wolff assumed positions as professor of law, vice-chancellor of the university, privy councillor, and, in three years, chancellor. In he was ennobled as baron von Wolff. The summons from Frederick the Great, prince of Enlightenment, confirmed Wolff's status as an Enlightenment philosopher. The characteristic aspect of Wolff's philosophical teaching was its strictly logical construction.

He had a manic capacity for arranging and systematizing everything, step by step, clearly and paradigmatically, accurately and in detail. He worked from the principles of contradiction principium contradictionis and of sufficient reason principium rationis sufficientis. He regarded the principle of contradiction as the first law of philosophy from which all other propositions could be derived. With the principle one could decide whether something was possible; that is, everything that might be held to have sufficient reason.

Philosophy was the science of the possible, with the task of showing how and why things are possible. In working out his science, the philosopher had to observe certain rules. No principles could be employed unless adequately proved, and no new ones allowed unless derived from proven principles. No departure could be made from the meaning that words had generally acquired, and if new words or concepts were required, they had to be accurately defined. Intrinsically different objects and phenomena had to be given different names. Starting with axioms, clear definitions, and distinctions, deductive methods would link truths with one another and thus reach irrefutable conclusions.

In this way results. Cogitationes rationales Frankfurt and Leipzig: Renger, , 1. In none of this did Wolff go beyond Leibniz, or, for that matter, Aristotle, Thomas Aquinas whose influence he acknowledged , Descartes, Spinoza, or Tschirnhausen, whose Medicina mentis he had studied in detail. The mathematical method nevertheless became known as Wolffian, because Wolff systematized it as never before. In his hands it became an all-purpose means for establishing truth in any sphere. Wolff's epistemology is quite simple. Human knowledge outside Christian revelation can be acquired in three ways: by experience historical knowledge , by reason mathematical knowledge , or by a combination of the two philosophical knowledge.

The last of these three methods is preferable; the other two have value only to the extent that they can be of use to philosophy. Our senses awaken our most general concepts, which are innate in our consciousness, and provide many fresh ideas; reason clarifies them and puts them into context. Thus every philosophical discipline has both empirical and rational components. For Wolff, philosophy came to mean the same thing as science, as the German term for philosophy, "Welt-Weis-sheit," suggests. Mathematics is not a part of Wolff's philosophy. Instead, it serves as an instrument of knowledge in its own right—a method, a means rather than an end.

Mathematics, in both form and inherent logic, provides a model for all areas of human knowledge. From this point of view, the mathematical method was identified with the philosophical one, and assumed a central role in the scheme of all Wolffian philosophers, even if they did not all see mathematics in the same subtle light as Wolff did. For the imitators, in fact, mathematics at times meant little more than computation. Wolff held dear the idea of a system of knowledge.

Knowledge was not merely a sudden insight or an idea, but arose from step-by-step deduction leading to reliable conclusions. The complex, reliable system therefore became an emblem of Wolff's entire philosophy—. Frankfurt and Leipzig: Renger, , 53—71; the "Discursus preliminaris" is the best explanation of Wolff's goal. For Wolff, mathematics was the method and philosophy the content.

This distinction is essential to an appreciation of his philosophy and its place in 18th-century thought. Wolff's working life falls into two periods. In the first he was active at Halle, wrote in his native German, formulated a more popular philosophy, and spoke so freely on religious matters that he was accused of atheism and banished. In the second period he lived in Marburg, wrote books in Latin, put forward a more theoretical philosophy explicitly addressed to the world of learning, and appeared in religious matters as an orthodox and unrelenting apologist.

The watershed came somewhere around In the earlier phase he followed the precepts of the Enlightenment; in the latter he opposed them. Wolff's German books aimed at a larger public are characteristic of his enlightened period. They have a pronounced practical and utilitarian tone and allot philosophy a "liberating" role, fully comparable to later manifestos of the French Enlightenment.

