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
4.2 Hobbesian Optics: The Visual Line and the Optic Axis in De Homine II
Hobbes’s chapters on optics in chapters II–IX of De homine (OL II.7–87) are oddly placed within his three-volume Elementa Philosophiae, which comprised three sections: De corpore, De homine, and De cive. Since these optical writings are purported to be about vision for all animals and not just vision for humans, it is strange to find them placed within that work, especially since discussion of uniquely human features does begin in chapter X (De sermone) of that work.8 This odd placement may result from the circumstantial manner in which De cive (1642) was published first, long before Hobbes was satisfied with De corpore (1655). Hobbes waited even longer to publish De homine (1658), and its publication was a topic of conversation for Hobbes’s correspondents.9
Such delay in publishing his optical work, which had already been sketched out in his unpublished Minute (1983), as part of the Elementa trilogy may just be haphazard editing work on Hobbes’s part. However, another possibility is that Hobbes developed his view of how tightly linked the methodology of optics, which was part of mixed mathematics, or subalternate science by his predecessors, was to natural philosophy only after De corpore had already been published. Indeed, we only find him making the claim, mentioned above, that “physics (I mean true physics), that depends on geometry, is usually numbered among the mixed mathematics” (Hobbes 1994b [1658], 42; OL II.93) three years after publishing his most significant work in physics (Part IV of De corpore). In Anti-White I.1 (1642/43) Hobbes had boldly asserted that “all the sciences would have been mathematical had not their