Posts Tagged ‘logic’

December 13th, 2010

Crosswise logic

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My previous post sought to humble the principle of non-contradiction, and thus the logic of consistency it defines, finding it inadequate for thinking the temporal world in which we live and breathe and have our being. Parmenides first articulated this principle, calling “equally deaf and blind” those who would not think consistently according to it, those “hordes without judgment, for whom both to be and not to be are judged the same and not the same, and the path of all is crosswise (palintropos).” Without compromise, he recognized the conflict between his principle and our world of change and diversity. Consistently, he rejected time and the logic needed to understand it. His target here was Heraclitus, who claimed that “a thing agrees in disagreement with itself; it is a crosswise harmony (palintropos harmoniē), like that of the bow and the lyre.” This post aims to explain his earlier, contradictory, but nonetheless more accurate logic.