Deductive Proof in the Theoria generationis (1759)
Shirley Roe (1979) argued that Christian Wolff’s philosophy of science influenced the methodology of Caspar Friedrich Wolff (1733–1794). We build on and further develop Roe’s interpretation. Wolff was educated at the University of Halle, 1754–1759 (Roe 1979, p. 13). Halle housed a significant number of Wolffians, although Christian Wolff’s influence waned over the course of the eighteenth century (Albrecht 2018, pp. 430–439). The Wolffian physicist Johann Peter Eberhard (1727–1779), whom we have discussed, became professor of philosophy at Halle in 1753 and of medicine there in 1756 (Klemme and Kuehn 2016, p. 176). Hence, at the time when Caspar Friedrich Wolff attended Halle’s medical faculty, there were Wolffian scientists working there, although he was of course exposed to Newtonian influences there as well (Jahn 1998–1999).
In his dissertation Theoria generationis (1759), C.F. Wolff developed an epigenetic theory of generation.Footnote 12 As Roe emphasized, Wolff’s Theoria generationis was written in accordance with Christian Wolff’s mathematical method:
One of the most striking aspects of Wolff’s writings, particularly the Theoria generationis, is their scholastic, deductive style of presentation. Wolff’s dissertation is a model of the “mathematical method” championed by Christian Wolff .... The Theoria generationis extends this method to embryology through a deductive scheme based on principles, definitions, scholia, and syllogistic reasoning. (Roe 1979, pp. 13–14)
Roe is correct to stress the impact of Christian Wolff’s axiomatic ideal of science on C.F. Wolff. However, her interpretation has been challenged by Zammito (2018, p. 155). We will return to Zammito while defending Roe’s interpretation below; here, we remark that we do not think that Roe sufficiently stressed the implications of Wolff’s axiomatic method. According to our reading, C.F. Wolff’s axiomatic treatment of embryology has the purpose to present embryology as a proper axiomatic science that conforms to Christian Wolff’s ideal of science. We argue that the axiomatization of embryology provided a small step in the emergence of biology as a special science.
Caspar Friedrich Wolff’s adherence to an axiomatic ideal of science becomes clear in his introductory remarks to the Theoria generationis. There, Wolff construes scientific explanations as deductive demonstrations from principles or laws. He argues that one only explains generation if one “deduces the parts of bodies and the mode of composition of these parts from principles or laws” (C.F. Wolff  1999, p. 4; Roe 1979, p. 14). Wolff can thus be said to accept conditions (3a) and (3b) of the classical model. Wolff further notes that in his theory of organic generation we specify the true causes of organic bodies, and thus are provided with philosophical, as opposed to mere historical, cognition of these organic bodies (C.F. Wolff  1999, p. 5). Here, Wolff employs the distinction between historical and philosophical cognition introduced by Christian Wolff (C. Wolff  1963, pp. 3–6; Roe 1979, p. 14). Historical knowledge is descriptive empirical knowledge of the world. It provides bare knowledge of facts and merely shows that something is the case. In contrast, philosophical knowledge is knowledge of the reason of things that explains why something is the case. C.F. Wolff attempts to provide philosophical knowledge of organic bodies: he explains why organic bodies are structured as they are. Wolff also claims that in his work he demonstrates truths from principles. Thus, for example, he claims that he has demonstrated growth from its principles, ex suis principiis demonstrata (C.F. Wolff  1999, p. 88). Christian Wolff reserved the term demonstration for deductive inferences proceeding from certain principles (C. Wolff  1978, p. 172). C.F. Wolff’s use of the term demonstration suggests, given his frequent use of Wolffian terminology, that he also views explanations as deductions from principles. Finally, C.F. Wolff states that a theory is true if one first demonstrates the principles and laws of the theory and then subsequently shows that from the principles the consequences necessarily follow (C.F. Wolff  1999, p. 4). This claim indicates that Wolff wanted to present his theory in a deductive axiomatic fashion. It also suggests that C.F. Wolff adopted Christian Wolff’s combined demonstrative analytic and synthetic method. We argue that this is indeed the case.
