Can One Think an Infinite Thought? - Some Thoughts on Descartes' Trademark Argument for God

The existence of God is a perennial question in philosophy and has been debated for centuries. There have been many kinds of arguments for God’s existence including the ontological, cosmological, and teleological arguments among others (Taliaferro 2019). In his famous Meditations, Descartes offers a peculiar argument for God’s existence which bears a resemblance to ontological arguments, but is in fact an attempted causal proof of God’s existence (Descartes et al. 12-19 1996). This argument, like ontological arguments, starts from the very concept of God, but, unlike ontological arguments, argues that this concept of God must be caused by God Himself given a basic principle of proportionate causality. It is a, seemingly, clever argument. Despite its cleverness, the argument was not without its critics. One of the most famous criticisms of Descartes’ argument came from Thomas Hobbes who argued that the argument failed in virtue of the fact that one cannot comprehend the concept of God since the idea of God is infinite, but the human mind is finite and thus cannot comprehend the infinite (Descartes et al. 100 2017). I will defend the cogency of Hobbes’ objection and argue that Descartes’ argument fails in virtue of the fact that human beings cannot comprehend the concept of God fully. This will be developed by explicating ideas of an infinite human intellect, bolstered by Spinoza’s conception of the knowledge of God and it will be responded to by exposing the consequences of allowing for an infinite human intellect. 

Descartes sets out to prove God’s existence in Meditation III. The context and placement of the argument he provides in Meditation III is necessary to understand the argument itself. In Meditation I, Descartes has provided reason to doubt all of the things which people ordinarily take to be knowledge. After having done this, Descartes begins to build a tower of knowledge beginning with the knowledge of oneself as a thinking thing in Meditation II. With these two Meditations in the backdrop, Descartes introduces his first argument for the existence of God. Descartes begins the Meditation by making it clear that he is only relying on the concept of God and not anything a posteriori: “I shall now close my eyes, I shall stop my ears, I shall call away all my senses, I shall efface even from my thoughts all the images of corporeal things,” (Descartes et al. 12 1996). Descartes also emphasizes that the ideas which his mind can comprehend are clear and distinct ideas. “Innate ideas” are incredibly clear for Descartes since there are no intermediate steps between the acquisition of the idea and the idea itself (Descartes et al. 14 1996). The concept of God is, for Descartes, an innate idea, but this is a fact is a result of Descartes’ examination of the concept of God as he conceives of “a supreme God” and finds that this God is “eternal, infinite, [immutable], omniscient, omnipotent, and Creator of all things which are outside of Himself, has certainly more objective reality in itself than those ideas by which finite substances are represented” (Descartes et al. 15 1996). In the next paragraph, Descartes assumes a form of the principle of proportionate causality: “there must at least be as much reality in the efficient and total cause as in its effect,” (Descartes et al. 15 1996). Descartes applies this to ideas and then says that ideas have at least as much reality as the mind-independent entities that they represent. From this, it follows that God exists as Descartes’ conception of God is which has “infinite . . . objective reality,” and since ideas must have at least as much reality as the mind-independent entities that they represent, the God which Descartes conceives must have “infinite . . . objective reality,” (Descartes et al. 15 1996).

One of the major critics of this argument was Thomas Hobbes. Hobbes focused on the fact that Descartes’ concept of God is the concept of an “infinite God,” but Hobbes thinks that “the human intellect is not capable of conceiving of infinity” (Descartes et al. 100 2017). The thought here is that since the human intellect is finite it is not in any way capable of doing infinite things, including the comprehension of ideas with infinite conceptual content, like Descartes’ concept of God. In responding to Hobbes, Descartes argues that if Hobbes is right, human beings are incapable of attributing infinity to any concepts since the human mind cannot attribute to a thing that which it does not comprehend, or at least that is Descartes’ reasoning (Descartes et al. 100 2017). In responding, Hobbes makes a distinction between attributing infinity to things in a way that “is suited to the scale of our intellects,” which Hobbes does not deny is possible, and attributing it to a thing after “a fully adequate conception of” the thing (Descartes et al. 100 2017). Hobbes’ reasoning is that Descartes needs to have “a fully adequate conception of” the concept of God in order for his argument to be successful. 

Does Hobbes’ objection succeed? It seems so. Firstly, Hobbes is correct in pointing out that in order for Descartes’ argument to work Descartes needs to have a complete comprehension of the concept of God. As Descartes says, the God of which he conceives has  “infinite . . . objective reality,” and then he moves from this, utilizing his principle of proportionate causality, to say that this idea of a being with “infinite . . . objective reality” must correspond to an entity which has  “infinite . . . objective reality”, given that ideas have at least as much reality as the mind-independent entities which they represent (Descartes et al. 15 1996). If Descartes merely had a finite conception of this being with “infinite . . . objective reality,” then he would be unable to make the inference from the principle of proportionate causality to the actual existence of God because a finite idea of a being with “infinite . . . objective reality” need not, necessarily, be caused by a being with “infinite . . . objective reality” (Descartes et al. 15 1996).

