Deduction–Abduction–Induction Chains in Plato’s Phaedo and Parmenides

Abstract

Plato is widely considered as the methodological progenitor of philosophy by introducing the rigorous pursuit of universal definitions through endless revisions and generating intricate deductive arguments. The dialogue format is ideal for displaying intricate arguments, with sub-arguments, rebuttals, revised arguments, revised rebuttals, and so on. These arguments are considered to display the paradigm of deduction. However, examining under the surface reveals that embedded in the deductive arguments are abductions of various sorts, such as hypothesis generation and inference to the best explanation, as well as inductive reasoning through persistent examples is in the crevices of these arguments. Hence, in Lorenzo Magnani’s Abduction, Reason, and Science, Processes of Discovery and Explanation (Kluwer Academic Publishers, New York, 2001) “abduction–deduction–induction cycles” are unveiled. In the Phaedo, with its four-staged argument for the immortality of the soul, and in the Parmenides, with the dilemma of participation and the largeness regress as two objections to Plato’s theory of Forms, though the overarching arguments are deductive ones, the author finds, in the layers of their independent premises, as well as in some of the inferences in the sub-arguments, an abundance of abduction of various varieties as well as induction. Magnani’s term can be employed for hybrid “deduction–abduction–induction” chains to characterize the arguments in these two dialogues. First, a descriptive synopsis of the main arguments is presented; then a linear quasi-diagrammatic display of the arguments in the context of the entire dialogues is sketched. The conclusion is that the overarching arguments in both the dialogues may be captured as a De⇒Ab—De—In structure in which the arguments are deductive with embedded abduction–deduction–induction cycles.