• Is 'I think therefore I am' a tautology?
    It is, but it is a concealed tautology. To discover it we have to apply Nietzsche's critique in Beyond Good and Evil to it, and reduce all of the controversial moves. The Cogito that remains after it dodges the critique is a tautology, but is where the necessity comes from.

    The short road to that argument is to point out that Descartes quite happily, in the second meditation, points out that he is nothing more than this thinking, such that if the thinking should stop, then he would cease to exist as well. This is how he get's around the objection that it hasn't been established that the thinking belongs to him (he could just be tuned into some radio frequency). He identifies the "I" with thought, saying they are the same thing.

    He then goes on to define thought in such a way that nothing escapes its definition: thinking (in language), perceiving, feeling, willing, denying, refuting, accepting..... Basically, anything that can be taken as self-presently existing - the "given" as such. He needs to define thought in this hungry way to avoid making a conceptual determination (that could always be doubted - how do you "know" thought is such and such, and how do you know that this such and such is an instance of thought, defined thusly?), which was Nietzsche's third criticism.

    So, if there is "something" then this something is called thought. If there is thought, then there is an "I". The "I" arises via the transitive property from the simple fact of existence, showing it to be a complex tautology.