Descartes: A Way Out of the Circle

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In this paper, I argue that Descartes arrives at the proof for God (the Ontological Argument) with normative certainty of all his clear and distinct ideas. Thus, his epistemology is in no way circular. Descartes proves the existence of God as a retrospective confirmation of his normative certainty of clear and distinct ideas. Furthermore, I argue that even if Descartes were required to prove the existence of God in order to grant his epistemology, he should not fear circularity because the Ontological Argument is a sound deductive argument.

To start, it is necessary to discuss the nature of the Cartesian Circle and how it arises. In the first meditation, Descartes reflects on the number of falsehoods he has believed during his life and on the subsequent faultiness of the body of knowledge he has built upon those falsehoods. Thus, he decides that in order to secure knowledge once and for all, he needs to start over, building up his knowledge anew on indubitable grounds. To this end, Descartes employs hyperbolic doubt. To attain an epistemology that resists even the most radical skeptics, Descartes decides to proceed in his investigation to find a secure point of reference by doubting literally everything. Everything that he has accepted as most true, after all, he has acquired from or through his senses. He realizes that the senses cannot therefore be a trustworthy source of knowledge. When he is dreaming, for example, Descartes experiences what seem to be real sensations and real objects. As he writes, he feels certain that he is awake and sitting by the fire, but reflects that he often has dreamed a similar scenario and has been convinced by it to be true. Descartes concludes, though he can doubt composite things, he cannot doubt the simple and universal parts from which they are constructed, such as shape, quantity, size, time, etc. While we can doubt studies based on composite things, such as medicine, astronomy, or physics, he concludes that we cannot doubt studies based on simple things, such as arithmetic and geometry.
On further reflection, Descartes realizes that even simple things can be doubted. At the beginning of the third meditation Descartes presents his most powerful doubt, which seems to be the root of what is known as the Cartesian Circle.


Some God could perhaps have given me a nature such that I might be deceived even about matters that seemed more evident. But whenever this preconceived opinion about the supreme power of God occurs to me, I cannot help admitting that, were he to wish it, it would be easy for him to cause me to err even in those matters that I think I intuit as clearly as possible with the eyes of the mind.” (Meditation III 36, p. 25)

To be specific, the Circle arises because, according to that line, an evil god, for example, could make even our ideas of mathematics false. One might argue that God is supremely good and would not lead him to believe falsely all these things. But this reasoning would clearly depend on dubious premises and thus the argument would beg the question. In other words, if an evil god has the power to deceive us into believing that 2+2=4 when in reality is not, then we are not entitled to mount any argument because the premises of that argument can be false.

That passage seems to have caused a great deal of trouble for Descartes. Many commentators have pointed to that passage as an insurmountable obstacle that prevents Descartes from acquiring normative certainty of any further propositions than that he exists. Michael Della Rocca, who defends an interpretation of the Meditations that allows Descartes to avoid circular reasoning, sets up the standard interpretation of Descartes’ problem this way: Supporters of the Cartesian Circle lament that before Descartes proposes his argument for the existence of God in the third and fourth meditations, he (Descartes) has merely psychological—and not normative—certainty of propositions in general. In other words, those who believe that Descartes reasons in circle claim that Descartes is not entitled to use God as a guarantor for acquiring normative certainty of any proposition because the conclusion that God exists and he is not a deceiver rest entirely on premises that can be doubted, i.e., that are not normatively certain, by Descartes’ own system. So, even if Descartes’ theological argument, i.e., the Ontological Argument is deductively valid, at this stage, all Descartes have is a series of premises that are merely psychologically certain, and thus can be false; consequently, the Ontological Argument appears to be unsound and thus unable to support its conclusion that God exists. However, this reading, I want to argue, is unduly uncharitable for at least two reasons. The first reason is that although Descartes’ increasing doubt requires that he suspend all judgments, we should not forget that in his second meditation, Descartes established a proposition that resists all skeptical attacks—even the alleged powers of a deceitful, evil god. That unshakable proposition, known as the Cogito, is normatively certain. In the second meditation, Descartes writes
I have convinced myself that there is nothing in the world — no sky, no earth, no minds, no bodies. Doesn’t it follow that I don’t exist? No, surely I must exist if it’s me who is convinced of something. But there is a deceiver, supremely powerful and cunning whose aim is to see that I am always deceived. But surely I exist, if I am deceived. Let him deceive me all he can, he will never make it the case that I am nothing while I think that I am something. Thus having fully weighed every consideration, I must finally conclude that the statement “I am, I exist” must be true whenever I state it or mentally consider it. (Meditation II, 25, p.18)

