Author:
Wade A. Tisthammer
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Date Posted: 01/ 9/04 10:52pm
In reply to:
Ben
's message, "Simply resolved" on 01/ 9/04 9:15pm
>The problem is very simple. You're treating infinity
>like a finite concept. In other words, you're saying
>the word "infinity," but then you're saying x and y
>are equal because they're both infinite.
Not exactly. I am saying that given an infinite number of years and an infinite number of days, we have a one-to-one correspondence, i.e. for every day that has passed there exists a different day that has passed and vice versa (year 1 and day 1, year 2 and day 2, year 3 and day 3 etc.). If you think this correspondence is incorrect, please provide a day/year that doesn't have one to "match up" with.
>X and y (I'm
>using these instead of your years and days) cannot, of
>course, be equal, since the very idea of years and
>days involves their being very different amounts of
>time.
The quantity of days and years are both infinite. This logically and necessarily follows from an infinite past.
>Infinity cannot be defined as a particular
>number, which is what you're trying to do with it.
There are number of problems with this criticism. First, which premise are you attacking? Merely saying "infinity cannot be defined as a particular number" (even assuming that is what I am doing) doesn't refute premise 1 (the one-to-one corresondence) or premise 2.
>Another problem is this idea of "existing outside
>time," which makes no sense at all.
It may be strange but it is logically possible. It may indeed be physically possible, but the outside agency could be atemporally timeless. Strange? Yes. Logically impossible? No. Besides, it seems to be the only thing that can account for the facts (e.g. a finite past).
>So your basic problems are that
>
>(a) you're creating a paradox that isn't there, and
>(b) you're misunderstanding the nature of time.
Saying the paradox isn't there doesn't make it go away. Your criticisms are much to vague to be of much use here. They don't clearly refute any premise, for instance.
Let's recap. Given an infinite past and Shandy's story:
- There is a one-to-one correspondence between years passed and days passed.
- 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.
To deny the conclusion you have to reject at least one of the premises. On what grounds do you reject, say, premise 1? Claiming that I'm treating infinity like a number doesn't change the fact that there would indeed be an infinite number of years and an infinite number of days, (if the past were infinite) for instance. Nor does claiming that a paradox isn't there change the fact that there is a one-to-one correspondence between years passed and days passed, nor does it alter the story of Tristram Shandy writing about a passed day in each year and thus (given the two premises) finishing his autobiography.
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