descartes' statement cogito ergo sum is just a tiny piece of this long history... the 3 words themselves aren't that important.
It's true that it these words aren't all of Descartes philosophy, what was important to him was to find a firm base, something on which you can rely on being true, because he reasoned without a firm base all reasoning is useless and anything that ignores this 'basic' assumption is not worth thinking on. Descartes also believe in intentionality, that all thoughts have object (but I can also be the object of thought) – another thing that modern philosophy shows us isn’t quite true.
Emma_85: Was Discours de la Méthode insufficient proof of Descartes’ own existence? (Why is his use of the first person a problem for you?)
We can't be sure that what is around us is real if we go about it as Descartes did 'de omnibus dubitandum', what we can be sure of is that these thoughts or impressions we have are real, not the objects are real, we can't prove that, but these impressions of them that we have in our brains are real. The table in front of you for example probably exists, but you can't prove it, you can't even tell me exactly what the table is, all you know of it is that at the moment in this light and with combined with your personal experiences what your impression of it is. The table is three dimensional in your mind, because your brain leaves you no option, it only lets you experience things three dimensionally, but that is no proof that the table really is three dimensional. But you can say that your impression of it is three dimensional, so it’s the impression you can say something about with certainty.
We now know that the thoughts exist, but why should be now say that an I too exists? Our impression we have of ourselves... I suppose you could say that exists, what ever that might be, but we can’t say that a consistent I exists. The I was one of the main things in western philosophy, but it’s just not something that exists.
Nietzsche wrote this about Descartes philosophy:
“Wenn ich den Vorgang zerlege, der in dem Satz „ich denke“ ausgedrückt ist, so bekomme ich eine Reihe von verwegenen Behauptungen, deren Begründung schwer, vielleicht unmöglich ist, - zum Beispiel, dass ich es bin, der denkt, dass überhaupt ein Etwas es sein muss, das denkt, dass Denken eine Thätigkeit und eine Wirkung seitens eines Wesens ist, welches als Ursache gedacht wird, dass es ein „Ich“ giebt, endlich, dass es bereits fest steht, was mit Denken zu bezeichnen ist, - dass ich weiss, was Denken ist.“
urgh... ok, my a bit shortened translation:
“When I take apart the sentence ‘I think’ I can find quite a few claims, that are hard to prove if not impossible – for example, that it’s me, who thinks, that there even has to be something that thinks it, that thinking is an action and an effect of a being, which you think of as the cause, that an ‘I’ exist, in the end, that it’s already certain what to call thought – that I know what thought is.”
He goes on to say that your perception of yourselves as an I is also a bit flawed. You should read up some Freud, he goes into great detail to prove that ‘I’ is made up of loads of different parts, and he tries to explain why we still think of ourselves as one being.