Author:
Wade A. Tisthammer
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Date Posted: 09/12/04 6:19pm
In reply to:
Duane
's message, "Tristam Understood" on 09/ 9/04 1:48am
>Wade:
>
>OK. I finally understand. Here's the nature of the
>paradox:
>
>These are statements provable in Cantor set theory -
>
>1) Two sets have the same cardinality (i.e., the same
>number of elements) if there exists a total,
>one-to-one and onto function mapping one set to the
>other.
>
>2) A set is countably infinite if it has the same
>cardinality of the natural numbers.
>
>Now, according to the Tristam "paradox," the following
>situation exists:
>
>The set of days is countably infinite
>
>The set of years is countably infinite
>
>Therefore, the set of days is the same size (that size
>being "countably infinite") as the set of years.
>
>These things are true. And they are weird. But the
>simple fact remains that they don't "prove" anything.
The initial argument (which I no longer hold on to) is that it would lead to the absurdity of Tristram Shandy being able to finish his autobiography. This is undisputedly absurd given the circumstances (takes him a whole year to write about one day etc.)
>The declaration of "absurdity" does not equal
>disproof. So I fail to see how the Tristam Shandy
>"paradox" says anything substantiative.
You might want to look into the current version.
- If an infinite past is metaphysically possible, then Tristram Shandy writing his autobiography for as long as time has existed should not lead to absurdities.
- If Shandy has been writing from eternity past (i.e. has been writing all along the infinite, beginningless past) he is either infinitely far behind or he finishes his autobiography at some point.
- Shandy finishing his autobiography, since it takes him a whole year to write about a day, is an absurdity and cannot possibly happen.
- Shandy being infinitely far behind means the present would never be reached (the day he wrote about last year is infinitely far away, there is no way to get from that day to the present), which is an absurdity and cannot possibly happen.
- All (both) possible options generate an absurdity, if Shandy were writing his autobiography from eternity past (2, 3, and 4).
Therefore an infinite past is not metaphysically possible (1 and 5).
The argument is valid, i.e. the conclusion logically follows from the premises. The only way to reject the conclusion is to reject at least one of the premises. So, which premise do you reject?
I did not merely "declare" them to be absurdities. I established the absurdities mathematically. Would you like me to do so again?
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