Pat Hayes wrote: (01)
> On Aug 11, 2009, at 5:51 AM, ingvar_johansson wrote: (02)
>> 1. Ratio scales, interval scales, and ordinal scales require different
>> formalisms.
>
> Surely not. We plan to produce an ontology all written in one formalism.
>
> Let me test my understanding of these terms. (03)
I can tell you how I have been using the terms, which I think is in
conformity with much philosophy of science writing on these issues. But I
can't promise that it is in conformity with everything that is written
today. (04)
> A scale is a set of items used to represent measurements. (05)
I would say: 'a set of NUMERALS+UNIT used to represent properties,
amounts, measurements or observations'. Even realists (not only
operationalists and pragmatists) accept scales. (06)
> An ordinal scale is a scale with a total order on its elements. (07)
I would say: 'a scale with ONLY a LINEAR order on its elements'. (08)
> An interval scale is a scale with a difference function from pairs of
> scale items to ... (what? Real numbers? (09)
I would say: an interval scale is from a formal point of view an ordinal
scale plus a function that tells what is to be regarded as EQUALLY LARGE
INTERVALS in the order. (010)
> Some other scale? Could there
> be an interval scale in which differences were restricted to natural
> numbers, for example?). (011)
In my opinion: yes. (012)
> A ratio scale is a scale which has a zero element and a multiplication
> operation by rational numbers. (013)
If it is a scale in physics, then the zero element has from a physical
point of view to represent an ABSOLUTE zero of the quantified dimension in
question. The interval scales of Celsius and Fahrenheit have a zero
element, but these are completely conventional. (014)
With your formal interests, I think you may benefit a lot from looking at
Henry Kyburg's "Theory and Measurement" (published 1984, but reprinted now
2009 by Cambridge UP). Since I am a relist with respect to universals, I
disagree with Kyburg's reduction of determinate properties to equivalence
classes of the corresponding property instances. But here are four views
of his with which I agree: (015)
1. Quantities are functions from objects to MAGNITUDES, not numbers (e.g.,
p. 10). (016)
2. A standard unit need NOT necessarily have the numerical value 1 (pp.
160, 166). (017)
3. "there are a larger number of quantities that can be measured directly
than many writers acknowleddge" (p. 111). For instance, area need not be
given the unit 'm x m'. (018)
4. Comparative relations are logically prior to classification (p.11). (019)
Best wishes,
Ingvar J (020)
>
> (My source for this is
> http://www.stat.sfu.ca/~cschwarz/Stat-301/Handouts/node5.html
> , by the way, found through google)
>
>>
>> 2. Out of every ratio scale an interval scale can be constructed,
>> and out
>> of every interval scale an ordinal scale can be constructed, but not
>> conversely.
>>
>> 3. In the late nineteenth century, physics was able to replace the
>> existing interval scales for temperature with a ratio scale for
>> temperature (the Kelvin scale).
>>
>> 4. There is no axiom or theorem to the effect that science can turn
>> all
>> ordinal scales into interval scales, and all interval scales into
>> ratio
>> scales.
>
> Right, all those make perfect sense.
>
> Pat
>
>
>
>>
>> Ingvar J
>>
>>
>> _________________________________________________________________
>> Message Archives: http://ontolog.cim3.net/forum/uom-ontology-std/
>> Subscribe: mailto:uom-ontology-std-join@xxxxxxxxxxxxxxxx
>> Config/Unsubscribe:
>> http://ontolog.cim3.net/mailman/listinfo/uom-ontology-std/
>> Shared Files: http://ontolog.cim3.net/file/work/UoM/
>> Wiki: http://ontolog.cim3.net/cgi-bin/wiki.pl?UoM_Ontology_Standard
>>
>>
>
> ------------------------------------------------------------
> IHMC (850)434 8903 or (650)494 3973
> 40 South Alcaniz St. (850)202 4416 office
> Pensacola (850)202 4440 fax
> FL 32502 (850)291 0667 mobile
> phayesAT-SIGNihmc.us http://www.ihmc.us/users/phayes
>
>
>
>
>
> (021)
_________________________________________________________________
Message Archives: http://ontolog.cim3.net/forum/uom-ontology-std/
Subscribe: mailto:uom-ontology-std-join@xxxxxxxxxxxxxxxx
Config/Unsubscribe: http://ontolog.cim3.net/mailman/listinfo/uom-ontology-std/
Shared Files: http://ontolog.cim3.net/file/work/UoM/
Wiki: http://ontolog.cim3.net/cgi-bin/wiki.pl?UoM_Ontology_Standard (022)
|