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