| Subject: Yes, but I'm beginning to think that maybe you don't... |
Author:
Duane
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Date Posted: 09/13/04 8:21am
In reply to:
Wade A. Tisthammer
's message, "Did you?" on 09/12/04 6:19pm
Wade:
I'm responding to this post, as well as the one below.
>>You of all people should recognize that "absurdity"
>>does not equal disproof. "Absurd" means that you
>>can't understand it.
>
>No, absurd means ridiculously unreasonable,
>irrational, unsound etc.
Right - absurd means:
ridiculously unreasonable TO YOU.
irrational TO YOU.
unsound TO YOU.
You're playing a game here, and that game is mathematical logic. And you seem to be missing the instruction booklet.
You need to mathematically define "absurdity" if you want to use it to "disprove" something. You've arrived at a conclusion, that Tristam's situation is "absurd," but how does that disprove infinite time?
Oh - that's one other thing. You can't "disprove" an infinite past without "disproving" infinite TIME. So let's be clear, that you're saying that you've proven that time is finite. As a quick "proof," assume that the past is finite - that there is a "day 1." Now assume that the future is infinite. Now consider the following statement:
"Today is a day that is infinitely far from day 1."
Clearly, if time is unbounded in one direction, it is unbounded in both directions.
So, to return to our discussion of "absurdity," YOU need to define what it means for a statement to be "absurd" if you want your argument to mean anything at all. If you want to use math to "prove" or "disprove" something, you have to play by ALL the rules, not just the ones you choose. So, you MUST define "absurdity" in a logical sense, since you're making a logical argument. So let's get you started:
1) What are the conditions required for a statement to be "absurd?"
2) If a statement is "absurd," is it always false?
3) If a statement is "absurd," but not false, then what is it? "Absurdly true?"
OK - I hope you get the point of this - when you're making a logical argument, there is only TRUE and FALSE. "Absurd" is neither explicitly true nor false. If you wish to restate your argument, replacing "absurd" with "false," please feel free to do so.
But you cannot say, "because statement X is absurd, it is therefore false" without defining absurdity. Since the common usage of "absurd" means "Relating to the belief that neither human life nor the universe have any real meaning," I can only assume you don't mean THAT. Since you ARE trying to talk about the universe and human life...
Huh. Maybe you mean absurd in the sense of, "ridiculously incongruous." Well, if that's what you mean, then you'd better just say "false" instead of "absurd." If something is inconsistent, then it is false. So maybe that's what you mean.
But if you mean "absurd" in the sense of, "C'mon, guys... Can't you see how silly this is? I mean, f'real!!! Shuh! Infinitely far behind? Geez... NOOOO Way! I mean, NOOOO WAY could THAT happen! Duh!" then you'd better just give up. Because, oddly enough, if you claim to prove something, you can't depend on the fact that we'll agree with your "sensibilities." You need to mathematically prove it.
So let's go to your argument...
I said:
>>The declaration of "absurdity" does not equal
>>disproof. So I fail to see how the Tristam Shandy
>>"paradox" says anything substantiative.
You responded:
>You might want to look into the current version.
Notably, you didn't respond in any way to my statement in the "current version." Your argument is logically and mathematically impenetrable and invalid, since you toss about the term "absurdity" without mathematically or logically defining it.
At its core, your argument an argument by contradiction. Those arguments go like this:
"We assume X. Statements A, B, C, ..., etc. follow from X. If we can show that they cannot all be true, then we've disproven X."
Properly stated, your argument is as follows:
Assumptions:
"Assume that time is infinite."
(which is a sloppy, non-precise way of saying the following:)
"Assume that the set D exists, where D contains all days, and is countably infinite."
"Assume that the set Y exists, where Y contains all years, and is countably infinite."
Conclusions:
"There is a one to one correspondence from set D to set Y"
"That means that the number of days = the number of years"
None of these things are false, according to modern set theory. There's no contradiction.
I'll agree with you that the conclusion saying that there are the same number of days as there are years seems strange to me, but based on the definition of infinity, it's not false. If we start to describe weird things that happen when this is true (like Tristam finishing his book, or Tristam being infinitely far behind), I (and any mathematician) would agree that they're weird, but that doesn't make them false.
Let's look at another example of something weird, but true. about set theory:
"The set of all natural numbers has the same number of elements in it as the set of only the even natural numbers."
Huh? How can that be? The set of all even natural numbers has, as far as we can tell, HALF the number of elements that the set of ALL natural numbers. Well, that would be true for finite sets, but since the set of natural numbers AND the set of only the even natural numbers are both countably infinite, they have the same cardinality (i.e., the same number of elements).
Yeah, it's weird - I might even say, "That's absurd!" but, because of the way we've defined set theory, number theory, and mathematics, it's demonstrably true!
Don't you see? The fact that something is "strange" and doesn't make intuitive sense to us means, in a logical, rational, mathematical sense, exactly NOTHING. Infinity is a weird concept, one that most (or actually probably NOone) really "understands." Yet, we've decided it exists, and defined its properties VERY clearly and explicitly.
Wade, if you want to state that you don't believe in the concept of "infinity," that's fine. But your personal beliefs don't "prove" anything.
One final response to a comment you made:
You said:
>I did not merely "declare" them to be absurdities. I
>established the absurdities mathematically. Would you
>like me to do so again?
Uhm... Actually, you didn't. If you'd established a mathematical concept of "absurdity," you'd be the first human ever to do it. The concept of "absurdity" is not a mathematically distinct concept. You could (and actually might) say that "absurd" means "false." If that's the case, then why even use "absurd?" Just say false!!! Or maybe you could say that "absurdity" means "contradiction," which is a clear mathematical concept. If that's the case, all you'd have to do is demonstrate the contradiction. No need to call it by a different name.
(by the way, contradiction stems from the concepts of TRUE and FALSE - like this:
"if X is true, then X is not true.
if X is not true, then X is true."
That's exactly what a contradiction is.)
So, I'm forced to conclude one of the following:
1) you don't understand the rules of logic and math
2) you've invented a new kind of mathematical logic, where "absurd" has a meaning that is independent of "TRUE" or "FALSE"
or
3) you're being intentionally deceptive
So which is it?
Duane
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