Originally published as “G.W.L. Epistola responsoria de Methodo Botanica ad Dissertationem A.C.G. Medici eximii [G. W. Leibniz’s Letter in Response to the Dissertation on Botanical Method of the Outstanding Physician A. C. Gakenholz],” in Monatlicher Auszug, April 1701, VIII S.68–80; reprint, Kortholt 4, 83–194; Dutens II ii, 169–72. LBr 293, Bl. 5–6; Ritterkatalog: A:52443; B:34667 in response to 52441; 52442.
Alexander Christian Gakenholz (also Gackenholtz, Geckenholz) was a physician and botanist from Celle, near Hanover. He submitted his doctoral dissertation, titled Disputatio medica inauguralis de Hydrope (Inaugural Medical Dissertation on Dropsy), to the faculty of medicine at Utrecht in 1698, and later went on to write, among other works, the Progymnasma botanicum de vegetabilium praestantia (Hamm, 1706). He wrote a letter to Leibniz, concerning mathematical questions, as early as 1694 (see A III vi, 229–32).
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I. On the optimal method of classifying plants. II. On the optimal method of classifying in general. III. On the method of classifying of recent botanists. IV. On the function of plants. V. On a different method of classifying plants. VI. On Joachim Jungius’s method. VII. On comparisons of plants not to be made only on the basis of their flowers. VIII. IX. X. On various important criteria in distinguishing plants. XI. On promoting the advancement of medicine, and on Ramazzini’s and Hoffmann’s achievements in this.
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I. I have well received your letter, which testifies to a knowledge and experience that are uncommon, as well as to the affection you show for me. I wanted to respond immediately, first of all in order to thank you and second of all in order to explain my thoughts on certain points at somewhat greater length. Clearly drawing arguments from facts, you corroborate my opinion by showing, by the example of the roots I had mentioned, which are capable of a great variety, that we should not be obliged to classify plants from their flowers alone. To the differentia that you mention could be added the juices of certain roots. And in this category it could be recorded that the genus of camphor, as they say, is obtained from the root of the cinnamon tree. Certainly, I do not disapprove of the ingenious diligence of eminent men in botany, who have found a method of classifying plants from their flowers more convenient than former ones; however, I wanted it to be considered that from a single principle of division the matter is not resolved, and that the secrets of the botanical doctrine are not sufficiently explained by this one method.
II. Indeed, as I already showed as an adolescent, a long time ago, in a little book called On the Combinatorial Art of the year 1666, combinations of things according to set numbers afford a correspondence with the genera of so many inferior species, so that it may be understood that there are as many genera of species as there are combinations of things. For example, let there be four inferior species, or species presumed to be inferior, beyond which it is not possible to subdivide any further: a, b, c, d. There will be the following genera: one, the highest, combining all of them a b c d; there will be genera of the second order, coming next to the sum of four and combining only three of the species, namely a, b, and c, or b, c, and d, or, finally, b, c, and d; and in consequence the four genera will (by designating each one by the three species which it alone combines) abc, abd, acd, bcd. The genera of the third order (in this place), nearest to the inferior species and combining two of them, are six in number, namely ab, ac, ad, bc, bd, cd. Whence again it arises, according to a single mode of dividing and subdividing, namely by dichotomies (which indeed, when it can be employed, is the most perfect mode of division), that not all subaltern genera can be obtained. For example, if you proceed as follows:
abcd or abcd a bcd ab cd b cd a b c d cd,
by the prior mode you will not have subaltern genera other than, at the second level, a single bcd (combining all and only b, c, d); and at the penultimate or third level, a single cd (or that which combines all and only c and d). Other genera will escape your attention. By the latter mode you will lose all of the second-level genera; from the third level you will obtain only two, while there are four others, which are omitted by these modes. Other people, establishing other processes of division, will bring forth new results. No one will bring forth all results by a single method of dividing. This brings it about that the combinatorial method (which in fact includes multiple divisions) is more fecund than the common method of division (which is content with a single division). Hence, various philosophers and jurisconsults, by various modes of subdividing, have tracked down various human appetites, or various species of moral virtues, or of laws, or other notions of such kind; and everyone has noted something of use in his own method of considering and dividing. Since in truth in a great number of species the variety of combinations and of the diverse methods of division is immense, it is clearly necessary for the art of method that the more useful comparisons be preferred, and that a method that is more evident and commodious be selected for assisting the memory. Thus dichotomy by way of opposing differentia came out among the first for the purpose of discovery and recording.
