Subject: Re: Logic deemed illogical! Area man protests.
From: Steven Gabriel (sgabriel@willamette.edu)
Date: Sat Jan 08 2000 - 06:52:16 EST
> Consider that cornerstone of formal logic, the principle of transitivity: if
> a > b and b > c, well then a > c. I maintain that transitivity holds for all
> quantities a, b, and c. It holds regardless whether it has us as an
> audience. It holds even when we tell it not to hold. Against all odds, it
> holds!
Ahh .... but transitivity of the operator '>' relies on '>' being already
defined, then it works, and not before.
It is a common mistake to think that the formal systems we create are more
than just creations. In the early 20th century mathematicians struggled
to find a basis for the formal system of mathematics. They failed. All
formal systems rely on a few simple definitions, assertions or rules.
These are never just known, but are created. Once we create a formal
system THEN we can say something like "transitivity for such-and-such
always holds" but we can't say that before we define the formal system,
and therefore it's a mistake to claim it was somehow fundamentally true in
a way that is not dependent upon some definition or created rule.
1 + 1 = 2, right? We might say that's fundamentally true, or like to say
that even if we try we can't make it not true. Hrm.
1 apple + 1 apple = 2 apples
1 raindrop + 1 raindrop = 1 raindrop
Oops. =)
It all just depends on how we set things up. BTW, I find it interesting
how I use a rational argument to plead the case for irrationality. =)
S. (who has been too busy getting himself into grad school to keep up with
mailing lists!)
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: Steven Gabriel -- sgabriel@willamette.edu :
: http://www.willamette.edu/~sgabriel :
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: "Sitting quietly doing nothing, :
: Spring comes and the grass grows by itself." :
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