Here Descartes proves beyond doubt the existence of a self. Granted, if an evil god exists and is able to deceive me, and he is deceiving me as we speak, I may well be deceived into believing that I have a physical body and that there is an external world independent of my thoughts even if in reality I have no body and what I perceive as being an external world is an illusion. However, the existence of myself becomes a necessary truth, which I perceive clearly and distinctly. Notice that the proposition “I exist,” is necessarily true and is affected by the law of contradiction like any mathematical proposition. That is to say, to deny that I exist, is to affirm that I exist—even if an evil, deceitful god exists and he is currently deceiving me. Now, many commentators failed to appreciate that the proposition “I am, I exist” or better known as “I think, therefore I am” is a normatively certain proposition that Descartes uses as a model or axiom to find other such propositions. Namely, if I find that a proposition cannot be false in any possible world, it follows that that proposition must be normatively certain. In other words, even if an evil god uses his powers to deceive me or I am dreaming (or I am in the matrix), there is no possible world in which I may be deceived but at the same time I do not exist. If that were possible, it would be tantamount to saying that the proposition P and –P is true or that something exists and does not exist at the same time. However there is no possible world in which something exists and does not exist at the same time. The fact that one can utter such a proposition does not make the proposition possible or even conceivable. One would not even be able to imagine what it would be like for something to exist and not exist at the same time. P and –P is in fact necessarily false in any possible world. The logical form of a proposition such as P and –P is the same as “I think, therefore I am” because there is no possible world in which a thinking thing wonders about its existence when in reality it does not exist. These propositions are generally referred to by Descartes as clear and distinct perceived ideas.

The second reason why I regard the standard interpretation, that which lament circularity in Descartes’ argument, as unduly uncharitable is that there is textual evidence showing that Descartes approaches the Ontological Argument with normative certainty of his current clear and distinct perceived ideas. At the outset of his third meditation, Descartes writes


When I turn to the things themselves which I think I perceive very clearly, I am so convinced by them that I spontaneously declare: let whoever can do so deceive me, he will never bring it about that I am nothing, so long as I continue to think I am something; or make it true at some future time that I have never existed, since it is now true that I exist; or bring it about that two and three added together are more or less than five, or anything of this kind in which I see a manifest contradiction. (Meditation III, 36, p. 25)

The passage above indicates that Descartes has normative certainty of those ideas and concepts he later uses to mount the Ontological Argument and, moreover, the passage shows that he does know to have normative certainty at that stage. That is why Descartes uses the logical form of his Cogito as an axiom that enables him to identify other similar logical forms. (I’ll return to this later) Mathematical propositions as well as propositions of geometry, for example, have the same force and logical indubitability as the Cogito. Namely, Mathematical concepts have the important feature that they never change. The number three is what the numeral “3” refers to. A numeral is a symbol that can be written down at a particular time and place. In contrast, a number is not the kind of thing that can ever be written down. This shows that, if numbers exist, they do not exist at some times and places as opposed to others. If a skeptic complains that perhaps, if we go along with Descartes’ evil god, it is possible that the number three were different 10,000 years ago. But what would that mean? That proposition is not just inconceivable but also nonsensical. To say that the number three was not really three but almost three or slightly less than three is tantamount to saying that at one point in time or in some possible world a triangle might have four sides. Clearly, there is a peculiar aspect of language that allows one to utter nonsensical propositions. These points about numbers are uncontroversial. However, one may still object that it is Descartes who, after all, admits that