Through providing a philosophical account of the structure of organic bodies, C.F. Wolff’s theory of organic generation provides us with what he calls “the science of the organic body” (C.F. Wolff  1999, p. 5). This shows that he wanted to ground embryology as a proper axiomatic science. In the next section, we will argue that the axiomatic treatment of embryology provided a small step in the emergence of biology as a special science.
Caspar Friedrich Wolff’s Account of Nutrition in Plants
We now turn to the question of how the axiomatic ideal influenced C.F. Wolff’s scientific theorizing. To achieve this end, we will sketch Wolff’s theory of organic generation. As Roe argued, Wolff presented a theory of the generation of plants and animals that was based on two factors: (i) the ability of plant and animal fluids to solidify, and (ii) a force called the vis essentialis (1979, pp. 5–6). The origin and formation of plants and animals are brought about by the secretion of fluids that solidify into structures. In animals, for example, the first structure that solidifies is the spinal column, which subsequently secretes, for example, the wings and legs (1979, p. 6). This theory of organic generation was based in part on Wolff’s account of nutrition and growth in plants and animals. Wolff took nutrition, growth and reproduction to be analogous processes (C.F. Wolff  1999, p. 6). Hence, an account of, for example, nutrition and growth, will shed light on the analogous process of reproduction. In the following, we will discuss Wolff’s account of nutrition in plants. This shows how Wolff attempted to treat embryology demonstratively.
Wolff’s account of nutrition in plants follows the analytic method, that is, he reasons demonstratively from consequences to their causes (just like Christian Wolff’s deductive demonstration of the proposition that air has an expansive force was an analytic inference). That a large part of Wolff’s work adopted the analytic method is explicitly stated in paragraph 71 of the Theoria generationis, where he remarks that he wanted to discover the principles and laws of generation a posteriori (C.F. Wolff  1999, p. 44; Roe 1979, p. 16). At the start of providing his account of nutrition in plants, Wolff introduces his famous vis essentialis. Wolff argues that plants take up nutritious fluids, that these fluids are distributed throughout the plant, and that these fluids evaporate. According to Wolff, there must be a force that is responsible for taking up fluids from the surrounding environment and that distributes these fluids throughout the parts of the plants. This force is the vis essentialis (C.F. Wolff  1999, pp. 11, 12). The vis essentialis is later called a principle that allows one to demonstrate or explain phenomena (C.F. Wolff  1999, p. 44).
Having described the vis essentialis, Wolff turns to a discussion of the channels through which fluids move in plants. Wolff notes that, when one places a root or a branch under a microscope, one observes vessels (Gefäße, vasa) and cylindrical fluid droplets contained in these vessels. Hence, these vessels are the primary means through which fluids move. However, in young leaves one does not find vessels: they merely contain vesicles (Bläßchen, vesiculae). Since these parts of the plants must also receive nutrients, Wolff concludes that the fluids move through the substance of vesicles and disperse throughout the plant. In other words, fluids move through the solid parts of plants with the same ease as they move through vessels. Wolff concludes by providing some remarks on the growth of leaves and roots of plants. He claims that leaves grow by new vesicles inserting themselves between old vesicles or by vesicles expanding, whereas roots grow by the insertion of new vessels between old vessels or by vessels expanding. Fluids must penetrate these vesicles and vessels as well as the spaces between the vesicles and the vessels (C.F. Wolff  1999, pp. 12–14).