A critical indication of his popular, liberal position was his vacillation between physicotheology and teleology, two doctrines not easily distinguished and therefore often confused. Physicotheology rested on the ingenious organization of the natural world in general, but it often singled out particular features in nature as evidence of a creator behind the order. This search for an all-ordering God behind the exquisite subtlety of nature could justify, and even motivate, all scientific research.

Where order served as a fundamental principle in physi-. Bissinger, Die Struktur , 49f. If everything fulfills a definite purpose, there must be at least an implicit ordering principle—a God who intended the order. Many physicotheologists came to confuse proofs based on general order and those based on intent, and to subsume teleology under physicotheology. In either case, a "popular" proof of the existence of a divine creator was secured. To see Wolff as a great representative of physicotheology, however, is to overplay his hand.

Wolff attacked both the physicotheological and teleological approaches. Wolff's method required that the theoretical foundation be established first. Had his views suddenly changed? No, he had distinguished between two sets of readers—academic and popular. Wolff's major works in Latin do not feature physicotheology. In a foreword to a translation of Nieuwentyt's well-known book on physicotheology , he referred to his own work in German and underlined that it was intended for readers who did not speak the languages of the erudite.

Whatever he said, in practice he inferred God's perfection from the usual inventory of the natural scientist. He described the cosmos and all its bodies, the sun and the fixed stars, the earth and the planets; he dealt with air and winds, different kinds of precipitation, rainbows, lightning, and thunder. The quantitative philosopher will want to know that his evidence includes "the number of heavenly bodies. In sum, although Wolff demanded strict standards of logical proof in his mathematical method, he allowed himself to break the rules when addressing an unlearned audience.

The end justified the means,. Bissinger, Die Struktur , f. He made an even more significant adjustment in his major work Theologia naturalis , an extended exercise in apologetics, rapidly becoming his specialty. He devoted more than pages to demonstrating the false steps and absurd notions of atheism. Just as he had previously used the mathematical method to lend positive support to philosophy or theology, he now used it to expose and exclude those who were not orthodox.

Fourteen years earlier he had been banished and accused of atheism; now Wolff attacked those who adopted the viewpoint he had then espoused. Yet he held fast throughout these sea-changes to his mathematical method and philosophical rationalism. Which side of Wolff attracted his contemporaries—the mathematical-rationalist or the teleological-apologetic? The answer must be that many accepted both sides, viewing them as two parts of the same entity. The mathematical method tied them together, and became the guiding principle for Wolff's pupils, even for those most inclined to apologetics.

His extensive Institutiones philosophiae Wolfianae 2 vols. Olms, , —, and Beck, Early German philosophy , — Bilfinger emphasized the twin foundation stones of reason and experience, and stood ready to point out correspondences between natural science and Christian faith. Alexander Gottlieb Baumgarten, first in Halle, then at Frankfurt, wished above all to apply Wolff's philosophy to aesthetics. His well-balanced Metaphysics , extremely faithful to Wolffian systematics, amounted to a reference book or compendium of Wolffian doctrine. In Denmark, Wolff's doctrines exerted influence through a number of mathematicians and philosophers: Christian Hee, who stayed for a time with Wolff at Marburg; Friedrich Christian Eilschow; and, above all, Jens Kraft, eminent as both a mathematician and a philosopher, who published a series of textbooks in imitation of Wolff.

The tendency of Wolff's disciples to tread confidently in their master's footsteps, to accept both his philosophical and his theological views, and to tie them together via the mathematical method, was muted in Sweden by resistance to the casual combination of philosophy and theology. Sweden's true introduction to Wolff came through. In a manual of arithmetic , Celsius spoke warmly of the existence of the mathematical method and also of its importance to other disciplines.

He praised not only Wolff's method but also followed the master in setting out his dissertation in traditional Euclidean form, with short propositions under such headings as axioma, theorema, definitio, observatio, demonstratio , and scholion. The dissertation argues that the soul can be proved to exist by means of Wolff's philosophical laws, and Wolff himself is called "the greatest philosopher of our time," philosophus nostra aetate summus.

