Author:
Wade A. Tisthammer
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Date Posted: 09/13/04 11:46pm
In reply to:
Duane
's message, "Yes, but I'm beginning to think that maybe you don't..." on 09/13/04 8:21am
>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.
I happen to accept epistemological objectivism. The world is flat, and you are a tuba. Yes, it's ridiculous to YOU...but it's also ridiculous in a more objective sense.
>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.
Creating a reductio ad absurdum argument requires no such thing. You're still free to disagree with the premises, of course.
>You've
>arrived at a conclusion, that Tristam's situation is
>"absurd," but how does that disprove infinite time?
I was arguing against an infinite past. If you don't see how the argument works, would you like me to construct a formal proof?
>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."
I don't believe that statement at all. It certainly doesn't make sense in a finite past (assuming “day 1” is the present or yesterday like it was in the TS story; you haven’t actually clearly defined what “day 1” is).
>Clearly, if time is unbounded in one direction, it is
>unbounded in both directions.
Except under a finite past there never is, and never will be, a day "infinity." It doesn't logically follow at all that the past is infinite merely because the future is potentially so.
>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.
You mean I have to play by the rules you choose? Listen, my argument is what it is. The mathematics were used only to justify the necessary repercussions of Tristram Shandy having written from eternity past. That's all. You can of course disagree that the implications are absurd, though I think you'd be hard pressed to justify "the present can never be reached" as a non-absurdity in the real world.
>You need to mathematically prove it.
No I don't. It was never meant to be a mathematical proof (though mathematics is obviously involved). It was a rational a priori philosophical argument. Now do you honestly wish to claim that the apparent absurdities are actually quite reasonable? For instance, how could Tristram Shandy finish his autobiography given the circumstances I described (taking him an entire year to write one day etc.)?
>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."
If a belief is absurd, it is probably false. Certainly there is rational reason for thinking it to be false. Now you can claim to that my so-called absurdities are actually quite rationally acceptable (thus denying premises 3 and 4 of the formal proof), in which case we might have to examine that further and resolve the apparent absurdities.
>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:)
A straw man here? Look, I do have a formal proof for its validity if you want it. Bottom line: to reject the conclusion you must reject at least one premise. So, which premise is it and why is it false? Claiming that I haven't rigorously mathematically defined "absurd" doesn't quite do the trick.
Are you familiar with the phrase ignoratio elenchi?
Now I suppose you could dispute premises 3 and 4, but given the circumstances I think that will require some justification.
>"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.
And that's not my argument at all. You have unwittingly created a straw man.
>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.
They are absurd and impossible. IF Tristram Shandy were infinitely far behind, it implies a point in the infinite past that is infinitely far away from the present. Perhaps that’s to be expected with a past of an infinite quantity of days, but it implies the present cannot be reached. It is similarly absurd and impossible for Tristram Shandy to finish.
>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.
That doesn’t even remotely match the absurdities in the TS story. Obviously the present can be reached, for instance. It is equally absurd and impossible for TS to finish. Suppose we’re at the day he finished. He obviously can’t have written about today yet or yesterday, considering it takes him an entire year to write about one day etc.
>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.
If you don’t believe you’re a tuba, that’s fine. But your personal beliefs don’t “prove” anything.
Naturally of course you are ignoring the premises and formal proof of the argument that I base my “personal belief” on. You think the argument to be unsound? Then let’s get to the premises!
Actually I don’t dispute “infinity” as such, just an infinite past because of the coherency problems it suffers. You still haven’t quite attacked a premise yet.
>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.
I should have phrased it differently. What I meant was that the implications I mentioned did in fact exist (i.e. TS is either infinitely far behind or he finishes at some point).
>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?
I’ll take option 4): you are seriously confused and have unintentionally avoided the crux of the argument.
Now how about those premises?
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