John F. Sowa schrieb:
I have no qualms about anything you say below. (02)
> I'm happy to accept the following position:
> IJ> 'Truthlikeness' is introduced as a notion *beside*
> > the bipolar notion of 'true-false' used in everyday
> > life and in two-valued logic. I have by no means claimed
> > that the introduction of 'truthlikeness' implies that
> > two-valued logic has to be replaced by many-valued logic.
> But I also believe that Peirce's notion of truth is useful
> to describe the ultimate goal that scientists are seeking,
> but may never attain:
> IJ> The notion of 'truthlikeness' is needed in order to make
> > sense of the history of science and to get a reasonable view
> > of the future of science.
> I believe that Peirce was influenced by the mathematical
> treatment of infinite series. For example, the following sum
> 1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + ...
> converges to the limit 2. However, any finite sum of terms
> is less than 2 by some small amount.
> For this series, I would say that the truth is "2", and
> that any finite sum is more and more "truthlike" as more
> terms are added.
> Although this particular series happens to have a very
> compact statement of the "exact truth", namely "2",
> many series, such as those that converge on an irrational
> number such as pi, have no exact statement of the "true
> value". But we can approximate it as closely as we like.
> This example illustrates a useful way of interpreting both
> words 'truth' and 'truthlikeness':
> - Truth, in Peirce's sense, is a precise goal, which might
> be beyond our ability to discover or even to describe in
> a finite string of symbols.
> - Truthlikeness, in Popper's sense, has a range of values,
> each of which can be stated in a finite number of symbols.
> It's possible that one of those statements might happen
> to be a precise description of the absolute truth, but we
> might never be able to know whether it is the final answer.
> Neither of these two senses is identical to the common meaning
> of the word 'truth', but the distinction is useful for clarifying
> certain debates, such as this thread.
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IFOMIS, Saarland University
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