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Article 2551 of comp.ai.philosophy:
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>From: dlyndes@gothamcity.jsc.nasa.gov (David Lyndes)
Newsgroups: sci.philosophy.tech,sci.logic,comp.ai.philosophy,sci.math
Subject: Re: Grasping concepts... is it polite?
Message-ID: <1992Jan8.170943.15772@aio.jsc.nasa.gov>
Date: 8 Jan 1992 17:09:43 GMT
References: <1992Jan2.131048.18412@news.stolaf.edu> <1992Jan6.092440.25451@etl.go.jp> <1992Jan6.130008.16471@news.stolaf.edu> <1992Jan7.214019.6969@neptune.inf.ethz.ch>
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Organization: Barrios Technology @ NASA/JSC; Houston
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|> Yes, but can you imagine it in the same way you can imagine 10? It is easy
|> to think of 10 marbles; it is nearly impossible (or completely) to imagine
|> aleph_0 marbles.

This is getting pretty weird.  Imagining, image-ing, grasping a concept,
abstract entities like aleph null, heavy going.  A few points:

(1) If you need an image to go along with the abstract entity, that great
    enemy of abstract ideas, George Berkeley provides you with a perfectly
    suitable way to get it.  The basic idea is that the general idea
    of "triangularity" is derived from individual triangles.  But you
    ignore many of the properties of the individual triangles.  The
    color of the triangle and specific angles are not relevant in a
    discussion of "triangularity, but number of sides, number of angles,
    are.  So any particular triangle can "stand for" triangularity if
    we ignore the "irrelevant" features.  David Hume used this theory
    in his treatise (sorry, but I don't remember the page numbers) and
    continues to this day in some interpretations of category theory
    and relative identity theory.

        "Sometimes the less you inspect a word the better
         you understand it."

(2) When discussing what it takes to grasp a particular concept like
    aleph-null, we should set some criterion such that if we meet it,
    then we have been successful in explaining what it takes to grasp
    the concept.  Just adding the adverb "really" n+1 times (as in
      "But you don't grasp it.",
      "But you don't really grasp it.",
      "But you don't really really grasp it.", ...)
    doesn't further the conversation.  Unless you can say something
    about what is missing.
  
    The phrases "gut understanding" fall in the same category.

(3) Grasping the concept of number (finite or transfinite) requires
    little more than grasping the concepts of "zero", "is the next item",
    and "correspondence."  Being able to conjure up an image in your
    imagination is not relevant to whether you've grasped the concept.

(4) Yes, understanding 10 apples is different from understanding aleph-null
    apples.  10 apples is a finite number of apples.  Aleph-null apples
    is an infinite number of apples.  Understanding the difference
    between 10 and aleph-null apples doesn't require understanding
    much else.

(5) I think part of the problem in this conversation is that there is
    a good bit of sloppiness in the use of verbs.  I've seen
       - think of
       - imagine
       - understand
       - grasp
       - see
    These are not synonyms.

-- 

	 +-----------------------------------------+
	 | David K. Lyndes                         |
	 | Barrios Technology                      |
	 | email: dlyndes@deltahp.jsc.nasa.gov     | 
         | "Its my opinion and you can't have it!" |
	 +-----------------------------------------+


