Abstract
In the elenchus of Meno, Socrates employs simultaneous algorithmic and abductive visual model-based reasoning. Even though the algorithmic method would quickly provide the answer, Socrates’ purpose is to make the slave boy recollect the Form of Diagonal. Recollection itself is abductive discovery and hypothesis generation. Contrary to standard interpretation true opinion rather than knowledge is recollected. For knowledge, a tether, an account or justification is required that cannot be recollected. Rather it involves abduction–deduction–induction chains of reasoning. The algorithm method is also deficient because whereas the squaring algorithm is easily grasped and employed by the slave boy, the inverse square rooting algorithm is not available to him and would be extremely difficult for him to grasp for he has not been educated in mathematics. The visual abductive model which involves counting as well as seeing is hence essential for the boy to acquire knowledge of a simple geometric proposition.
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Notes
- 1.
Some of the words of Shelley’s poem ‘To a Skylark’ [26] have been changed, the spirit is maintained.
- 2.
This diagram is obviously drawn by Socrates but is not shown in the dialogue, but only the square at the next stage with the bisectors is shown.
- 3.
Like the very fist square this square is not drawn by itself by Socrates in the dialogue but the completed square with the square of side three also displayed in it drawn as a composite.
- 4.
Accessed from [16, p. 218].
- 5.
Accessed from [16, p. 207].
- 6.
Accessed from [16, p. 199].
- 7.
Keith Lehrer and Thomas Paxson Jr. take ‘S is completely justified in believing that h’ to be one of the necessary conditions of knowing [11, p. 225].
- 8.
Again, the words from the last verse of Shelley’s ‘To a Skylark’ have been changed. [26].
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Jetli, P. (2014). Abduction and Model Based Reasoning in Plato’s Meno . In: Magnani, L. (eds) Model-Based Reasoning in Science and Technology. Studies in Applied Philosophy, Epistemology and Rational Ethics, vol 8. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37428-9_13
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