Podwójna negacja w B 2 poematu Parmenidesa


  • Piotr Błaszczyk
  • Kazimierz Mrówka


Parmenides’ poem, Euclid, Elements, Diogenes Laertius, Stoics, negation, double negation, hypernegation, privation, denial


Double negation in B2 of Parmenides’ poem: In our article we focus on the analysis of the structure of double negation in the poem of Parmenides, paying attention to the fragment B 2. The starting point of the analysis is submitted to the classification of varieties of negation contained in Diogenes Laertius (VII.69-70): negation, denial, privation and double negation. We write an example of double negation given by Diogenes as: “Not (is not a day) ↔ it is a day”. In terms of the poetic expression the law of double negation serves to strengthen the goddess’ speech. However, in the context of Parmenides’ ontology, the law of double negation serves as an affirmation of “is”. Our goal is to give a detailed analysis of the structure of double negation. In the next step we introduce Euclid’s proofs by contradiction. We show that all four forms of negation indicated by Diogenes occur in the Elements and there is a richer set of the linguistic forms used as expression of negation, including the double negation. 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, a double negation 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 not like that (…. is not around …) ↔ is around” (Elements VI.26); and in Parmenides: “is ↔ not (is not to be)” (B 2, v. 3). Contribution of the co-authors: contribution to the general conception of the paper (K.M. 50%, P.B. 50%); a part addressing Parmenides (K.M. 100%); a part addressing Euclid (P.B. 100%); translation of the analysed passages form Greek into Polish (K.M. 50% i P.B. 50%).