space indeed, because a mere phantasm, yet that very thing which men call so” (EW I.93). Hobbes is emphatic that whereas the magnitude of body is real, imaginary space is not: “For imaginary space is the effect and magnitude is the cause; this an accident of the mind, that of body existing out of the mind” (OL I.93; EW I.105). Place or locus is likewise merely an abstraction from magnitude: “place is nothing out of the mind, nor magnitude anything within it … place is feigned extension, but magnitude true extension” (OL I.93; EW I.105). So it is not surprising that Hobbes is antagonistic toward ancient (e.g., Lucretian) and modern (e.g., Torricellian) demonstrations of local vacuums (EW I.411–26) and dismissive of void space beyond the world: “there is no real space outside it; but there is no imaginary space either” (Anti-White III.2; 1976, 41).
Hobbes also heaps abuse on Cartesian a priori arguments against the vacuum: “to argue that that there can be no vacuum ‘because vacuum is nothing’ is as cogent as maintaining that ‘no man can fast because to fast is to eat nothing’ … and nothing cannot be eaten” (EW I.109; Cf. Anti-White III.3; 1976, 42). Furthermore, Hobbes affirms that merely imaginary space is sufficient to separate one body from another: “if there intercede any imagined space, which may receive another body, then those bodies are not contiguous” (EW 1.108). He even holds there is real distance in imaginary space: “The ‘distance’ between two bodies, or even between two vacant spaces, is the shortest space lying between them. So if some intermediate part is removed from a continuous body the distance between its extreme parts is not thereby removed” (Anti-White III.3; 1976, 42).
Hobbes’s quasi-realism about imaginary space is highly reminiscent of the Stoics’ conception of pure space as one of the problematic “incorporeals.” As materialists they officially insist that the void is strictly non-existent or “nothing” (Stobaeus; SVF 2.503/LS 49A; 1987, 294). Accordingly, like Hobbes, they make place corporeal: “place is what is occupied by an existent and made equal to what occupies it (by ‘existent’ they mean body)” (Sextus Empiricus; SVF 2.505/LS 49B; 1987, 294). And, like Hobbes, although the Stoics deny the actual existence of local vacua, they do not rule them out a priori. As Galen puts it: “they leave void in the nature of existing things even if they deny its presence within the world” (Galen, SVF 2.503/LS 49E; 1987, 295). There is good reason to think the void extends infinitely beyond the world since it is there capable of receiving body: “it is incorporeal and without contact, neither has shape nor takes on shape, neither is acted upon in any respects nor acts, but is simply capable of receiving body” (Cleomedes, SVF 2 542; LS 49C; 1987, 294). So this “incorporeal” non-existent “subsists” as the possible places of bodies: “void is what can be occupied by an existent but is not occupied, or an interval empty of body, or an interval unoccupied by a body” (Sextus Empiricus; SVF 2.505/LS 49B; 1987, 29). This is just how Hobbes characterized imaginary space: “no man calls it space for being already filled but because it may be filled” (EW I.93).
2.2.2 Time and Mind
For Hobbes, just as our conception of space is derived from the image of body, our notion of time is derived from perceived motion: “a moved body leaves a phantasm of motion, namely an idea of that body passing out of one space and into another by continual succession. And this idea or phantasm … is that which I call TIME” (OL I.83; EW I.94).10 He insists that his own definition of time – “the phantasm of before and after in motion” – is in conformity with Aristotle’s canonical definition – “the number of motion with respect to before and after” (OL I.84; EW I.94; see also Anti-White XXVII, 1976, 339–40; Aristotle, Physics, Bk. IV, Ch. 11; 220a25-6; Aristotle 1971, Vol. 1, 373) – since “numbering is an act of the mind” (OL I.84; EW I.95).
