 The language of this fragment shows that Philolaus is firmly in the tradition of Presocratic philosophy. Aristotle refers to the Presocratics as the physiologoi, “writers on nature,” and it is precisely nature (physis) that is the first word of Philolaus’ book. Physis here means “nature” or “real constitution” and finds a good parallel in Heraclitus’ famous saying that “nature loves to hide” (fr. 123). Philolaus uses it universally to refer to the natures of all individual things in the world as well as the nature of the cosmos as a whole. For an alternate view see Zhmud (2018) who argues that it means “all the things that have come into being and exist.” Zhmud points out that Philolaus is the first thinker to make physis the main subject of his book. The next words show that Philolaus, like his Presocratic predecessors, regarded the natural world as a cosmos, as an order, and saw it as his central problem to explain that order. His answer to that problem, however, is quite unlike earlier answers. Earlier Presocratics had tended to explain the natural world in terms of material elements such as water or air, or groups of elements such as the earth, air, fire and water of Empedocles.  Opposites such as the hot and the cold or the rare and the dense also played a prominent role. Instead of these concrete and tangible substances Philolaus appeals to things which are unlimited, “unlimiteds,” and things which limit, “limiters.” The basic problem in understanding Philolaus’ philosophy is thus to determine what he means by limiters and unlimiteds. In the surviving fragments, he never provides a definition of these terms nor does he provide an explicit example. Nonetheless he uses them repeatedly. In Fragment 2 he argues that the basic elements of the world must logically be either all limiters, all unlimiteds or both limiters and unlimiteds. He is emphatic here and argues further in Fr. 3, evidently against some of his predecessors, that the basic elements cannot be simply unlimiteds. Since the world around us manifestly contains some things that limit, some that are unlimited and others that are both limiting and unlimited, we must suppose that the elements from which the world arose included both limiters and unlimiteds (Fr. 2). How could a limiter arise from an unlimited or an unlimited from a limiter? In Fr. 6 Philolaus argues that we cannot say anything more definite about the ultimate principles of reality (“nature in itself” and “the being of things”). We can only go so far as to say that they must have included limiters and unlimiteds in order for the world we see around us to have arisen. Beyond this description the basic principles of reality admit only of divine and not of human knowledge. Thus, it is a matter of principle that Philolaus does not identify any particular set of limiters and unlimiteds as the basic principles of the world; identification of such a set is beyond human capability. On the other hand, he clearly thinks that we can recognize limiters and unlimiteds in the world around us and repeatedly appeals to this fact. If the cosmos and everything in it is put together from limiters and unlimiteds, we ought to be able to identify some of them.