On Sep 28, 2009, at 1:54 PM, Gunther Schadow wrote: (01)
> Is there some way we can converge on something?
>
> Could we make a list of requirements described by examples
> for each of the capabilities of the theory.
>
> 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.
>
> 1 = 1 : true or false?
>
> 1 N.m = 1 N.m : true or false? (02)
Both obviously, necessarily, logically true. (03)
>
> 1 m = 100 cm : true or false? (04)
true (05)
>
> 1 L/L = 1 kg/kg : true or false? (06)
No idea until you tell me what you mean by division or ratio here. In
one understanding, L/L would be a pure number, making the equation
true. But I suspect you do not mean this. (07)
>
> 1 m = 1.00 m : true or false? (08)
Depends on whether you consider 1 = 1.00. In other words, its nothing
to do with meters. But I'd say, yes. (On the grounds that I presume
this is meant to address issues of precision in quantity
specifications, and I believe they should be relegated to another
topic.) (09)
>
> 1.0 m = 1.001 m : true or false? (010)
Similar, but I'd say false in this case. Certainly 1.0 =/= 1.001 (011)
>
> 0 m = 0 kg : true or false? (012)
false. (013)
>
> 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.
>
> 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. (014)
We could, but I think this would be a step backwards. Even if we all
agree, we will still not know if we have a common ontology; and if we
disagree, the discussions will only reveal the divergences of thought
that we are already discussing. (015)
Pat Hayes (016)
>
> 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?
>
> thanks,
> -Gunther
>
>
>
>
>
>
> 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
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