Whenever this pre-conceived opinion of the pre-eminent power of God occurs to me, it is not possible for me not to allow that if He wishes, it is easy for him to bring it about that I err, even about those things which I think I intuit as evidently as possible by the eyes of the mind. (Meditation III, 36, p. 25)

Here I want to suggest a reading of Descartes saying something like this: God can make me err when I count my 5 fingers on my right hand and then I count my 5 fingers on my left hand and I end up with the number nine. Surely it would be petty of God, even for an evil God, to deceive me like such, but an omnipotent, evil God could nonetheless do it. However, let us say that he deceived me into believing that, say, after counting to five fingers on my right hand, evil God erases my memory of counting to five and replaces with a false one whereby I have counted to four. Then, when I count my fingers on my left hand I arrive at the number nine. As I said, it seems an unlikely scenario even for an evil God, but if this were to happen, evil God deceived me but did nothing to change the reality of numbers. So, if I am dreaming, or an evil God wants to deceive me about things that I deem true, then I do not possess normative certainty of any proposition. But if I pay close attention, in this case I attend to the concepts of mathematics or geometry, I will find that based on pure self-evident logical axioms, I clearly and distinctively realize that five and five are ten or that a triangle has three sides, and other such truths, which are tautological. When I realize this, when I attend to these axioms, even an evil God in his immense power cannot actualize that five and five make nine when in reality they make ten. In fact, Descartes is not unaware of this difficulty and, in this regard, in a conversation with Burman, who points out that Descartes’ argument appears to be circular, Descartes writes,


[Descartes] does use those axioms in the proof, but he knows that he is not deceived with regard to them, because he is actually paying attention to them. And for as long as he does pay attention to them, he is certain that he is not being deceived, and he is compelled to assent to them. (The Philosophical Writings of Descartes, Vol. 3, p. 334)

Thus, Descartes realizes that it would be easy for an evil God to deceive him in a way I pointed out above with the example of counting fingers. But he says that he knows he is not being deceived about certain axioms because he is paying close attention to them. And as long as he is attending to these axioms and realizes that they are self-evident, he is compelled to accept them as normatively true. But one might want to push the issue and question God’s omnipotence. That is, if God is omnipotent, and the creator of all truths, isn’t it the case that he can do anything he wants even to the extent that he creates a world in which no absolute truths exist? For example, if God is omnipotent, can he create square circles and four-sided triangles? As I pointed out already, I think that because one can utter the words “A square circle” or “A triangle has four sides” or “Two and two make five”, whether God or human, those words do not actually refer to anything that could be the case in any possible world. But Descartes does not seem to take the same position. In my opinion his assertions are the product of the fact that in those times one could be burned at the stake for saying the wrong thing about God or saying that there are things that even God is not able to bring about.
However, if traditionally the concept of omnipotence is taken to mean that God can do whatever he wants, it does not mean that God can create a round square or a rock so heavy he cannot lift. According to classical monotheism, God—despite being infinitely powerful—cannot bring about what is illogical. In any case, Descartes seems to consider the possibility that if God wanted to, he could “make a mountain without a valley, or bring it about that 1 and 2 are not 3” as he writes in the Letter for Arnauld of 29 July 1648 (The Philosophical Writings of Descartes, Vol. 3, p. 358-359) Thus for Descartes, God could somehow bring it about that perhaps in some possible world 2 and 1 are not 3 or that mountains come without valleys. But in the end, God decided to bring it about that 2 and 1 are 3 and that mountains do have valleys. Nonetheless, Descartes says that these truths are necessary because God willed so: “I do think that [the mathematical truths] are immutable and eternal, since the will and decree of God willed and decreed that they should be so.” (The Philosophical Writings of Descartes, Vol. 2, p. 261). And he later continues that “It is because He [God] willed that the three angles of a triangle should necessarily equal two right angles that this is true and cannot be otherwise; and so on in other cases.” (p. 261) One interesting aspect of what Descartes is willing to say about the power of God, i.e., that “he could make a mountain without a valley…” is that Descartes adroitly avoids saying that God, in his infinite power, could bring it about that I think I exist although I do not exist.


