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I've learned about Descartes' universal doubt and as I understood it, he says mind that is supposed to interact with God isn't part of res extensa and therefore isn't part of the senses we can doubt. On the other hand, I know that his argument for the existence of God was founded on our natural senses. So did Descartes really doubt the existence of God?

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    Short answer: NO. – Mauro ALLEGRANZA Sep 22 '17 at 11:25
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    You can find many useful posts regarding D's Cogito argument on this site. – Mauro ALLEGRANZA Sep 22 '17 at 11:26
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    But there are "certainities": "[A]rithmetic, geometry and other subjects of this kind, which deal only with the simplest and most general things, regardless of whether they really exist in nature or not, contain something certain and indubitable. For whether I am awake or asleep, two and three added together are five, and a square has no more than four sides. It seems impossible that such transparent truths should incur any suspicion of being false. (Med. 1)" – Mauro ALLEGRANZA Sep 22 '17 at 12:58
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    "I recognize that it would be impossible for me to exist with the kind of nature I have — that is, having within me the idea of God — were it not the case that God really existed. (Med.3)" – Mauro ALLEGRANZA Sep 22 '17 at 13:03
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The answer depends on the meaning of "really". The structure of Meditations is that Descartes sets out to doubt everything, no holes barred. At this point he is presumably doubting the existence of God as well. But is he "really"? God is never specifically addressed at this point. Eventually, Descartes finds himself unable to doubt cogito ergo sum, which is the one thing specifically so addressed. Thus, he does distinguish between permitting (feigning?) doubt and being able to doubt. Cogito starts the ascending arc of meditations leading to the "clear and distinct ideas" and "God is not a deceiver" locked into the Cartesian Circle of mutually justifying each other (Descartes had responses to the charge of circularity, but they are not wholly convincing). To move along the circle Descartes uses a version of Anselm's ontological argument, and given the dubious assumptions needed to make it work it is hard to believe that one can be convinced of God's existence based on that alone. At this point we are in the area of inability to doubt, albeit accompanied by rational arguments. So, did Descartes "really" doubt the existence of God?

Peirce spent multiple pages analyzing, one could even say psychoanalyzing, Cartesian doubt, see Peirce on Cartesian Doubt, and he concluded that it is "paper doubt" that rests on a peculiar combination of flawed reasoning and willful self-deception:

"Descartes thinks he must be persuaded that shape and motion do not belong to his nature, or anything else but consciousness. This is taking it for granted that nothing in his nature lies hidden beneath the surface. Next, Descartes asks the doubter to remark that he has the idea of a Being, in the highest degree intelligent, powerful, and perfect. Now a Being would not have these qualities unless he existed necessarily and eternally. By existing necessarily he means existing by virtue of the existence of the idea. Consequently, all doubt as to the existence of this Being must cease. This plainly supposes that belief is to be fixed by what men find in their minds... He fails to remark that this is precisely the definition of a figment.

[...] "Many and many a philosopher seems to think that taking a piece of paper and writing down "I doubt that" is doubting it, or that it is a thing he can do in a minute as soon as he decides what he wants to doubt. Descartes convinced himself that the safest way was to "begin" by doubting everything, and accordingly he tells us he straightway did so, except only his je pense, which he borrowed from St. Augustine. Well I guess not; for genuine doubt does not talk of beginning with doubting.

[...] "We cannot begin with complete doubt. We must begin with all the prejudices which we actually have when we enter upon the study of philosophy. These prejudices are not to be dispelled by a maxim, for they are things which it does not occur to us can be questioned. Hence this initial skepticism will be a mere self-deception, and not real doubt; and no one who follows the Cartesian method will ever be satisfied until he has formally recovered all those beliefs which in form he has given up... Let us not pretend to doubt in philosophy what we do not doubt in our hearts."

So on Peirce's view Descartes did not "really" doubt much of what he believed, least of all God. Needless to say, some scholars disagree. Haack writes, for example, that Descartes’s "method is relevantly different from what Peirce takes it to be, and that it does not require, what Peirce insists is impossible, that one voluntarily set out to doubt what one initially believes." Johanson rehabilitates "paper doubt" as "philosophical doubt" (in contrast to the "heartfelt doubt") and argues that the former is not out of place in philosophy:"Descartes has open the possibility of saying that what he is doing is subjecting his indubitable (and dubitable) beliefs to criticism and imaginary experimentation, to see which of them can withstand the test of feigned hesitancy." And in the sense of "feigned hesitancy" Descartes did indeed doubt the existence of God, see Peirce’s Critique of the Cartesian Maxim.

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Descartes wrote, "I think it proper to remain here for some time in the contemplation of God himself-that I may ponder at leisure his marvelous attributes-and behold, admire, and adore the beauty of this light so unspeakably great, as far, at least, as the strength of my mind, which is dazzled by the sight, will permit."" We learn from experience that a like meditation is the source of the highest satisfaction of which we are susceptible in this life."

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