Indefiniteness, Infinity, and Descartes’s Cosmological Argument

By Charlie Schmidt, University of Colorado Boulder

1. Introduction

Descartes’s Third Meditation presents a cosmological argument that has likely received more attention than any other alleged proof of God ever written. His argument is as follows:

[P1] “In order that an idea should contain some … objective reality … it must without doubt derive it from some cause in which there is at least as much formal reality as this idea contains of objective reality” (III. ¶15).

[P2] “I [have an idea of] a supreme God, eternal, infinite, [immutable], omniscient, omnipotent, and Creator of all things” (III. ¶14).

[C1] “God necessarily exists” (III. ¶24).

Accepting this argument to be valid and its first premise to be true, its overall soundness relies on that of [P2]. Thus, it is necessary to ask the question: is the idea of God in Descartes’s second premise truly sufficient to yield [C1]? It is my position that Descartes successfully proves the existence of some infinite substance in his Third Meditation; though, considering his characterization of God as an infinite being who is causally responsible for Himself, I contend that this substance cannot possibly be God. In this paper, I will argue that the only infinite substance whose existence is proved by Descartes’s work is the indefinite plurality of causal relationships (IPCR). I plan to show that Descartes misrepresents the indefinite as a negative feature (characterized by the lack of absolute negation) when, if it is represented as IPCR, it is, instead, a positive feature (characterized by implicit verification) (Schechtman 503). IPCR, in being an infinite and positive feature not conflicting with any of his other premises, is the only infinite substance whose existence his logic defends.

2. Descartes’s Causal Principles

Causal principles are foundational of [P1] and Descartes’s ontology, both of which are essential to his cosmological argument. [P1], which is referred to by Anat Schechtman as Descartes’s Principle of Objective Reality (POR), is essential to Descartes’s cosmological argument because it provides a means by which the Meditator may confirm the existence of things beyond his own thoughts (491). Without such a means, the Meditator would have no hope of confirming the real existence of anything outside his own mind, much less the existence God. Descartes’s ontology, on the other hand, is essential to the cosmological argument in a more subtle way: it provides the framework through which, according to Descartes, God can both exist and be clearly perceived. To provide context for this statement before further exploring the causal principles invoked by Descartes’s POR and ontology, the following is an elaboration on the role of Descartes’s ontology in the cosmological argument.

According to Descartes, the three levels of being are substance, attribute, and mode. Every perceivable thing can be categorized into one of these three levels of being (Schechtman 490). Each level of being depends on the one before it; modes may not exist without attributes, and attributes may not exist without substances (Principles I. 53). The role of Descartes’s ontology in his cosmological argument becomes clear upon examination of both the properties and variations of substances. The most significant property of substances in relation to the cosmological argument is that they are the only things which may be clearly and distinctly perceived by the Meditator. Additionally, there are two kinds of substances: finite and infinite. Finite substances are only allowed to exist because of the existence of an infinite substance (Meditations III. ¶26). This infinite substance is, of course, according to Descartes, God. Without this framework to differentiate between the different levels of being, Descartes would not be able to claim that God’s existence could be clearly perceived, nor would he have the verbiage to attempt to prove the existence of an infinite substance. He would have no terms with which to make his argument, so it could not exist.

Descartes’s TOR explains the relationship between objective reality and formal reality. Objective reality is the reality contained in ideas alone, while formal reality is the reality contained in the things on which those ideas are based. The relationship between the two concepts is clearly causal:

The stone which has not yet existed not only cannot now commence to be unless it has been produced by something which possesses within itself, either formally or eminently, all that enters into the composition of the stone.… Further, the idea … of a stone, cannot exist in me unless it has been placed in me by some cause which has within it at least as much reality as that which I conceive to exist in … the stone. (III. 15)

In the above quotation from the Third Meditation, Descartes likens the causal relationship between a stone and its necessarily real cause to the causal relationship between ideas and their necessarily real subjects. Notably, he does not simply make an analogy between the two relationships; he implies that they are exactly the same kind of relationship. As obviously as a causal principle governs the production of a stone, the same causal principle is responsible for the content of the Meditator’s ideas.

To clarify the relationships between each level of being, Descartes’s Principles of Philosophy uses the following example: mind is a substance whose principal attribute is thought, and modes of thought are specific ways of thinking (I. 53). These modes of thought, specifically, can be doubt, understanding, conception, affirmation, denial, will, refusal, etc. (Meditations II. ¶8). Upon close consideration, the relationships between modes, attributes, and substances, are causal in more or less the same way as the relationships between stones and the processes which form them or ideas and their subjects. Modes of thought may not exist without the capacity for thought, and the capacity for thought may not exist without a mind. Since each level of being on Descartes’s ontological ladder “presupposes” the existence of the one(s) on which it depends, it may likewise be affirmed that each level of being is causally responsible for the one(s) which depend(s) on it (Principles I. 53). When one puts Descartes’s previously mentioned example of mind in this context, it indeed seems reasonable: mind, a substance, causes thought; and thought, an attribute, causes doubt, understanding, conception, and any other mode of thought.

