Eleatic Arguments

Abstract Diogenes of Apollonia, often called ‘the last pre-Socratic’, began his book with these words: ‘It seems to me that anyone beginning any account ought to make the starting-point [or principle) indisputable (chreon einai ten archen anamphisbeteton) and the explanation simple and dignified’ (64B1 ). 1 Having no context for the fragment, and not knowing how it continued, we do not know if Diogenes went on to explain his requirement of indisputability.2 Did he mean that first principles must be either self-evident or capable of being demonstrated (and thus placed beyond dispute)? Or did he perhaps mean that the author of a theory must give whatever arguments are needed to place the first principle beyond dispute? It seems that this latter is what Diogenes meant, for he goes on, in fragments 2–5, to argue for his own first principle, air. These fragments appear in Simplicius’s commentary on Aristotle’s Physics, and Simplicius tells us that B2 appeared ‘immediately after the introduction’ (although it is not known if the introduction included more than fragment r). Fragment 2 is an argument that the first principle must be one, that ‘all the things that are, are alterations of the same thing and are the same thing’. Diogenes claims that ‘this is very clear’ (kai touto eudelon), thus apparently satisfying his criterion for indisputability laid down in B1; but he nevertheless goes on to provide an argument that purports to demonstrate that ‘all things are the same thing’. The argument is a reductio with a suppressed premiss: if each thing that is had a nature peculiar to itself (idia phusis), there would be no mixing, no benefit or harm from one thing to another, no growth for plants, no animals, or anything else.