absorbed into natural philosophy under Hobbes’s First Philosophy.
5 5 Alessandro Piccolomini and subsequent Aristotelian mathematicians reclassified mechanics, the art of machines, which was traditionally considered a craft, as a mixed mathematical science (Hattab 2009, 93–8). Marcus Adams discusses Hobbes’s treatment of physics as a mixed mathematical science, which following the Aristotelian tradition of such sciences, borrows its principles from the more fundamental science of geometry, and applies them to nature to deduce physical effects (Adams 2017, 84–6). This is also the sense in which Descartes considers his natural philosophy mathematical and mechanical and appears to be a common thread in the so-called early modern “mechanists” (Hattab 2009, 120–35, 2019).
6 6 The English edition misleads since it mistranslates cognitio with “science” in the last sentence, falsely implying that Hobbes counts experience as scientific knowledge: “But we are then said to know any Effect, when we know, that there be Causes of the same, and in what Subiect those Causes are, and in what Subiect they produce that Effect, and in what Manner they work the same. And this is the Science of Causes, or as they call it of the διότι. All other science, which is called the ὅτι, is either Perception by Sense, or the Imagination, or Memory remaining after such Perception” (EW I.48–9).
7 7 This aspect of the generic method generates a persistent misreading of Hobbes’s specific method of analysis as akin to the first phase of Jacopo Zabarella’s regressus, which further gets conflated with a different sense of method in which Zabarella appeals to analysis. For example, see Hanson (1990, 587–626), MacPherson (1968, 25–9), Röd (1970, 10–15), Hungerland and Vick (1981, 25–7), Watkins (1973, 63–5), and Duncan (2003). J. Prins demonstrates how differences between Hobbes’s and Zabarella’s views on logic affect their views on method and scientific knowledge (Prins 1990, 26–46). Jesseph revised his view noting that any number of extant views on analysis and synthesis could have influenced Hobbes’s (Jesseph 2004, 191–211). I show that the regressus, a proof enabling one to deduce a possible natural cause from observed effects, and then in turn, deduce that the possible cause is the actual cause of the natural effect, does not map onto Hobbes’s method. Linking the two stems from substantive confusions between the regressus and what Zabarella calls “method as order.” Zabarella only discusses “analysis” in the context of method as order. Wherever Hobbes gets this label, his sense of “analysis” is unrelated to the regressus and closer to later Scholastics uses than Zabarella’s (Hattab 2014).
8 8 Most Scholastic Aristotelians accept Aristotle’s claim at the start of Nicomachean Ethics that practical matters do not allow for the same precision as theoretical matters and hence require a distinct method (Aristotle 1984, 1730).
9 9 Zabarella notes, when we define mathematical entities, our definitions are advanced as principles “since they are heard and understood at the same time, and are known per se” (Zabarella 1597, 159). This is because things like “line” and “surface” are simple accidents, so the declaration of merely the word suffices to signify the essence. In other words, in mathematics, nominal and essential definitions of the object coincide; thus, in mathematics, one has a perfect definition once one obtains a nominal definition. This view was shared by seventeenth-century mathematicians, like the Jesuit Josephus Blancanus, who claims that most mathematical definitions bear the advantage of being both nominal and essential definitions: “when it is said that an equilateral triangle is one having three equal sides, at once you see the cause for both the name and the thing” (Blancanus 1996,181). Blancanus’s work is cited in Marin Mersenne’s early publications, making it likely that Hobbes was exposed to Blancanus’s mathematical theory, via the Mersenne Circle. On this theory, definitions of mathematical objects carry the distinct advantage that their names concurrently tell you how the object is caused.
10 10 As Karl Schuhmann points out, both Hobbes and Spinoza appear to adopt Hero of Alexandria’s generative approach to defining geometrical objects (Schuhmann 1987, 72).
11 11 Marcus Adams, following Pérez-Ramos, calls this “maker’s knowledge” and argues that it constitutes the causal knowledge of scientia for Hobbes. On his interpretation, Hobbes’s commitment to maker’s knowledge accounts for why geometry and civil science are the only instances of science for Hobbes (Adams 2019, 2). Since both the geometer and the political philosopher construct their actual object, the same procedure can be applied in these domains, a procedure not available to the physicist who studies objects generated by natural processes.
12 12 Oddly, Hobbes’s example to reveal the parts into which we resolve our conception of the individual nature of a square does not indicate that these parts would combine to generate the square in the same manner. “Plane” and “line” do not generate a square in the way a point in motion generates a line. The same can be said of the definition of a triangle that Hobbes introduces in De corpore, I, vi.11 and again in Leviathan chapter 4 (2012, 54; 1651, 14). Adams (2014, 55–8) proposes a possible explanation for these two different kinds of definitions.
13 13 Adams gives the strongest defense of the first implied possibility, arguing that the simple conceptions at the foundation of both natural and political philosophy enable an ensuing construction in both that can be thought of as a demonstration, in the sense that Hobbes regards the construction of a geometrical figure, like a square, from its elements as a “demonstration.” Adams concludes, “The structure, in civil philosophy and geometry, of thought experiment, definition by explication, and generative definitions allows Hobbes to see himself as providing a demonstration by synthesis in both cases” (Adams 2019, 19). Physics, which does not admit of this kind of geometrical demonstration, lies outside scientia. However, Adams also defends the view that physics counts as a science for Hobbes in the Aristotelian sense of a mixed mathematical science (Adams 2017, 84–6). Others embrace the second possibility pointing to inconsistencies in Hobbes’s texts (see Sorell 1999).
14 14 Moreover, seventeenth-century works were rife with analogies between the natural world and machines. As I show in Hattab (2011), they often did not signal a commitment to what we mean by mechanistic explanations. For different seventeenth century senses of “mechanics” and “mechanical demonstration,” see also Gabbey (1993) and Hattab (2019).
15 15 Sorell sums up the apparent tensions within Hobbes’s texts (1999, 5–7, 14–15), and Adams (2014, 4–6) gives a good overview of the two previous main lines of interpretation, which he calls the “deductivist” and the “disjoint” accounts – neither resolves the tensions. Sorell’s solution is to argue that civil science can be autonomous, resting solely on experiential foundations: “There is a philosophical or scientific understanding of the motions of the mind, arrived at from a prior acquaintance with principles given in physics. There is also a pre-scientific understanding, available to anyone who bothers to introspect and observe within himself the passions that move him” (Sorell 1999, 7). Adams is more sensitive to the fact that merely arriving at the same insights through alternative means does not qualify the result as scientia since a certain methodical procedure is integral to Hobbes’s view of scientific knowledge. Adams argues that natural and civil philosophy are unified, on the one hand, by a common method, borrowed from geometry, for constructing their definitions, and on the other, in that each science borrows its principles from more fundamental science in the way that Aristotelian mixed mathematical