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Re: [ontolog-forum] Visual Complexity

To: patrick@xxxxxxxxxxx, "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
Date: Tue, 06 Feb 2007 22:26:26 -0500
Message-id: <45C946E2.6090207@xxxxxxxxxxx>
Patrick,    (01)

That is obvious.  I don't know anybody who would make any
claim to the contrary:    (02)

 > What I resist is the suggestion that any formal language
 > or model (cf. John's response) can be constructed that
 > states the basis for every claim it makes.    (03)

Leibniz made the point that everything in the universe has
some influence, however small, on everything else.  For that
reason, he said that mathematics is the only science in which
certainty can be reached in a finite number of steps.  For the
physical world, he said that only an infinite mind such as God's
could determine anything with absolute certainty.    (04)

Kant made a related point:    (05)

    Since the synthesis of empirical concepts is not arbitrary
    but based on experience, and as such can never be complete
    (for in experience ever new characteristics of the concept
    can be discovered), empirical concepts cannot be defined.    (06)

    Thus only arbitrarily made concepts can be defined
    synthetically. Such definitions... could also be called
    declarations, since in them one declares one's thoughts or
    renders account of what one understands by a word. This
    is the case with mathematicians.    (07)

C. S. Peirce said    (08)

    It is easy to speak with precision upon a general theme.
    Only, one must commonly surrender all ambition to be certain.
    It is equally easy to be certain. One has only to be
    sufficiently vague. It is not so difficult to be pretty
    precise and fairly certain at once about a very narrow subject.    (09)

Alfred North Whitehead said    (010)

    Human knowledge is a process of approximation. In the focus
    of experience, there is comparative clarity.  But the
    discrimination of this clarity leads into the penumbral
    background.  There are always questions left over.  The
    problem is to discriminate exactly what we know vaguely.    (011)

    Both in science and in logic, you have only to develop your
    argument sufficiently, and sooner or later you are bound to
    arrive at a contradiction, either internally within the argument,
    or externally in its reference to fact.    (012)

    The topic of every science is an abstraction from the full
    concrete happenings of nature.  But every abstraction
    neglects the influx of the factors omitted into the factors
    retained.    (013)

    The premises are conceived in the simplicity of their individual
    isolation.  But there can be no logical test for the possibility
    that deductive procedure, leading to the elaboration of compositions,
    may introduce into relevance considerations from which the primitive
    notions of the topic have been abstracted.    (014)

For more discussion of these and related issues, see    (015)

    The Challenge of Knowledge Soup    (016)

John    (017)

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