# 代写数学作业范文：Analysis on Tristram Shandy's Paradox

According to an Encyclopedia entry on NationMaster.com (2009) it is generally considered that the publications of Laurence Sterne’s The Life and Opinion of Tristram Shandy, Gentleman had a dominant effect on literature of that time. Like his contemporary writers, Sterne debated publicly upon the boundary between literature and philosophy, that’s why his book is filled with allusions and references to philosophers, critics and writers of the 17th and 18th centuries namely: Pope, Locke, and Swift. It seems that those leading thinkers influenced Sterne’s The Life and Opinion of Tristram Shandy, Gentleman immensely. For instance, sagacious “Locke’s Essay Concerning Human Understanding (1690) contributed ideas and frameworks that Sterne explored throughout his novel, thus showing his engagement with the science and philosophy of his day:

Pray, Sir, in all the reading which you have ever read, did you ever read such a book as Locke’s Essay upon the Human Understanding? –Don’t answer me rashly–because many, I know, quote the book, who have not read it–and many have read it who understand it not:–If either of these is your case, as I write to instruct, I will tell you in three words what the book is.– It is a history.–A history! of who? what? where? when? Don’t hurry yourself–It is a history-book, Sir, (which may possibly recommend it to the world) of what passes in a man’s own mind; and if you will say so much of the book, and no more, believe me, you will cut no contemptible figure in a metaphysick circle. (Tristram Shandy, ch. 1 XXVII, p. 40)

请问，先生，在您所读过的所有书中，您有没有读过像洛克的《人类理解论》这样的书?不要轻率地回答我——因为我知道，有许多人引用这本书，他们没有读过——也有许多人读过但不懂它:——如果你有上述情况，我写信告诉你，我会用三个字告诉你这本书是什么。这是历史。——历史!是谁?什么?在哪里?什么时候?别着急——这是一本关于一个人内心想法的历史书，先生(它可能会向世人推荐它);如果你对这本书只说这么多，别再说了，相信我，你就不会在形而上学的圈子里留下可鄙的形象。(尚迪，第一章二十七节，第40页)

Many people believe that Sterne’s novelThe Life and Opinion of Tristram Shandy, Gentleman differs drastically from the contemporary literature of both Defoe and Richardson by his methods of narrative construction and exploration of the external world. Tristram Shandy is presented in the very act of creation and change by rejecting realism, but examining inner states of consciousness. In addition, what sets Tristram Shandy apart from its contemporary fiction is the use of language.

许多人认为，斯特恩的小说《绅士》在叙事建构和对外部世界的探索方面，与笛福和理查森的当代文学有很大的不同。特利斯特瑞姆·尚蒂通过拒绝现实主义而审视意识的内在状态，呈现在创造和变化的过程中。此外，《特利斯特瑞姆·申蒂》与当代小说的不同之处在于语言的运用。

It appears to me that this novel is an example of “process writing to the moment” where time is tied to and belongs to the protagonist. That kind of process writing in Lawrence Sterne’s novel, where the persona of author is trying desperately to write his autobiography, leads to one of the time paradoxes. It takes Tristram Shandy one year to record the events of a single day of his life. Tristram laments that, at this rate, he will never finish.

I am this month one whole year older than I was this time twelve-month; and having got, as you perceive, almost into the middle of the fourth volume–and no farther than to my first day’s day–‘tis demonstrative that I have three hundred and sixty-four more days to write just now, than when I first set out; so that instead of advancing, as a common writer, in my work with what I have been doing at it–on the contrary, I am just thrown so many volumes back–was every day of my life to be as busy as this–And why not?–and the transactions and opinions of it to take up as much description–And for what reason should they be cut short? at this rate I should just live 364 times faster than I should write–It must follow, an’ please your worships, that the more I write, the more I shall have to write–and consequently, the more your worships read, the more your worships will have to read” (Tristram Shandy, ch. 2 XVLIII, p. 126)