3. IPCR and Descartes’s Principles

According to the rules which Descartes establishes at the outset of the Meditations — namely, that literally everything the Meditator knows must be cast into doubt — if the above established causal principles are not clearly and distinctly perceived, then the Meditator may not use them in any further pursuit of truth (Meditations II. 1). Yet, as I have shown, these causal principles are implicit and foundational of premises which the Meditator has already shown to be clear and distinct: namely, the distinction between substance, attribute, and mode, and the relationship between objective and formal reality. If the Meditator cannot accept these causal principles to be clear and distinct perceptions, then he must forego these essential premises and be left with no hope of finding a way out of his initial hole of Cartesian doubt. He would even be unable to prove that he is a thinking thing, as it would not necessarily follow from the existence of his ideas that they have any source. Consequently, I may say with relative comfort that the existence of an indefinite causal principle is as certain as anything else which is clearly perceived by the Meditator. It is, therefore, unintelligible to suggest that modes are not always caused by attributes, that attributes are not always caused by substances, and that ideas with objective reality are not always caused by things with formal reality. Upon reflection, such truths only become clearer and more distinct; the immutable nature of these causal relationships is as distinct a perception as the Meditator can possibly have.

If the nature of Descartes’s indefinite causal principle is immutable in the way that it must be in order for the Meditator to retain any of his progress from prior to the Third Meditation, it necessarily follows that the number of individual causal relationships between particular modes, attributes, and substances is indefinite; limitless. This may seem like quite a jump, but no other conclusion can be reached, provided that one is willing to accept the following two pre-established premises: first, that causal principles govern the relationships between all modes, attributes, and substances, and second, that every existing thing is classifiable as either a mode, attribute, or substance. There is surely an indefinite number of existing things (the Meditator has still not accepted [P2] and does not yet have an idea of infinity, so this number may only be said to be indefinite), and wherever things exist, there are — and have been — at least as many causal relationships as existing things. This can be verified by the causal principle of Descartes’s POR, which, as established earlier, can be applied to both ideas and physical objects (likes stones, provided that such objects can be proven to exist).

Though the number of things which are governed by causal relationships is only indefinite, the idea of IPCR that exists in the Meditator’s mind contains, I contend, infinite objective reality. I believe this contention is substantiated, again, by the causal principle invoked by Descartes’s POR. One existing thing may have had many causes, and, therefore, may be the product of many causal relationships. Even if it appears to have a single cause, that single cause must have had a cause, and so on. The number of causal relationships which exist, therefore, must always be larger than the already indefinite number of perceivable things which exist. The indefinite number of perceivable things in existence is indefinite instead of infinite only as a consequence of the mind’s so-far limited capacity conceive of infinity; yet, this indefiniteness, the Meditator must have already concluded, is inherently exceeded by IPCR. If something inconceivably large is adjudged by the Meditator to be indefinite simply by failure to perceive its real limits, and there is a second thing which is, by its nature alone, larger than the inconceivably large, indefinite thing, then the Meditator’s idea of the second thing is as infinite an idea as he can possibly have. That is to say the Meditator’s idea of IPCR contains infinite objective reality. If this claim is true, then IPCR may take the place of God in both [P2] and [C1] of Descartes’s cosmological argument, resulting in the conclusion that IPCR is an existing infinite substance.

At least initially, I do not think Descartes would accept my claim that the Meditator’s idea of IPCR has infinite objective reality and is entitled to replace his argument’s notion of God. In the next section, I will address what I believe would be his most likely objection to my argument. However, presently, I will consider exactly how IPCR, as an infinite substance, would be compatible with Descartes’s ontology (provided that one accepts my argument from the previous paragraph). If the substance is IPCR, its principal attribute is causation, as, when one considers what follows most necessarily from IPCR in the same way that thought follows most necessarily from mind, no other conclusion may be reached. Minds are known to be minds because they think, and IPCR is known to be IPCR because it causes. Its modes, then, are all existing things. Doubt, affirmation, will, refusal, etc. are all necessarily products of thought in exactly the same way that things are all necessarily products of causation. I do not see any inherent problems with this ontology, though I will now explore what I would anticipate to be Descartes’s most significant objection to my argument from the previous paragraph.