But there is another, more radical, sense in which Hobbesian time is imaginary or subjective: “when people speak of the times of their predecessors, they do not think that after their predecessors are gone their times can be anywhere else other than in the memory of those that remember them” (OL I. 84; EW I.94).11 Likewise, in the other temporal direction, “this word future is a name but no future thing has yet any being … nevertheless, since our thought is used to conjoin [subnectere] things past with things present the name future serves to signify such conjoining” (EW I.17; OL I.15). Despite this apparent presentism, Hobbes seems to grant mind-independent reality to time. For “it is inconceivable that anything can be moved without time” (OL I.97 EW I. 110)12 and he clearly regards motion as mind-independent. Motion, after all, is the real cause of the image of time just as magnitude or “real space” is the cause of imaginary space: “time is the image of motion and has the same relation to real motion as a reflection in a mirror to the true face and a mirrored shape to a true shape” (Anti-White XXVIII.2; 1976, 339). Furthermore, Hobbes frequently treats the successive duration of motion as mind-independent. Sense, for example, is “some internal motion in the sentient generated by some internal motion of the parts of the object” (Anti-White XXVIII.2; 1976, 339). Indeed, the internal motions in the brain themselves “remain there for some time” (OL I.320; EW I.393).13 This persistence of sensory motions, which enables memory, is precisely what separates us from mindless objects. So rather than reduce motion and time to the mind, mental processes are themselves explained by motion and time.14
The Stoics are ambivalent about time for similar reasons. For one thing, it is not a body: “in their view time is one of the incorporeals, which they disparage as inactive and non-existent and subsisting merely in thought” (Proclus, SVF 2.521/LS 51F; 1987, 305). Furthermore, they are presentists. Thus, according to Stobaeus, Chrysippus held “only the present belongs; the past and the future subsist but belong in no way” (Stobaeus, SVF 2.509/LS 51B; 1987, 304; see also Plutarch, SVF LS 51C; 1987, 305). And yet, like Hobbes, they recognize that time is essential to motion: “time is the dimension of motion according to which the measure of speed and slowness is spoken of, or the dimensions accompanying the world’s motion” (Stobaeus, SVF 2.509/LS 51B; 1987, 304; see also Sextus Empiricus, LS 50F; 1987, 299). And there is no indication in Stoic physics that the motion of the universe, or its parts, require imagination. So they classify time, like the void, as an “incorporeal”: something subsisting, which we can speak about and quantify in science and in ordinary life, but lacking independent existence (Sextus Empiricus SVF 2331/LS 27D; 1987, 162).15
Some scholars have perceived in Hobbes’s philosophy of space and time an anticipation of Kant (Herbert 1977); others (more plausibly) have detected the influence of late scholastic Aristotelianism and nominalism.16 But the guiding principles of Hobbesian metaphysics, materialism, and (what Brandt calls) “motionalism” (Brandt 1917, 379), are what most inform and complicate his treatments of space and time. Without resorting to a “subsistent” incorporeal kind of being, Hobbes nevertheless followed the Stoics in giving time and space a sufficient reality to employ them as independent parameters of mechanistic physics.
2.2.3 Causality
For Hobbes, the knowledge of effects from their causes, and vice versa, is the defining feature of philosophy (EW I.3). His own analysis of the causal relation, presented mostly in chapter IX “Of Cause and Effect” in De corpore, is rich and somewhat neglected.17 Here, I will explore one important aspect of this analysis, which is strongly reminiscent of the Stoics’. Together with Spinoza, Hobbes is perhaps the strictest early modern “necessitarian” about the causal connections among bodies. A cause “simply” or “entirely” is a collection of accidents such that “when they are all thought to be present it cannot be understood but that the effect is produced at that same instant. And if any of them be wanting it cannot be supposed but that the effect is not produced” (EW I.122). Men call things “contingent, whereof they do not perceive the necessary cause” (EW I.130). Hobbes argues the conceptual inter-dependence of simple causes and their effects is crucial for several principles at the foundation of his physics, including “no action at a distance” (EW I.125), “same cause/same effect” (EW I.125-6), and the inertia of both motion and rest (EW I.125).
The Stoics are