In any event, there is a connection between BR and Tristram Shandy....
http://bertrandrussell.org/brsbb/index.php?topic=314.5;wap2
Bertrand Russell had very much to say on this. I bring up the Tristram Shandy paradox. What of our infinite number of days? Mortal individuals posse 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:
Observed History: 1 day, 2 days, 3 days, 4 days, 5 days, . . .
Recorded History: 365 days, 730 days, 1095 days, 1460 days, 1825 days, . . .
It would seem mathematically impossible for Shandy to complete writing on all the days passed. Since each day yields an additional 365 days to write then It would seem that the longer Shandy wrote, the further behind he would get. Russell solves this mathematical problem by suggesting an actually infinite number of years in order to complete it. As a side note, the symbol often used to refer to a mathematical infinite is the Aleph Null (represented here as X0 due to HTML limitations). As one observes the following equation, it appears to suggest something not true of usual, finite numbers.
X0 + 1 = X0
The implication here is that since any number added to infinity is still infinity, then the principle that the whole is greater than the parts does not apply here. One component of the equation (X0) is quantitatively equal to the sum of both components (X0 and 1). Russell asserts that given an infinite number of years to write plus the infinite number of days obtained results in an infinite amount of time transpired. Thus, the amount of time to write if obtained would be equal to the amount of time given to write about. Therefore (d = days to write on; y = years to complete; t = time obtained),
(y x X0) + (d x X0) = X0(t)
Russell believes that when the presence of infinity is seen all at once, then the concept of infinity is something that can exist as a quantitative property (he does not mean exist in the Platonic sense).
We have seen Bertrand Russell attempt to prove the possibility of achieving an actual infinite through successive addition. Even though the Tristram Shandy paradox of the slow autobiographer was designed to show why such a successive addition is not possible, Russell believed that the solution required Shandy to have an infinite number of days to complete his task. Quentin Smith agreed with Russell's contention and suggested the notion of sets and proper subsets to prove the point. William Craig suggested that Russell had focused on the wrong issue and that the problem rested not in the necessary time to complete it but, rather, on the sufficiency of consecutive counting.
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