This paper revisits the learning paradox first posited by Socrates in his famous dialogue with Meno. The paradox of new knowledge has been steadily attracting the attention of educational researchers (e. g. see Bereiter 1985; Petrie 199 1; Prawat 1999). My paper briefly examines Kierkegaard's classical solution in terms of the necessity of the decisive moment, arguing that, contrary to Kierkegaard, there is no miraculous knowledge. The paper justifies this assertion by suggesting a two-fold approach towards re-solving the Socratic paradox: first, using Charles Sanders Peirce's triadic scheme and his semiotics that incorporates the logical category of abduction; and second, by extending his notion of diagrammatic reasoning and suggesting a model for a cognitive structure constructed on the complex (Gauss) plane. Peirce pointed out that his categories of Firstness, Secondness and Thirdness are the "conceptions of complexity" (Peirce CP 1. 526). The paper concludes by asserting that the problem of new knowledge debated in antiquity by Socrates and Meno can be solved by adopting the geometry of complexity as a representation of the logic of the included middle, constituting the core of triadic semiotics.
Paideia: Education in the Global Era, Volume 1 p. 207-221