The Challenge of Plenitude
The plenitude of being was a constant cause for religious as well as scientific amazement. John Ray's famous The wisdom of God manifested in the works of creation (1691) opens by quoting Psalm 104:24—"How manifold are thy works, O Lord! In wisdom hast thou made them all"—and continues by changing the exclamation into a question. Ray called attention to the number of stars and planets, then calculated the number of animals. His estimate that there are 2,000 insect species in Britain alone, and 20,000 in the whole world, must have seemed very bold at the time, and likewise the figure 40,000 to 45,000 for all plants and animals together. He also discussed the proportions between the number of species, showing that the less perfect genera contain more species than the more perfect, a matter he went on to explain with many insights into the interplay of nature. To him, as to many of his contemporaries, the microscope had proved the plenitude of creation. We should note a typical 17th-century conceit: the greater the number of variations, the greater the glory of Man, since the Lord made them for human pleasure. As Ray put it: "another reason why so many kinds of creatures were made, might be to exercise the contemplative Faculty of Man; which is nothing so much pleas'd as in the variety of objects."
Compare Ray's numbers with the estimates given by Pieter van Musschenbroek half a century later. Following Hermann Boerhaave's lead, Musschenbroek reckoned the number of plant species at 13,000. He allowed 5 insect species to each plant. This made 65,000 insects
and (he guessed) 72,500 species in the entire animal kingdom—or, rather, twice that many, since each animal serves as food for another. Suddenly, the number has reached 145,000, and, again, the figures should be doubled since so little of the earth had been explored. We have in all 291,000 species, magnificent proof of the skill of the creator. Musschenbroek referred to Antony van Leeuwenhoek, to Henry Baker's book on microscopy, and to René Antoine Réaumur's entomology. It may be objected that Musschenbroek, a professor of physics, reasoned too much like a mathematician to win the confidence of the natural historian. Still, both had recourse to physicotheology.
At first, Linnæus probably did not estimate nature's multitude as extravagantly as had Ray. He inherited the task of describing the 6,000 species in Caspar Bauhin's Pinax (1623) from his predecessors, Olof Rudbeck, father and son, who planned to publish pictures of every known plant. (Their project was stopped by the great fire in Uppsala in 1702.) Anyone shouldering such a task would try to keep the numbers down. According to Linnæus, botanists should be able to remember at least all genera. Hence this second Adam, as Albrecht von Haller called him, must have believed it possible to survey nature taxonomically. In his Oratio de telluris habitabilis incremento (1743), he supposed that in the beginning the world was a paradise island containing all species. The only thing that had happened since then was the constant increase of individuals—and land.
The number of new discoveries during the 1740s forced Linnæus to change his mind. He had to fit these novelties into the context of his already published textbooks. The characters of the fresh-water polyps and the corallines, and later different fungi, seemed to contradict the taxonomical borderlines of nature. Critics labeled the
sexual system scholastic and artificial and contrary to the notion of nature's great chain. As an answer, Linnæus sketched an evolutionary hypothesis in Genera plantarum (1764), which also expressed his views about the natural system of plants. The more Linnæus peeked into the secret depths of nature, the more he found intricate connections. He now preferred the concept of mappa naturae over the simple hierarchical arrangement of the scala naturae.
Still more material flooded into Linnæus' study. The Systema naturae expanded from twelve folio pages in the first edition to almost 2,000 pages in the twelfth. He classified some 7,700 plants, 6,200 animals, and 450 mineral species. Altogether Linnæus' nature contained no more than 15,000 species, but that, as he knew, was but a beginning. Systema naturae goes from God to gravel, aiming at nothing less than a complete inventory or encyclopedia of the world. To Linnæus, nature's multitude must have been both a wonderful ongoing revelation and a terrible curse. He must have been one of the greatest optimists of all time. His library, now in the Linnæan Society of London, is filled with volumes of additions scrawled in the margins of his books.