After discussing the trajectory of nutritious fluids in plants, Wolff provides a comparison between the vessels and vesicles in young (parts of) plants and older (parts of) plants. He notes that in young plants, the vesicles are moveable parts that can be designated as pores or cells, whereas the vessels are moveable parts that can be designated as canals. Moreover, in young plants the substance that exists between vesicles and vessels is a homogeneous soft substance that is permeable. In older plants, this substance has solidified. According to Wolff, this solidification process is responsible for the growth of plants, which, as we have seen, occurs by new vesicles inserting themselves between old vesicles and through the insertion of new vessels between old vessels. Wolff argues that the soft substance that exists in the spaces between the vesicles contains a fluid that expands and solidifies and forms a new vesicle. Likewise, the soft substance that exists between the spaces of vessels contains a fluid that expands and solidifies to form new vessels. Solidification of nutritious fluids is thus the process through which the growth of plants is explained (C.F. Wolff  1999, pp. 16–17). Here we see that the ability of plant and animal fluids to solidify, which was used by Wolff to explain the generation of plants and animals, was already introduced by Wolff in his account of nutrition and growth in plants.
In summary, Wolff has argued that (i) the vis essentialis is responsible for distributing nutritious fluids through plants, (ii) these fluids run through vesicles and vessels as well as through the matter that exists in between the spaces of these vesicles and vessels, and (iii) the fact that nutritious fluids run through the matter that exists between vesicles and vessels causes an expansion of this matter, which, together with the solidification of the nutritious fluid, gives rise to new vesicles and vessels. Hence, nutritious fluids form new vesicles and vessels. Wolff concludes by noting that the formation of the first vesicles and vessels must also be due to the solidification of nutritious fluids (C.F. Wolff  1999, pp. 16, 20–21).
Wolff’s account of nutrition in plants is experimental: his conclusions follow from microscopic observation of plants. It is also meant to be a demonstrative theory. After establishing propositions experimentally, Wolff presents his argument as a deductive inference. For example, in paragraph 21, Wolff argues that: from the fact that the spaces between the vesicles and vessels are filled with soft substance (established in paragraph 20); from the fact that leaves grow through new vesicles inserting themselves between old vesicles, whereas roots grow through the insertion of new vessels between old vessels (established in paragraph 9); and from the fact that vesicles are nothing but pores or cells filled with fluids, and vessels are canals filled with fluids (established in paragraph 20), it “follows with necessity” that the soft substance occupying the space between vesicles is expanded through the fluids it contains and that vessels are formed in a like fashion (C.F. Wolff  1999, p. 17; see also Zammito 2018, pp. 157–158). The claim that propositions follow with necessity from each other supports the idea that Wolff is presenting a deductive inference here. Note that Wolff’s method is analytic: he reasons from the consequences to their causes. In later chapters, Wolff reverses the direction of inquiry and adopts the synthetic method, reasoning deductively from grounds to their consequences. For example, in a later chapter on the growth of plants, Wolff establishes laws (axioms) that govern growth and subsequently deduces particular phenomena on the basis of these laws (C.F. Wolff  1999, pp. 34, 37–38). All of this suggests that Wolff wanted to present his theory in an axiomatic fashion.
The idea that C.F. Wolff strictly followed Christian Wolff’s ideal of axiomatic science has been challenged by Zammito. Although Zammito acknowledges some influence of Christian Wolff on C.F. Wolff, Zammito writes that C.F. Wolff was an eclectic and that it is doubtful that he was “a rationalist in a sense that rendered building inferences drawn from observation and experience superfluous, or that construed rational deduction a priori as the ultimate and only `science’” (Zammito 2018, p. 154). Zammito stresses Wolff’s experimental work and contrasts this to Christian Wolff’s axiomatic or demonstrative ideal of science. Zammito offers the following justification for his reading, which is based, like our reading, on Wolff’s account of nutrition in plants:
there is no derivation a priori in this account. It is entirely a matter of experimental observation and concrete description. The first twenty propositions of part 1, then, are entirely empirical, not derived from axioms in some logico-deductive manner. In paragraph 21, Wolff did draw an inference that he claimed was necessary (“thus it follows with necessity”) .... I can take this only as an inductive inference, not a deduction, and the “necessity” Wolff claimed can only be a matter of what we would call inference to the best explanation, not demonstrative logic. (Zammito 2018, pp. 157–158)
