John F. Sowa wrote:
> Wacek,
>
> 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.
>
> 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. (01)
This is all very fine. We have graded precision here. But we do not
have graded truth. We may have different coverage and accuracy when
using different statements, but the truth remains ungraded. (02)
In fuzzy logics we have all sorts of membership functions that allow you
map a crisp value onto a fuzzy variable together with a measure of
membership in the corresponding fuzzy set. The measure is often called
the 'degree of truth', but I find it misleading: to say that a car has
a high speed with the degree 0.5 is not really to say that 'the car has
a high speed' is 0.5 true; it is to say that we are equally satisfied
as dissatisfied with calling the speed of the car 'high'. We do not
grade truth, we grade our satisfaction. And since fuzzy logics can be
seen as an extension of multivalued logics, I *suspect* that mvl involve
some nonclassical definition of truth which allows one to speak of
degrees of truth, but then it is truth in a different sense that I try
to keep to here. (03)
vQ (04)
>
> John
>
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> (05)
--
Wacek Kusnierczyk (06)
------------------------------------------------------
Department of Information and Computer Science (IDI)
Norwegian University of Science and Technology (NTNU)
Sem Saelandsv. 7-9
7027 Trondheim
Norway (07)
tel. 0047 73591875
fax 0047 73594466
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