Several theses reminiscent of Celsius' approach appeared over the next few years, all of them loud in praise of the mathematical method and bearing the imprint of the mathematical form favored by Wolff. Presented first pro exercitio , two years later all four dissertations were defended pro gradu , under Celsius and Klingenstierna as tutors. Several of the dissertations describe the mathematical method without employing it; one stresses that certain philosophical knowledge is impossible without it. Other dissertations under Celsius follow the same pattern. One deals with the subject of "incomprehensible books," which provided.

Klingenstierna, resp. Wallerius Stockholm, , 4, 7, De demonstratione , pres. Alstrin, resp. Wallerius Stockholm, The philosophy that can promote profit and happiness is contained in logic and mathematics. Hence the mathematical method is superior to earlier instruments and Wolff is the greatest of philosophers, outshining lesser lights like Plato, Aristotle, and Descartes. With Wolff's method, the author "brushes aside the weapons of atheism and defends the truths of the Christian religion.

Samuel Klingenstierna had already earned a name for himself as a mathematical genius when he set off to study abroad in He went first to Marburg to hear the much admired Wolff. It is recorded that the pupil much impressed the teacher. When the chair of mathematics at Uppsala became vacant, Klingenstierna applied for it. Because Marburg was within the native state of King Fredrik I of Sweden, Wolff had access to the king and recommended Klingenstierna in the strongest terms.

Appointed to the post in , Klingenstierna did not take up his professorship until , when he returned to Sweden with newly purchased books and fresh reports on the fashionable new philosophy. His were popular lectures, and students sought him as tutor for their doctoral theses. These theses are filled with quite simple Wolffian propositions about the excellence of the mathematical method or the role of contingency in the creation of the world, and frequently make reference to Wolff and Bilfinger. Mathematics thus linked up with philosophy, notably in Klingenstierna's seminars in philosophiam naturalem.

Celsius, resp. Quotations from and references to Wolff abound. But enthusiasm for Wolff and the use of mathematics in philosophy went too far. Alert theologians, worried by the excessive spread of rationalism, castigated Wolff as "heathen and atheistic. The professors responded with promises to be careful and to protect their young students.

Two years later the tone of admonition grew sharper. The chancellor decreed that professors should not preside at theses outside their own disciplines, a rebuke directed particularly at the professors of mathematics, who had been so ready to interpret the Wolffian philosophy. A year later, students were required to give a declaration of faith when enrolling at the university, to guard the purity of the doctrine.

Such censorship and official criticism encouraged attacks on Wolff. His opponents asserted that mathematics and philosophy did not belong among the fundamental sciences; they saw all questions as ultimately teleological in nature. Philosophy, they insisted, should stick to its time-honored role as the handmaiden of faith. The situation soon changed radically. Cronhielm was succeeded as chancellor by Gustaf Bonde, known for his deep interest in mysticism, alchemy, and Platonic mathematics.

An admirer of physicotheology and of Wolff, he later published three volumes of "reflections on the wonders of God in nature. Bonde went even further when he engineered an offer to Wolff of the most highly regarded professorship in the university which Wolff declined. Bonde's permissiveness sanctioned latent interests among the faculty. By the time of his death in , he had presided over a hundred theses, a third of which were Wolffian through and through.

He praised mathematics for its ability to clarify and present problems in easily grasped diagrams and figures, and he insisted on the importance of the Wolffian philosophy to theology. He vehemently attacked all tendencies toward deism or "indifferentism"; true to the later Wolff, he used rationalism as a defense of orthodoxy and against the ideas of the Enlightenment. An even louder champion of Wolffianism was Nils Wallerius, who started out as a mathematician and physicist, continued as a philosopher, and ended up as a theologian.

The Quantifying Spirit in the 18th Century

Within the compass of philosophy he included logic, metaphysics, psychology, and natural theology, all slavishly arranged in accordance with Wolff's system. The mathematical method was fundamental in all philosophy, but mathematics must yield to theology, lest it lead to materialism and atheism.

