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Hobbes reflects on the relationships among the areas of his philosophy in several places in the corpus, but his most extensive reflection upon these relationships is in De corpore VI.6. At first glance, it may seem that Hobbes is advancing a reductionist program along the following lines: all natural phenomena are reducible to minute bodies in motion. If this reductionist picture is correct, then it looks as though the parts of philosophy can be organized from first philosophy to physics, and from “morals” to civil philosophy, with first philosophy serving as the foundational discipline for all philosophy, as displayed in Figure 4.1.

Figure 4.1 Hierarchy of the parts of philosophy.

Indeed, in De corpore VI.6, Hobbes details how one should begin from the knowledge of the “universals” of first philosophy, such as the knowledge of what “place,” “body,” and “motion” are, and then use that knowledge to develop geometrical definitions. For example, using the knowledge of such universals as these one can form the definition of “line” as that which is “made by the motion of a point” (OL I.63; Hobbes 1981, 297). After working in geometry, which he says studies motion simpliciter, Hobbes suggests that there should be a general study of “those things which occur from the motion of the parts” (OL I.64; Hobbes 1981, 299). This will lead to considering “sensible qualities” such as light, color, sound, odor, and flavor, but before these can be explained the human senses that perceive these qualities must be understood. These third and fourth parts of philosophy together constitute physics (physica).

Finally, Hobbes notes that “[a]fter physics we come to morals” in which desire and aversion, and passions generally, are examined as “motions of the mind” (OL I.64; Hobbes 1981, 299). He explains that the reason why the study of the passions follows physics is that the passions have their “causes in physics” (OL I.64; Hobbes 1981, 299). Hobbes concludes this reflection on the relationships among the parts of philosophy by claiming that anyone who attempts to engage in natural philosophy without taking principles from geometry will be making vain attempts. Furthermore, he declares that anyone who engages in such useless activity will “abuse their listeners” (OL I.65; Hobbes 1981, 301).

This reflection Hobbes offers about natural philosophy and its relationship to the other parts of philosophy suggests a deductive relationship, and many Hobbes scholars have argued that such a view was Hobbes’s (Martinich 2005; Peters 1967; Shapin and Schaffer 1985; Watkins 1965). An even stronger view sees Hobbes as a type of reductionist (for example, Hampton 1986; Ryan 1970). For example, Alan Ryan offers a version of this reductionist interpretation of Hobbes as follows:

Hobbes believed as firmly as one could that all behaviour, whether of animate or inanimate matter, was ultimately to be explained in terms of particulate motion: the laws governing the motions of discrete material particles were the ultimate laws of the universe, and in this sense psychology must be rooted in physiology and physiology in physics, while the social sciences, especially the technology of statecraft, must be rooted in psychology.

(1970, 102–3)

As is clear from the De corpore VI.6 passage discussed already, there is some textual support for this understanding of Hobbes’s philosophy. If this view that ultimately all behavior of matter is explained in terms of the most basic physical laws is correct, then we might expect that in Hobbes’s actual practice he would provide explanations that appeal to more “basic” particles and laws about how those particles behave. Furthermore, we would expect him to provide bridge principles stating how statements about macroscopic entities, like human bodies or commonwealth (artificial) bodies, reduce to statements about microscopic entities.

A significant difficulty faces the deductivist and reductionist interpretations: How would a deduction or reduction actually work between, say, a statement in “morals” and statements in geometry or physics? Consider the concept of “endeavor,” which Hobbes introduces in De corpore XV.2 (in Part III on geometry) and then uses again within civil philosophy to describe the motions of human bodies, since the passions are endeavor (2012, 78; 1651, 23). Although endeavor is used in geometry, moral philosophy must add information about human passions understood as endeavor. As will be discussed, Hobbes describes this very need to supplement with additional information in De homine X.5 as needing to have “knowledge of the subject” (in Hobbes’s description of the relationship between pure geometry and mixed mathematics; Hobbes 1994b [1658], 42; OL II.93). In particular, the properties “appetite” and “aversion” are added, but these properties obviously do not apply to all bodies in general. As a result, endeavor in human bodies (the passions) will not be reducible to endeavor in geometry (for similar discussion, see Malcolm 2002, 147). Were this reduction what Hobbes had in mind, we would expect him to provide bridge principles to show how “endeavor” in human bodies can be reduced to “endeavor” in bodies in general.

Two additional statements that Hobbes makes in the surrounding context of De corpore VI.6 further complicate things for the deductivist or reductionist interpretations. First, after making the link between physics and morals, he advises that what he has described is the order of investigation:

That all these things ought to be investigated in the order I have said [Haec autem eo ordine quem dixi investiganda esse] consists in the fact that physics cannot be understood unless the motion which is in the minutest parts of bodies is known and such motion of the parts unless what it is that effects motions in another thing is known, and this unless what simple motion effects is known.

