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1 ¹ Hobbes exhorts those with a sincere desire to be philosophers to “let your reason move upon the deep of your own cogitations and experience; those things that lie in confusion must be set asunder, distinguished, and every one stamped with its own name set in order; that is to say your method must resemble that of the creation. The order of the creation was, light, distinction of day and night, the firmament, the luminaries, sensible creatures, man; and after the creation, the commandment. Therefore, the order of contemplation will be, reason, definition, space, the stars, sensible quality, man; and after man is grown up, subjection to command” (EW I. xiii). Hobbes echoes the appeal to two parallel, but separate, sources of insight into truth prevalent in seventeenth-century Calvinist Scholastic textbooks and Francis Bacon’s work: the book of nature and Holy Scripture. Schmidt-Biggemann explains that for seventeenth-century Calvinist Scholastics, “Knowledge was understood as an inventory of the Revelation made available to humankind, as knowledge found in the Bible, History, and Nature. These three ‘books’ were the field of experience which according to God’s creation plan is inventoried in knowledge” (Schmidt-Biggemann 2001, 394; translation mine).

2 ² Meteorology, Optics, and Music were all mixed mathematical sciences in the Scholastic tradition; logic was considered the instrument of philosophy, not part of natural philosophy proper.

3 ³ See Hattab (2009, 93–8).

4 ⁴ Hobbes’s division most resembles that of early seventeenth-century Calvinist Scholastic textbooks in which “The framework of metaphysics was theological, not the other way around. Hence one counted metaphysical concepts within natural theology and in this way, natural philosophy and metaphysics were made broadly coextensive” (Schmidt-Biggemann 2001, 394, translation mine). For Hobbes, likewise, topics of traditional Aristotelian metaphysics, like the first cause, its eternity, and the immortality of the soul are relegated to Theology. Remaining metaphysical topics, like the nature of substance, its accidents and causation are 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 sciences relied on the principles of pure mathematics (Adams 2014, 6–7).

16 ¹⁶ Adams advances 2a) in combination with a looser structural unity than strict deductivism.

17 ¹⁷ Sorell advocates 2b) arguing for “the autonomy thesis” (Sorell 1999, 7–13). Adams agrees that Hobbes is not committed to the idea that, for every context of inquiry, the same foundational principles constitute the absolute starting points for a hierarchically ordered series of deductions in each branch of philosophy: “if we understand Hobbes as holding that the simples for a science are determined by our explanatory needs – a materialism that does not privilege a single level for explanations – then we can understand why Hobbes grounds civil relations in human bodies apart from civil relations” (Adams 2019, 20). However, Adams also advocates 2a) arguing that the simple conceptions at the foundation of first philosophy and civil science are attained by a common method of thought experiments following fixed steps (Adams 2019, 19).

18 ¹⁸ For example, Zabarella’s seminal writings on logic divide method, taken broadly, into order and method properly speaking. The task of method in the proper sense is to lead us from a known thing to knowledge of another, unknown thing, as when we are led from substantial change to knowledge of prime matter or, from eternal motion to knowledge of an eternal unmoved mover. By contrast, method as order does not cause us to infer one thing from another, but rather arranges (disponere) the things to be treated, as when the order of teaching demands that we first discuss the heavens and then the elements. It arranges the parts of a discipline. Order takes precedence because one must divide a discipline into parts, before one can articulate the method that will lead us from the known to the unknown that is sought within each part (Zabarella 1597, Vol. I, 139). Scholastic Protestant philosophers, known as systematics, took up Zabarella’s teachings to develop a middle path between Aristotelian and Ramist systems of logic. Bartholomaeus Keckermann and Franco Burgersdijk wrote logic texts in this tradition that were influential in England at the time Hobbes wrote the first part of De corpore. They make the same distinction between universal and particular method as Zabarella (Burgersdijk 1626, 380; Keckermann 1613, 578–9). Burgersdijk, like Hobbes, claims that the order of discovery is the same as the order of teaching (Burgersdijk 1626, 380–1).

