On Sep 28, 2009, at 10:13 AM, ingvar_johansson wrote: (01)
> 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. (02)
Hmm. But 'similar to' is typically not transitive, so not an
equivalence relation. (03)
> 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 (04)
'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. (05)
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. (06)
> ; and the dimension
> mass can be regarded as the class of all such equivalence classes
> whose
> instances are physical-chemically comparable. (07)
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. (08)
Best (09)
Pat Hayes (010)
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? (011)
>
> Best,
> Ingvar
>
>
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> (012)
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