(OL I.64–5; Hobbes 1981, 299–301)

Labeling this as about the order of investigation suggests that one should engage in preparatory work in First Philosophy and geometry before attempting to provide explanations in natural philosophy or about the human passions. As will be discussed, understanding these comments as about the order of investigation, and not as advocating for a deductivist or reductionist mode of explanation, makes sense of Hobbes’s actual practice of natural philosophy where one borrows (already known, and thus first in order) causal principles from geometry for use within an explanation.

Second, Hobbes’s discussion in De corpore VI.7 further confounds claims that he held a deductivist or reductionist view. There Hobbes states that although civil philosophy is connected to “morals,” the latter of which is connected to the other parts of philosophy, civil philosophy can be “detached” from it because the “causes of the motions of the mind are not only known by reasoning but also by the experience of each and every person observing those motions proper to him only” (OL I.65; Hobbes 1981, 301).

How is this flexibility for learning the “principles of politics” possible according to Hobbes? Elsewhere, Hobbes distinguishes between two paths that one can take in philosophizing – synthesis and analysis – and he incorporates these two paths in definitions of “philosophy” in De corpore (for example, in De corpore I.2; OL I.2; Hobbes 1981, 175). Hobbes uses synthesis and analysis simplistically, sometimes calling them compounding or composing and resolving and other times calling them adding and subtracting (for example, De corpore VI.1; OL I.59; Hobbes 1981, 289). For example, he describes how the conception “square” is resolved in analysis into “plane,” “bounded by a certain of lines equal to one another,” and “right angles,” which parts of “square” are further resolved into the “universals or components of every material thing: line, plane (in which a surface is contained), being bounded, angle, rectitude, and equality” (OL I.61; Hobbes 1981, 293). Then, those component parts are put back together (in synthesis), and by doing so learns that these parts are the “cause of square.”²

Applying these two paths of synthesis and analysis to the issue at hand, Hobbes says that one can proceed (in the order of one’s investigation) synthetically by beginning in First Philosophy with (already known) conceptions such as “space” and “motion simpliciter” and working through geometry, physics, and morals, adding the relevant concepts proper to each discipline along the way, until coming to the principles of politics (OL I.63–5; Hobbes 1981, 297–301). Alternatively, Hobbes claims that “those who have not learned the earlier part of philosophy … can nevertheless come to the principles of civil philosophy by the analytic method” (OL I.65; Hobbes 1981, 301). How does this analysis work for such individuals? Hobbes suggests that whenever the everyday person without prior philosophical training is presented with a question (such as “whether such and such an action is just or unjust”), they are capable of resolving or analyzing the conceptions in that question into component parts. This analysis will break apart “unjust” into “fact” and “against the laws” and by continuing to resolve these conceptions will arrive at “the fact that the appetites men and the motions of their minds are such that they will wage war against each other unless controlled by some power” (OL I.66; Hobbes 1981, 303).

Hobbes optimistically claims that once the everyday person arrives at this knowledge of humans in their natural state simply by analysis from a question like “is X just or unjust” that they will be able to determine whether any possible action is just or unjust “by composition” (OL I.66; Hobbes 1981, 303). Thus, the everyday person will engage in both analysis and synthesis. The picture that emerges is that by either means one may arrive at the principles of civil philosophy, and that either path (in Figure 4.2) is a legitimate means of doing so.

Figure 4.2 Orders of knowing to arrive at civil philosophy.

Against the portrayal of Hobbes as a reductionist or deductivist, Hobbes’s claims about these two orders of knowing eschews reduction or an attempted strict derivation from one “level” to another. On the first path of synthesis (the left inverted pyramid in Figure 4.2), one begins in First Philosophy and clarifies conceptions like “space,” “place,” and “motion simpliciter.” These conceptions are then used within geometry when making figures such as lines and squares. Those geometrical figures incorporate the conceptions from First Philosophy but are in no way reducible to them; indeed, geometry adds to these earlier conceptions as it makes figures and determines their natures. Continuing upward, as it were, geometry will be used within physics but physics must add to geometry when it treats features of actual bodies in nature, such as “the action of shining [bodies]” (Hobbes 1973 [1642–1643], 106; 1976 [1642–1643], 24–5). This “adding to” activity, as has been discussed already, constitutes synthesis for Hobbes.

However, Hobbes held that an alternative order of knowing from the everyday experience of one’s own mind to the principles of civil philosophy was an equally legitimate way to arrive at the principles of civil philosophy. In this case (the right inverted pyramid in Figure 4.2), one subtracts or resolves the questions made salient in one’s personal experience, such as “is X just or unjust?” by considering one’s conception of “just” and examining its component parts. This subtracting or resolving will continue until reaching a claim about humans in their natural state. Then moving from that claim – in synthesis – one can determine whether any action would be just or unjust.³ Hobbes does not assume that those moving from everyday experience to the state of nature have stopped in an inferior place compared to the starting point for those beginning in First Philosophy. In other words, he does not claim that ideally there should be a further reduction; these two orders are simply different means for reaching the same result.