我这个月比我去年这个时候大了整整一岁十二个月;如你所见，我已经差不多读到第四卷的一半了，而且还不到我入职的第一天，这说明我现在可以写的时间，比我刚出书时多了三百六十四天。作为一个普通的作家，在我的工作中，我非但没有前进，反而扔了那么多的书回去——我的生活每天都这么忙碌——为什么不呢?还有关于它的交易和看法，要尽可能多地加以描述，为什么要把它们缩短呢?以这种速度我应该比我应该写必须遵循活快364倍,一个“请你的崇拜,我写的越多,我越要编写,因此,崇拜你读得越多,就越崇拜必须阅读”(崔斯特瑞姆姗蒂,ch。2 XVLIII, p . 126)

In order to link Tristram Shandy’s writing process with time paradoxes, I will briefly outline the background to Bertrand Russell’s theory. In his book The Principles of Mathematics,chapter XLIII on the philosophy of the infinite his analysis consists of the inquiry “whether any contradiction can be found in the notion of infinite.” In this specific chapter Russell’s crucial points are focused on the semantical and set-theoretical paradoxes or “antinomies” as he calls them. The twentieth century philosopher, Bertrand Russell claimed that if Tristram Shandy were immortal he would be able to finish his autobiography. Russell’s assertion that Tristram would be able to complete this seemingly impossible task is the source of the Tristram Shandy paradox. And thus Russell concludes:

为了将尚蒂的写作过程与时间悖论联系起来，我将简要概述伯特兰·罗素理论的背景。在他的《数学原理》，关于无限哲学的第XLIII章中，他的分析包括了“在无限的概念中是否存在矛盾”这个问题。在这一章中，罗素的关键观点集中在语义和集合理论的悖论上，或如他所说的“二律背反”。二十世纪的哲学家伯特兰·罗素声称，如果特利斯特拉姆·尚蒂是不朽的，他就可以完成他的自传。罗素断言崔斯特瑞姆能够完成这个看似不可能的任务，这就是崔斯特瑞姆·尚蒂悖论的来源。因此罗素总结道:

Tristram Shandy, as we know, took two years writing the history of the first two days of his life, and lamented that, at this rate, material would accumulate faster than he could deal with it, so that he could never come to an end. Now I maintain that, if he had lived for ever, and not wearied of his task, then, even if his life had continued as eventfully as it began, no part of his biography would have remained unwritten. This paradox, which, as I shall show, is strictly correlative to the Achilles, may be called for convenience the Tristram Shandy. (Russell, p. 358)

我们都知道，特利斯特拉姆·申蒂花了两年时间写了他生命最初两天的历史，他悲叹道，以这样的速度，材料的积累速度会超过他的处理能力，所以他永远也写不完。现在我认为，如果他永远活着，不厌倦他的任务，那么，即使他的生活像开始时一样充满了事件，他的传记也不会没有写完。这个悖论，正如我将要说明的，是与阿喀琉斯理论密切相关的，为了方便起见，可以称之为特里斯特拉姆·尚蒂。(Russell, p . 358)

Russell’s theory consists of two powerful components in the Tristram Shandy paradox—the number of days that Tristram lives and the number of days required writing about those days. The sum of those two quantities will logically give us the number of days Tristram needs to complete his autobiography. Assuming that Tristram were indeed immortal, then the number of days in his life would be infinite. If that were the case, the second quantity, the number of days it takes him to write about his life, would also be infinite as well as the sum of those two quantities. Thus we can conclude that, Tristram needs an infinite number of days to finish his autobiography. Given he were immortal, he would have an infinite number of days in which to write. Therefore, the key aspect of Russell’s argument is the capability of an immortal Tristram Shandy finishing his autobiography, since the number of days in his life is equivalent to the number of days required to write about his life as they are both infinite.

As far as Russell’s argument is concerned, it is not totally accepted. Many of his critics contend that Tristram Shandy could not possibly finish his autobiography – even if he were immortal. Again, assuming that it takes Tristram one year to record the events of one day of his life, then each day that Tristram lives adds a year to the time needed to complete his task, thus causing him to fall another year behind with each passing day. As a result, in this situation the amount of time needed for Tristram to write his autobiography is increasing faster than the amount of time he actually has in which to write. It would simply cause him to fall infinitely far behind. Hence, according to critics of Russell’s argument the immortality would not allow the protagonist, Tristram, to complete his task.

