Prima facie, proposition 2P7 in Spinoza’s Ethics presents the counter-intuitive claim that there can be no ideas without extended objects accompanying them. That is, ideas cannot exist without correlative bodies. However, Spinoza offers 2P8 to address the possibility of singular things that do not exist, while preserving his mind-body parallelism.
The ideas of singular things, or of modes, that do not exist must be comprehended in God’s infinite idea in the same way as the formal essences of the singular things, or modes, are contained in God’s attributes.
Spinoza contends this proposition is evident from 2P7 (the doctrine of parallelism) and its scholium, in which attributes are posited as different expressions of the same substance (a circle in Nature and the idea of the existing circle are the same thing), which in turn is proven by 1A4, a concise statement of the principle of sufficient reason. The corollary to 2P8 elaborates the proposition by arguing that if singular things only exist through comprehension in God’s attributes, their objective being (i.e. being in relation to an object), or ideas, only exist through God’s infinite idea. On the other hand, when things exist in duration as actualized objects, their corresponding ideas also have duration, an additional property of reality and being.
One way of interpreting 2P8 is to argue that Spinoza is simply accounting for things that used to exist (memories of the dead, historical figures and places, thoughts about dinosaurs) or will exist (people and animals not yet born, species evolved 1000 years from now). According to this interpretation, bodies have duration along with their ideas, but their infinite ideas in God, or their essences, do not. It is only necessary that things exist as they do when they do. Things exist virtually in God’s idea, before, after and during their actualized duration as finite modes. This interpretation facilitates commensurability between 2P8 and Spinoza’s necessitarianism. However, 2P8 also seems to suggest that literary characters, unicorns, false sensations and alternative events that could have been – things that exist in possibility, but will never exist as actualities in extension – also have ontological status.
The scholium for 2P8 – an analogy or an “inadequate” heuristic device in which an infinite number of unconstructed rectangles are imagined within, and formed by the chords of, a circle – seems to support this more complex version of nonexistent things. Because the relationship between the circle and its rectangles is, according to Spinoza, analogous to that between God’s infinite idea and nonexistent singularities, the nonexistent particular is enabled by the laws of God’s infinite idea. The laws of extension enable the individual rectangles, which nevertheless remain nonexistent because no cause has effected their actualization. The rectangles do not exist, but it is possible to imagine a series of events leading to their construction and existence. The (nomo)logically possible, in other words, is distinct from the experientially possible.
Another (if slightly anachronistic) example from Leibniz perhaps gets at the same issue more clearly than in Spinoza’s example (which Bennett, in his translation, dismisses as unhelpful). In his “Justification of the Infinitesimal Calculus by that of Ordinary Geometry” (1701), Leibniz draws the diagrams reprinted above. In each transformation, the singular, actual, quantifiable and metric dimensions of EAC and YXC change. However, the relations that make their construction and morphology possible remain constant. If the hypotenuse EY is moved such that it intersectspoint A, EAC disappears as an actuality, its dimensions being zero. However, the relations still remain latent, possible or virtual. As Leibniz contends, the triangles never reach absolute zero.
Spinoza’s subsequent use of 2P8 in the Ethics supports the contention that he is positing two existences: one quantitative the other absolute. In 2P9D, he refers to 2P8 to prove singular modes of thinking as distinct from each other. In 2P11D, Spinoza employs 2P8 to argue that ideas of nonexisting things cannot occur (at least without ideas of existing things also) in human minds, while 2P15D uses it to contend that each component of a body has a corresponding idea in God. If these two propositions only suggest two different types of existence, 2P45D explicitly posits them. Spinoza writes, “The idea of a singular thing which actually exists necessarily involves both the essence of the thing and its existence (by P8C).” Finally, Spinoza’s reference to 2P8 in 5P23D reinforces this double existence by noting that human minds have duration only while the corresponding body endures, suggesting that duration plays a role in the order and connection of series in relation to human, but not divine, minds, the latter of which exists infinitely rather than in time.
Spinoza continually draws a distinction between essential and durational, formal and objective, abstract and quantitative, pure existence and existence in time or place. Formal essences are contained in God’s attributes, apart from things, while existence requires duration. While this distinction helps explain why time is not an attribute (it is incommensurable with the infinite and timeless nature of essences), this theory of double existence still appears to challenge Spinoza’s monism.
As such, another way of articulating this phenomenon is by drawing a distinction between essence and existence without positing two distinct types of existence. Essence (by 1P24C) “involves neither existence nor duration,” so eternal being in no way implies actual, durational existence. Every finite mode has an essence comprising an idea, in the infinite intellect, of its bodily constitution. Therefore, as part of the infinite intellect, the essence of a finite mode is eternal. God comprehends eternal essences even if those things do not exist right now.
In addition, the theory that these nonexistent modes have ontological status as possibly existing yet actually nonexisting things expressing God’s essence introduces contingency as a blatant contradiction to Spinoza’s thorough necessitarianism. Therefore, it would only follow that an essence comprehended in God’s attribute is still, for Spinoza, an actuality – a real being – and any notion of double existence is epistemological rather than ontological. Our minds perceive things in duration because they inadequately assume bodies to exist only now. That is, the duration of the body is existence as inadequately pictured, while the eternity of the body, its idea and its essence comprise existence adequately apprehended as an affect of God.
2P8’s notion of an essential reality without determinate existence, as well as adequate and inadequate knowledge, in addition to clarifying some doubts concerning the doctrine of parallelism, also explains the ostensible ambiguity accorded the attributes as articulated in part one of the Ethics. The attributes (by 1D4) are “what the intellect perceives of a substance, as constituting its essence,” but (by 1P15D) they are denied ontological status when Spinoza writes, “But except for substances and modes there is nothing.”
Attributes, in other words, are ontologically situated much differently from substance and modes, but are productively related to ideas, and (by 2D3) an idea is “a concept of the mind which the mind forms because it is a thinking thing.” The explanation for 2D3 goes on to mark conception as an active dimension opposed to the passive nature of perception, which reflects Spinoza’s previous distinction between natura naturans as active, identified with God and the divine attributes, and natura naturata as derivative and identified with the modes.
Moreover, Spinoza affords the attribute of thought a special status deriving from intentionality, which is significant, because, as Spinoza writes in 1P15S5:
So if we attend to quantity as it is in the imagination, which we do often and more easily, it will be found to be finite, divisible, and composed of parts; but if we attend to it as it is in the intellect, and conceive it insofar as it is a substance, which happens [NS: seldom and] with great difficulty, then (as we have already sufficiently demonstrated) it will be found to be infinite, unique, and indivisible.”
This distinction between active conception and passive perception in thinking, as well as the infinite and finite, reflects 2P8’s important distinction (in 2P8C) between things that exist insofar as they are comprehended in the attributes of God and insofar as they are said to have duration. Containment in God signifies existence in which ideas are finite and readily apparent as such through the imagination. However, they are simultaneously eternal and always existing, which is less apparent and only accessible through intellect. This immanent, as opposed to transitive, constitution of existence is difficult to comprehend, but 2P8 suggests that thinking actively of nonexisting things allows us to access the mental essences produced by the absolute nature of the attribute of thought – a radically different means of expression than we find in finite existing things. While durational objects have more reality and being, actively conceptualizing nonexistent things brings us closer to God or Nature, which makes the “must” in 2P8 an ethical obligation.