| Subject: Your first premise actually proves an infinite past!!! |
Author:
Duane
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Date Posted: 05/25/04 5:42am
In reply to:
Wade A. Tisthammer
's message, "Proof against an infinite past?" on 01/ 9/04 5:47pm
Wade:
Sorry to kick this dead horse. I was idly thinking the other day, and remembered this discussion - came up with another thought about what it actually proves.
I must apologize in advance, though. I haven't read through the huge list of responses, and if someone else has brought this up already, then feel free to ignore this.
O.K. - on to the post.
- There is a one-to-one correspondence
between years passed and days passed.
- In each year Tristram Shandy records a
different passed day.
If you'll allow one assumption about your argument, I think that you actually proved, rather than disproved, an infinite past.
Here it is:
The premises of this argument are true on any given day of Shandy's life.
== PROOF ==================================================
Let D be the set of all days prior to today, consisting of integer values such that each element of D corresponds to a day before today, and is equal to the number of days that must pass to reach today. (i.e., 0 is today, 1 is yesterday, 2 is the day before, etc...)
Now, let us construct D recursively. (Please excuse the verbosity - I'm too lazy to figure out how to write in the set symbols.)
-- Basis --------------------------------------
x(0)=0, x(0) is a member of D
-- Recursive step -----------------------------
x(n) is a member of D if
x(n) < f(x(n-1))
where
f(j) = (j+1)*365
Since the inequality above is true for all n > 0, D consists of all non-negative integers, and is infinite.
== END PROOF ===========================================
O.K. - so, in English, the above is, basically this:
Start with today. Number it zero. Since there is a 1 to 1 correspondence of days passed to years passed, there is at least one year prior to today.
O.K. - since a year has passed, we know there was a yesterday, so let's "travel back in time" to yesterday. *ZAPP!!!* Since we're now in "yesterday," there must be at least two years that have passed prior to "today." (Actually, one year and 364 days to be exact). Etc., etc.
Every day we "go back," we automatically add on another year. We can never "run out of days," since each one that has existed in the past corresponds to a whole year that has passed.
So we can "count back" to infinity. The first premise of your argument actually proves that there *is* an infinite past!
Let me know what you think about this.
Duane
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