Wacek, (01)
It's important to distinguish truth and precision: (02)
> ... but this still does not seem to give support to the view
> that truth can be graded. Approximations, yes. (03)
Following is a statement by Peirce: (04)
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. (CP 4.237) (05)
This point allows true statements about the same subject with
different levels of precision. They can all be equally true,
even though some may be more precise. (06)
As Wittgenstein said, (07)
One might say that the concept 'game' is a concept with blurred
edges. -- "But is a blurred concept a concept at all?" -- Is an
indistinct photograph a picture of a person at all? Is it even
always an advantage to replace an indistinct picture with a sharp
one? Isn't the indistinct one often exactly what we need? (08)
Frege compares a concept to an area and says that an area with
vague boundaries cannot be called an area at all. This presumably
means that we cannot do anything with it. -- But is it senseless
to say: "Stand roughly (ungefähr) there"? (P. I., Sec. 71). (09)
As another example, I might say that the sun is 93 million miles
from the earth. For many purposes, it is pointless to give a more
precise statement, and for some purposes, it would be less useful. (010)
For example, the earth's orbit is not perfectly circular, but with
a sufficiently large margin of error (slightly over a million miles),
93 million miles is a true statement that is independent of the time
of year. A more precise statement with qualifications for different
times would be important for plotting the trajectory of a satellite,
but it would be less useful for many other purposes. (011)
John (012)
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