Did Linnæus ever indicate the possible "size" of nature's kingdoms? Perhaps. In the fifth edition of Genera plantarum (1754), he introduced the idea of an alphabet or letters of the botanical language. These 26 letters combined two at a time were to cover all parts of the flower with the help of four "certain and mechanical principles," namely number, position, figure, and relative position. By a combination of these characters, botanists could give a good description of the genera, which in difficult cases should be checked by the concept of "habitus," the over-all impression of the plant. The largest possible number of genera is 26 × 26 × 4 or 2,684. Linnæus' evolutionary hypothesis of 1764 seems to end up in a similar number. At the beginning God created the "natural orders," which Linnæus elsewhere counted as 58. The next level, of the genera, came into existence by "mixing" the orders two by two: 58 × 58 makes 3,364
natural genera. The third step, another multiplication by 58, gives us the number of possible species "mixed" by nature. There is also a fourth step, when "casus" or change mixes the species, which constantly happens and to such an extent that the botanist should not bother about all the resultant "varieties." Thus, the successive unfolding of types is caused by God, nature, and chance. The orders and the genera deserve special study. To keep up with the rest will be almost impossible. Here Linnæus seems to have retreated from his earlier optimism about human possibilities. If his reasoning seems odd, consider this from his fellow Swede Christopher Polhem, the great technical innovator. A descriptive name can be constructed by using letters in a prescribed order. For instance, an initial "p" could mean man, a "b" animal, "k" grass, while vowels might stand for the different senses, "a" for sight, "e" for hearing, "i" for smell. Further letters could indicate medical effects. With this system, Polhem guaranteed 1,406,250 possibilities; "more differences should not exist." If they do, it would be easy to add one or more variables or letters.
Linnæus' critic, Buffon, had to face the same problems. At the outset of his series on birds, he admitted a problem in acquiring all existing species. He and his collaborators worked for twenty years, constantly enlarging the collections of the Cabinet du Roi but never approaching completeness. Still, he could offer three times as many species of birds as were found in the tenth edition of Systema naturae (1758). (These figures depended on species definition and are not strictly comparable.) There are two competing strains in Buffon's writing: his early fascination with individuality in nature and his later encyclopedic ambitions. These tensions are even more obvious in the writings of Linnæus' second major French critic, Michel Adanson. Adanson faulted Linnæus for, among other things, grossly
underestimating the number of species of coquillages in Senegal. We will return to Adanson. Here he exemplifies awareness of nature's tropical abundance, while Buffon represents the contention that this abundance cannot be counted.
Linnæus and Buffon both received credit in an unusually unbiased way in Haller's preface to the German translation of the Histoire naturelle (1750). In view of his old quarrel with Linnæus about who was the better naturalist and who had collected more plants, this sympathetic judgment might seem surprising. It may be explained by the message of the essay, that is, the blessings of hypotheses for the progress of science. "Laws in botany are arbitrary," Haller stated, "but they have done us an unbelievable service. Now we can distinguish ten thousand plants more easily than the Ancients did their six hundred." Linnæus' new theory performed the greatest service. At present, botany was advancing its lead over all sciences. "Not only is it nearest to completion, and has little by little determined the nature of almost all its classes and resemblances; it has [also] spread its laws throughout the entire Kingdom of Nature. Zoologists and mineralogists have received their laws from it and accepted them as the Romans did from the Areopagus." This last allusion is not a poor piece of flattery. Haller certified that botany would soon be finished, that all the work of collecting material and its description would be brought to their happy end. Success was guaranteed by the model he gave for natural history research: just as a land surveyor begins a map by determining some locations without the positions of places in between, the natural historian starts off with an initial sketch, which later knowledge will fill. The analogy is typical for an era of geographical exploration. It hardly implies the notion of an infinite or a dynamic nature, but rather only the hope of completing the process of exploration.
A similar promise of prompt success (if only governments and princes would offer enough financial support) appeared in an article with the upbeat title, "Have we still to hope for a complete system of nature?" The author, entomologist Johan Samuel Schröter, did so hope, provided natural historians adopted his rules. In Schröter's scheme, only one person should be responsible for each major natural group and should be endowed with dictatorial powers to suppress quarrels among naturalists. Schröter held that only a group of specialists in natural history, and not a single person alone, could fulfill the Linnæan task. Other necessary preconditions were "ability, leisure, and money."
The most ambitious attempt of the 18th century to secure exact figures for the contents of the natural world, however, was made by Eberhard Zimmermann in his book, Geographische Geschichte des Menschen und der allgemein vierfüssigen Thiere (1778–83). Zimmermann combined macroscopic information from the explorers with inspiration from the microscopists' overfilled world. As professor of mathematics—he taught Gauss at Braunschweig University—he excelled in calculations about the size of the known world in relation to the number of known animals. These ratios show an impressive knowledge of zoological detail but also have strong similarities with the more unrealistic parts of political arithmetic as well as with Musschenbroek's calculations. Zimmermann vigorously pursued the Linnæan project, and equally vigorously attacked Buffon's "complete ataxia." But Zimmermann's calculations made the works of the Lord too manifold for the grasp of His creatures.