We think Zammito’s argument is mistaken for two reasons. On the one hand, we note that Zammito is forced to explain away Wolff’s claim that his conclusion “follows with necessity.” For someone with Wolff’s philosophical background, inductive and abductive inferences do not yield “necessity”; for most authors in this period, only deductive, i.e., demonstrative, inferences necessitate their conclusion. On the other hand, we believe Zammito is led to this interpretation because he is mistaken about what the axiomatic method meant to an author like C.F. Wolff. As we argued in the previous section, Christian Wolff allowed for the possibility that some propositions in natural science are discovered experimentally and have empirical content, while insisting that after we have found these empirical propositions experimentally we must order them demonstratively. Hence, it is not the case that inferences drawn from observation and experience are superfluous within Christian Wolff’s axiomatic conception of science. C.F. Wolff adopts the same method: he first establishes propositions experimentally and then orders them deductively. We can also explain why Zammito is unable to find a synthetic argument from axioms in the first twenty propositions of the Theoria generationis. If C.F. Wolff is following Christian Wolff’s method, these first paragraphs can be read as an analytic part of the argument, in which Wolff reasons from consequences to their grounds and to the axioms. It is only in later chapters that Wolff adopts the synthetic method, reasoning from axioms to their consequences. Thus, as we have said, in later chapters Wolff establishes laws (axioms) that govern growth and subsequently deduces particular phenomena on the basis of these laws. We conclude, therefore, that Zammito wrongly challenges Roe’s interpretation of Wolff’s work because (1) he mistakenly believes that empirical or experimental propositions cannot play a major role in an axiomatic conception of science, and (2) he does not acknowledge that Wolff first establishes propositions experimentally and then orders them deductively. We showed that these assumptions are mistaken as assumptions about the axiomatic method proposed by Christian Wolff. As a result, the peculiarities of C.F. Wolff’s presentation to which Zammito draws our attention are entirely to be expected if C.F. Wolff is in fact following Christian Wolff’s prescriptions. We add one disclaimer: it may be the case, as Zammito’s analysis suggests, that C.F. Wolff sometimes presents what are really inductive inferences as deductive inferences. In addition, if we let a logician analyze Wolff’s work, we would no doubt find many implicit premises and leaps of inferences. However, there is ample evidence that C.F. Wolff wanted to treat embryology axiomatically, that is, that he followed Christian Wolff in accepting the ideal of axiomatic science. Zammito may be right that the axiomatic ideal of science is an illusion and provides a faulty conception of how science actually works (see Zammito 2017), something we know from our modern vantage point. However, this ideal did influence philosophers and scientists.
Although C.F. Wolff follows Christian Wolff’s prescriptions for science, there are important differences between the two men’s use of the axiomatic method in the life sciences. C.F. Wolff’s account of nutrition in plants is based on fundamental concepts, such as the vis essentialis, the notions of a vessel and vesicle, and of nutritious fluids that can solidify. On the basis of these fundamental concepts, Wolff attempts to explain nutrition in plants. As we have seen, Christian Wolff referred to general physical laws to explain phenomena such as nutrition and growth. C.F. Wolff, in contrast, refers to the action of the vis essentialis, which is operative in organic nature, rather than general physical laws. Hence, C.F. Wolff articulated principles that were specific to theorizing in the life sciences and attempted to explain organic processes in terms of these principles.
The idea that life sciences must have principles specific to these sciences was endorsed by many life scientists after Wolff. Johann Friedrich Blumenbach (1752–1840), for example, based his theorizing on the notion of a vital force. Vital forces, which were operative only in the organic domain and accounted for the vital properties of organisms, were distinguished from physical and chemical forces, to which all bodies are subject (Blumenbach 1817, pp. 16–17; van den Berg 2014, pp. 195–196). Since, according to Blumenbach, vital properties cannot be accounted for in terms of physical or chemical forces, life scientists should appeal to vital forces in order to explain the vital properties of organisms. Hence, Blumenbach introduced principles that were specific to the life sciences. The vital materialism that was adopted by many biologists at the end of the eighteenth century is an important factor in the emergence of biology as a special science (see Gambarotto 2018).
