More moderately: I think, therefore I am isn’t the best translation of Descartes’s famous pronouncement cogito, ergo sum.
I’m thinking, therefore I am is better than I think, therefore I am, but it’s still not right.
The reason I’m thinking is better than I think is as follows: it’s only because Descartes is actually thinking at that moment, and not just because he’s something that is capable of thinking, that he can be certain at that moment that he exists.
But I’m thinking, therefore I am is still not right. This is because Descartes doesn’t mean what we mean by ‘think’. He uses the Latin word ‘cogito’ and the French word ‘penser’ to mean any sort of conscious experience; not just what we today call thinking. Pain is thinking, given Descartes’s use of the term ‘think’. So is having an itch, as the Descartes scholar Gary Hatfield has pointed out. [1] I’m in pain, therefore I am (exist) is as good as I’m thinking, therefore I am (exist).
Here are a few quotations from Descartes that confirm his wide use of the word ‘think’
“Thinking. I use this term to include everything that exists within us in such a way that we are immediately aware (conscius) of it. Thus all the operations of the will, the intellect, the imagination, and the sense are thoughts” [2]
“Understanding, willing, imagining, having sensory perceptions … all fall under the common concept of thinking or perception or consciousness” [3]
“By the term ‘thinking’ I understand everything which we are aware of (conscius) as happening within us, insofar as we have awareness (conscientia) of it. Hence, thinking is to be identified here not merely with understanding, willing and imagining, but also with sensory awareness”, [4]
including awareness of hunger, thirst, pain, [5] and all emotions or passions, which are ‘confused thoughts’. [6]
So the best translation of cogito, ergo sum is
I’m conscious, therefore I am (exist)
or
I’m conscious right now, therefore I am (exist).
2
It’s true that the conscious experience Descartes has when he thinks his famous thought is a thought in our narrower sense of the word as well as in Descartes’s broader sense; it isn’t a pain or an itch. It’s also true that I’m in pain is itself a thought in our narrower sense of the word, not a pain. So Descartes would have been thinking in the narrower sense if he’d thought I’m in pain. But I’m in pain would have worked just as well as I’m thinking to establish his point. He needn’t have been thinking that he was thinking, when he thought I’m in pain, as well as thinking that he was in pain, in order to establish his point.
For these reaons it seems to me that “I’m thinking, therefore I exist” isn’t just an inadequate translation of cogito ergo sum, given what ‘think’ means in present-day English. It’s wrong. It’s wrong even though Descartes thought that all you’d be able to do, if your mind was somehow separated from your body was think in the narrower sense of the word. [7], [8]
3
The use of ‘think’ in Descartes’s broad sense to mean any kind of conscious experience is extremely widespread in philosophy after his time. This has probably caused a lot of misunderstanding. As late as 1890, William James explicitly states that he is going to use ‘think’ in Descartes’s way—“I use the word thinking … for every form of consciousness indiscriminately” [9], and the broad use survives well into the twentieth century. Eddington uses it in this way in 1928, when he’s talking about those who accept that consciousness is a matter of physical brain activity but think that consciousness is not part of the basic nature of matter. “It seems rather silly”, he says, to prefer to attach … thought [i.e. consciousness] … to something of a so-called ‘concrete’ nature inconsistent with thought [i.e. the brain conceived of as made of essentially non-conscious matter], and then to wonder where the thought comes from”.[10] It seems silly, in other words, not to endorse some species of ‘panpsychism’.
notes
[1] Gary Hatfield (2011) ‘Transparency of Mind: The Contributions of Descartes, Leibniz, and Berkeley to the Genesis of the Modern Subject’, in H. Busche (ed.), Departure for Modern Europe: A Handbook of Early Modern Philosophy (1400-1700) (Felix Meiner Verlag), pp. 361–375, p. 372.
[2] Descartes (1641) Second Set of Replies AT7.160, C2.113. ‘AT’ refers to the Adam and Tannery edition of Descartes’s works, Oeuvres de Descartes (Paris: Cerf, 1897–1910). ‘C’ refers to The Philosophical Writings of Descartes, three volumes, translated by John Cottingham, Robert Stoothoff, Dugald Murdoch, and Anthony Kenny (Cambridge: Cambridge University Press, 1985–1991).
[3] Descartes (1641) Third Set of Replies AT7.176, C2.124.
[4] Descartes (1644) Principles of Philosophy §1.9 AT8A.7, C1.195.
[5] Descartes (1641) Sixth Meditation AT7.81, C2.56. ‘Pain exists only in the understanding’ (‘la douleur n’est que dans l’entendement’) AT3.85.
[6] Descartes (1644) Principles of Philosophy §4.191 8A.317, C1.281.
[7] He thought that this separation was possible, at least in principle, because he thought of the mind as something non-material.
[8] There are a few places where he suggests that you might be able to do a bit more than think in the narrower sense of the word if your mind was separated from your body.
[9] William James (1890/1981) The Principles of Psychology (Cambridge, MA: Harvard University Press), p. 219–220.
[10] Arthur Eddington (1928) The Nature of the Physical World (New York: Macmillan), p. 259.


The main problem with obsessing too much over this is that Descartes never says it in Meditations. It does come up in Objections and Replies, but the fact that it is not in Meditations shows immediately that it is not what he considered to be a central premise.
In fact, what it really is is a (tacit or explicit) premise of a reductio ad absurdum argument to the simple conclusion "sum". And the important thing about "sum" is that it is the very first proposition that Descartes initially believed that survives his skeptical test: he shows by reductio that he could not falsely believe "sum", whenever he believes it, although he could falsely believe "I am awake" or "There is a fire in the fireplace".
(note: Descartes does not arrive at "Sum" by first establishing "Cogito" and then inferring "Sum" by Modus Ponens. If he did, then "Cogito" not "Sum" would be the first proposition to escape the skeptical onslaught. The first established proposition is "Sum", established from zero premises by reductio.)
As far as its role in the reducio, "cogito" could certainly be replaced by "credo" (I believe), which would be a narrower category of mental act. All he needs is something that he must do n order that he believe that he exists. The argument is that he must exist to do that thing, and hence he could not falsely believe he exists: that yields a contradiction.
One main mistake, beside thinking that specifically "Cogito ergo sum" plays a central role in the Meditations, is the belief that just because of the "Cogito" bit Descartes jumps to the conclusion that thinking—rather than other activities—are essential to his nature or existence. But that's plainly false: having established that he is, he then systematically goes about trying to figure our what he can be sure he is. And the first thing he can be sure he is capable of doing is thinking. But that does not mean he needs to be thinking to exist, much less that thinking exhausts his essential nature. He does, eventually, come to that conclusion, but via some rather detailed argumentation.
There was also Turing’s “polite convention that everyone thinks,” which he framed as anti-solipsism...