Let him [God] deceive me all he can, he will never make it the case that I am nothing while I think that I am something. Thus having fully weighed every consideration, I must finally conclude that the statement “I am, I exist” must be true whenever I state it or mentally consider it. (Meditation II, 25, p.18)

It seems clear to me that when Descartes here believes that in fact even God could not bring about a world in which thinking things do not exist. Granted, God is the one that created me, but in doing so he created an eternal truth, i.e., that a thinking thing cannot not exist. With regard to geometry and mathematics, Descartes seems to be saying that they are not independent of God, but he nevertheless made them as eternal truths.
At this point, I want to return to the original question of whether Descartes has normative certainty of some propositions, which allows him to mount his theological argument. The proponents of the Cartesian Circle defend an interpretation of Descartes according to which Descartes lacks normative certainty of the premises required to prove God’s existence. According to these proponents, Descartes’ clear and distinct perceptions, prior to the Ontological Argument—on Descartes’ own account—are not free from doubt. But in light of the passages above, it seems that we have strong textual evidence that affords Descartes a way out of the Circle. Still, the initial doubts, we might say, partially stand. All the truths concerning the existence of an external world might not be certain, i.e., they are at best psychologically certain. But the truths or axioms required by Descartes for the premises used in his version of the Ontological Argument, as shown by textual evidence, are normatively certain. And an important reason for this is that those truths that Descartes declare eternal are independent of the physical world and independent of the self. Namely, the truths of mathematics and geometry, as illustrated earlier, are self-evidently true and true in all possible worlds. Thus Descartes is able to start with the normative claim that if he thinks, he must exist. This claim or axiom serves as a model to find other such axioms that, like the Cogito, are eternal truths. Descartes now moves forward using these axioms in arguments for the existence of God; and he is sure that God exists because he attends to the arguments that prove it. Therefore, God becomes a retroactive guarantor of any further knowledge and the memory of all the clear and distinct perceptions when not thinking of them directly.

Although I presented an interpretation of Descartes that dispenses him from circularity, based upon well-grounded textual evidence, it is not to say that Descartes’ troubles are over. Granted that Descartes has normative certainty of the premises to his theological arguments, i.e., granted that these premises are self-evident truths that even an omnipotent God cannot change, still many philosophers do not regard the Ontological Argument as sound. Hence, they lament that Descartes never successfully extends his knowledge outside of the solipsistic corner of the self. Therefore, here I want to suggest a way to look at the Ontological Argument as deductively sound; and if it is so, this argument is able to afford Descartes with retroactive normative certainty of all previously clear and distinct perceived ideas. With that in mind, at this point it would be helpful to see how exactly Descartes makes use of the aforementioned axioms in his theological arguments. The most important argument is known as Ontological. But before Descartes proposes the famous Ontological Argument, he actually offers two other very interesting arguments, both of which are based on the principle of contingency. I point this out because it seems to me that many critics of Descartes, and critics of his version of the Ontological Argument, fail to appreciate that Descartes offers a rich cumulative case for the existence of God. That is to say, Descartes’ Ontological Argument should not be considered in isolation, but rather as the culmination of a cumulative case produced by a cluster of arguments.

