Podwójna negacja w B 2 poematu Parmenidesa

In our article we focus on an analysis of the structure of double negation in the poem of Parmenides,paying attention to the fragment B 2. The starting point for the analysis is the classificationof varieties of negation contained in Diogenes Laertius (VII.69-70): negation, denial,privation and double negation. We provide an example of double negation as given by Diogenes: “Not (is not a day) it is a day”. In terms of the poetic expression the law of double negationserves to strengthen the goddess’ speech. However, in the context of Parmenides’ ontology, thelaw of double negation serves as an affirmation of “is”. Our goal is to give a detailed analysis ofthe structure of double negation. In the next step we introduce Euclid’s proofs by comparison.We show that all four forms of negation indicated by Diogenes occur in the Elements and thereis a richer set of the linguistic forms used as an expression of negation, including that of doublenegation. Finally, we show that Parmenides applies consciously the law of double negation,and the poem is the first philosophical text confirming the use of this law. In short, doublenegation can be summarized as follows: for the Stoics, in Diogenes Laertius (VII.69-70): “not(is not a day) is a day”; for Euclid: “not (is not-equal) is equal” (Elements, I.6). “is notlike that (.... is not around ...) is around” (Elements VI.26); and in Parmenides: “is not(is not to be)” (B 2, v. 3).