The Origin of Species —Part II:
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 1'existence réelle de 1'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 a meaningful 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.

Chapter 11
Infinite Series and Finitization,
pp 117-119.