I strongly believe that both arguments outlined above are consistent as well as logically valid due to the case of the Tristram Shandy paradox. Nevertheless bearing in mind the previous points it could be said that the paradox discovered by Bertrand Russell in 1901 suggested that actual infinity was not an issue to dismiss due to the uncertain nature of infinity. I suppose that Tristram Shandy’s paradox emphasizes the basic problem in getting to grips with infinity which has always been a remarkable enchantment for great philosophers and writers throughout history in its notion of unending space and distance, God and eternity, time and duration.

我强烈相信，由于特利斯特瑞姆·尚蒂悖论，上述两个论点都是一致的，在逻辑上也是有效的。然而，记住前面的观点，可以这样说，伯特兰·罗素在1901年发现的悖论表明，由于无限的不确定性，实际的无限并不是一个可以忽略的问题。我认为，特利斯特拉姆·尚蒂的悖论强调的是，如何把握无限的基本问题。无限的概念，无限的空间和距离，无限的上帝和永恒，无限的时间和持续时间，在整个历史上，对于伟大的哲学家和作家来说，都是一种非凡的魅力。

“To understand what time is aright, without which we never can comprehend infinity, insomuch as one is a portion of the other–we ought seriously to sit down and consider what idea it is we have of duration, so as to give a satisfactory account how we came by it. –What is that to any body? quoth my uncle Toby. (Vide Locke.)” (Tristram Shandy, ch. 2 XI, p. 84)

It is necessary to note that Aristotle, the ancient Greek philosopher, provided a main key by introducing the terms actual infinite and potential infinite in an attempt to distinguish between the two. He strongly believed that the completed or actual infinite could not exist. While on the other hand, potential infinite might be represented as a manifest in nature. There has been debate as to whether infinity is a reality or an idea. Rucker in his chapter 1 on Infinity helps us in characterizing it as follows “Aristotle would say that the set of natural numbers is potentially infinite, since there is no largest natural number, but he would deny that the set is actually infinite, since it does not exist as one finished thing.”(p. 3) Later on Rucker ends up suggesting that Aristotle’s belief is a “doubtful distinction” agreeing with Cantor’s opinion that “…in truth the potentially infinite has only a borrowed reality, insofar as a potentially infinite concept always points towards a logically prior actually infinite concept whose existence it depends on.”(p. 3) In other words an actual infinite is not like a potential one which is growing to the infinity as a limit, although giving a collection which is finite in time at every point.

If this is the case that potential infinite is growing to the infinite limit then I do believe in its existence. But as far as completed infinite is concerned, my supposition will be negative. I oppose to the fact that actual infinite exists. The concept of actual infinite seems to me as an idea or a succession of ideas in our mind while the notion of potential infinite is represented by the future. Granted that Tristram Shandy wrote one day of his autobiography for 365 days then in general what this will indicate is the sum of the two equivalents which would be constantly finite but increasing to the infinity as a limit. Thus I assume that a profound analysis of the Tristram Shandy’s paradox explained by Russell proves my suggestion that the narrator, Tristram Shandy, would never reach the completed or actual infinite. Hence he would never finish his autobiography.

如果是这样，无限潜能增长到无限极限，那么我相信它的存在。但就完全无限而言，我的假设是否定的。我反对真正的无限存在这一事实。"实际无限"的概念在我看来是一个概念，或者是我们头脑中一连串的概念，而"潜在无限"的概念则是由未来所代表的。假设特里斯特拉姆·珊迪自传的一天写了365天，那么总的来说，这将表明两个等量的和，它们是不断有限的，但作为一个极限增加到无穷大。因此，我假设罗素对尚蒂的悖论的深刻分析证明了我的观点，即叙述者尚蒂永远不会达到完全的或实际的无限。因此，他的自传永远也写不完。

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