Descartes attempts to establish the existence of an infinite higher being, namely God, via the method of causal proof. Causal proof is built on a basis of two forms of reality and the transferring of said realities between a cause and its effect. Formal realities are most aptly characterized as tangible realities and are ranked from least to most real as Modes/Properties, Finite Substance, and Infinite Substance. Objective realities are simply the ideas we have of the aforementioned three Formal realities. The key relationship between the two is the following: the cause of an idea must have at least as much formal reality as the effect (the idea itself) has objective reality. Starting from the fact that he has an idea of a perfect being, Descartes is able to use causal reasoning to conclude that a God of infinite Formal reality must exist to cause an idea with infinite Objective reality. However, Descartes’ method was not without its objections. Pierre Gassendi objects to the presumption that infinity is even conceivable, and even if it is, whether God can be characterized by it. Descartes responds by emphasizing that a flawless understanding of infinity is neither possible nor necessary for the existence of God, and he urges Gassendi to acknowledge God rather than attempt to imagine his scale.
Gassendi’s first objection states “the human intellect is not capable of conceiving of infinity, and hence it neither has nor can contemplate any idea representing an infinite thing” (CSM II 200 AT X 286). This first objection is an attempt to sweep the legs of the causal argument, drawing into question whether the launching point of Descartes’ argument is even possible. Effectively, Gassendi is claiming that the highest level of Objective reality according to Descartes, the idea of an infinite substance, does not exist. Even if the idea of infinite is attempted to be understood within a human capacity through its definition as the negation of a limit, Gassendi claims ,“ just as the thing extends beyond any grasp of it he can have, so the negation of a limit which he attributes to its extension is not understood by him” (CSM II 200 AT X 286). To Gassendi, the negation of a limit is itself a conception of infinity. When comprehending infinity, an infinite number of possible limits exist along the way. To negate all limits ultimately still requires a conception of the infinite limits possible and is hence still outside the grasp of human capability.
Gassendi’s second objection states that even if God is a collection of certain attributes taken to an infinite extent, he is still a collection of a finite number of infinites. He first establishes that God is an enumeration of perfections ,“taken from things which we commonly admire in ourselves, such as longevity, power, knowledge, goodness, blessedness and so on” (CSM II 200 AT X 287) which is a finite list. The damning argument comes when Gassendi notes that ,“the idea representing all these things does not contain more objective reality than the finite things taken together” (CSM II 200 AT X 287). Gassendi’s second argument can both serve to extend or catch any fallacies within his first argument. In the case that his first argument is true and the conception of infinity is not possible, then our idea of God is a finite number of attributes taken to a finite extent, which is concretely and absolutely finite. In the case that his first argument is proved false and the conception of infinity is possible, our idea of God is then composed of a finite number of attributes taken to an infinite extent. However, this God is still not the same as true infinity and is closer to the definition of indefinite, laid out by Descartes himself, where limits exist and are simply not recognized. Nonetheless, Gassendi’s argument implies that the idea of God need not have been caused by something with infinite Formal reality as the idea itself does not have infinite Objective reality regardless of how you look at it. Interestingly, Gassendi never attacks Descartes’ most abstract assumption that a cause must have as much reality as its effect, opting instead to topple all possible notions that God is an infinite idea which Descartes swiftly refutes.
Descartes’ first counter argument seeks to explain that a perfect conception of infinity is not a requirement for infinity to exist. He states ,“Here you fail to distinguish between, on the one hand, an understanding which is suited to the scale of our intellect and, on the other hand, a fully adequate conception of things” (CSM II 252 AT X 365). Descartes uses the tactic of generalizing Gassendi’s concern regarding lacking perfect conception to any and all ideas, stating ,“no one has this sort of conception either of the infinite or of anything else, however small it may be” (CSM II 252 AT X 365). Descartes demonstrates how foolish the inadequate conception argument is when applied to objects of clear formal reality which our minds still struggle to fully comprehend. This tactic is closely tied with the wax passage in Meditations II where Descartes examines his likely faulty idea of the modes of the piece of wax, yet never doubts that the wax exists and contains a degree of Formal reality greater than the Objective reality of his idea of it. Though it is certainly more difficult to acknowledge the existence of infinity than it is to acknowledge the existence of a piece of visible and tangible wax resting on a table, neither’s existence can be denied as both are still objects with which the cogito statement may be applied to ascertain existence.
Once it has been established that perfect conception of infinity is not a necessity of its existence, Gassendi’s second argument hangs on by the thread that God, a composition of a finite number of attributes to the infinity, is not absolutely infinite. This is where Gassendi’s lack of attention to the crux of Descartes’ causal proof, namely that the cause must have at least as much reality as its effect, leads to the breakdown of his objections. Descartes uses causal proof to support the idea that God is indeed infinite, asking ,“how could we have a faculty for amplifying all created perfections (i.e. conceiving of something greater or more ample than they are) were it not for the fact that there is in us an idea of something greater, namely God?” (CSM II 252 AT X 365). Essentially, Descartes is claiming that if within us there is both an attempt to and a means of amplifying certain attributes towards infinite (which can be seen as the effect), and the cause must have at least as much objective reality as the effect, then the cause must have been an idea of at least infinite, which is equivalent to saying the idea of infinity. Altogether, Descartes urges Gassendi not to limit the concept of God to a set of worldly attributes and to simply equate the idea of God with the idea of absolute infinity.
Ultimately, Descartes would claim that where Gassendi’s arguments begin to fundamentally collapse is where Gassendi first tries to imagine rather than understand God. Imagination is nothing more than a crude attempt to understand an object via the anticipated sensory details of an object. However, these sensory details have long been established as deceptive, and exist on the lowest order of reality. The highest level of understanding according to the cogito passage lies simply in actively thinking and acknowledging the existence of an object. Descartes’ analogy for this is as follows: God is to us as an elephant is to a man who has never seen an elephant before. If told to imagine the elephant, the man might think of an absurd and large-looking creature, choosing to focus on a shallow and uncertain level of sensory reality regarding its scale. The only certainty the man can establish is that this massive animal exists. All other efforts to paint a more vivid picture are fruitless.
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