ingvar_johansson wrote:
> I think the solution is to accept the existence of both properties and
> tropes (property instances). So: two sticks, one property, two property
> instances, one length value of that property that are instantiated twice.
>
I think we are coming to broad agreement with this. The problem is that
we have not yet written clear definitions of the 4 or 5 concepts
involved, and we have not agreed on the association of terms to concepts. (01)
Q1 = a measurable aspect of a particular physical thing, e.g., the
height of the Eiffel Tower, the length of stick A, the weight of a
specific pack of cigarettes, as distinct from the weight of the next
pack of cigarettes in the same carton. (Q1 = 'particular quantity', a
subtype of 'property instance' = trope) (02)
Q2 = each instance of Q2 is a category of Q1 in which all instances of
the category are comparable. The instance of Q2 is the measurable
aspect that they all share, e.g., length. (Q2 = 'quantity kind', a
subtype of 'property'?) (03)
Q3 = the measurement/abstraction of a Q1 that is comparable to the
measurement of another Q1 that is of the same Q2, e.g., an "amount of
length", that abstraction of the height of the Eiffel Tower that can be
compared to the distance between the Eiffel Tower and the Arc de
Triomphe. The Q3 is what is the same about the weight of the two
identical packages of cigarettes. It is what is being compared when we
say "the distance to the Arc is longer", "stick B is shorter than stick
A". (Q3 = 'specific quantity'?)
(Each Q3 is an "equivalence class of Q1s", e.g., of all length
measurements that are the same. Each Q3 is also an "equivalence class of
quantity values", except that the abstraction exists without the values.) (04)
Q4 = each instance of Q4 is a category of Q3 in which all instances of
the category are comparable. The instance of Q4 is the measurable
aspect that they all share, e.g., length. There is a 1-to-1
correspondence between instances of Q4 and instances of Q2, I think. So
it may be unnecessary to distinguish them. (05)
measurement unit = a Q3 that is defined by reference to a Q1 and used as
a reference quantity in constructing quantity values, e.g., the metre.
Note: the metre is not the wavelength of some specific emanation of the
Cesium atom; it is defined to be the abstraction/magnitude of that Q1,
an amount of linear displacement that can be compared to other amounts
of linear displacement. (06)
quantity value = an expression of a Q3 in terms of a number and a
reference measurement unit, such that the ratio of the Q3 represented to
the Q3 that is the measurement unit is the number, e.g., 183 metres.
Two quantity values are equivalent iff they express the same Q3 (in
different measurement units). (Conversion is therefore a rule for
identifying an equivalent quantity value.) (07)
I don't care what we call them, but we need to sort out these notions.
We can call one (and only one) of them "quantity", but we need to agree
on which one. And we also have to decide where to mark the
specialization to scalar quantities, as distinct from vector quantities. (08)
Further, if we call "length", "width", "height", and "road distance"
_different_ Q2s, then there is a subtype of Q2/Q4, which we shall call
Q5, such that if A and B are two different instances of Q5, then no
instance of A is comparable to any instance of B. So "length" and
"mass" are Q5s but "width" and "height" and "road distance" are not.
VIM 'base quantity' is a subtype of Q5, or a 'role' of Q5 in a 'system
of quantities'; and similarly, VIM 'derived quantity' is a disjoint
subtype/role of Q5. And I think the union of 'base quantity' and
'derived quantity' covers Q5 in any system of quantities. (That is, I
would distinguish the Q2 as the "aspect being measured" and Q5 as the
"nature of the aspect being measured". I have said before that I think
VIM 'kind of quantity' is Q5.) (09)
The point is that there is no widespread agreement on the vocabulary in
this area. We have to list the concepts we need and assign terms to
them. And as Pat pointed out, we have to formulate the axioms that make
the concepts clear, regardless of what we call them. (010)
-Ed (011)
--
Edward J. Barkmeyer Email: edbark@xxxxxxxx
National Institute of Standards & Technology
Manufacturing Systems Integration Division
100 Bureau Drive, Stop 8263 Tel: +1 301-975-3528
Gaithersburg, MD 20899-8263 FAX: +1 301-975-4694 (012)
"The opinions expressed above do not reflect consensus of NIST,
and have not been reviewed by any Government authority." (013)
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