RUSSELL, INFINITY, AND THE TRISTRAM SHANDY PARADOX by Shandon Guthrie
INTRODUCTION Mathematicians have puzzled for centuries what precisely we mean when we refer to the concept of infinity . Some have suggested that infinity is merely something that exists in the mind. Yet others maintain that infinity possesses some ontological status in the real world. In an attempt to demonstrate the difference between the reality of an infinite and the idea of an infinite, Aristotle had suggested the terms actual infinite (the completed whole value of infinity) and potential infinite (susceptible to infinite addition). Analytic philosopher Bertrand Russell believed that an actual infinite could be achieved as long as the counter possessed an actually infinite number of years to do it. In the example given in Sterne's novel, we have the example of Tristram Shandy. Sterne writes about Tristram Shandy as an individual committed to writing an autobiography. However, he is so slow that it takes him one year in order to complete only one day. This means that the most recent event that could be recorded is the day that occurred one year ago. As Shandy writes an additional day, it takes him an additional year to complete the events of that day. Russell uses this example and believes that an actual infinite can be achieved through successive addition only if Shandy has an infinite number of days to complete it.
RUSSELL'S ASSESSMENT OF THE TRISTRAM SHANDY PARADOX Bertrand Russell (1872-1970) suspects that the Tristram Shandy paradox can be solved. For Russell, it is the individual who possesses an infinite number of days. Of course mortal individuals possess merely a finite number of days. According to Russell, this is the key in solving the apparent problem. For a precise view of the problem, I will show the paradox numerically. The paradox posits an autobiographer who writes on every day passed. Since it takes Shandy one year (=365 days) to complete one day, then in terms of a one-to-one correspondence it would appear to be futile on a finite level: