Just a minor nit. Though widely believed, Descartes never wrote cogito, ergo sum. I'm not sure who came up with that, but what Descartes wrote was je pense, don

Just a minor nit. Though widely believed, Descartes never wrote cogito, ergo sum. I'm not sure who came up with that, but what Descartes wrote was je pense, donc je suis, and the meaning is subtly different even if we define "so" (donc) as "therefore." What Descartes intended was not a logical proof of existence. What he meant was, "I am, I exist, whenever I think it." There is no "therefore" or quod erat demonstrandum involved.