Finally, we may note that, in the third part of the Theoria generationis, Wolff specifies universal properties of organisms and universal principles of organic generation. This part contains the axioms of the life sciences. For example, Wolff specifies that a universal property of organisms is that individual parts of organic bodies cannot exist without the existence of other organic parts, or that they obtain nutrition from other organic parts (C.F. Wolff  1999, p. 145). From this fundamental principle, Wolff deduces consequences, such as the proposition that every organic body possesses a part through which the nutrition of all other parts is mediated. As an example of a fundamental principle of organic generation, Wolff mentions the familiar principle that the parts of organic bodies are formed through fluids (C.F. Wolff  1999, pp. 146, 150) which again functions as a principle from which consequences are derived. The final part of the Theoria generationis thus again provides evidence for our reading that Wolff first attempted to analytically discover the propositions of his theory of generation proceeding from empirical propositions, while subsequently ordering these propositions synthetically.
Axiomatics in the Theorie von der Generation (1764) and the Emergence of Biology
In 1764, C.F. Wolff wrote a follow-up to his dissertation, called Theorie von der Generation, in which he again explained his theory and debates with Albrecht von Haller (1708–1777) and Charles Bonnet (1720–1793) (Roe 1979, p. 8; on the Haller-Wolff debate, see Roe 1981 and Detlefsen 2006). We will explain the impact of axiomatics on the Theorie von der Generation and explain the importance of Wolff’s axiomatic embryology for the emergence of biology as a special science.
As Roe has emphasized (1979, pp. 15–16), Wolff’s methodological views in his Theorie von der Generation (1764) are the same as those articulated in his dissertation of 1759, and show the impact of Christian Wolff’s philosophy. In the section Begriff einer Theorie von der Generation, C.F. Wolff again introduces Christian Wolff’s distinction between historical and philosophical cognition (C.F. Wolff 1764, pp. 8–9). Wolff’s embryology is supposed to provide philosophical as opposed to historical cognition of organic phenomena, that is, explanations for why organic phenomena occur. Wolff also notes that his theory of generation provides the sufficient ground of the parts and the composition of organic bodies (C.F. Wolff 1764, p. 11). Roe notes that the notion of a sufficient ground was used by Christian Wolff but does not explain this notion. Christian Wolff construed a sufficient ground as the set of all the (certain) grounds that make a proposition true (C. Wolff  1983, 2: 434–436; Madonna 1987, p. 19). Thus, the notion of a sufficient ground is tied to the idea of axiomatic science: if we have a complete demonstration of a proposition terminating in certain axioms, we know its sufficient ground. That C.F. Wolff wanted to specify the sufficient ground of organic phenomena suggests that he wanted a demonstration of these phenomena from certain principles. C.F. Wolff also again states that his theory is based on principles (Grundsätzen). In his debate with Haller, Wolff shows that his theory is based on true principles that explain phenomena, and he stresses the importance in his dissertation of the axiomatic presentation of his theory (C.F. Wolff 1764, pp. 32, 75, 76, 79). Finally, whereas C.F. Wolff, like Christian Wolff, recognized the role of hypotheses in science, he notes that he provides a stronger proof than proof by hypotheses (C.F. Wolff 1764, pp. 41, 63) and refers to his theory as a certain truth proved on the basis of true principles (C.F. Wolff 1764, pp. 35, 42, 60–62, 76, 111–112).
A large part of the Theorie von der Generation is taken up by providing experiments that provide proofs for Wolff’s theory. However, this does not indicate a departure from the ideal of axiomatic science. As we have argued, C.F. Wolff wanted to combine experimental research with an axiomatic and demonstrative presentation. Moreover, even in the Theorie von der Generation we can find deductive explanations that fit Christian Wolff’s ideal of science. Roe cites the explanation of the fact that animals have hearts whereas plants do not, which she presents as a deduction from experience (Roe 1979, p. 16).
