Descartes’ aim is to build a good foundation for knowledge by rejecting all the false beliefs he might have. He does this by applying a general method: anything which is not certain should be rejected. (One cannot simply inspect beliefs for falsity: to believe is to believe to be true. So the alternative would be the piecemeal re-forming of beliefs on the basis of evidence in each case: an impossibly lengthy task.)
It may well be that Descartes thinks that knowledge is certain (and Cartesians have typically assumed that) so if we do not think that, his method may worry us. It will also get rid of any bits of knowledge which are not (quite) certain. But on the other hand: better safe than sorry. It will ensure that nothing that remains is not knowledge. (That is, unless you follow Wittgenstein’s idea that no knowledge is certain. See later.)
The methods of generating doubt, and hence for rejecting forms of knowledge as whole types, concern:
the unreliability of the senses,
dreaming and
the evil daemon.
In class it was suggested that perhaps one's senses never deceive. All that happens is the wrong interpretation is placed on their deliverances. One counter-worry, though, is that if the senses deliver content (if they represent the world to be in some way or any way) then such content can surely be wrong. It would be rash to assume that the reason they never deceived was because they were very good. So the counterpoint to the counter-worry is the claim that the senses do not deceive because they do not tell us anything: they are silent. For an expression of this thought see J.L. Austin’s Sense and Sensibilia and Charles Travis' very difficult paper ‘Silence of the senses’.
But even ignoring that idea, the first point does not seem to provide a general argument for the unreliability of the senses since the problem is identified by comparing across the senses (the stick looks bent but feels straight). So it does not seem to be an argument for general scepticism, just fallibilism: any of our judgements may be wrong but not all of them together. (Cf any pupil may be above average height but not all of them.)
The latter two methods – and hence Cartesian scepticism – threaten our grasp on the external world as a whole, opening up a gap between it and what we experience. The sceptical argument of these two works by describing a ‘ringer’ for our pre-philosophical view: an alternative that we cannot distinguish from that pre-philosophical view. For all we know, it might be true.
(A ringer is a horse substituted for another of similar appearance in order to defraud the bookies. This word originated in the US horse-racing fraternity at the end of the 19th century)
But if that is the case, then we cannot know that it is not true and thus, goes the argument, we cannot know any of the empirical facts we take ourselves to know about the external world which are incompatible with it.
Note that the ringer concerns the external world. So the resulting scepticism is limited to that. It does not, for example, appear to threaten a priori truths such as mathematical truths. (It is hard to come up with a ringer that would run counter to our mathematical beliefs without us spotting it.)
This reflects the ground rules for thinking about scepticism. Especially because scepticism is unbelievable, the sceptic owes us an argument for why we cannot, after all, have the knowledge we think we have, pre-philosophically and naturally. Unless there is an argument for scepticism, nothing speaks in its favour. The argument based on a ringer is just such an argument. Once it is in play, it looks impossible to stop.
Note also that there is another source of radical scepticism: the Agrippan Trilemma. But we won't focus on this.