1Messieurs,

2After introducing in the first lesson the foundations of scientific development in the eighteenth century; highlighting in the second lesson the most remarkable periods of the history of sciences in the same century; and sharing the outline of my lecture, I gave a broad presentation on the two great authors who practically dominated the entire eighteenth century. I presented the main characteristics of Newton’s life, showing his most important discoveries. We noticed that his method was always based on observation and experimentation, what I called peripateticism.

3We will now focus on Leibniz who followed different principles but nonetheless had a major influence on sciences in the eighteenth century. His influence still endures: naturalists following the philosophy of nature, supporters of idealism and pantheism still rely on the ideas advanced by this extraordinary man.

4Leibniz (Gottfried Wilhelm) was born in Leipzig on 3 July 1646, four years after Newton. He had a universal mind. We saw that, on the contrary, Newton focused on mathematics and physics and their application to astronomy, devoted some effort to chemistry, and worked only towards the end of his life on chronology and theology. Leibniz embraced all branches of human knowledge: he was incomparably the most encyclopedic mind since Aristotle.1 At fifteen, he was well educated in languages, mathematics, and philosophy. At eighteen, he published a philosophical comparison of the dogmas of Aristotle and Plato2 while earning his doctorate in law at the age of twenty.

5Knowledge taught in public schools was not enough for his intellectual activity. He became aware of the interest of secret societies for chemistry and alchemy,3 and learned that a recommendation written in mystical terms was required to be admitted. He wrote and sent a letter to the Rosicrucianists4 —an order that used specific symbols unknown to outsiders— a compendium of mystical alchemy terms that he did not understand himself. Mystified, the society admitted him. But he soon realized, through the experiments he witnessed, that the Rosicrucianists were not any closer to metal transmutation and discovery of the universal panacea than their predecessors. In need of a situation, he followed a career in law, which had great benefits. Knowledge in public law was useful as German princes had continuous conflicts to be brought before the imperial court.

6Leibniz attracted some attention with the publication of a small volume on the learning and teaching jurisprudence.5 In 1669, he published a work in favor of the Prince of Neuburg, one of the claimants to the throne of Poland.6 He also thought of restructuring Alsted’s Encyclopedia.7 In 1671, he sent his theories of abstract and concrete motions8 to the French Academy of Sciences,9 already including the theory of active forces that stirred up physicians in the first half of the eighteenth century. Finally, he went to London where he met Boyle10 and Oldenburg.11 After the death of the Elector of Mainz,12 his protector, he entered the service of the Duke of Brunswick13 as courtly advisor and librarian. He held the latter position until his death.

7At the request of the Duke of Brunswick to work on the history of the House of Brunswick,14 he collected documentation dating back to ancient times. He even investigated the causes that shaped Brunswick,15 and subsequently the Earth, producing a geogony16 under the title Protogaea.17 We will explore this geogony in detail once we get to the different systems of geology published at the time. Today, suffice to say that Leibniz’s system was certainly one of the best, most ingenious and credible, for a period when knowledge was lacking. We will see that it even contains most of Buffon’s ideas on the same subject.18 Anything that a genius touches yields benefits.

8I will not talk about Leibniz’s historical works, which are unrelated to our subject.

9Leibniz was given the esteem he deserved. He received titles and pensions from the German Emperor,19 the King of Prussia,20 and Peter I, Tsar of Russia,21 who appointed him to advance the state of knowledge in his empire and to establish an academy. The academy was only opened after Leibniz’death. Leibniz was the first president of the Prussian Academy of Sciences and Humanities,22 established according to his plan. His ideas on the relationships among the sciences were also followed for the creation of the Institute of France. He went to Vienna to establish a similar academy but faced insurmountable obstacles from the Austrian government. He returned to Hanover. In 1714, the Elector of Hanover became the King of Great Britain,23 therefore giving the country the two greatest geniuses of the time: Newton and Leibniz. Leibniz died at the age of seventy in 1716, a few years before Newton.

10In the previous lesson, I thoroughly explained how the last years of these two great men were disturbed by the arguments among themselves and their disciples over the ownership of the differential calculus, certainly the most important issue on which such powerful minds could argue. I will only repeat that Leibniz discovered the differential calculus in 1676 and had the merit of presenting it clearly. Therefore, his terms and notation were applied everywhere, except in England. Once his discovery was published, it was applied to the major components of astronomy and mechanics.

