本文是数学专业的留学生作业代写范例，题目是“Analysis on Tristram Shandy's Paradox(尚蒂悖论分析)”根据国家master.com(2009)上的百科全书条目，人们普遍认为劳伦斯·斯特恩的《特利斯特瑞姆·香蒂的生活和观点》的出版，《绅士》对当时的文学产生了主导影响。就像他同时代的作家一样，斯特恩公开辩论文学和哲学之间的界限，这就是为什么他的书充满了典故和引用，哲学家，批评家和作家的17和18世纪，即:蒲柏，洛克和斯威夫特。这些主要的思想家似乎极大地影响了斯特恩的《特利斯特瑞姆·尚蒂的生平与观点》。
Tristram Shandy’s Paradox崔斯特瑞姆姗蒂悖论
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)
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.
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:
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.
“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.