The following section and the next turn away from Hobbes’s statements about how the parts of his philosophy fit together and focus instead on Hobbes’s actual practice of providing explanations. Scholarly attention has mostly been directed toward the former, but in actual practice we find Hobbes weaving together principles from geometry into explanations that simultaneously rely upon everyday experience and geometry. What could allow him to do this, assuming his statements and practice are consistent with one another? Before turning toward Hobbes’s practice, I will first discuss briefly what Hobbes describes in De homine as “true physics” (Hobbes 1994b [1658], 42; OL II.93).

The starting point for considering what Hobbes calls “true physics” is a division that he makes in De corpore VI.1 between knowing with certainty (scientia) and more mundane forms of knowing (cognitio):

We are said to know [scire] some effect when we know what its causes are, in what subject they are, in what subject they introduce the effect and how they do it. Therefore, this is the knowledge [scientia] τοῦ διότι or of causes. All other knowledge [cognitio], which is called τοῦ ὅτι, is either sense experience or imagination remaining in sense experience or memory.

(OL I.58–9; Hobbes 1981, 287–9)

Essentially, Hobbes divides all human knowledge into two parts: scientia, for which we possess knowledge of the causes (i.e., knowledge of the “why”), and cognitio, for which we have mere sense experience or the remnants of sense experiences in the form of imaginations (i.e., knowledge of the “that”). These two parts provide different levels of certainty to knowers. Since scientia is knowledge of the actual causes of some effect, knowers possess certainty concerning how that effect came to be.⁴

How could Hobbes, with his reliance upon sense as the source for all ideas (e.g., 2012, 22; 1651, 3), hope to lay claim to epistemic certainty? The move he makes is that humans possess scientia only in cases where they act as the maker of some effect, and so geometry and civil philosophy are the only contexts in which this is possible, a claim Hobbes makes in Six Lessons (EW VII.184) and in De homine (OL II.93–4; Hobbes 1994b [1658], 41). In both geometry and civil philosophy, human knowers begin from abstract objects, such as bodies in imagination considered as geometrical points or human bodies in imagination considered as being in their natural state. There are no such entities in the natural world, as Hobbes’s criticisms of Euclid make clear (e.g., EW VII.202), but humans can create them by considering their imaginations in certain ways. Human knowers next move around those abstract objects in their imagination and consider the effects of combinations of those bodies and the motions of those bodies. In doing this, they create some effect, such as “lines and figures” in geometry (EW VII.184) or “the principles – that is, the causes of justice (namely laws and covenants) …” in civil philosophy (OL II.94; Hobbes 1994b [1658], 42). They possess scientia of those effects because they, as makers, brought them about as they actively constructed them.

The second part of Hobbesian human knowledge – cognitio – provides the basis for nearly all human decisions. When I hear a sound outside at night, suspect that sound is a coyote, and decide to check the security of the chicken coop, this results in a conjecture. The conjecture I make is only as good as my prior experiences: those of nocturnal animal noises, my comparison between the current sound and those in the past, and the linkages related to what happened to the coop following my hearing of past sounds from coyotes (stored as “Transitions from one imagination to another …” from past sense experiences; see Leviathan 3; 2012, 38; 1651, 8). The likelihood that my conjecture “The hens are about to be eaten!” will be accurate will thus depend upon the quantity and quality of those past experiences, what Hobbes describes in Leviathan 3 as “Foresight, and Prudence, or Providence; and sometimes Wisdome” (2012, 42; 1651, 10).

Hobbes recognizes that conjectures of this sort can be “very fallacious” because of the “difficulty of observing all circumstances” (2012, 42; 1651, 10). His example of such a conjecture is when someone “foresees what wil become of a Criminal,” and he seems to mean that if someone saw all of the linkages between every criminal and the punishment each of those criminals received for each crime (an induction by simple enumeration), then that person would have certainty about statements like the following: “This criminal will be sent to the gallows.” Were human knowers able to observe “all circumstances” in this way, then the distinction between scientia and cognitio would dissolve. However, since humans have different experiences from one another, both in terms of quantity and quality, Hobbes states that prudence comes in degrees: “by how much one man has more experiences of things past, than another; by so much also he is more Prudent” (2012, 42; 1651, 10).