4. Indefinite vs. Infinite

Descartes would likely object to my claim that the Meditator’s idea of IPCR contains infinite objective reality by drawing the same distinction between the infinite and the indefinite that he drew in both a 1649 letter to Claude Clerselier and Principles of Philosophy. The distinction is presented in the following passage from the Clerselier letter:

I never use the word ‘infinite’ to signify the mere lack of limits (which is something negative, for which I have used the term ‘indefinite’) but to signify a real thing, which is incomparably greater than all those which are in some way limited. (“To Clerselier” 377)

The true distinction between the infinite and the indefinite, then, comes down to the distinction between positive and negative things, as well as the premise that the indefinite is negative while the infinite is positive. To further clarify the difference between negative and positive features, Descartes explains in his Principles of Philosophy that “[God is] the only thing that our understanding positively tells us doesn’t have any limits,” but, for other things, “the most we know … is the negative information that we can’t find any limits” (I. 27). Given Descartes’s preference to consider the indefinite negatively and his belief in the inability of negative features to be infinite, I believe he would say it is unreasonable for me to claim that an idea of something indefinite may contain infinite objective reality.

Yet, I am troubled by Descartes’s classifications of the indefinite as inherently negative. My trouble with this classification becomes clear upon examination of an example he uses in Principles of Philosophy to justify it: “No matter how numerous we imagine the stars to be, we think that God could have created even more; so we’ll suppose that there’s an indefinite number of stars,” which is distinguishable from the infinite reality of God (I. 26). Descartes seems to be implying that, since God is the substance which would be responsible for the creation of stars in excess of those we might imagine to exist, God is infinite and the number of stars — which we can imagine to be as large as any number we can conceive of — is indefinite. I would challenge Descartes, however, to consider whether IPCR, in the exact same way as God, could be responsible for the creation of stars in excess of those we imagine. I have, I believe, already provided a parallel argument in section III to substantiate my belief that it, indeed, could: causal relationships necessarily exist in excess of everything which can be perceived, as each thing which can be perceived must have, at the very least, more causes than itself alone. Every perceivable thing — which can be related in this instance to the number of stars one may imagine — is indefinite; yet IPCR, a substance which is causally responsible for every existing thing, is infinite in exactly the same way Descartes claims is unique to God.

My quarrel with Descartes is, however, not as significant as it may at first seem. I simply contend that, when Descartes refers to God, he means to refer to IPCR. There is really precious little difference between the two notions; they are both, in theory, infinite substances which are causally responsible for all existing things. They are both theoretically omniscient and omnipotent. God is a problematic notion only because it implies a finality to the causal relationships between things which is, I believe, incompatible with the necessarily immutable causal principles which are foundational of Descartes’s argument in the first place. It is surely necessary for Descartes to prove the existence of an infinite substance if his Meditator is to make any logical process. But, since this can be done without negating the causal principles which govern so much of his argument, it should be done. If it is not, his proof of an infinite substance becomes significantly less viable.

5. Conclusion

Descartes’s notion of God causes subtle foundational problems with his otherwise sound cosmological argument in the Third Meditation. It requires an exception to the immutable causal principles which are clearly established in Descartes’s POR and ontology: an exception which, if allowed, undermines his entire argument. If the infinite substance Descartes proves is, alternatively, IPCR, then he is not required to undermine his own argument and is still able to provide a basis for the existence of all finite substances, their attributes, and modes. After adjudicating his supposed distinction between the indefinite as a negative feature and the infinite as a positive feature, IPCR’s existence as an infinite substance became clearly plausible. In order for Descartes’s proof of an infinite substance to be as strong as possible, it must be considered a proof of IPCR; not a proof of God.

Works Cited

Descartes, René. “Principles of Philosophy.” Early Modern Texts. Ed. Jonathan Bennett. Early Modern Texts, Jan. 2012. Web.

Descartes, René. “To Clerselier, 23 April 1649.” The Philosophical Writings of Descartes: Volume 3, The Correspondence. Trans. John Cottingham, Robert Stoothoff, and Dugald Murdoch. Illustrated, Reprint ed. Vol. 3. N.p.: Cambridge UP, 1991. 376-78. Print.

Descartes, René. “Meditations On First Philosophy.” Trans. Elizabeth Haldane. Internet Encyclopedia of Philosophy. N.d. Some Resources for Self-Paced Logic. Web.

Schechtman, Anat. “Descartes’s Argument for the Existence of the Idea of an Infinite Being.” Journal of the History of Philosophy 52.3 (2014): 487-517.



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