There are also deductive arguments which Roe does not discuss, but which demonstrate C.F. Wolff’s debt to Christian Wolff. In Chapter 6 of the Theorie von der Generation, Wolff discusses what he calls imperfect leaves of plants, that is, leaves that are less developed (C.F. Wolff 1764, p. 231). When discussing the anatomy of plants, Wolff notes that there exist grades of imperfection of leaves: the leaves of the flower (Blume) are more imperfect than the leaves of the sepal (Kelch), the leaves of the pistil are more imperfect than the leaves of the flower, and so forth. Wolff calls this phenomenon the weakening of vegetation in plants. He then proceeds to provide what he calls an a priori proof of this phenomenon (C.F. Wolff 1764, pp. 232, 233). We have seen this terminology being used by the Wolffian physicist Eberhard, who took a priori proofs to be demonstrations from principles. This is exactly what C.F. Wolff provides, namely a demonstration based on certain and empirically established principles. He reasons as follows (C.F. Wolff 1764, pp. 234–235): (i) If (a) a plant is healthy and (b) there is a sufficient supply of nutritious fluids, a plant begins to grow and produce new parts. (ii) If there is no growth and production of new parts, or a lack of growth and production of parts, it must be the case that either (a) or (b) are not satisfied. (iii) If a plant does not grow, or there is a lack of growth and production of new parts, but is nevertheless healthy, this must be due to a lack of nutritious fluids. (iv) Consider a healthy plant, called A, that is affected by a lack of growth and production of new parts. (v) The lack of growth of A must be due to a lack of nutritious fluids, a conclusion that can, on the basis of premise (iii), be generalized to all healthy plants affected by a lack of growth and production of new plants (Q.E.D.). This is clearly meant as a deductive demonstration from principles, and it can be reconstructed as a valid deductive argument. Wolff notes that this proof secures the truth of the conclusion. However, after providing this proof, Wolff also provides experiments that support his conclusion (C.F. Wolff 1764, pp. 235, 236–243). Hence, C.F. Wolff adopted the method of Christian Wolff and Eberhard: he demonstrated truths from certain principles while also providing confirmation of these truths through experiments, striving for a harmony between reason and experience.
Having discussed C.F. Wolff’s main works, we may consider the excellent work of Detlefsen (2006), who, like Zammito, is sometimes skeptical of Roe’s interpretation. Detlefsen agrees that C.F. Wolff accepted Christian Wolff’s ideal of demonstration as demonstration from principles (Detlefsen 2006, p. 254). However, she also doubts Roe’s interpretation on the grounds that C.F. Wolff was an avid experimentalist. Building on the work of Duchesneau (1982, p. 330)Footnote 13 and Rudolph (1991, p. 78), she describes C.F. Wolff’s method as a form of experimental demonstration (Detlefsen 2006, p. 256), because the conclusions follow from experiments. We think the term experimental demonstration is apt to characterize Wolff, because Wolff actually was an experimentalist, and we generally agree with Detlefsen’s account of experimental method in Wolff. However, we argue that C.F. Wolff also wanted to present his theory demonstratively. Remember Christian Wolff’s method: (i) in experimental physics, we construct experiments. (ii) Then, we reconstruct experimental inferences as analytic deductive arguments. (iii) Finally, we adopt the synthetic method and show how consequences follow from the axioms. C.F. Wolff clearly accepts this method. In other words, the strict dichotomy between experimentalism and a demonstrative ideal of science, which Zammito and Detlefsen seem to accept, is not apt to interpret Christian Wolff and C.F. Wolff, both of whom wanted to unify experimental science with demonstrative science.