A prima facie worry concerning Hobbes’s bifurcation of all human knowledge into scientia and cognitio is that, so far, it appears that natural philosophy may merely be the result of prudence. Indeed, Hobbes is explicit in Six Lessons that unlike in geometry and civil philosophy human knowers fail to possess knowledge of the causes of natural phenomena, since they are not the Creator: “But because of natural bodies we know not the construction but seek it from the effects there lies no demonstration of what the causes be we seek for but only of what they may be” (EW VII.184). Likewise, in De corpore XXV.1 he emphasizes that he will not offer explanations of how natural phenomena are generated by rather how they may be generated (OL I.316; EW I.388). In that same context, he identifies the explananda of natural philosophy as the phenomena, or effects of nature, which are “known through sense [per sensum cognitis]” (OL I.316; EW I.388), harkening back to his bifurcation of knowledge by using a cognate of cognitio.

What sets apart an explanation in natural philosophy, say, of the possible cause of some phenomenon like the sun warming a rock, from my conjecture, relying upon prudence, that the hens are about to be devoured by a coyote? The difference, Hobbes holds, lies in the source of the inference that we make. Rather than merely relying upon past associations from experiences stored as trains of imaginations, when I provide a possible cause for some phenomena in natural philosophy I borrow the cause from geometry.⁵ Since human knowers can possess scientia in geometry, when I use a geometrical principle within a natural-philosophical explanation what I provide is transformed from being a potentially “very fallacious” conjecture to what we may call suppositional certainty (Adams 2016, 47; 2017, 104). I cannot be certain that the cause borrowed from geometry is the actual way that nature brings about a given appearance, but I can be certain that if nature behaved according to the geometrical principle borrowed then the phenomenon would follow necessarily. The two case studies below will give examples of this borrowing that provides suppositional certainty.

Thus far, we have seen how natural philosophy is distinct from and lies epistemically between scientia and cognitio; indeed, explanation in natural philosophy involves mixing something from both. In an ideal natural-philosophical explanation, one will rely upon sense experience to show that some phenomenon occurs and then borrow a causal principle from geometry to provide a plausible reason for why it occurs. This understanding of natural philosophy as mixing places value on both the “that” and the “why,” and Hobbes admits in De homine XI.10 that “histories are particularly useful, for they supply the experiences/experiments [experimenta] on which the sciences of the causes [scientiae causarum] rest” (OL II.100; see also OL I.9). Hobbes thinks about this mixing in light of discussions preceding him of the relationship between mathematics and natural philosophy, and his use of Greek terminology suggests that he had Aristotle’s view in mind, though he did not apply it strictly (Adams 2016; see also discussion of Hobbes and mixed mathematics in Biener 2016).

Hobbes explicitly identifies explanations in natural philosophy as a mixing these two types of knowledge in De homine X.5, where he argues that

since one cannot proceed in reasoning about natural things that are brought about by motion from the effects to the causes without a knowledge of those things that follow from that kind of motion; and since one cannot proceed to the consequences of motions without a knowledge of quantity, which is geometry; nothing can be demonstrated by physics without something also being demonstrated a priori. Therefore physics (I mean true physics) [vera physica], that depends on geometry, is usually numbered among the mixed mathematics [mathematicas mixtas].

Therefore those mathematics are pure which (like geometry and arithmetic) revolve around quantities in the abstract [in abstracto] so that work [in them] requires no knowledge of the subject; those mathematics are mixed, in truth, which in their reasoning some quality of the subject is also considered, as is the case with astronomy, music, physics, and the parts of physics that can vary on account of the variety of species and the parts of the universe.⁶

(Hobbes 1994b [1658], 42; OL II.93)

Hobbes is clear: ideally physics of the proper sort – what he calls “true physics” – should be classified as part of “mixed mathematics.” According to Hobbes, the difference between pure mathematics and mixed mathematics is that for the latter in addition to quantity “some quality of the subject is also considered.” For example, rather than treating refraction and reflection of bodies in general – “in the abstract” (EW I.386) – like Hobbes does in De corpore XXIV, in optics one must also include reference to the behavior of light and light-producing bodies as well as to the properties of the parts of the eye, such as the crystalline humor, processus ciliares, and retina. In Anti-White I.1, Hobbes makes this point by describing mixed mathematics as treating “quantity and number, not in the abstract [non abstracte], but in the motion of the stars, or in the motion of heavy [bodies], or in the action of shining [bodies], and of those which make sounds” (Hobbes 1973 [1642–1643], 106; 1976 [1642–1643], 24–5).

This move Hobbes makes drastically expands the purview of mixed mathematics, or what Aristotle the subalternate sciences, beyond domains such as optics, harmonics, and mechanics. Indeed, in Posterior Analytics Aristotle holds that one should ideally not attempt to “prove by any other science the theorems of a different one, except such as are so related to one another that the one is under the other – e.g. optics to geometry and harmonics to arithmetic” (Posterior Analytics I.7, 75b14–17; Aristotle 1984, 122).⁷