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Article 2505 of comp.ai.philosophy:
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>From: andreas@etl.go.jp (Andreas Knobel)
Newsgroups: sci.philosophy.tech,sci.logic,comp.ai.philosophy,sci.math
Subject: Re: Grasping concepts... is it polite?
Message-ID: <1992Jan6.092440.25451@etl.go.jp>
Date: 6 Jan 92 09:24:40 GMT
References: <1991Dec23.112144.6884@husc3.harvard.edu> <1991Dec30.172852.3305@csc.canterbury.ac.nz> <1992Jan2.131048.18412@news.stolaf.edu>
Organization: Electrotechnical Lab.
Lines: 27

In article <1991Dec30.172852.3305@csc.canterbury.ac.nz> chisnall@cosc.canterbury.ac.nz writes:
>But "10^10^10" is an exceedingly compact representation for the number
>it denotes.  It is a mere 8 ascii characters, and the function "^" can
>be defined fairly succintly.  Can your mind grasp, say, the base 10
>representation of "10^10^10"? 

Courage, mes braves (aimed at the readers of *.tech and ai.*), why stop
at a lousy finite number like 10^10^10? I can imagine aleph_0, it starts
here with 0, 1 is next and then it sort of peters out in the distance.
I would contend that I can even see aleph_0^aleph_0, hey, and if I really
strain my eyes (or use the binoculars recently recommended in rec.birds),
(aleph_0^aleph_0)^aleph_0, and so on. I remember a set theory course given
by Ernst Specker where we discussed this concept of `seeing cardinals',
and if I remember correctly, came to the conclusion that we could `grasp'
the cardinals produced by successive applications of ^aleph_0, but not 
the limit. I guess this is because we can see finite segments of these
cardinals.

Andreas




-- 

Andreas Knobel                      e-mail andreas@etlcom.etl.go.jp
ETL, Tsukuba, Japan.