III. Transferring these general precepts of the art of meditation into the present matter, I do not so much condemn the recent botanists’ effort to assist memory by any method of dividing into classes that they judge the more suitable. I sooner praise their approach, as long as they do not adhere to it too rigidly and almost uniquely. Although, in advance of knowing the interior constitution of these machines of nature, no accurate method can be instituted, nonetheless a certain substitute method may be employed for the sake of our comprehension and progress in theory. In our effort to bring into order the works of nature, we resemble this methodical man from the ranks of the Ramists, who, ignoring the demonstrations, wished to classify the geometrical figures. This man, estimating everything from its external aspect and lacking experience of the causes, would give a certain superficial, and I would say impoverished, treatment of geometry; and nevertheless he should be praised for his diligence, and for being useful to those who are incapable of anything more. Such is our own activity, as it is, in the three kingdoms of nature.
IV. Plants, animals, and, if I may say it in a word, organic bodies that are produced by nature, are machines fitted for the perpetuation of certain functions; they bring about this perpetuation through the propagation of the species, as well as through the nourishment of the individual, as well, finally, as through the accomplishment of these operations which it is the special function of each to assume. And indeed it is manifest that the human body is a machine suited for the perpetuation of contemplation. In all other bodies we have not sufficiently explored the full extent of the ends of nature. It is however not at all doubtful that a great part of nature’s ends are purported to serve for human use, that is, to facilitate contemplation, or, what is the same, to excite in us the admiration of divine wisdom. And thus whatever can be derived from plants or produced for the uses of humans must be included among the ends [of nature], and we must above all explain by what mechanisms they tend to that fulfillment. That this reason for botanical investigation should not be neglected in setting the principles of it is thus made evident.
V. Of course, as in geometry, the theoretical part is one thing—and this in turn is dual: either Euclidean, which demonstratively explains the causes of figures and the properties deriving from these; or Ramist, which divides the classes of configurations and the obvious properties according to the external aspect [specie]—, and another thing is practical geometry, which develops uses; and this in turn is dual: namely, either more esoteric or more popular. Thus plants or animals can be divided either theoretically, according to certain sensible differentia, or indeed practically, according to human usage; and both of these methods are more popular when the inner aspects are not in sight. Although I do not despair but that we will be able to come to something more profound, both theoretically—if men duly followed the endeavors of Jungius, Malpighi, Hooke, Swammerdam, and Leeuwenhoek with a dedication greater than what, to my surprise, is presently done—as well as in medical practice, if, where our instinct and sense do not suffice (for we have lost a good part of this natural instinct of ours which a physician advocates in a little book of his written in French, because of our artificial way of life, unless one believes that barbarians should be consulted as still nearer to their origin in Mother Nature), the sense and instinct of other animals may be invoked in an auxiliary fashion. For indeed it is very probable that whatever plants are pleasing for the nourishment of the same insect (of other animals I shall say nothing now) are of a cognate nature and possess similar properties.
VI. Further, in this theoretical part (I omit now the practical distinctions that are inferred from sensual, mechanical, alimentary, or medical uses), although I support an ordering into classes according to one certain criterion that is widely variable, I would reckon that other criteria for ordering and comparing plants should not be neglected. Joachim Jungius, who flourished in the century that just ended, a man who is to be counted among the most learned of his century, in his posthumous Isagoge Phytoscopia, which is but a small record of his lost meditations, elegantly taught to discern, and to express with apt names, the figures of leaves, since he saw that in these nature descended to the greatest varieties and those most suited for drawing distinctions. Now, I aver, learned men transfer this method with some success to the leaves of flowers, for it is with the flowers that the generation of plants is most closely connected, and it is above all useful to discover variety in the principles of generation, as indeed Aristotle understood when he undertook to relate the varieties of animals mainly by means of this criterion.