19 ¹⁹ Sorell notes of analysis and synthesis “Neither method trades on specialized knowledge” and describes what Hobbes does in Elements of Law and Leviathan as follows: “One way in which the doctrine is supposed to improve on what we know already, is by imposing an order on it. From a mass of moral lore, common sense psychology, rudimentary information about law and the average citizen’s knowledge of which people in the state hold offices of authority, Hobbes purports to sift out what is basic and what is not, what has to be known before other things are known … Relations of dependence are thus revealed between truths that might otherwise seem on the level” (Sorell 1999, 11). He then adds: “But deductive or demonstrative order is not the whole story” (Sorell 1999, 12). Sorell recognizes that the purpose of analysis and synthesis is to order knowledge but reconstructs the rest of the story differently than I do. Adams likewise identifies two different levels at which Hobbes unifies sciences but takes as central a method of construction that enables the explanations one finds in the mixed mathematical sciences (Adams 2014, 7).

20 ²⁰ A third sense of analysis and synthesis found in logistica, Hobbes’s geometrical method, lies outside the scope of philosophical method. William Sacksteder and Richard Talaska concur that, for Hobbes, analysis and synthesis do not function, in philosophy, as they do in geometry. Philosophical propositions arrived at, through analysis, are not, as in geometry, convertible in the corresponding synthesis (Sacksteder 1980, 131–46; 1988, 643–7; Talaska 1988, 207–37).

21 ²¹ Keckermann and Burgersdijk likewise take the natural order to be one where what is most universal is both prior by nature and prior to us (Burgersdijk 1626, 380; Keckermann 1613, 582–3).

22 ²² As Adams (2019) shows, one may have to employ thought experiments to get at the most universal features of all.

23 ²³ It is odd that Hobbes speaks of “universal notions” and “pictures” since universals appear to be neither real things nor abstract general ideas. He writes, “when a living creature, a stone, a spirit, or any other thing is said to be universal, it is not to be understood that any man, stone, & c. ever was or can be universal, but only that these words, living creature, stone, & c. are universal names, that is, names common to many things; and the conceptions answering them in our mind, are the images and phantasms of several living creatures or other things” (EW I.20). Such universal notions or pictures could consist in several particular ideas that we link to each other and to an abstract name.

24 ²⁴ Hobbes seems to assume that our universal notions mirror the underlying faculties of real things. He shares this assumption with the Portuguese Jesuit philosopher, Pedro da Fonseca, and early seventeenth-century German Scholastics influenced by Fonseca’s metaphysics. Walter Sparn observes of the latter, “Their approach assumes ontologically that subtilitas [acuteness/mental penetration] is suited to experienced things, i.e., there is kinship and internal reference to God, both among things and in relation to the human intellect, by virtue of which they [things] exist in it [the human intellect] as especially representable and abstractable into general concepts. In this manner, the first principles of their knowledge can be drawn from the proportional being of things” (Sparn 2001, 481, translation mine).

25 ²⁵ Notably, Hobbes claims that in moral science, instead of proceeding from the definitions of human will and passions obtained in physics, we can directly resolve our conception of an unjust action into “fact against law” and the notion of law into “the command of him or them that have coercive power” (EW I.74). Power will be further resolvable into the wills and passions of humans constituting the power, but these can be cognized by experience rather than demonstrated from the principles of physics. Hobbes also uses thought experiments to get clear on basic concepts, like space, possibly because simples are not resolvable. Adams draws an interesting parallel between the annihilation thought experiment in De corpore and the state of nature device to reveal the concept of equality (Adams 2019, 9–11).

26 ²⁶ It is, admittedly, less clear how one would deduce natural laws using this particular method. This requires more research.

27 ²⁷ Nor is analysis2 a resolution into universal notions since a medium and sentient body are both more specific than matter in general. However, it loosely resembles strict analysis in that it distinguishes something complex into parts.