In this paper, I present a detailed analysis of Aristotle’s criticism of dichotomy in Parts of An... more In this paper, I present a detailed analysis of Aristotle’s criticism of dichotomy in Parts of Animals, A2–3 to provide a foundation for a new interpretation and understanding of the two cruxes in that text: What is Aristotle criticizing? Against whom is Aristotle directing his criticism? First, I demonstrate how Aristotle criticizes both division by a single differentia and division by multiple differentiae in one single line and in many lines. Second, in taking issue with an unidentified dichotomist, I argue that Aristotle is targeting Plato’s application of dichotomy in the Statesman and Sophist as well as Speusippus’ use of dichotomy in his division practice. After clarifying what and whom Aristotle is targeting, I conclude that Aristotle’s criticism is not only destructive but also constructive. In closing, I offer some remarks on the relationship between division and definition by explicating how Aristotle’s metaphysical concern with definition and the unity of definition influences as well as dominates his criticism of dichotomy.
In this paper, I aim to explore the structure of the exercise in the second part of the Parmenide... more In this paper, I aim to explore the structure of the exercise in the second part of the Parmenides. In analyzing the transitional section, I claim that in addition to diairesis, there is another method of division, namely, cross-division, which Porphyry terms chiasmus. On this basis, I explain how Plato uses chiasmus to divide the exercise into eight hypotheses, in which the subjects of the paired hypotheses (I-VI, II-V, III-VII, and IV-VIII) are the same and those of the nonpaired hypotheses differ. In closing, I reconstruct the universal scheme of the exercise on the basis of Plato's use of chiasmus.
In this paper, I articulate three kinds of division that Plato and Aristotle acknowledge to be pr... more In this paper, I articulate three kinds of division that Plato and Aristotle acknowledge to be proper, valid methods of division, namely, diairesis (vertical division), parallel division, and chiasmus (cross-division). I attempt to explain the relationship among the three kinds of division, namely, how they transform from one to another. Starting with Plato’s division of constitution in the Statesman, I illuminate that from ostensible diairesis emerges a parallel division, and the parallel division causes a cross-division to occur. Thus, the sixfold division of constitution is not a diairesis (as it appears to be) but rather is a 3 x 2 cross-division. Inheriting the three kinds of division from Plato, Aristotle advances the form by providing a theoretical explanation to the transformation of the three kinds of division.
In this paper, I present a detailed analysis of Aristotle’s criticism of dichotomy in Parts of An... more In this paper, I present a detailed analysis of Aristotle’s criticism of dichotomy in Parts of Animals, A2–3 to provide a foundation for a new interpretation and understanding of the two cruxes in that text: What is Aristotle criticizing? Against whom is Aristotle directing his criticism? First, I demonstrate how Aristotle criticizes both division by a single differentia and division by multiple differentiae in one single line and in many lines. Second, in taking issue with an unidentified dichotomist, I argue that Aristotle is targeting Plato’s application of dichotomy in the Statesman and Sophist as well as Speusippus’ use of dichotomy in his division practice. After clarifying what and whom Aristotle is targeting, I conclude that Aristotle’s criticism is not only destructive but also constructive. In closing, I offer some remarks on the relationship between division and definition by explicating how Aristotle’s metaphysical concern with definition and the unity of definition influences as well as dominates his criticism of dichotomy.
In this paper, I aim to explore the structure of the exercise in the second part of the Parmenide... more In this paper, I aim to explore the structure of the exercise in the second part of the Parmenides. In analyzing the transitional section, I claim that in addition to diairesis, there is another method of division, namely, cross-division, which Porphyry terms chiasmus. On this basis, I explain how Plato uses chiasmus to divide the exercise into eight hypotheses, in which the subjects of the paired hypotheses (I-VI, II-V, III-VII, and IV-VIII) are the same and those of the nonpaired hypotheses differ. In closing, I reconstruct the universal scheme of the exercise on the basis of Plato's use of chiasmus.
In this paper, I articulate three kinds of division that Plato and Aristotle acknowledge to be pr... more In this paper, I articulate three kinds of division that Plato and Aristotle acknowledge to be proper, valid methods of division, namely, diairesis (vertical division), parallel division, and chiasmus (cross-division). I attempt to explain the relationship among the three kinds of division, namely, how they transform from one to another. Starting with Plato’s division of constitution in the Statesman, I illuminate that from ostensible diairesis emerges a parallel division, and the parallel division causes a cross-division to occur. Thus, the sixfold division of constitution is not a diairesis (as it appears to be) but rather is a 3 x 2 cross-division. Inheriting the three kinds of division from Plato, Aristotle advances the form by providing a theoretical explanation to the transformation of the three kinds of division.
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