Zimmermann began small, with minerals, whose maximum number he put at 750. The variety of plants is much greater; recent estimates reached to almost 30,000 known species, only a fraction of the total quantity, which Zimmermann by various calculations raised
to 175,000. He showed even more interest in the number of animals. Erxleben, Schreiber, Johann Friedrich Blumenbach, and others had set the quantity of known species at 10,000. Following Roesel von Rosenhoff and Linnæus (Pandora insectorum, 1758), Zimmermann proposed that there must be at least five insect species specialized on each plant species. Immediately we have 175,000 × 5 or 875,000 insect species of which only 51,000 had been described; entomologists had work to do. Nature abounds with parasitic and intestinal worms, with polyzoa and infusoria, and the sea is crammed with life to an extent almost impossible to grasp. "Who can follow the flying fish?" Probably the variety of sea organisms is two or three times that of land organisms. Zimmermann provided for invisible organisms, small and pellucid, on which the insects feed, and also for atmospherical fauna. Bearing all this in mind, he reached seven million species of animals, perhaps more. Then there are the innumerable specimens of each species. In the universe our planet is just a small spot unknown even to the inhabitants of Jupiter. And yet it has such multitude and magnificence! Zimmermann ended his essay with "a paean of thanks" to the Creator, the traditional natural-theological envoi . Following the natural-philosophical tradition as well, he offered calculations of the number of mammals undiscovered in different parts of the world, but despite the obvious interest of these estimates for the history of biogeography we leave them out.
This account of Zimmermann's work sums up several of the features of late Enlightenment natural history. He enthusiastically accepted the Linnæan project of species-hunting. Several times he appealed to princes for support for its completion. He was also intoxicated by the idea of nature's plenitude. As Ray did a century earlier, he compared the plenitude of this world with the plenitude of the universe. But we must note the enormous difference in the numbers they gave. And Zimmermann turned the whole architecture of the chain of being upside down. Whereas Ray (and Linnæus in Oratio , 1743) claimed that the ratios between nature's kingdoms were such
that the lowest—the mineral—was more numerous than the vegetable, the vegetable more than the animal, Zimmermann proudly formulated a different and "remarkable law: the total of types of organized bodies increases with the degree of sensation and life." Throughout Zimmermann supported the idea of the chain of being, but obviously that notion was collapsing—so to speak—under its own weight. Zimmermann's discussion reflected many of the components of 18th-century natural history, but his figures neither fit the Linnæan project nor supported the single-line chain of being. His account did not visibly change the direction of natural history, but it forced two themes to the surface: the dramatic growth of numbers and the pessimistic prospects for complete knowledge.
So much for external problems; the Linnæan system has internal ones as well. It was fundamentally mathematical in a very simple way, based on the numerical principles of the sexual system as well as on zoological taxonomy. The naturalist counted stamens and pistils, teeth and nipples, toes, scales, antennas, everything. Among other advantages, mathematics afforded brevity and exactness. Linnæus was in every respect an economical man, who had to budget both time and space for his enormous undertaking to map the whole natural world. Without the Linnæan reforms the natural historian would not have been successful in surveying nature; with them, however, nature might appear to be one long list of numbers.
It was reasonable to question the validity of the criteria. Buffon did, in his famous criticism of Linnæus in the "Premier discours" of the Histoire naturelle in Buffon (1749). There Buffon argued that species as well as higher taxa are simply constructions of the taxonomist, while nature by contrast only consists of individuals. For Buffon, the counting of stamens and pistils has nothing to do with the true study of nature. He found no room for mathematics in natural history, the more remarkable considering his background in
that discipline. Nor did he use numbers to reason about nature's continuity. Indeed, he did not stress continuity in his writings as strongly as is generally thought. He of course made references to the great chain of being; but he rejected the idea of animal reason and opposed linking human and animal via the ape as a link to man. At bottom, however, what makes Linnæan taxonomy impossible in Buffon's eyes is that the number of natural "groups" must be infinitely great, since the only natural entity is the individual. The only way to treat nature, the only "method" or plan in the Histoire naturelle , is to accept subjectivity and to arrange descriptions according to how we normally get to know the animals.
In many ways Buffon adhered to the observer tradition, as did the master entomologist Réaumur, who advocated a similar concentration on the individual in contrast to more or less complete taxonomic surveys. Since we never will know everything, Réaumur wrote, we should not regret that some thousands of insects do not figure in our inventories. Instead, we should concentrate on the truly interesting wasps and butterflies. Observations rather than coherent systems are what matter.