Wallerius shared the concern of both philosophers and theologians over theologia polemica —the struggle against Enlightenment philosophy. In Wallerius received a new chair in theology devoted to uncovering and combatting heretics. The new professor was to repudiate all freethinkers, "such as atheists, naturalists, deists, anti-scripturalists, indifferentists and other unbelievers. In an essay on the repulsiveness and wickedness of materialism, Wallerius ranted at the ancient atomists Democritus, Epicurus, and Lucretius and their modern successors Thomas Hobbes and Pierre Bayle.

Wallerius, resp. Eurenius Uppsala, , 4, 7, Wallerius' guiding ambition was to reconcile mathematics, philosophy, and theology. At hand were all the necessary tools: a professional graps of mathematics, philosophy, and theology; a passion for system; and Wolff's method. His eminent elogist in the Royal Swedish Academy of Sciences, Torbern Bergman, showed restrained appreciation of Wallerius' contribution, and a like opinion was expressed in another contemporary biography: "Had he lived fifty years earlier and in a more scholastic era, his memory would have been even more illustrious.

Wolff's use of mathematics usually made the best impression on those who knew the least mathematics. During the late s, in a celebrated dispute between the supporters of Newton and those of Wolff, Pierre Louis Moreau de Maupertuis was the main adversary of the Wolffians. The most telling attack on Wolff came from Kant, however, who as usual went right to the core and challenged the mathematical method itself. The Berlin Academy had posed the question of whether metaphysical truth could be equated with mathematical truth and, if it could not, what sort of truth it then was.

Salvius, , Reimer, — , 2. Schneider, ed. The treatise of marked his rejection of the mathematical ideal in philosophy. In it Kant draws his well-known distinction between analytic and synthetic propositions, and concludes that metaphysics is not synthetic like mathematics but rather analytic. The synthetic structures of mathematics cannot be transferred to philosophy and its "mathematical method," for philosophy, unlike mathematics, does not have at its disposal definitions and axioms from which to proceed methodically. Application of the mathematical method to the field of philosophy had thus given rise to errors and mistakes: no dogma in philosophy could be likened to the definitions and axioms of mathematics.

Kant's criticism swept away the very foundations of Wolff's influence. Wolff's mathematical method depended on the possibility of applying procedures of mathematical proof to all philosophical and theological questions. Now Kant argued that the basic structures of mathematics and philosophy were different. Wolff's system crumbled. Several conclusions emerge. Wolffian thinking became a fashionable philosophy in the first half of the 18th century, and its exponents and detractors both saw the mathematical method as the essential element of his doctrine.

It is important to distinguish between form and content in our analysis of the Wolffian mathematical method, and to recognize that Wolff's philosophy fulfilled different functions in different situations. While "rationalism" and "mathematical method" were popular rhetorical flourishes in the 18th century, they also stood for a well-defined means of attaining certain intellectual objectives. Both friends and enemies of the Enlightenment appropriated that method, since mathematics as a method of proof promised results in all areas of human knowledge.

That it collapsed so readily under Kant's attack reflected that Wolff's mathematical method had already proved inadequate: it failed to provide tools for revamping critical philosophy, or for creating instrumentalist science, or for solving practical problems facing the bureaucratic states of the late 18th century. The form and content of mathematics itself, however, would continue to speak to these needs.

The word "quantitative" applies to natural history during the second half of the 18th century in two distinct but related ways: as characteristic of the object and of the method of study. These features—the overwhelming flow of information and the determination to inventory and survey it for useful purposes—characterize much of the learned activity of the late Enlightenment. I then turn to natural history, reporting the inflation of information and some of the problems of keeping it together.

Finally, I look at the paradoxes of natural history at the turn of the century. The classificatory project of 18th-century natural history runs parallel to and was in many ways inspired by the development of the encyclopedic enterprise of the same period. Natural historians and encyclopedists shared similar ambitions for totality, coherence, and order.

Both camps had to ask the same questions: How much is there in the world to know? Is it proper to measure all the riches of creation? If so, by what "method" should they be described? Is there a correspondence between what we can know and the fundamental nature of things? Parallel to the rapid increase of information. Natural history as well as general encyclopedism moved from the finite world of the baroque to the infinite world of modern times.

