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)
http://www.jfsowa.com/pubs/challenge.pdf
The Challenge of Knowledge Soup (016)
John (017)
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