by Richard Lee
In Meditation II1 Descartes offers a version of his famous "cogito ergo sum" argument. I follow Descartes in putting the argument in the first person ("I" instead of "he").
IP2. If I can be sure of p, then I know p.
IP3. If there is a ground of doubt for a belief p, then there is a possible situation in which I believe p, but p is not true.
Assume there is a ground of doubt for my belief that I exist. (Call this assumption A.)
Then, by IP3 there is a possible situation in which (a) I believe that I exist but (b) I do not exist. (Call this IC1.)
But, P1 states: if I believe that I exist, then I exist.
So, by P1, there is no possible situation in which I believe that I exist but I do not exist. (Call this IC2.)
IC1 and IC2 contradict one another.
So, by reductio, assumption A is false. (Call this IC3.)
So, according to IC3, there is no ground of doubt for my belief that I exist.
Then by a substitution into IP1 and IC3 it follows, via modus ponens, that I can be sure that I exist. (Call this IC4.)
Finally, by a substitution into IP2 and IC4 it follows, via modus ponens, that I know that I exist. And this is the conclusion, C.
|. . . p . . . [where "p" appears as a variable]|
|. . . Q . . . [where "Q" is a specific claim]|
|If p, then q.|
|IP3||If there is a ground of doubt for a belief p, then there is a possible situation in which I believe p, but p is not true.||implicit premise|
|IP3*||If there is a ground of doubt for my belief that I exist, then there is a possible situation in which I believe that I exist but I do not exist.||substitution of "I exist" for "p"|
|A||There is a ground of doubt for my belief that I exist.||assumption for reductio|
|IC1||There is a possible situation in which (a) I believe that I exist but (b) I do not exist.||modus ponens from IP3* and A|
|Q and not Q. [for some claim Q]|
Premise P1 seems unobjectionable: If I am believing anything then I must exist. (Descartes is quite clear that this doesn't mean my body or even my brain exists, of course.)
But are the implicit premises true?
IP3 seems a good definition of "ground of doubt."6
But IP2 may be questioned. Maybe more is necessary for knowledge than certainty. Might not a man be subjectively quite certain ("sure") of something and yet be wrong? If so, then he did not really know it, although he thought he did. Descartes doesn't just want the conclusion that he thinks he knows he exists.
And IP1 may be questioned as well. What if there is some belief for which there is no ground of doubt, but there is also no positive reason at all to believe? Just because there is no reason to doubt it might not be enough reason to believe. This is almost the fallacy of "appeal to ignorance."
And on the subject of fallacies, if Descartes is simply trying to prove he exists, then this argument perhaps begs the question since it presumes the questioner exists. (But notice that the premises are all conditional statements, so it seems that no premise by itself presupposes the existence of the "I.") And as formulated here, the conclusion is not "I exist," but "I know that I exist," and that is certainly not presumed in the premises, so I do not see any begging of the question here.
2. "... am I not at least something?" "Then there is no doubt that I exist ..." "`I am, I exist' is necessarily true every time it is uttered by me or conceived in my mind." (P 133b)
3. "... there is no doubt that I exist, if he deceives me. And deceive me as he will, he can never bring it about that I am nothing so long as I shall think that I am something." (P 133b)
4. Descartes speaks more specifically of a particular (albeit powerful) ground of doubt he is concerned with, namely the possibility of an "evil genius," but it seems to me his argument actually is intended to, and does, eliminate not just that one ground of doubt, but also the deceptive senses, insanity, dreaming and all other possible grounds of doubt for the belief.
5. Actually substitution is valid only for so-called "extensional" contexts, but I won't get into that here.
6. Thanks to John Perry of Stanford University for that analysis of "ground of doubt."