11Leibniz focused on all branches of natural history and addressed one of the most interesting questions: the human race. Languages were among the most plausible elements to address this question (as the facts came before civil history). Relationships among languages, common etymologies, show that nations and peoples derive from one another.24 Leibniz originally expressed this aspect, later developed by Adelung25 and other linguists. From the age of sixteen, Leibniz worked on a universal language meant to be intelligible to all peoples and that he called pasigraphy.26 He said to have found his inspiration in the Chinese language but he died without completing it.

12Leibniz also left a dissertation on the origin of rivers in which he exposed the theory of rain. In physiology, he had mechanical theories about animal secretions, and various ideas on the configuration of the parts that dominated this science for a while. We will come back to his discussions with Stahl27 when we broach physiology.

13He also worked on botany and presented his opinions on methods, recommending the approach of a contemporary physician, Burckhard.28 Linnaeus used this method for his sexual system, which was described in a letter from Burckhard to Leibniz.29 Leibniz later presented a dissertation on fish and plant imprints found in black schist in Halle.30 They were thought to be the products of natural occult forces. Leibniz and Scilla,31 whom I previously mentioned, were the ones who demonstrated the best that these imprints were effects and testimonies of earthly motions.

14These are, Messieurs, Leibniz’s works on natural history. However, his metaphysics on continuum and scale had a completely different influence on sciences. Many metaphysical ideas were expressed in the second half of the eighteenth century. Descartes’s ideas32 on the full and the formation of bodies with atoms or elements of various shapes were the foundations, adopted almost everywhere, of general physics. One of the most pointless challenges against this hypothesis looked at the nature of the elements of matter, examining whether matter could be infinitely divided and if it were not the case, what the limits of its divisibility were. You would understand that the answer to this question would be useless for physics itself and that ingenious minds could pursue these discussions for centuries. Descartes admitted the infinite divisibility of matter while defining it as impenetrable, which is contradictory.33 However, assuming infinite divisibility, how can it be conceived that extremely minimal parts would form limited bodies that fill a determined space? This was the main issue for physicians. Leibniz’s answer consisted of ideas on space that were later developed by Kant.34 He described space as having no existence, saying that it existed only in relation to our existence and that it was not possible to appreciate its nature and cause beyond the phenomena at the source of our perceptions. Leibniz imagined that matter and the entire universe were originally composed of simple substances, not as extremely small as Epicurus’s atoms,35 but independent of everything else and characterized by an abstract metaphysical simplicity. He called such substances monads. Each monad can have a correspondence with the whole universe and, if adequately placed, could acquire the perceptions of other monads. Bodies are composites of monads and not of atoms because the latter imply space, an attribute that monads do not have. Monads are indestructible in the natural order and only the divine power could annihilate them.36

15You can see that with these more or less clever ideas, which are rather irrelevant for my subject, he did not address the infinite divisibility of matter but rather the materiality or immateriality of the thinking principle. Such hypotheses only had the advantage of avoiding the objections faced by Descartes’s system and by materialism, which was even more contested.

16Leibniz established relationships between simple and composite substances, which form an infinite chain linking the most basic elements to the very highest perfection. This necessary link between beings, their reciprocal action and reaction constitute in his eyes a chain of causes and effects, from which he derived his philosophical principle: there is no effect without a cause and there is nothing without a reason. This principle of sufficient reason, which dominates Leibniz’s philosophy, linked present and past beings with respect to time, as well as past beings and subsequent ones until the end of time. He called this relationship the chain of being.

17Under Leibniz’s system, simultaneous beings are also linked but not necessarily by causality. For instance, the correspondence between the determinations of the soul and the motions of the body does not depend on reciprocal influence but on what Leibniz called pre-established harmony. I will not go into detail about what he meant by pre-established harmony. I would only say that any of Leibniz’s ideas that was vaguely expressed and even more vaguely interpreted gave way to systems inconsistent with his thinking. This was the case for the chain of being that may have led to useful research but resulted in the greatest number of misconceptions.

18According to Leibniz, links between beings only consist of relationships based on sufficient reason, cause and effect, and pre-established harmony. There are no relationships based on shape that imply consecutive steps between one shape and another, meaning that to go from one shape to the next, there would be an intermediary link and no gap. However, Bonnet37 and other philosophers of the eighteenth century assumed that Leibniz thought so and on this basis, they presented their famous system of the Chain of Being,38 in part to support Leibniz.

