Explaining the Constancy of Species: Linneaus, Buffon, and Leibniz

The transition from the transcendent to the immanent view can be traced in each aspect of the life problem . . . . We now turn to the transformation of the theory that is to explain the species characteristics of a life-form and their constancy through the generations.

The pure typical case of a transcendent explanation is Linnaeus’ theory, according to which God created at the beginning of the world the various animal species and endowed the individuals of each species with the ability to bring forth their own kind; in fact, the species was the quintessence of the individuals who have descended from each other through procreation; in theory the species was coined by God’s creative hand. When fixity of the species was understood in this way, there was hardly any reason to look for the inner causes of the individual’s character; the reference to God as the transcendent creator of the world in its thusness was sufficient.

Of all the theoreticians of biology of his day, Linnaeus was most deeply immersed in the Christian worldview. Linnaeus believed that the world actually had a definite beginning; there was a day and an hour when the world, in the organization of its existence, emerged from the chaos through God’s creating hand. When this belief died, the teaching of the species and its duration became questionable, leading to those transformations in the theory with which we must now concern ourselves.

When the world was no longer believed to be the creation of a higher being, the act of creation was no longer the real starting point in time of the world and its many species. The “world” was no longer a finite event that was on some level actually delimited in time by a transcendent being. And while the similarity of individuals had been understood as caused by a similar pressure of the divine hand, the theory of the fixity of the species was now also shaken. The succession of generations no longer had a finite beginning in the creation or an origin of its specific laws; instead, the succession could be traced from any individual back into infinity without this regression coming up against a point of origin for the law of the species.

The result was a peculiar, undecided state. The concept of creation was replaced by the idea of infinity. Preformist theory, which envisioned the germs of all individuals contained in the first progenitors of each species–for example, the human ones in the body of Eve–had to change, and replace this real definite beginning with the series of infinite encapsulations.

Now if the image of the created finite succession of generations is supplanted by the idea of an infinite succession without any real beginning, the idea that the law of this succession was created transcendentally at the beginning of the succession of generations becomes meaningless, and speculation forces us moreover to the formulation of that law in such a way that the law of the species can be directly discerned in each individual of the species.

A shift of the cause of the fixity of the species to infinitely distant specimens became pointless because according to the law of the infinite succession it must be assumed that each individual was descended from a predecessor. This led to the speculative leap to the lawfulness of the species as a real cause [Realgrund] that is at work in all individuals of a species, thus necessarily also in the one currently under observation, without having to be traced back to preceding ones.

This finitization of the law of the species in turn invalidates the idea of infinity that, for one speculative moment, served as the explanatory cause of the species–that is, for the moment when the act of creation had ceased to be the starting point of the succession of generations and it was still believed, in accord with the rationalistic encapsulation theory, that the regression to the preceding individual could explain the one descended from it. This open, undecided moment came to an end with the abolition of the idea of infinity and with the adaptation of the concept of law to the finite style of the new concept of the organism . . . .

Buffon Dissolves the Problem of Infinity

In his four propositions Linnaeus presented the species as created all at once and then subdivided into the generations of its individuals; the how of this process of individuation did not seem open to question. The succession became a problem only when biological inquiry starts with the individual and finds its attempt to explain the individual caught up in the infinite regress of encapsulations of preformed germs without coming any closer to an understanding of the concrete individual in its self-contained existence.

In this succession, in the continuous renewal and duration of the species, lies the mystery of nature, as Buffon argues when he attempts to fathom the nature of these succeeding generations and to elucidate the underlying problem. The ability to produce offspring of one’s kind, this curious lasting, apparently eternal unity–this to Buffon was the unfathomable mystery. The permanence of the species, which Linnaeus held to be the indisputable, God-created unitas of the series of individuals, becomes a problem for Buffon, who wants to understand the individual in its organic unity as a totality and as a totality of a specific kind.