VII. But the comparison of animals is conducted more usefully also with a view to other parts, as comparative anatomy shows, to such a degree that in the lungs or organs of respiration a connection has been discovered between plants themselves and animals, as well as a certain continuity [series] and a kind of transition from plants to large animals by way of intermediary insects, if I may so call them, according to what Swammerdam advises. Thus it can easily be understood that the comparisons of plants themselves should be instituted not only on the basis of the flowers, but also on the basis of most other major parts taken separately. It is not as though, on the basis of any single criterion, a complete distribution of all species should be undertaken: this would take up too much space in a textbook of Institutions (although in a book of Pandects it should be preferred). But this should be done in order that no useful comparison or combination be rashly neglected.
VIII. And these could be like corollaries of a certain primary ordering that will be of use in the future to lovers of botany, because it is necessary that plants, as you well remind us, be distinguished according to features other than the flowers, which are not always visible. I mentioned the root to you as an example, which is the primary instrument of nutrition, and which is always visible and in nearly all plants, as you rightly note, with the possible exception of those plants which, swimming in water, constitute with their orbicular leaves a vegetation under the name of duckweed, though even in these an analogue (of the root) might not be lacking. Further, the structure of the whole plant should not be neglected either, from which first arises the division into trees, bushes, and grasses. Coming to the parts of the plant, what a multitude of criteria for division are to be found there, either in the solid parts, as in the roots (of which I have already spoken to you), the trunk (its interior and its bark), the leaves (either of the plant or of the flower), the fruit (in which the seeds are discovered), and in other solid parts; or in the fluid parts, such as the marrow, the water that flows out, the resin, and, finally, in the humid substance that is pressed out, or, more precisely, in the odor or vapor that is emitted; meanwhile different plants are chiefly distinguished by different parts that they contain or to which they give rise; some by the flower, others by the root, others by the bark, some by the sap, etc. And there is none of those parts from which a certain comparison could not be drawn with wide application throughout the vegetable kingdom. If one point of comparison should be discovered to be analogous to another, this would provide much light.
IX. It pertains to the structure of the whole that very often from the prevalent part we name the whole plant a root or a flower, either because the function of the part that gives the name is more important, or because its mass or form is more preeminent, so that they are more usefully placed in a single genus and enumerated under a single heading. How many are the species included under the single name “grass,” in all of which there is something that imitates the genus of grains? How many are the species of reeds, in which the stalk predominates? Why do we not group together the plants that yield berries in the same way that we do the grain-yielding ones? Why not in the same way the whole genus of ferns? In jurisprudence there are certain primary dispositions of the matters according to the various genera of moral persons—real, personal—, and nevertheless, from these diverse genera, common ones are usefully abstracted by the mind, as when the doctrine of conditions arising from wills and contracts is reduced to one genus, which happens by establishing proper criteria concerning the interpretations of acts, the times, the places, the various things and persons juridically treated, the privileges of churches, women, and soldiers, and the other innumerable topics which provide arguments for academic dissertations. Similarly, it is more relevant concerning nature that it be considered in all aspects, that all manners of comparison be instituted, since the investigation of it is more difficult than that of civil matters.