19Leibniz did notice that countless forms existed in nature, some related to others, which proved how clever he was. He predicted some discoveries made much later after him. For instance, he declared that it might be proven one day that some animals multiply like plants, which was verified with the discovery of the propagation of polyps by Abraham Trembley,39 fifteen years after Leibniz’s death. We will see that some of his predictions on cosmogony and geology were fulfilled. However, his remark on the relationships between some animal shapes is far from Bonnet’s system. According to Bonnet, all beings are on a single line, starting with the most basic ones, such as amorphous minerals, followed by more refined crystals —to Bonnet, their symmetry seemed to indicate a transition to the regular shape of organized bodies— simple plants, more complex plants, zoophytes, worms, fishes, birds, quadrupeds, man, and, on the last ring of the terrestrial chain, the various celestial intelligences communicating to the divine and forming a descending chain from heaven to earth. Taken strictly, this system, no matter how beautiful, would give a false idea on creation. Before proving so, we will recall the reasoning of naturalists who still support this system. According to them, organized beings, animals in particular, consist of a considerable number of organs. The combinations of such organs could almost be infinite. If classified by degree of complexity, they would produce a series of organizations with the most basic being linked to the most perfect animal. They go further by saying that there are still gaps in the chain of being, to be eventually cleared up as natural science is enriched with new discoveries.

20Ultimately, if the combinations of organs were free and independent from the mutual relationships between these organs, nature would offer countless organized beings but it would still not be possible to place them on a single line. Let us take the letters of the alphabet to represent the organs and let us assume the first ones were combined with the last ones in every way possible. These millions of combinations could not be placed on a single line but would form unlimited beams within an intercrossed network.

21However, animal economy does not even include this network; organs cannot be combined based on all existing abstract and mathematical hypotheses. Some organs are mutually exclusive while others attract each other. When one organ is absent, its correlatives are also lacking. These are the elements of compared anatomy. It is clear for example that for a given shape or nature of intestines, there has to be an analogous shape or nature of mouth, teeth, food, mastication, and locomotion organs. I will reiterate that such correspondences could not be infinite as many are impossible due to the nature of things; the countless combinations of mathematics do not apply to physiology.40 Thus, the number of beings is determined. It cannot be as considerable as assumed because it is limited by the very nature of organs that can only be combined in certain ways. You see that there are blanks, gaps, and intervals in the chain of being. It is a geometric demonstration. Only an incomplete knowledge would lead to the conclusion that Bonnet and others had reached of a continuous chain of being or their distribution on a single line. When their system is confronted with reality, it can be seen that they only focused on certain relationships and neglected many others. The links between beings only occur on one or two points of the organization.

22Let’s take the group of quadrupeds as an example. We will see that there are gaps even within individual components. There are no interconnected intermediaries between ruminants and non-ruminants. But this discussion would require us to go into much detail so let’s just focus on the presumed relationships among the main natural groups. It is claimed that mammals are related to birds through bats, that birds are linked to quadrupeds via the ostrich, and that cetaceans constitute the link between mammals and fishes. If such relationships were true, there would not be one single line, but two collateral lines leading to mammals: the bird lineage through bats and the fish lineage through cetaceans. To support his system, Bonnet cited the flying squirrels, the flying lemurs, and the bats.

23It is true that bats stay in the air like birds but do they use the same means? Is the organization of these beings identical? The answer is no. Birds fly thanks to an arm with several extensions, an extremely reduced hand with two fingers close to each other. The surface maintaining them in the air is due to their feathers, organs that are specific to the bird class and not found in any other class, despite a semblance of similarity to the wings of butterfly. Bats on the other hand have hair; they fly thanks to their fingers, which are real stretched mammal fingers and not bird fingers. Their flight apparatus consists of an extended arm and a thin membrane from the body to the fingertips, serving as a parachute.

24The wings of flying fishes are amplified fins. The flight apparatus of flying dragons is a horizontal extension of false ribs covered by the teguments of the flank. Therefore, there is no similarity in structure, but only in name and use, between the wings of birds and those of other flying animals.

