Ingvar, (01)
I'm happy to accept the following position: (02)
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. (03)
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: (04)
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. (05)
I believe that Peirce was influenced by the mathematical
treatment of infinite series. For example, the following sum (06)
1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + ... (07)
converges to the limit 2. However, any finite sum of terms
is less than 2 by some small amount. (08)
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. (09)
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. (010)
This example illustrates a useful way of interpreting both
words 'truth' and 'truthlikeness': (011)
- 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. (012)
- 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. (013)
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. (014)
John (015)
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