Homer recounts how, trapped inside a monster's cave with nothing but his wits, Ulysses once saved himself by twisting his name. Odysseus called himself Outis: "no one," "no man," or, to force a translation, "not-" or "non-one." The ploy was a success. He blinded his barbaric host and eluded him, and in doing so became anonymous, at least for a while, even as he bore a name. This act illustrates a fundamental rule of language. Every time the particle "non-" is attached to a word, a single event in speech may be discerned: a term is denied, and its denotations are suppressed. In that refusal, a realm of meaning is disclosed: one that has no positive designation, although it is delimited. To exhaust this undefined expanse, one would need to traverse the entire domain of signification that a given expression implicitly excludes. Perhaps a god could do it. But in the non-man's cave, as at the hero's telling, no god is present. The thinkers who came after Odysseus did not forget the lesson that he taught. From Aristotle and his commentators in Greek, Arabic, Latin, and more modern languages, from the masters of the medieval schools and their early modern successors to Kant, Schelling, Hegel and those who came after them, philosophers have been drawn to the possibility that the seafarer laid bare. This book, then, reconstructs the adventures of a particle in philosophy. Yet its aims are not solely historical. It also seeks to show how, in its equivocations, a possibility of grammar can be an incitement to thinking. Speaking without being aware of the rules by which we speak, reasoning in our mother tongues without reflecting on the logic and illogic that they imply, we can draw on a faculty that is obscure to us, without examining it as such. 0.