Is there some way we can converge on something? (01)
Could we make a list of requirements described by examples
for each of the capabilities of the theory. (02)
So, from my UCUM perspective, I would want to know, for
every operation what the result would be. It's like a list
of unit test cases that I would use to test my implementation. (03)
1 = 1 : true or false? (04)
1 N.m = 1 N.m : true or false? (05)
1 m = 100 cm : true or false? (06)
1 L/L = 1 kg/kg : true or false? (07)
1 m = 1.00 m : true or false? (08)
1.0 m = 1.001 m : true or false? (09)
0 m = 0 kg : true or false? (010)
We would make a table of these statements, and add any sort
of detail to them that we want to exemplify cases in which
the equivalence (or any other) relation holds. (011)
Then we can use that to come down to one list of requirements
and we only need to formulate the theory around those
requirements. We can also challenge the requirements right
then and there and argue why the relation should or should
not hold in that case. (012)
I feel like unless we do this, any candidate theory that we
look at here can be shot down because it fails to distinguish
something that some (but not all) on this list would want to
distinguish. So, can we make a table? May be on the Wiki where
we can maintain a nice table of examples? (013)
thanks,
-Gunther (014)
Pat Hayes wrote:
> On Sep 28, 2009, at 10:13 AM, ingvar_johansson wrote:
>
>> Dear Pat,
>>
>> you wrote:
>>> Agreed, but they too often stray from being an arriving at a common
>>> understanding, into what might be called a confusion of amateur
>>> ontology-hacking. The current noise about 'equivalence classes' (with
>>> no mention of any equivalence relations) is a good example.
>> If you were thinking of me, I took it for granted that the relation
>> is a
>> similarity relation.
>
> Hmm. But 'similar to' is typically not transitive, so not an
> equivalence relation.
>
>> Take mass as an example. If one wants to take one's departure in
>> individual instances of mass (what VIM calls quantity values of mass),
>> then generic quantity values such as 1.53 kg and 137.999 kg can be
>> regarded as being classes of exactly similar instances
>
> 'similar' in what sense? The only useful sense that I can determine is
> that they are both measures of the same quantity. So all this
> equivalence-class talk does not eliminate the idea of kind of
> quantity, or reduce it to something conceptually simpler or ontology
> more fundamental.
>
> BTW, the fact that one has to start with 'individual instances of
> mass' is itself a large mark against this POV, as these individual
> instances are ontologically useless and intuitively very opaque. I
> personally do not think they exist. If they do, then each act of
> measurement measures a distinct one of them, distinct - indeed,
> *necessarily* distinct - from those measured by all other acts of
> measurement. Regardless of the authority of the VIM, this seems to me
> to be close to incoherent as a basis for a theory of measurement.
>
>> ; and the dimension
>> mass can be regarded as the class of all such equivalence classes
>> whose
>> instances are physical-chemically comparable.
>
> Well, perhaps it can, but what is gained by this re-regarding? This
> account is certainly not simpler or easier to formalize than the one
> which has kinds-of-quantity as an explicit concept. If we are going to
> be strictly mathematical about it, in fact, they are exactly
> equivalent (each can be defined from the other, with some basic
> mathematical assumptions such as the axiom of choice); but the
> equivalence-class way of talking is less natural and more long-winded,
> without adding any insight or expressiveness.
>
> Best
>
> Pat Hayes
>
> PS. Another remark about QVMs. You appeal to a similarity relation of
> 'being a measurement of the same quantity kind'. But there are many
> other possible such relations, among them 'being made using the same
> apparatus', 'being a measurement made at the same time of day', etc..
> These are all mathematical equivalence relations, and all could count
> as 'similarity' relationships. What is that distinguishes your
> particular relationship form the many others?
>
>> Best,
>> Ingvar
>>
>>
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--
Gunther Schadow, M.D., Ph.D. gschadow@xxxxxxxxxxxxxxx
Associate Professor Indiana University School of Informatics
Regenstrief Institute, Inc. Indiana University School of Medicine
tel:1(317)423-5521 http://aurora.regenstrief.org (016)
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