Sean Barker
0117 302 8184 (01)
> -----Original Message-----
> From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx
> [mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of
> Waclaw Kusnierczyk
> Sent: 11 May 2007 17:07
> To: [ontolog-forum]
> Subject: Re: [ontolog-forum] {Disarmed} Reality and Truth
>
>
>
> Barker, Sean (UK) wrote:
> >
> > Sean Barker
> > 0117 302 8184
> >
> >
> >> -----Original Message-----
> >> From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx
> >> [mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf
> Of Waclaw
> >> Kusnierczyk
> >> Sent: 11 May 2007 11:57
> >> To: [ontolog-forum]
> >> Subject: Re: [ontolog-forum] {Disarmed} Reality and Truth
> >>
> >> Once we are here, I have the following metaphor in mind.
> >>
> >> 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.
> >
> > Even in Euclidean 2D, one might ask which of (0, 1)x(0, 1) and {0,
> > 1]x[0, 1] (the open and closed sets) is a square, and if
> one, why not
> > the other.
>
> Of course; but in both cases, a particular figure is a square or not.
> (02)
The point is, that a precise definition of a square would include one
and not the other - both a square but only one is a square - and
presumably the other is squarelike (03)
>
> The question is, is Euclidean 2D space the only place where
> > we want to use the concept square?
>
> Surely not, but how does it matter here? (04)
It matters because by choosing a well defined system that relies on
classical logic, it then makes other things not squares, such as a
straight-line figure with four corners, all of them right angles on the
surface of a sphere. (05)
>
> >
> >> 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.
> >
> > I order a square cover for a hole. In engineering terms, this is
> > specified by two identical dimensions, together with
> tolerances, and
> > the constraints which make it a square - angles at corners, plus
> > tolerances on the accuracy of the angles, or equivent
> specifications
> > such as how parallel the edges are.
> >
> > I suspect that by arguing in terms of 2D Euclidean space - which
> > assumes manipulation through classical logic - that you
> have assumed
> > the hypothesis that you are trying to demonstrate.
>
> This was just a metaphore, no attempt to prove any theory.
> (06)
The problem is that the metaphor is inappropriate (07)
>
> >> 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.
> >
> > Or - it depends on the "squarelikeness" function the
> observer selects.
> > What this says is that there is not an ideal "squarelikeness"
> > function, or, if you prefer
>
> Yes; what would 'ideal' mean? (08)
There does exists a partial ordering of
squarelikeness functions
A1, A2, ... s.t. A1(x) < An(x) for all n > 1, all x, x a figure
with A1 the ideal (09)
>
> >
> > There does not exist an unique ordering of
> squarelikeness functions
> > A, B, ... s.t. A(x) < B(x) for all x, x a figure
> >> 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.
> >>
> >> 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.
> >
> > You seem to want to restrict all discussion to formal
> systems, which
> > would mean that the ontology 101 pizza example is not an ontology.
>
> Not quite sure what you mean by 'formal systems' in this context.
> How does it imply that (I would mean that) the pizza ontology
> is not an ontology? (But yes, an ontology which tries to
> convince me that a pizza is a concept is not of much interest to me.)
>
>
> >
> >> 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.)
> >
> > This is based on a claim that only two valued logic are
> valid, which I
> > would claim is invalid at the 99% level.
>
> Again, what would 'valid' mean here? I acknowledge mvl, and
> fuzzy logics, but as argued earlier, it seems to me that
> speaking of degrees of truth in these logics is a misunderstanding. (010)
My apologies, but I feel impelled to hurl an insult at this point -
Platonist!
More seriously, it depends on your understanding of language - does
language model the world? or does it talk about the world? (Plato v.
Aristotle, or Tractatus v. Philosophical Investigations if you're in to
Wittgenstein) (011)
>
> vQ
>
> >
> >> Ingvar seems, to me, to have the wish to call squarelikeness
> >> 'squareness'.
> >>
> >> vQ
> >>
> >>
> >>
> >>
> >>
> >>
> >>
> >> 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 from an
> >>>> external partner or the Global Internet.
> >>>> Keep this in mind if you answer this message.
> >>>>
> >>>> 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
> >>
> >> ------------------------------------------------------
> >> Department of Information and Computer Science (IDI) Norwegian
> >> University of Science and Technology (NTNU) Sem Saelandsv. 7-9
> >> 7027 Trondheim
> >> Norway
> >>
> >> tel. 0047 73591875
> >> fax 0047 73594466
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>
> --
> Wacek Kusnierczyk
>
> ------------------------------------------------------
> Department of Information and Computer Science (IDI)
> Norwegian University of Science and Technology (NTNU)
> Sem Saelandsv. 7-9
> 7027 Trondheim
> Norway
>
> tel. 0047 73591875
> fax 0047 73594466
> ------------------------------------------------------
>
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> (012)
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