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Chapter 30: The Mathematical Model in Plato and Some Surrogates in a Jain Theory of Knowledge
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30 The Mathematical Model in Plato and Some Surrogates in a Jain Theory of Knowledge One of the generative questions in Benjamin Nelson’s late work was: What accounts for the breakthrough insights that permit the reduction of all quality to quantity, the proclaiming of a mathematical reality behind the experiential immediacies of experience and the affirmation of a homogeneous time and space throughout the universe , insights that characterize Western science? It is a question that exercise both Nelson and Joseph Needham; both consider it from an intercivilizational perspective. To put the matter in Needham’s terms: ‘‘What was it that happened in Renaissance Europe when mathematics and science joined in a combination qualitatively new and destined to transform the world?’’1 Nelson first answers these questions by examining Western orientations and institutions of the twelfth and thirteenth centuries. He shows that in a ‘‘sacro-magical if sacramentalized’’ reading of creator and cosmos ‘‘there appears a stress upon the need and ability of men to know and explain natural phenomena by the principles of natural philosophy; to offer rational justification of their acts and opinions.’’2 In the same context, Nelson speaks of a two-fold commitment to the ‘‘concrete individual person’’ and to an ‘‘objective Universal.’’ Armed with Nelson’s questions (the subject of fruitful conversations long before the appearance of the article cited) I pondered the issues of whether these factors, already nascent in the epistemic structure of Plato’s dialogues concerned with the Ideas, could not be displayed 464 against an Indian system remarkably similar in hierarchical structure and philosophic intent. Only in the light of these similarities, I thought, would the key difference—the existence of an ‘‘objective Universal’’ in one and not the other—emerge. The same aim governs both Platonic and Jain epistemologies: the overcoming of sense experience in order to attain a more adequate access to truth. But in the former structures of universalization—the ideas of number and geometric form—lead to this overcoming, while in the latter certain ad hoc extensions of sense are made to play this part. I shall not attempt to ground larger claims, such as the existence of an ongoing tradition unbroken from Plato to the twelfth century. Nelson would be the first to puncture so ominously unhistorical a claim. I attempt, rather, to bring out the difference between a system that engages the constructs of a contemporary mathematics and eventuates in an objective Universal and one that fails to do so. Both Plato and a Jain text, The Tathvārthādhigama Sūtra of Śri Umāsvāti, with the commentary of Śri Pujyapada,3 argue that the knowledge of sensibles is merely preliminary to higher forms of knowing and that these in turn culminate in a highest or ultimate form of knowledge. Furthermore, both Jain and Platonic systems concur in claiming necessity, apodicticity, and comprehensiveness or totalizing power for such knowledge. In the light of these common considerations, I argue here that a difference in what are considered possible objects of knowledge by each system accounts for the positing of differently conceived faculties of knowledge. I argue, further, that the faculties alleged to attain higher knowledge in Jain epistemology are compatible with the Jain understanding of the objects of knowledge. Thus, an internally consistent account of knowing is provided in a scheme that (1) assumes the actuality of the material world, but (2) presupposes that knowledge of the world in some sense falls short of ultimate truth, and (3) lacks mathematical paradigms for providing a means of transition between the world of ordinary experience and that of final knowledge. In order to support these claims, it is important to clarify in advance how the possible objects of knowledge are understood in each system and how the transition from lower to higher knowledge is effected . In the Platonic account, the move from lower to higher epistemological levels is achieved by conferring a unique status upon a class of objects, number and figure, which facilitates a transition between apprehension of the empirical world and the world of Ideas. When applied to practical ends, these objects are still encumbered by The Mathematical Model and Some Surrogates 465 [54.161.130.108] Project MUSE (2024-03-28 08:17 GMT) visible images, but when divested of their concrete applications, they are themselves Ideas. The assumptions of arithmetic and geometry do not themselves constitute the ultimate ground of certainty, for mathematical hypotheses, which may appear certain...