In another line of attack, Linnæan mathematics was met with more mathematics. Adanson attacked the essentialistic and scholastic elements in Linnæan taxonomy and recommended an overall statistical evaluation of the plant's character, a method appropriate for modern computers. It is uncertain how far he himself used his method. It is not only extremely time consuming, it also stands in strong contrast to his predilection for completeness and universality. Thus Adanson's suggestions, although in many ways interesting, were a dead end in practice. Practical taxonomy could function only in connection with some sort of essentialism, while nominalism seemed to belong more to philosophy.
The philosophical core of these objections and of 18th-century natural history in general was the idea of the great chain of being. In his thematic study, Lovejoy singles out the species problem, the interest in missing links, and the studies of the microscopists, all of which involved philosophical problems such as continuity and causality. By the end of the century, the idea had suffered many changes. Lovejoy emphasizes what he calls the temporalization of the chain, brought about by the study of fossils. More might well have been said about continuity . In general, both philosophers and natural historians adhered to the Cartesian-Leibnizian idea of continuity without any leaps or bounds. Action by contact keeps the world together and makes it go around. The Newtonian model of a void universe operating by distant forces did not appeal to natural historians. If there is continuity along the whole chain, then it should be possible to use the same classificatory devices and characters to judge all organisms. But, as Charles Bonnet objected, humans lack the right perspective and must satisfy themselves with "classifying classes," with specializing within fairly broad limits. Linnæus could stretch his scheme through botany only with difficulty—the sexual system was hardly useful for the cryptogams—and new principles were invoked for the other kingdoms of nature. Natural historians could see only fragments of the great chain before it twisted or disappeared from sight.
The related problem of plenitude , so beautifully demonstrated by the observations of the microscopists, also meant continuity along the
chain. Its main impact on classification, however, was the implication that God created an unlimited number of individuals rather than "types" or species. The vast numbers that came into being through the laws of generation were studied by Leeuwenhoek and other animal demographers. How to impose limits on this continuity? The question was similar to Zeno's paradox and, if taken seriously, could have led to taxonomy's suicide. The 18th-century natural historian had to deny the physicotheological premises that underpinned his work. To be sure, some very straightforward observations could strengthen him in his denial. As Voltaire wondered shrewdly, why is there no link between animals with two feet and with four? Johann Hermann, in his admirable Tabula affinitatum animalium (1783) (affinity had become the new catchword for genetic, evolutionary, or taxonomic relationship), emphasized symmetry in the animal world. To him, the chain was not linear but rather like a net with many intermediary and vacant steps. The number of possible types between two species of bug became almost impossible to estimate. Working with only ten variables, he found 10,172,640 possible varieties. Where, then, is the species limit? His conclusion seems to be that, apart from the possibility of an innumerable quantity of species on other planets, about which we know nothing, the Creator must have condensed his unlimited multiplying ability into a limited number of multifaceted species. As a solution of the plenitude dilemma,
Hermann's suggestions seemed good enough. But they were purely defensive and conjectural.
Kant's criticism of Linnæan natural history also deals with the problems of continuity and plenitude. Either we work from logical entities as Linnæus did in Systema naturae , or we work with categories like time and space, that is, with Naturbeschreibung or Naturgeschichte based on geography. The Linnæan method did not attend to geographical dispersion. Kant sharpened his view: "The systems of Nature so far proposed should more correctly be called Aggregates of Nature; for a system presupposes the idea of the whole , from which the multiplicity of things can be derived. Really we have no Systema naturae . In our present systems, things are just placed together." This criticism, delivered in a lecture in 1756, was sooner or later bound to affect the ethos of natural history.
We conclude this section with two examples of pessimism, or rather modesty, on the part of late 18th-century epistemologists. The Swedish-Finnish chemist Jacob Gadolin observed that scholars stumble and fumble through the unknown regions of knowledge hoping to find a chain like the Linnæan method to follow. "If every country had its Linnæus, there would be no end of discoveries since Nature is an unfathomable treasure." So far optimism—but as Adam after the Fall was to experience, "the more we open our eyes the more we see that we are naked." Gadolin combined epistemological skepticism with traditional biblical pessimism. Again in a combination of religion and chemistry, Joseph Priestley confessed that for himself he found it impossible "to produce a work that shall be anything like complete ." "In completing one discovery we never fail to get an imperfect knowledge of others, of which we could have no idea before; so we cannot solve one doubt without creating several new ones." "The greater is the circle of light, the greater is the boundary
of the darkness by which it is confined." The awareness of this truth is the other side of the belief in progress.