The first stage toward the Ontological Argument is Descartes’ proposition that there are three types of ideas, which are referred to as innate, fictitious, and adventitious. I find it easier to rename these ideas respectively as necessary, impossible, and contingent. Necessary ideas are true independently of us and are true in any possible world: e.g., propositions of math and geometry. (These are what will later be called Relations of Ideas by Hume and Analytic by Kant) Impossible or invented ideas come from our imagination: examples include unicorns, round squares, mermaids, etc. And contingent ideas are those that come from experiences of the world. He argues that the idea of God is necessary and placed in us by God, and he rejected the possibility that the idea of God is impossible or contingent. On this note, let us see how Descartes make use of these concepts in the following arguments:

Argument 1(Origin of Ideas)

1. From nothing, nothing comes.
2. The cause of an idea must have at least as much formal reality as the idea has objective reality.
3. I have in me an idea of God. This idea has infinite objective reality.
4. I cannot be the cause of this idea, since I am not an infinite and perfect being. I don’t have enough formal reality. Only an infinite and perfect being could cause such an idea.
5. So God, having infinite formal reality, must exist cause my idea of him.
6. An absolutely perfect being is a good, benevolent being.
7. So God is benevolent…
8. So God would not deceive me, and would not permit me to err without giving me a way to correct my errors.

Argument 2 (On The Existence of the Self)

1. I exist.
2. My existence must have a cause.
3. The only possible causes are
a) Myself
b) My always having existed
c) My parents
d) Something less perfect than God
e) God
4. Not a. this is simply nonsensical: it would mean that when I did not exist, I brought myself into existence. But if I was not there, it would be impossible to cause myself to exist.
5. Not b. This does not solve the problem. If I am a dependent being, I need to be continually sustained by another.
6. Not c. This leads to an infinite regress.
7. Not d. The idea of perfection that exists in me cannot have originated from a non-perfect being.
8. Therefore, e.
9. Therefore, God exists.

Argument 3 (Ontological)

Descartes now advances his version of the Ontological Argument according to which the fact that one cannot conceive of God without existence inherently rules out the possibility of God’s non-existence. Simply put, the argument is framed as follows:
1. God is defined as an infinitely perfect being.
2. Perfection includes existence.
3. So God exists.

Descartes had already claimed to have confirmed God’s existence through previous arguments, but this one allows him to put to rest any discontent he might have had with his “clear and distinct” criteria for truth. With a confirmed existence of God, all doubt that what one previously thought was real and not a dream can be removed. In other words, Descartes, as shown in the previous section, possessed normative certainty of his clear and distinct ideas prior to his entering the Ontological Argument. And since the premises used in the argument are doubt-free, normatively true, axioms, these premises are true. Consequently, the Ontological Argument is deductively sound. With the existence of God in place, Descartes produces what Della Rocca, in his paper, refers to as “normative retrospective certainty of his [Descartes’] clear and distinct ideas.

But what are we to make of the ontological argument? Why are so many philosophers troubled by it? To be sure, the Ontological Argument is one of the most controversial argument in the history of philosophy. Its controversy stems from its sheer simplicity. Ontology deals with existence, and the argument in question claims that the existence of God is implied by the concept of God. To put it in a modern term, the existence of God is an analytic proposition, just like “All bachelors are unmarried man.” Descartes starts by considering what God means. By God we certainly mean an entity that possesses all qualities or perfections: he is all-knowing, all-powerful, and all-loving, in short, the greatest of all possible beings. Also, being the creator of time, he must exist outside time. And since he created everything that is extended in space, he must exist outside space. Such a being would, accordingly, less perfect if he did not exist, and therefore he exists. Descartes, as I mentioned earlier, relies upon his previous arguments of the origin of ideas and existence. Still, many philosophers have criticized it as being a fallacious argument, though they never quite articulated what goes wrong with it. Kant for example criticized the argument by pointing out that existence is not a real predicate, a real quality. A predicate is that part of a statement that states the properties about the subject. The predicate “exists” is not conferring real existence on the subject term. This idea was anticipated by Gaunilo in his arguments against Anselm’s version back in the 11th century. Consider the following statement: “God exists.” Kant thinks the real existence of a thing, be it God or anything else, is presupposed in that thing’s having any properties at all, since anything having properties must exist in order to have them. Thus, to say that God exists is to assert a thing with properties—God—that also possess a further property—existence. But since having any properties at all is only possible if the thing having those properties exists, it follows that existence is not an additional property of the thing, but presupposed. Hence, existence is not a predicate. So the question “Does God Exist?” according to Kant is really not a question of logic at all. It is a question that lies entirely beyond what empirical science can determine.

