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Saturday, May 10, 11:38:19pm [ Login ] [ Main index ] [ Post a new message ] [ Search | Check update time | Archives: 1, 2, 3, 4, 5, [6], 7, 8, 9, 10 ]
Subject: Proof against an infinite past?


Author:
Wade A. Tisthammer
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Date Posted: 01/ 9/04 5:47pm
 Is it? You be the judge. The essence of the argument is that an infinite past implies an absurdity and therefore cannot be correct. The implications for this paradox (if it cannot be resolved) are highly significant for the cosmological argument. If you have a finite past, some kind of outside agency that transcends time had to create the universe.

Suppose we have a man Tristram Shandy who is writing his autobiography and it takes him one year to write about one day. It seems clear that Shandy can never finish his autobiography because the number of days passed will always outrun the number of years that have gone by, at least with any finite scenario.

Before moving on something needs to be mention about Shandy being able to finish a set of days. Suppose we have three years (set 1) and three days (set 2). If Shandy writes about a different day in each year (in year 1 he writes about a day, in year 2 he writes about a different day etc.), it follows that he can record all the days in set 2. (The only way not to write about all the days in set 2 is if he was writing about days that were not that set.) The same holds true if we have 100 years and 100 days, a thousand years and a thousand days, a million years and a million days etc. In those cases there is a one-to-one correspondence between years passed and days passed, i.e. for each day that has passed there exists a different year that has passed and vice versa (there is year 1 and day 1, year 2 and day 2, year 3 and day 3 etc.). Given a one-to-one correspondence between years and days, and if Shandy writes about a day in each year, he can write about all those days. However, if Shandy wants to record all the days of his life he runs into a problem: the number of days passed will always outrun the number of years that have gone by, at least with any finite scenario. For instance, after two years of writing he records 2 days, but he is now 728 days behind.

Suppose the past is infinite and suppose Tristram Shandy has been writing from eternity past. It takes Shandy one year to record one day of his life, and every year he does so and continues to do so until he’s finished recording all the days that have passed. Additionally, Shandy never writes about a day more than once, each year he records a different day. With an infinite past, we of course have an infinite number of years and an infinite number of days. There is thus a one-to-one correspondence between years passed and days passed (for each and every day there is a year). Because we have a one-to-one correspondence between years passed and days passed, and because in each year Shandy records a different day, it logically follows that Shandy records all the days that have passed; he finishes his autobiography. But how can that be given that Shandy can only get further and further behind? Additionally, it becomes immediately clear that Tristram Shandy could not possibly have written about today yet or yesterday, given that it would take him a whole year to do so and he couldn’t have started writing about a day before the day happened. Yet with an infinite past, we have an absurdity generated; because there would be the same amount of years as days, an infinite past provides the means for Tristram Shandy to complete his autobiography. Therefore, it can be argued that an infinite past cannot exist.

Can the paradox be resolved? It seems impossible for Tristram Shandy to finish his autobiography and yet the argument regarding an infinite past says otherwise. Let’s look at the part of the argument that claims an infinite past implies Shandy being able to finish his autobiography:


  1. There is a one-to-one correspondence between years passed and days passed.
  2. In each year Tristram Shandy records a different passed day.


Therefore Tristram Shandy records all the days that have passed (follows from 1 and 2); he finishes his autobiography.

Because the above is a deductive argument, it can fail in only one of two ways. Either the argument is invalid (i.e. the conclusion does not logically follow from the premises) or at least one of the premises is incorrect. Neither avenue looks particularly promising. For instance, if the argument is invalid and Tristram Shandy didn’t write about all the days that have passed, then given the one-to-one correspondence between years passed and days passed (remember, in each year Shandy writes about a different day), Shandy would have had to write about days that never existed, but since this is not the case (he only writes about passed days) he does indeed finish his autobiography. And yet he can’t finish his autobiography because there’s no way to write about yesterday etc. One could deny the existence of the one-to-one correspondence between years passed and days passed (the first premise), but that too is ridiculous since we can easily prove otherwise given an infinite number of years and an infinite number of days (for each day that has passed there exists a different year that has passed, and vice versa). The second premise cannot be rationally denied either, since it is a given from the story. Thus, the paradox thus seems impossible to resolve.

Can you think of a way to resolve it? I cannot. Let me know what you think.
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Replies:
Subject Author Date
Simply resolvedBen01/ 9/04 9:15pm
Foggy definitionsDamoclese01/10/04 8:54am
Guess who's back (guess who's back (guess who's back))Duane02/11/04 9:39am
A Tristram Shandy argument proved invalid.Wade A. Tisthammer03/13/04 10:11pm
A Tristram Shandy argument proved invalid.Wade A. Tisthammer03/13/04 10:14pm
Your first premise actually proves an infinite past!!!Duane05/25/04 5:42am

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