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 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.
>>
>
> 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 (01)
Wait. 'both a(re?) square but only one is a square' -- what is it?
If 'square' is taken to mean an equiangular, equilateral and
quadrilateral figure in which the edge is included, than one of the
above is square and thus is a square, and the other is not square and is
not a square. And likewise if the edges are to be excluded. (02)
You apply two different definitions of squareness at the same time, and
announce inconsistence. Sure, you're right. (03)
Or correct me if I misinterpret your statement. (04)
>
>> 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?
>
> 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)
I take 'well-defined system' to mean that we have a good definition of
the system, i.e., we have a description of the system which we think
captures precisely and correctly its nature. The example above is of a
system which is not only well-defined in this sense, but is also defined
by me, so I not only describe the system, but actually create it. (06)
But if you want to argue that matters are different (i.e., truth must
take degrees) in non-well-defined systems, then the response is that
'non-well-defined' means just that, a system which we do not have a
precise description of -- but then it is not truth that takes degrees,
but our uncertainty as to how the system is. (07)
So what about figures on a sphere? (08)
>
>>>> 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.
>>
>
> The problem is that the metaphor is inappropriate (09)
Perhaps it is; let us see another one that is appropriate and shows why
truth would have to take degrees. (010)
>
>>>> 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?
>
> 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 (011)
Why would this be ideal? It would clearly be optimistic or pessimistic,
depending on how you interpret lower vs. higher values. (012)
>
>>> 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.
>
> 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) (013)
Not sure what you read. What I mean is that even if mvl or fuzzy logics
explicitly involve truth-degrees, it may be a misnomer: these degrees
reflect the degree of our certainty about the truth of a statement, not
the degree of truth of the statement. (014)
Suppose that we have the linguistic variable 'tall'. Suppose you assign
to it a fuzzy set with a membership function f such that f(x) = 0 if x <
160, f(x) = 1 if x > 180, and f(x) is linearly increasing from 0 at 160
to 1 at 180. Suppose my height h is 170. Thus, f(h) = 0.5. Would you
say that it is 50% true that I am tall? That the truth of 'wk is tall'
is a 50% truth? (015)
vQ (016)
>
>> 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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>>>>>>
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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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>
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--
Wacek Kusnierczyk (018)
------------------------------------------------------
Department of Information and Computer Science (IDI)
Norwegian University of Science and Technology (NTNU)
Sem Saelandsv. 7-9
7027 Trondheim
Norway (019)
tel. 0047 73591875
fax 0047 73594466
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