I have heard that Descartes' "cogito ergo sum," while intuitively compelling, is actually a logically flawed argument. Can someone explain how/why it is logically flawed? I have heard the argument that anything that has any properties at all has the property of existence automatically, so existence is not a substantive property (have I put that correctly?). Even if that is true, why should it matter so as to make the cogito argument flawed? And are there any other, perhaps better logical arguments against Descartes' proposition?

Descartes' cogito is perhaps the best known argument in the history of philosophy and one of the most discussed. Criticisms are many, even in Descartes' times (Gassendi replied to him by saying that "ambulo ergo sum" is as good an inference as "cogito ergo sum" - which is in line with the objection you mention in your question). It is even unclear whether what Descartes had in mind was to draw a logical inference: he says that the conclusion that I exist from the fact that I'm thinking is a self-evident perception of my state of being, an intuition that I have more than a logical deduced thought. A possible objection is that the method of doubting that underlines the whole argument presupposes a being who doubts, that is, presupposes the conclusion it apparently allows to draw. A very influential treatment of Descartes' argument is the one put forward by the philosopher Jaakko Hintikka in a 1962 paper: Cogito ergo sum: inference or performance? (Philosophical Review, vol. 7). ...