Once we are here, I have the following metaphor in mind. (01)
In geometry we speak about figures (say, we constrain the world to
figures in a Euclidean 2D space). There are squares; I assume we do not
disagree on the definition of a square. (02)
A particular figure is a square, or it is not. We may look at it from
different distances, angles, etc., and decide that it is a square or not
(or, rather, decide whether we think it is a square or not); the figure
is or is not a square, independently of our decision and our confidence
in that the decision is correct. (03)
Consider non-square figures. These figures are not squares. But they
may be squarelike, and they may be squarelike to different degrees. But
how squarelike they are is not merely a function of how they are, but is
dependent on the observer. Squarelikeness parasites on both the figures
and the observer: a polygon might be seen as more squarelike than a
circle in that a square is a polygon, but a circle is not; a tetragon
might be seen as more squarelike than a pentagon, in that it has four
rather than five edges; an equilateral tetragon (a rhombus) might be
seen as more squarelike than an eqiangular tetragon, or vice versa. (04)
Nevertheless, any non-square figure is not a square. It is not a square
at all. It may be squarelike. You might also say that a square is
perfectly squarelike, in that it is square. But you might also say that
a square is less squarelike (and is not square) than, say, a non-square
rectangle, if you look from some particular angle -- this does not,
however, change the fact that the square is square and the non-square
rectangle is not. (05)
And here I see an analogy to truth: truthness is like squareness, and
truthlikeness is like squarelikeness. The latter may be more useful in
that we decide whether something is more or less truthlike, while we may
never be able to decide (in the sense of forming a belief rather than
making orders) whether something is true or not. (So John might say
here that this notion of truth is mystical, religious, and inapplicable.) (06)
Ingvar seems, to me, to have the wish to call squarelikeness 'squareness'. (07)
vQ (08)
Barker, Sean (UK) wrote:
> Sean Barker notes:
>
> 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.
>
> 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.
>
> 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).
>
> 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)....
>
>> -----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
>>
>>
>> *** WARNING ***
>>
>> This mail has originated outside your organization, either
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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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--
Wacek Kusnierczyk (010)
------------------------------------------------------
Department of Information and Computer Science (IDI)
Norwegian University of Science and Technology (NTNU)
Sem Saelandsv. 7-9
7027 Trondheim
Norway (011)
tel. 0047 73591875
fax 0047 73594466
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