X. Moreover, new comparisons of plants, which will be of great importance, will be provided by new observations (if they are further confirmed) concerning the imitation of a double sex in plants, on which Rudolph Jacob Camerarius, a man most eminent among those who are curious about nature, has begun to work most assiduously, and which recently the young Mr. D. Burckhard, a recognized expert in these matters, who wrote me a learned letter about this, decided to further investigate. For they look in the very subtle pollen of flowers for the analogy of the male seed, and deny that anything of this sort is lacking in any plant, even if it is not always perceived by the naked eye; capsules are present for receiving the pollen that are to be compared to the female ovary; a stylus or something analogous, like the vagina of the uterus, emerges from the capsule. From the flower, which the heat of the sun has opened, the pollen, through the aid of a blowing wind, would transfer and apply to the highest tip of the stylus. From the grains of pollen, something spirituous would lead to the ovary and then, if I may say so, penetrate the pod and fecundate the eggs or the seeds therein; a strong indication of that process is provided by the fact that no generation follows when the pollen is prematurely removed. If this is further attested by diligent observation, it will corroborate a conciliation between the doctrines of Kerckring and Leeuwenhoek, a conciliation that always seemed to me most probable: namely, that something subtle, which was already organic, and which could already be denoted by the name of plant or animal, reaches the female’s eggs from the male seed, and there, as if transformed in its proper soil and made to grow by feeding, develops into a fetus, through a process that may be called generation. In such an operation of nature, learned men report that plants behave quite differently. For commonly both semina are produced in the same flower and stalk, sometimes in distinct branches of the same plant, as in the hazel and the walnut trees; and sometimes different male and female plants have to be joined, which happens in hemp. Indeed, with the male part removed by force, the female plant never brings forward the semen responsible for generation, nor the prolific fruit. There is moreover much variety both in the receptacles and the figures of the pollen, as well as in the ovarian capsules and in the seeds contained there, and in the measures of the stylus or the vagina of the uterus, not to mention the figures both of the grain of pollen as well as of the eggs, commonly referred to as semen. Whence you see to which extent the field of comparison of plants is opened up, as certainly of great importance, even if reached to a lesser degree, and less extensive in our narrow experience than the field of what is disclosed in the figure of flowers.
XI. Besides, the numerous suggestions you cautiously provide in your letter to me concerning the improvement of medicine show no less your ability to judge than your knowledge of the art; these suggestions shall concern me less, who in the art of medicine—than which none is more excellent or difficult—can avail myself of neither that ability nor that knowledge. Nor do I interfere with these studies beyond what those outside of it are capable of. You know indeed that it pertains eminently to the activity of those who are engaged in civil affairs to have some measure of the health of the citizens. And thus formerly I urged Ramazzini, and now the celebrated Hoffmann, to pursue that investigation most useful to the human race: the natural history of the climate. For a number of years Ramazzini provided a Physico-Medical History, with one year dedicated to me (out of that kindness he is endowed with) and while he had been remiss in the most recent years, he wrote to me last year that he would soon publish all of them in a single volume. But in the year 1700 of the common era (which is to say in the secular sense the last of the century) Hoffmann most recently gave me, in a little book dedicated to me (which is an expression of his benevolence), a meteorological description that was at once an epidemiological one, admirably observing (beyond the variations of the barometer and the thermometer) the widest range of mutations of storms and of the wind (in which the essential of it is to be found) and from there which changes follow in human bodies and, if I may say, in the manner and condition of the illnesses. If these are continued and established in several places, with distinguished men exchanging information and with observations being compiled, not only shall we progress in understanding illnesses that proceed in singular and not yet investigated fashion, but a vast thesaurus of the most beautiful observations will soon be compiled, which will be of much use to the human race, so that I know nothing next to the practice of virtue that can be professed to be more pious and in agreement with Christian charity. Nor do I doubt that you, as well as the distinguished men with whom you are in contact, will contribute their share to the common good. And in fact it is not required that, as did those two men whom I mentioned for establishing and initiating that practice, each one should compose entire volumes, but rather each should bring out a maximum of available and notable facts. It is not a great affair to have a barometer, a thermometer, or an anemometer, and to repeatedly cast one’s eyes upon them, noting the smallest mutations of these instruments and of the air, or for these notations to make use of someone else’s labor who would not lack diligence (for intelligence is needed for noting as well as using notations), or to enquire about the plants and animals in that year, but it is to relate everything to the effects upon the human body and to the use of the art (as you yourself do in a praiseworthy manner). Farewell and favor [me in friendship]. Sent from Hanover, April 23, 1701