John F. Sowa wrote:
> It's important to distinguish truth and precision:
> > ... but this still does not seem to give support to the view
> > that truth can be graded. Approximations, yes.
> Following is a statement by Peirce:
> 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)
> 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.
> As Wittgenstein said,
> 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?
> 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).
> 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.
As for this example, if I have $99 and say that I have approximately
$100, then I am either correct or not, depending on what 'approximately'
is supposed to mean. I may have trouble with a crisp definition of
'approximately', and say that my statement is only 0.9 true, but this
0.9 is not a measure of the truth of my statement, but rather of my
satisfaction with saying that $100 is approximately $99. And if I say
that I have $100, I am simply wrong, irrespectively of how close $99 is
to $100 wrt. what I could possibly have, say, $1M. (02)
You statement that the distance between the Earth and the Sun is 93
billion miles may be pretty satisfactory or useful for some purposes,
but it does not make it true. It may be true, irrespectively the
degree of our satisfaction with it. (03)
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