Perhaps Spinoza can help Descartes here as Spinoza had a unique conception of the knowledge of the infinite. In proposition 47, book II of his Ethics, Spinoza boldly asserts that “the human mind has an adequate knowledge of the eternal and infinite essence of God,” (Spinoza 61).  Spinoza had great optimism about the capabilities of the human intellect because of his analysis of knowledge. Spinoza argued that true knowledge required a perfect knowledge of a thing and in this perfect knowledge was included a certainty of the truth of the knowledge: “He, who has a true idea, simultaneously knows that he has a true idea, and cannot doubt of the truth of the thing perceived” (Spinoza 58). The thought here is that in order to know something, there must be a complete apprehension of the relevant truths, otherwise one would still be searching for information so there would not be a complete apprehension of thing and this complete apprehension entails that knowledge is infallible because, for Spinoza, complete knowledge involves knowledge not only of why a thing is the way it is, but also why the thing could not have been different. However, this account of knowledge ultimately entails that complete knowledge of a thing will include a knowledge of the whole of reality, which, for Spinoza, is infinite. This way of allowing for the possibility of an infinite thought has a plausible starting point because it begins from the assumption that one can have complete knowledge of finite things, which is intuitive, and with this view of knowledge Descartes' argument may be able to get off the ground.

Despite this, Hobbes still seems to be correct when he says that the human intellect is incapable of conceiving of the infinite as the consequences of positing an infinite human intellect are very problematic, especially for Descartes. It seems that if the human intellect is finite, as Hobbes thinks, then Descartes cannot conceive of God in the way which is necessary for his argument. However, perhaps the human intellect is infinite and so can comprehend a being with “infinite . . . objective reality” (Descartes et al. 15 1996). For the sake of argument, Descartes’ picture of the mind as a non-extended, immaterial entity can be assumed (Hatfield 2014). On this view, the possibility of the intellect being infinite seems more feasible since it does not have the limits of extension. However, even with this non-extended, immaterial account of the mind assumed, it does seem plausible that the human intellect is finite and this can be shown through a thought experiment. 

Suppose that, indeed, the human intellect is infinite. This would have the consequence of the human intellect being as great as God’s intellect since, in this scenario, both the human and Divine mind would be infinite. This has some undesirable consequences for Descartes. Firstly, this would strictly entail that in some sense human beings and God are equal in greatness since they are equal in intellect, but this threatens the uniqueness of Descartes’ God. Moreover, if the human and Divine intellect are equal in greatness, then it seems hard to account on Descartes’ view why God is all-knowing, while human beings are not. This has the further consequence of calling into question Descartes’ fundamental methodology, skepticism, since if the human intellect is infinite, why must humans be so skeptical of what they take to be knowledge. 

Secondly, Descartes may want to avoid this issue by appealing to some difference in the natures of the human and Divine intellect. However, it is hard to see what difference there would be between these two intellects since infinite things which are infinite in the same respect, as the two intellects would be in this case, have no difference between them in this respect in virtue of the fact that infinite things have no limits insofar as they are infinite. So, if Descartes wants to explain this issue by appealing to some difference between the human and Divine intellects, he will likely have to say that the human intellect is finite. Once he does this, though, it’s hard to see how he can maintain his argument in Meditation III since this concession does not allow for the human intellect to be capable of comprehending an infinite thought. Given this, Hobbes’ objection to Descartes' argument seems to be cogent.

The question of the existence of God has been a central issue in philosophy of millenia. Descartes’ argument for God in Meditation III is exceedingly clever and is an important contribution to the debate over God’s existence. However, Hobbes’ objection to the argument is successful as the human mind cannot think of an infinite thought, which is what Descartes needs in order for his argument to work. Spinoza, seemingly, offers support for Descartes’ argument through Spinoza’s account of knowledge. Despite this, the consequences of positing an infinite human intellect leads to significant issues for Descartes’ views. So, while Descartes’ argument in Meditation III is worthy of consideration, it should not be considered a powerful argument for God’s existence.

Works Cited

Descartes René, et al. Discourse on the Method and Meditations on First Philosophy. Yale University Press, 1996. 

Descartes René, et al. Meditations on First Philosophy with Selections from the Objections and Replies. Cambridge University Press, 2017. 

Hatfield, Gary. “René Descartes.” Stanford Encyclopedia of Philosophy, Stanford University, 16 Jan. 2014, https://plato.stanford.edu/entries/descartes/. 

Spinoza, Benedict de, et al. Ethics. Penguin, 1996. 

Taliaferro, Charles. “Philosophy of Religion.” Stanford Encyclopedia of Philosophy, Stanford University, 8 Jan. 2019, https://plato.stanford.edu/entries/philosophy-religion/.