Abstract: Wittgenstein’s Tractatus has always been and remains a puzzle and that from its first page onwards. According to its initial assertions, the totality of facts constitutes the world and the totality of states of affairs defines the space of logical possibilities. But what are facts? What are possible states of affairs? And why do we need to consider their totality? Frege and Russell were the first to grapple with these interpretational questions. The ever-growing secondary literature on the Tractatus shows how easy it is to become absorbed in its hermeneutics. More important, however, is the question what substantively philosophical lessons we can extract from Wittgenstein’s words. There are, it turns out, at least, three of them. The first is, that the concept of fact, on which Russell and the Wittgenstein of the Tractatus relied so much, is philosophically brittle and that we must turn our attention, instead, to the broader notion of the factuality of the world. The second lesson is that we can and must think about the world in both factual and modal terms but that in doing so we must treat the idea of possibility, not that of necessity, as primary and we must conceive of possibilities as merely virtual, not as factual. The third is that we must consider the world as a whole, if we are to make sense of logic, science, and ethics.
