It's a classical logical argument -- Ben's Message Board

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Subject: It's a classical logical argument

Author:
Damoclese

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Date Posted: 03/20/04 10:25pm
In reply to: Wade A. Tisthammer 's message, "* Sigh * Fine." on 03/20/04 9:24pm

>
>My response to this argument is that it is non
>sequitur. The argument is invalid (which, BTW,
>wasn't the case with the Tristram Shandy argument,
>since I provided a formal proof establishing its
>deductive validity). If we first travel a half-mile,
>then a quarter, then an eighth etc. it is true that if
>we follow this pattern we will never traverse a mile.
>But we can take different steps (e.g. traversing an
>eighth of a mile each time, rather than cutting the
>distance by half each time).

I suppose you could, but traveling a mile at the pace of 1/8 of a mile each time implies you'd have to travel all those distances smaller than an 1/8 of a mile first. It's the same situation.

This argument isn't a non-sequitor at all. It's a classical paradox that endured for many centuries, and still does as the answer that was reached is less than satisfactory.

Calculus was the answer, and the reason the answer that calculus derives isn't obvious is because the nature of infinity and distance and time isn't at all clear, although everyone has some mental conception of each concept.

The same goes for your Shandy argument. The premises a deductive argument rests on can be perfectly sound inasfar as they are understood, but they fail miserably where ignorance is concerned, and ignorance is all too prevalent in the paradox you've provided with Shandy, although calculus could also theoretically answer it in the same way it answers this paradox.(which I find to be wholly unsatisfactory)

So the bottom line is this, you've played around with infinity and beginningless tasks which are areas of intense grey. The conclusion could be true, provided the conceptions of what infinity is and beginningless tasks are true. I don't think they are, and I don't think reality mirrors them, therefore I think the argument fails, and it isn't because some particular premise is necessarily wrong. It's because they are asserted where things are impossible to know in the first place, though we can certainly play with them and the wordings therein until the cows come home but in the end we haven't proven anything one way or the other.

Your argument fails because it presumes to know the unknowable, and that is it's main and ultimate shortcoming.

It's as if you've made an elaborate argument about what life forms must do who live in six dimensional planes. Who knows what they must do? How could we? How can you know what logic a beginningless task entails, or for that matter an infinite past? You can't. It all rests on the assumptions you are willing to adopt, which may or may not be true.

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