Sean Barker notes: (01)
In computational geometry, it is useful to distinguish between
what is inside a shape and what is outside. Basic topology defines what
is -in- or -out- in terms of open sets (or closed sets), however the
computational space of floating point numbers is not a metric space, and
this tends to make the boundary "fuzzy", that is, it seems appropriate
to define set membership in terms of fuzzy logic. (02)
In practice, fuzzy sets are painful to reason over, particularly
because applications of computational geometry, such as CAD, use a large
number of set operations (intersection, union, set difference) to
construct complex shapes out of simple primitives. It is more convenient
to quantize the logic, e.g. into -in-, -on- and -out-. Set operations in
geometry then become operations using a three value logic, which,
conveniently enough, turns out to be the Logic of Partial Functions (or
strictly, one of the LPF's). This approach explicitly defines the
quantisation function, which is the point at which one changes the value
of "truthfulness" in quantized logic system. (03)
The question of truth v. truthfulness seems to me to be a
discussion on the criteria for selecting a two-valued logic over a
multi- or continuous-valued logic. The selection of a continuous valued
logic, such as fuzzy logic, does not imply that things are not TRUE. In
fact, one might strongly assert something is TRUE if it is TRUE for all
quantization functions (for all uncertainties in the boundary between
true and false). (04)
And, btw, once you have decided on the criteria (C1) for
selecting a two-valued logic over any other logic, then you get to
debate the criteria (C2) for deciding the criteria (C1) on which you
based that decision. And then, the criteria (C3).... (05)
> -----Original Message-----
> From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx
> [mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of
> Ingvar Johansson
> Sent: 11 May 2007 10:50
> To: [ontolog-forum]
> Subject: Re: [ontolog-forum] {Disarmed} Reality and Truth
>
>
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> Waclaw Kusnierczyk schrieb:
> > Ingvar Johansson wrote:
> >
> >> John, who endorses
> >> Peirce's view that the scientific community *approaches* truth,
> >> equally stubbornly simply refuses to consider my (originally
> >> Popper's) proposal
> >>
> >
> > Hm. Might it be that you present your own preferred views
> as if they
> > were Popper's? (Pardon me my ignorance.)
> >
>
> They may by some be taken to differ in one detail, but I
> think they are essenntially identical. I mentioned Popper in
> order not to become accused of having stolen any idea. In
> what follows, I will simply defend my own views.
>
> >> to introduce a notion of 'truth' according to which truth is a
> >> determinable that can take degrees. I don't know what blocks them,
> >> but here are some further words that might help to make
> the notion of
> >> 'truthlikeness' clearer.
> >>
> >
> > Fine. I agree with you that this theory might be seen as a
> reasonable
> > one. I don't see it this way, which does not appear to me to be a
> > proof of its falseness -- which is completely coherent with my
> > previous social constructivism, call it as you like. I
> think we were
> > discussing what truth *is*, and then I simply stick to my
> own beliefs.
> > If it were obvious to me that we discuss how truth *could*
> be, I would
> > (I think) agree with you.
> >
>
> Statements are *about* something. What they are about depends
> on the concepts used. *Different concepts* are now and then
> (in everyday life, in science, and in philosophy) embodied in
> the *same graphical sign*. In this discussion the graphical
> sign 'truth' has been used both for the concept of bipolar
> truth and the concept of truth as a determinable that can
> take degrees. I have tried to show that the latter concept is
> (i) a semantically coherent concept, and (ii) a concept that
> makes it possible in a simple way to speak about science as
> progressing towards 100%-truths.
>
> Given 'truth as truthlikeness', one can meaningfully ask:
> "what *is* this truth or truthlikeness?" And then my
> short-hand answer is:
> "truthlikeness is an internal relation between a proposition
> and a truthmaker". This means, among other things, that to
> ascribe a certain truthlikeness to a proposition is *not* to
> ascribe it a monadic property, but a *relational property*.
>
> Ingvar
>
> >> On my proposal, of course, the term 'truth' becomes *out of
> >> context* ambiguous. It can then mean (i) 'truth' in the
> bipolar sense
> >> (which does not take degrees), (ii) 'truth' in the
> determinable sense
> >> (which takes degrees), and (iii) complete and absolute
> truthlikeness
> >> (which does not, just like any determinate truthlikeness,
> take degrees).
> >>
> >> '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. 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. When,
> >> *within* an empirical science, reseachers are discussing
> theories and
> >> hypotheses and what observable consequences they might yield,
> >> ordinary two-valued logic functions well.
> >>
> >
> > Good, but you did make claims that it is truth that takes
> degrees. It
> > appears to me that both John and me (and now you?) see
> truthlikeness
> > as distinct from truth, and calling it 'truth' (as in (ii) above,
> > where you seem to speak of determinate truthlikeness while
> proposing
> > to name it
> > 'truth') is simply begging for problems -- and thus the discussion.
> >
> > vQ
> >
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>
>
> --
> Ingvar Johansson
> IFOMIS, Saarland University
> home site: http://ifomis.org/
> personal home site:
> http://hem.passagen.se/ijohansson/index.html
>
>
>
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> (06)
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