25Even if a bat wing were similar —and it is not— to a bird wing, bats would still not be birds because their digestion, mastication, breathing, lactation, reproduction, and hearing organs are common to the quadrupeds and not the same as those of birds.

26Similar functions or some common characteristics do not constitute sufficient bases for classification. Mammals, birds, reptiles, and fishes form perfectly distinct and defined groups. However, despite the clear distinction, they present some similarities. Birds, which present numerous organization characteristics not found in the three other classes, have a similar cranial composition as individuals in the reptile and fish classes. They also present other similarities, for example by laying eggs as a reproductive method, and are therefore called oviparous.

27The four classes I mentioned above also have in common a vertebral column containing the central nervous system. This column, consisting of a series of vertebral centra, gives their common name of vertebrates. In summary, a group might be similar to another one for some of its parts but not so close as to conclude that there is an imperceptible link between them.

28I could apply this principle to other natural history groups. For instance, mollusks have a brain,41 a stomach, nerves, sometimes even eyes and ears. Based on this already complex organization, they can be classified after fishes. However, what is the huge difference between the most perfect mollusks, or what are considered mollusks, such as cephalopods, and the simplest fishes? (It is not important to know what the simplest fishes are. There is no chain between reptiles and fishes and there is no chain between fishes. Fishes are divided like mammals and cannot be ranked). No higher mollusk has a backbone or a vertebra, even less a spinal cord. Nerves from the brain spread organically or sympathetically unlike the brain and spinal nerves of vertebrates. The layout of the viscera, gills, heart, and reproduction organs of mollusks is also different. There is no need to go into further detail. The dissimilarity between mollusks and fishes is obvious.

29The complex eyes of the cuttlefish, bigger than fish eyes, might give a different impression. Their constitution is different in the arrangement of membranes and the distribution of retinal nerves. Descending to gastropods, bivalves, and oysters, there is no similitude observed. The layout is entirely different: the heart is on the back side and not on the chest side; gills are placed differently; breathing and digestion organs have a common entry for vertebrates when there is no link between breathing and deglutition organs for mollusks. Finally, there is absolutely no resemblance between the hard parts of vertebrates and invertebrates. A quick assessment of the last two zoological divisions yields the same results.

30I spent a long time on this subject, as my intention this year is to address, as they arise, all the important questions that divide naturalists, therefore adding the philosophy of natural science to the history of natural science. Today, I started the discussion on the Chain of Being because it is believed Leibniz initiated it. I hope to have proven the system false and shown that it is irrational to say that one animal could form a link between two groups if those two groups shared a function. The ostrich, for example, mentioned earlier, moves its wings to run. Is this single characteristic enough to affirm that the ostrich forms the transition between the bird and the quadruped classes? The answer is no. Besides the motion of the wings that are too short for flight, the ostrich is in all respects a bird: it has feathers and its wings present, like all other birds, two or three small characteristic fingers. Inside, like other birds, its lungs are partly fixed to its ribs and air moves through them on one side. The head is the same. Its sternum is in truth simpler: it only has two pieces instead of five but because its wings do not serve for flight, this part of the thorax is not as developed as the thorax of other birds where the large wing muscles are attached. Finally, the ostrich has the trachea, the ribs, and the feet of a bird. In other words, the further we analyze the question of a continuous chain of being, the less rational we will find it to be. I will reexamine this subject from the point of view of the derivation of beings from one another, a question as serious and important as the ones raised on cosmogony systems.

31Leibniz was the first to present sound ideas on cosmogony, the birth and development of the world, and the different circumstances of its organization —several philosophers did consider the Earth to be an organized being. You easily see that these questions must have been disturbing. Once some knowledge of the structure of the Earth layers was acquired, the question was raised on why so much marine life was found at different depths. Noting that water covered the Earth, and therefore that beings, at least the terrestrial ones, could not have existed then,42 similar assumptions as those on the chain of being were raised in haste to explain the mystery of their existence and to prove the ideas on their formation. All these systems are linked to the history of scientific advances and we will perform a thorough analysis. Every time there are big mistakes to report, the type of mistakes that grasped the minds and dominated scholars, we have to examine them in detail and disprove them. This will be my focus this year.

32I will address the cosmogony systems in the next session. I will start with this science as it embraces the generalities of nature and is therefore of major interest. We will then get to chemistry that will lead us to mineralogy and physiology.