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Source: p 38, Think: A Compelling Introduction to Philosophy (1 ed, 1999) by Simon Blackburn
Caution: I modified Blackburn's syntax and organisation to ameliorate readability; I added all numbering.

  It was one of his contemporaries, Antoine Arnauld (1612-94), who cried "foul" most loudly at this point, accusing Descartes of arguing in a circle, the infamous "Cartesian circle". Descartes seems committed to two different priorities.

  1. If we clearly and distinctly perceive some proposition p, then it is true that p.
    1.1. Symbolise 1 as:    If p is clear and distinct ("CD"), then it is true ("T").
    1.2. Then further symbolise 1.1 as:   CDp ⟶ Tp.

  2. Now abbreviate the following sentence as G:  God exists and does not deceive us.

  3. Then the circle is that at some points it seems that Descartes holds:
    I can know that (CDp ⟶ Tp) only if I first know G.

  4. But at other points he holds: I can know that G only if I first know (CDp ⟶ Tp).

It is like the familiar impasse in the morning, when you need to have some coffee to get out of bed, and you need to get out of bed to fix the coffee.
  One or the other has to come first. There is a whole literature trying to understand whether Descartes actually falls into this trap. Some commentators cite passages in which it seems that he does not really hold the first [ie: 1].

  1. The major suggestion is that G is necessary only to validate memory of proofs.

So while you actually clearly and distinctly perceive something, you do not need to trust anything at all, even G, to be entitled to assert its truth.

  1. But later, when you have forgotten the proof, only G underwrites your title to say that you once proved it, so it must be true.

I doubt 5 and 6: how is G needed for remembering a proof?

For example, remembrance of a mathematical proof means the ability to reproduce the proof now and instantly. Otherwise, this assertion appears meaningless and deceptive (if the asserter really meant a past lapsed ability to prove the proof, but cannot do it now). Notice that this example does not concern G: so why does G matter?

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    Before answering, I'd like to know: Have you read Descartes or are you depending entirely on this secondary source? For Descartes, G is the only guarantee against an evil demon manipulating thoughts on a fundamental enough level to screw with "remembrance" ergo G matters to Descartes... – virmaior Jan 17 '16 at 22:57
  • @virmaior Sadly, I have not read Descartes's original works; I am depending entirely on this secondary source. (Reason here). Yes, I do understand your last sentence above, but how does an Evil Demon and his manipulations matter to memory of proofs? If the student doubts her remembrance, just prove the proof again anew! No need to depend on memory. – Greek - Area 51 Proposal Jan 17 '16 at 23:04
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    But for Descartes the radical demon in Med I can manipulate my internal thought process ... In other words, Descartes does not share you belief about your pure ability of reason to move forward. I'd also suggest you look at philosophy.stackexchange.com/questions/31571/… -- Descartes is a philosopher where you can read him "right off the bat." – virmaior Jan 17 '16 at 23:07
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    right off the bat = without reading a secondary source to prep .. / Also, I'm not saying you have to agree with Descartes just that this is a central part of his argument and setup – virmaior Jan 18 '16 at 0:06
  • @LePressentiment The Meditations are short, very accessible, and freely available on the internet. I'm sure you've read much longer, more obscure writing about Descartes by now. There's absolutely no excuse to continue not having read them if you actually want to engage with Descartes. I can't understand this fear of primary sources --in philosophy, they can be much more clear than the commentaries, which are quite often misleading (or have an axe to grind). – Chris Sunami Feb 8 '16 at 15:47

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