The ontological argument, I want to argue, has two aspects, one arrogant and one humble. Most criticisms are based, in my view, on the arrogant aspect of the argument or, I may say, on an uncharitable interpretation thereof. I think the humble is helpful here. The arrogant aspect is what Kant highlighted with regard to existence. But what Kant and others failed to appreciate is a point that Descartes, as well as Amselm who had proposed an Ontological Argument before Descartes, namely, that the existence of God, regardless of whether existence is an attribute, is neither impossible nor contingent. Thus it must be possible. And if it is possible, it follows that God is necessary. Let me illustrate how this works: the idea of God is not an incoherent one. I think that virtually all philosophers agree that, in the end, it is possible that a God exists. The idea of God existing is not barred by the same logical contradiction inherent in the idea of a square circle. At least, if the idea of God were absurd or self-evidently false, God would be, immediately and self-evidently false. But this is not the case. I think it is impossible to show that the existence of such a being as God is absolutely impossible. Furthermore, for obvious reasons, if God existed, his existence could not be merely contingent, since the existence of contingent beings depend on external causes. But accordingly, God is an uncaused being. What remains, then, is that God is necessary, and thus exists. I can illustrate what I call the humble aspect of the argument as follows:

1. It is possible that a being that has maximal greatness (God) exists.
2. If it is possible that a being that has maximal greatness exists, then that being exists in some possible world.
3. A being has maximal greatness in a given world only if it has maximal greatness in every world.
4. A being has maximal greatness in a given world if it has omniscience, omnipotence, and omnibenevolence in that world.
5. Therefore, God—an omnipotent, omniscient, and omnibenevolent being—exists in the actual world.

This presentation of the argument, in my view, is a more charitable interpretation of Descartes’ version of the Ontological Argument. This way of expressing the argument is important for at least two reasons. The first is that this formulation avoids the need to suppose that existence is a perfection or great-making property. And the second is that it does away with all criticisms that try to invalidate the argument by conjuring up a greatest of all possible islands or greatest of all possible pizzas or unicorns or what not. That is to say, many philosophers have tried to invalidate the argument by claiming that it is possible to replace “God” with any other object, a pizza, for example. But that is a misunderstanding of the argument. If one supposes that there exist a maximally great pizza, one is obviously not referring to an actual pizza. What could it mean that a pizza, a physical object, could be maximally greatest? In order to be so, that pizza should be metaphysical, omnipotent, omnibenevolent, and omniscient—in other words, “pizza” would be an uncanny name for God. In fact, pizzas or unicorns as we know them are not necessary beings; a unicorn can be fruit of the imagination. One need not assume that a unicorn exist in reality. A pizza, on the other hand is a contingent object. So, a maximally great pizza would be a metaphysical pizza, and thus impossible to be eaten. Conversely, when we think about the idea of God we can either say that he exists or he doesn’t. But we cannot say that the existence of God is merely contingent. And since there is no self-evident contradiction in the existence of God, since his existence is possible, then it follows that it is necessary, and thus the Ontological Argument is deductively valid and sound.

In the foregoing discussion, I presented an exposition of the reasons according to which some readers lament circularity in Descartes’ reasoning. I hope to have shown that those readers adopt an uncharitable interpretation of Descartes. I also hope to have shown that there is an alternative interpretation based on well-grounded textual evidence. This alternative sees Descartes as having normative certainty of his clear and distinct ideas prior to his exposition of the Ontological Argument. As a result, Descartes uses these normatively certain truths as axioms to extend his knowledge outside his own self. God enters in the picture later, as it were, as a retrospective guarantor that all ideas clearly and distinctively perceived outside the self are normatively certain. Surprisingly, Descartes, in my opinion, is one of the first philosophers in the history of thought that uses the existence of God to grant all future scientific knowledge and at the same time to separates science from religion.


Author: Carlo Alvaro


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