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The Meditator knows the following: he exists as a thinking thing; what he clearly and distinctly perceives is true; God exists (which means the Meditator is not alone and there is at least now a greater possibility that an external world of things exists); the Meditator—not a deceiving God—is the source of error; and when his idea lacks clarity and distinctness, he must refrain from making a judgment.
In the Second Meditation, the Meditator ascertained not only the certainty of his existence as a thinking thing but also that the thinking substance is immaterial and finite. In short the essence of his existence is thinking, and thinking is entirely distinct from anything material that may exist. Moreover, while he does not know that any bodies exist, if they do, he learned from the wax example in the Second Meditation that its essence is to be extended and changeable.
In the Third Meditation the Meditator concluded God exists. This is because the essential attributes that make up the idea of God means the idea cannot have been caused by the Meditator himself. God alone is its cause.
In the Fifth Meditation, the Meditator returns to the topics of God and matter. As has been his approach in the previous Meditations, the Meditator turns first to his ideas of material things rather than starting with an investigation into whether or not such things exist. He has all sorts of ideas of material things, but this does not guarantee they are real.
The Meditator's analysis shows that the gap between mind and world—and so the bodies that would occupy it—can be bridged by mathematics. He notices he has distinct images of "continuous quantity," or extension. Extended things have parts. These parts have "various magnitudes, shapes, positions, and local motions" of various durations. The clarity and distinctness of these ideas strikes him as "so much in conformity with [his] nature" that they are not new.
To the extent that mathematics presents clear and distinct ideas, it shows such truth is "immutable and eternal ... not invented by [him], and does not depend on [him]." The Meditator thinks, in establishing the essence of material things, he has established at least the plausibility of their reality.
Given what he has learned about mathematics, he realizes there are ideas whose content is necessarily true. The Meditator goes on to consider if his idea of God is of this sort. The contents of this idea include "a supremely perfect being," which includes existence. In other words the essence of God includes (real) existence. Just as the what-it-is-to-be-a-triangle cannot exclude three sides, so also the what-it-is-to-be-God cannot exclude reality.
The Meditator goes on to explain it is not the thinking of God as existing that guarantees God's existence, "for [the Meditator's] thought imposes no necessity on things." Instead it is when thinking of God the thought necessarily includes existence, since such is an essential feature.
At the end of the Fifth Meditation, the Meditator once again asserts (as he did in the Third Meditation) that knowledge depends on God and is possible through clear and distinct ideas, since God is not a deceiver.
The main question in this meditation is whether or not material things exist independently of the Meditator's mind. He still cannot rely on sense perception since the veracity of that information is in doubt. Still, here he gets closer to an answer by way of considering the idea of a material entity.
Of these ideas some are clear and distinct, and some are not. Among the former are mathematical ideas—in some cases, specifically geometric ones. This means that extension is the essential attribute. When someone has an idea of shape, for example, they have extension—it is just part of the idea of shape. Of course, whether the shape is circular or rectangular, for example, is not an essential part of the idea of shape.
Whether or not these ideas exist independently of the Meditator, it is still the case that they exist as mental entities—they have some degree of reality. Moreover, this reality does not depend on the person. In other words the idea of shape is not a fiction generated out of combinations of other ideas. If one asks, "Does shape have green hair?" the answer cannot be discovered but instead made up. That made-up-ness is the nature of self-produced ideas. On the other hand when one considers "square" one must think about extension. Moreover, one can find the answer to the question, "If one side is 2' long, what is the area?" just by thinking about it. No invention is necessary—in fact just the opposite. And if one calculates correctly, one will always get a correct number (the sentence expressing that number will be true).
The idea of a material thing is clear and distinct since the essence of that thing is geometric, and thus extended. Therefore, if there are material things independent of the Meditator's idea of them, there is a possible science of these things. The Meditator just needs to determine if there is a formal reality corresponding to the objective reality of the idea. Ideas are real to the extent they are ideas, but if they purport to represent an entity external to the mind then fail to do so (much like a leprechaun idea), they are not as real as they would be if they existed outside the mind.
The analysis of the idea of material things gives rise to the ontological proof of God's existence. The reader will recall that a distinction has been made between essence and existence—the essence of the thinker is thinking, whereas the essence of the idea of material things is extension. These essences do not, however, commit the Meditator to assert these things exist independently of his ideas. According to the Meditator, the idea of God, however, is something else entirely. Here, existence is part of God's essence. This was also the case in the idea of God presented in the Third Meditation, but the type of argument proceeds differently. There, the focus was on what can be inferred about causes from effects. In the Fifth Meditation the focus is on the type of being God is.
Italian theologian and philosopher Anselm presented the ontological argument in the 11th century. After having been roundly criticized two centuries later by another Italian theologian and philosopher, Thomas Aquinas (1225–74), it fell out of favor until Descartes resurrected a version of it. The main difference between the two is that Anselm's version proceeds from an analysis of "God" to the conclusion that God necessarily exists independently of the mind. Descartes's focus is more mathematical. He compares his version of the ontological argument to geometric proofs.
Descartes has the Meditator claim that "existence can no more be separated from the essence of God than we can separate from the essence of a triangle that the sum of its three angles adds up to two right angles." In other words these ideas are analytically true, as is the idea that "existence is inseparable from God." Talking about a supremely perfect entity, the Meditator asserts, necessarily includes real (formal) existence. The argument can be encapsulated in a syllogism (major claim, followed by a minor claim, followed by a conclusion):
Why should the reader be convinced necessary existence and perfection are related? It is not the same as contingent existence, where something comes into being and passes away. Necessary existence is existence that cannot be otherwise.
A simple answer has already been suggested in the causal argument from the Third Meditation, as has the evil genius device. An exclusive mental reality is not as real as (or as good as, in some cases) a reality independent of the mind. One can think about the most delicious pizza possible, but this idea is not as real (or as tasty) as one that can be eaten.
So while the Meditator cannot think about a mountain without a valley, he can doubt that any mountain exists. Why can't he do the same for the God idea? Why can't he say, "When I think of the idea of a supremely perfect being, I also think of existence, but that doesn't mean God really exists"? According to Descartes, the Meditator isn't free to do so. If existence is part of the idea, denying it would be self-contradictory, in the way that asserting "a bachelor is not a married man" is self-contradictory.
One final noteworthy feature of the ontological argument is its movement from essence to existence. In the First Meditation, for example, the line of skeptical reasoning first establishes existence—for example, "I am, I exist"—before moving on to draw a conclusion about an essence—for example, "I am a thinking thing." The ontological argument moves from an analysis of the essential nature of God as "a supremely perfect being" similarly to the (mathematical) essence of body. However, whereas the essence of a body does not guarantee its real existence, the essence of God does. Hence the inextricable move from essence to existence.
With the ontological argument returns the worry of circular reasoning. More specifically, it is the use of the rule or principle of clarity and distinctness in connection with this proof (and the causal proof from the Third Meditation) that generates the concern: A person's clear and distinct idea validates God's existence, and God's existence alone validates their clear and distinct idea.