Necessity of Non-Being. On Plato’s Sophist - Chiurazzi, Gaetano (Religija ir kultūra, 2013)
The main idea of this article is that there is a relation between the definition of Being as dynamis in Plato’s Sophist and the coeval discussion about the incommensurable magnitudes. This is argued by showing that some arguments Plato uses in order to affirm the unsustainability of the quantitative definition of Being (One, Many) are referring back to the argument of the decomposition of even and odd numbers, through which the irrationality of the diagonal of the square is demonstrated. As a consequence, the article tries to show that the definition of Being as dynamis is necessary in order to “save the differences”, that is, in order to prevent the one being equal to the two, as it happens, according to Plato, in the theories of the monist and pluralist schools. This logical and ontological collapse is also a consequence of the negation of the irrationality of the diagonal. Dynamis (a name by which Theaetetus called the irrational numbers), as a middle term between Being and Non-Being, that is, as a modal negation (difference), is then required in order to preserve the very possibility of every other difference.
Keywords: Plato; Sophist; incommensurable; difference; dynamis; One–Many