To conclude, we discuss the importance of C.F. Wolff’s work for the emergence of biology as a science. Wolff presented embryology axiomatically, in line with Christian Wolff’s prescriptions for science. Why is this important for the emergence of biology as a science? As an anonymous referee pointed out to us, a historical-epistemological condition for the emergence of biology as a special science seems to be the idea that there is a difference between organic and physical phenomena, along with the idea that this difference applies to living nature as a whole. C.F. Wolff accepts the idea that organic phenomena must be explained by the so-called vis essentialis, which is operative in organic nature, and marks a difference between the physical and the organic. This is clear from his 1789 Von der eigenthümlichen und wesentlichen Kraft, where he argues that the essential force is peculiar to living matter (Roe 1979, pp. 21, 25, 26). However, as our referee pointed out, a stress on the difference between physical and organic phenomena was already present in Stahl’s work and was widespread in the eighteenth century (see, for example, Zammito 2018, pp. 13–36). What, then, is Wolff’s contribution to the emergence of biology? We think that it was precisely Wolff’s formal and axiomatic treatment of embryology that constituted a small step in the emergence of biology. To see this, we must again emphasize the differences between Christian Wolff’s account of the life sciences and C.F. Wolff’s views on life science.
Recall that Christian Wolff took anatomy to be the fundamental life science. For Wolff, explanations in the life sciences are based on anatomical propositions and on laws of physics. There are no fundamental concepts and propositions specific to the life sciences. For Christian Wolff, then, life sciences are not special sciences and the life sciences should be treated as forms of applied physics. C.F. Wolff differed from Christian Wolff in the following respects:
C.F. Wolff specified fundamental concepts and propositions, such as the vis essentialis, that were specific to the organic domain. Hence, he specified true axioms of embryology, and he believed that embryology has axioms that do not reduce to physical laws (as Christian Wolff thought). This made it possible to argue that there are genuine laws concerning “life” that are specific to the life sciences and that life sciences are not mere forms of applied physics.
Christian Wolff’s conception of science entailed an axiomatic hierarchy of sciences: lower sciences are subordinated to higher sciences. C.F. Wolff’s treatment of embryology was motivated by the intention to explicate the axiomatic hierarchy of the life sciences. For Christian Wolff, anatomy was one of the fundamental life sciences. However, C.F. Wolff’s theory of generation explained why organic bodies are structured as they are and thus provided the reasons why certain anatomical structures occur. Accordingly, as C.F. Wolff stresses, anatomy is not the fundamental life science, embryology is (C.F. Wolff  1999, p. 5). Thus, Wolff shows that embryology provides the foundation of many life sciences, such as anatomy and physiology. By providing a novel account of the foundations and hierarchy of the life sciences, C.F. Wolff showed how multiple life sciences are related and can potentially be treated in a unified, systematic, and scientific way. Through his formal treatment of the life sciences, and his attempt to specify an axiom that grounds multiple life sciences, Wolff thus made a step toward the emergence of biology. As we shall see, Treviranus undertook a similar project.
C.F. Wolff took all the propositions of embryology and the life sciences to concern a specific domain of beings, namely organic nature. By contrast, Christian Wolff interpreted the fundamental propositions of the life sciences as physical laws concerning matter in general (although he may have believed that some of the non-fundamental life-sciences employ propositions that do not stem from physics). For C.F. Wolff, the formal treatment of the life sciences matched the ontological conviction that there was a difference between the organic and the physical. According to the axiomatic ideal of science, sciences are distinguished from one another through their different domains (see condition (1) of the classical model). C.F. Wolff’s axiomatic treatment of the life sciences allows one to distinguish the life sciences from other sciences by noting that the propositions of the life sciences concern a specific domain of organic objects, one that is distinct from the domain of objects to which the propositions of physics refer. If one accepts the axiomatic model, this is a precondition for treating biology as a special science.
To conclude: Wolff’s axiomatic treatment of embryology constituted a small step in the emergence of biology as a science. Of course, not all German biologists were concerned with treating the life sciences axiomatically. If we survey the works of Blumenbach and Johann Christian Reil (1759–1813), we see that the life sciences were not always treated axiomatically in the latter half of the eighteenth century (on Blumenbach and Reil, see Richards 2000, 2002, Chaps. 5 and 7; on Blumenbach see van den Berg 2018). However, the ideal of an axiomatic science of life did not disappear.