He held those creatures to be individuals of a species who perpetuate themselves through copulation and thus preserve the image of the species. Individuals who do not produce offspring of their kind when they copulate must be regarded as belonging to different species. Thus, the chain of successive individual existences of the same species constitutes l’existence réelle de l’espèce. The infinite succession of generations with the same species characteristics is thus identical with the species itself, and Buffon then has to wonder whether seeing the individual as a part of this succession contributes anything to an understanding of the individual as a selfcontained being. Buffon answers in the negative and justifies his position by dissolving the problem of infinity.

He presents an excellent explanation of the genesis of the concept of infinity through the gradual addition of finite steps and demonstrates that the concept of infinity becomes meaningless if we keep in mind that the infinite regression is made up of finite steps. The infinite is nothing more than the finite realm with the boundaries removed; these boundaries are by nature a matter of quantity. As a result the infinite has become an intrinsically absurd concept. There is no actual infinite–that is, something infinite cannot be a subject of finite thinking. Regarding the problem of species this means that the inquiry has to start with the self-contained unity of the individual, which is determined by its species.

Several such unities of the same species form a finite series or succession, and from here theory (at any rate the preformation theory) makes the leap of attempting to explain the nature of the species on the basis of the infinite succession. However, according to Buffon, this infinity does not really exist; it is no existence actuelle but an abstraction. By nature extension is finite; to assume an actually infinite extension is a contradiction in terms. Those who nevertheless make such an assumption, according to Buffon, have to confine themselves to saying that the infini de successions et de multiplications is nothing more than an extension with an indefinite upper limit–not an infini but an indéfini.

Pointing out the infinite divisibility of matter also does not hold good; rather this argument must be countered with the point that the same illusions connected with the infinite divisibility are also associated with all other kinds of mathematical infinity: these infinities do not exist in actual fact but are merely intellectual abstractions. Therefore, dissolving the species into an infinite regression is not a sufficient answer to the question of how we are to understand the nature and reproduction of life-forms.

We can understand Buffon’s reasoning only if we assume a complete breakdown of the idea Linnaeus had still considered valid, namely, that of a finite, self-contained world created by God. In this self-contained worldview, the creation of the species unit by God is a completely adequate explanation of the species characteristics of the individual.

It is only when the rampartlike boundaries of this world are breached and the succession of generations extends into infinity that the problem of actual infinity becomes discernible in ameaningful way. It is only when the dogmatic framework breaks down and the empirical stance attempts to understand the isolated individual in its particularity that the problem Buffon presents arises.

Leibniz and Speculation on the Infinite

At the end of the chapter of Buffon’s Histoire naturelle (p.250) that contains the investigations of the problem of infinite we find the date February 6, 1746; the volume was published in 1750. For further details concerning his ideas, Buffon refers the reader to the foreword of his translation of Newton (not available to me), which appeared in 1740, and thus to the larger mathematical context of the problems associated with the analysis of infinity in his time.

The most significant and most concise fundamental formulations of the problem are found in some letters from Leibniz to Bernoulli (published in 1745). For our purposes the letter of July 29, 1698,is especially important because it contains a statement referring to the problem of preformation. There Leibniz speaks about the division of matter, arguing that no indivisible elements or smallest particles can ever be arrived at, only ever smaller ones that can be split into yet smaller ones.

By the same token, increasing a dimension will never lead to the largest one or to infinitely large ones or to ones whose dimensions cannot be increased further. Applying these principles to the problem of preformation, Leibniz concedes that the germs may be encapsulated but denies that it is possible to arrive at an infinitely small one, much less at an ultimate one.

The regression of encapsulation is thus extended into infinity, and the act of creation loses its significance as an absolute beginning. Another passage in a letter of August, 1698, shows even more clearly that in the infinite regression for each member we must necessarily envision another one, and thus the concept of an absolute infinity is a contradiction in terms. The passage is formulated with particular felicity because it distinctly shows the connection between the problem of the infinitely large with that of the infinitely small; from the vantage point of empirical finite facts, speculation on infinity leads to meaninglessness in both directions.¹

Notes

This excerpt is from The History of the Race Idea: From Ray to Carus (Collected Works of Eric Voegelin 3) (Columbia, MO: University of Missouri Press, 1998)

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