Natural history opened out similarly. But that is what often happened. This emphasis is constantly moving from the general to the particular, from principles to phenomena. But the basic assumptions remain. The rationalistic postulate of uniformity dominates the mind of this age. The 18th century manifested its rationalism in encyclopedias.

Natural history helped to determine their structure. The same ambition to take possession of what had been discovered, indeed conquered, characterized both the Systema naturae and the great French. New York: Columbia University Press, It was not mere coincidence that d'Alembert's and Diderot's great work began at the same time that Georges Louis Buffon's Histoire naturelle and the geodetic survey of France started. Both he and Ephraim Chambers, the author of the Cyclopedia , arranged their works not systematically but alphabetically, though, to be sure, not without long discussions about the systematic aspect: "It may be even said, that if the system be an improvement upon the Dictionary, the Dictionary is some advantage to the System; and that this is perhaps the only way wherein the whole circle, or body of knowledge, with all its parts and dependencies, can well be delivered.

The classic had so little to compare itself to that it could devote all its attention to order and its own perfection, whereas the latter—"since experiments are endless"—will never reach so far. The opposition Chambers developed was connected with the decline of rationalistic systems of sciences in the Leibniz-Wolff. Zedler, —54 , 8 , Rees London, ; original ed.

Knapton, , "Preface," xxii. It was not clear, however, how he supposed the tree of knowledge to grow—did logical division or historical development control the branching? His ideals were those of a geometer, believing in a regular universe and operating with axioms and principles. How well these combinations in the end corresponded to the tree of knowledge was problematic.

It responded to accusations that the first volumes did not have the coherence promised in d'Alembert's essay: "It is impossible to improve the arbitrariness of this great original profusion. The universe presents us only with individual things, infinite in number and with almost no fixed and determined division [among them]; none of them can be called the first or the last; everything is connected to everything else by insensible gradations.

Diderot insisted on the value of irregular articles. When Diderot defended this openness in contrast to closed systems, he also defended the alphabetical arrangement, which predominated thereafter. This arrangement represented an important step toward secularization of knowledge and agnosticism toward taxonomies of knowledge. To quote a recent interpretation: "As the zero degree of taxonomy, alphabetical order authorizes all reading strategies; in this respect it could be considered an emblem of the Enlightenment.

The encyclopedic business thrived on this tension between knowledge and information. The first edition of Encyclopedia Britannica —71 was more weighted toward information, whereas the success of the Brockhaus Conversationslexicon provoked charges of superficiality. Nils Afzelius Stockholm: A. Bonnier, , To Hegel, an encyclopedia should be a summarized introduction to scientific knowledge.

An heroic attempt to combine these different traditions, literally identified with the heritage from Francis Bacon and Plato, is found in the "General introduction" to the Encyclopedia metropolitana The objective is no less than a reconstruction of "the circle of knowledge in its harmony" to provide that "unity of design and of elucidation, the want of which we have most deeply felt in other works of similar kind, where the desired information is divided into innumerable fragments scattered over many volumes, like a mirror broken on the ground, presenting instead of one, a thousand images, but none entire.

Whatever its organization, an encyclopedia required supplements to stay current. Too much had to be altered or added. A two-volume Supplement to Chambers' work was published in London in Four supplementary volumes completed d'Alembert's and Diderot's great work in —7. This constant adding made an encyclopedia something like a journal.

Diderot wrote to the point. Journals are only a passing account of books and authors. Fellowes, —45 , 1 , The increase of information that perplexed encyclopedists also vexed lexicographers. In his Plan for an English dictionary , Dr. Johnson declared it to be his purpose to "fix" the language once and for all, because "all change is of itself evil. He now thought that "fixing" the language was as futile an effort as "embalming" it. He too had to deal with the problematic relation between words and things.

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Emanuel Swedenborg also had something to say about the growing awareness of never-ending knowledge. In an undated note from the middle of the century he wrote: "I was allowed to enter a library where there was a great number of books. In the inner parts of still more libraries were books written by adherents of the old churches and still farther were books from the oldest.