Ed Barkmeyer wrote: (01)
> 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 is 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. (02)
Dear Ed,
I agree that a fourfold distinction as yours below between Q1-Q4 is
necessary. However, to me you are using 'category' in an unusual sense,
and I think that in order to avoid confusion one should distinguish
between two senses of 'being an instance of', and then use different terms
for them. On the one hand we have 'an instance' as a spatiotemporally
located individual entity, this I will call 'an instance'; on the other
hand we have 'an instance' as a determinate of a determinable (red is an
instance of color, 14 kg is an instance of mass, etc.), this I will call
'a determinate'. In my opinion, VIM confuses these two senses. (03)
Furthermore, the fourfold distinction in question applies even to
non-quantified properties, and I think that to bring this out can help to
clarify the issues at hand. Let me exemplify with the determinable 'shape'
and one of its determinates, 'spherical'. A necessary requirement for a
quantification is that all the determinates of certain determinable can be
and are linearly ordered, and this has not yet been done for the shape
determinable. (04)
Q1-spherical = the spherical instance of ball A at t, the spherical
instance of the planet B at t, etc. That is, Q1 = determinate property
instances. (05)
Q2-shape = the shape instance of ball A, the shape instance of the planet
B, etc. That is, Q2 = determinABLE property instances. (06)
Q3-spherical = the determinate universal 'spherical' if you are a realist,
and the equivalence class of 'spherical property instances' if you are a
resemblance nominalist. That is, Q3 = determinate universal or determinate
equivalence class. (07)
Q4-shape = the determinable universal 'shape' if you are a realist, and
the equivalence class of 'shape property instances' if you are a
resemblance nominalist. That is, Q4 = determinABLE universal or
determinABLE equivalence class. (08)
And here are some axioms: (09)
A1: Necessarily, if a Q1-instance (e.g., a spherical instance) then also a
Q2-instance (shape instance). (010)
A2: Necessarily, if a Q2-instance (e.g., a shape instance) then also an
instance of a determinate of Q2 (instance that is spherical, or square, or
star-formed, etc.). (011)
A3: Only quantified determinates of the same determinable can be added and
subtraced (in a physically menaingful way). (012)
A4 (for many but not all determinables): Two Q2-instances cannot possibly
exist in the same spatiotemporal region. (013)
The ideas I have put forward go back to the Cambridge philosopher W. E.
Johnson’s book "Logic" (three volumes, 1921-24). I have also earlier in
some of my writings tried to rehabilitate and develop his
determinable-determinate distinction. See for instance the papers "(Review
of E. J. Lowe) The Four-Category Ontology" (2006) and "Determinables as
Universals" (2000) in section 1 on my home page
< http://hem.passagen.se/ijohansson/index.html > (014)
Ingvar J (015)
> 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)
>
> 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'?)
>
> 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.)
>
> 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.
>
> 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.
>
> 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.)
>
> 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.
>
> 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.)
>
> 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.
>
> -Ed
>
> --
> 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
>
> "The opinions expressed above do not reflect consensus of NIST,
> and have not been reviewed by any Government authority."
>
>
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