You will notice that earlier in this essay we have emphasised that there are no self-existent finite entities. The finite essentially refers to an unbounded background. We have now arrived at the converse doctrine, namely, that infinitude in itself is meaningless and valueless. It acquires meaning and value by its embodiment of finite entities. Apart from the finite, the infinite is devoid of meaning and cannot be distinguished from non-entity. The notion of the essential relatedness of all things is the primary step in understanding how finite entities require the unbounded universe, and how the universe acquires meaning and value by reason of its embodiment. Among philosophers, Spinoza emphasised the fundamental infinitude and introduced a subordinate differentiation by finite modes. Also conversely, Leibniz emphasises the necessity of finite monads and based them upon a substream of Deisitic infinitude. Neither of them adequately emphasised the fact that infinitude is mere vacancy apart from its embodiment of finite values, and that finite entities are meaningless apart from their relationship beyond themselves. The notion of understanding requires some grasp of how the finitude of the entity in question requires infinity, and also some notion of how infinity requires finitude. This search for such understanding is the definition of philosophy. It is the reason why mathematics, which deals with finite patterns, is related to the notion of the Good and to the notion of the Bad. The great religions illustrate this doctrine. Buddhism emphasises the sheer infinity of the divine principle, and thereby its practical influence has been robbed of energetic activity. The followers of the religion have lacked impulse. The doctrinal squabbles of Christianity have been concerned with the characterization of the infinite in terms of finitude. It was impossible to conceive energy in other terms. The very notion of goodness was conceived in terms of active opposition to the power of evil, and thereby in terms of the limitation of deity. Such limitation was explicitly denied and implicitly accepted. ix The history of the science of algebra is the story of the growth of a technique for representation of finite patterns Algebra is one chapter in the large technique, which is language. But, in the main, language indicates its meanings by means of casual associations as they arise in human history. It is true that language strives to embody some aspects of those meanings in its very structure. A deep sounding word embodies the deep solemnity of grief. In fact, the art of literature, vocal or written, is to adjust the language so that it embodies what it indicates. But the larger part of what language physically presents is irrelevant to the meaning indicated. ... from Mathematics and the Good one of Whiteheads last essays c. 1940
Posted on: Thu, 20 Mar 2014 07:51:03 +0000
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