ingvar_johansson wrote:
> 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.
>
>
I didn't realize that I was using "category" in an unusual sense. I
used the term to express the inverse of the subsumption relationship: A
'is a category of ' B iff B subsumes A. And in that I meant to imply
that A is a unary relation (a class, the sense of "category" that I
assume is "usual") in its own right, i.e. that A(x) is true if the
individual x has the characteristics that define A and false otherwise.
I would be happy to change all occurrences of 'is a category of' to 'is
a subtype of'. I am less comfortable using 'is a kind of', because I
think it has an ambiguous model. (01)
I never use "'an instance' as a spatiotemporally located individual
entity". I prefer the term "individual" for things that appear in the
domain of discourse (which is a potentially larger population than
"spatiotemporally located individual entity"), in order to avoid
precisely the confusion you identify. Further, I hope I only used
"instance" in the relation "is an instance of", with the
interpretation: x 'is an instance of' A iff (x is an individual in the
domain of discourse) and A(x) is true. You may use "determinate of a
determinable" for that relation if you please, but I doubt that it will
be easily comprehended by much of our audience. (02)
> 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.
>
> 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.
>
> Q2-shape = the shape instance of ball A, the shape instance of the planet
> B, etc. That is, Q2 = determinABLE property instances.
>
>
The examples are confusing, but the definition "Q2 = determinABLE
property instances" is what I meant. I think the example of Q2-shape is
"spherical" or "sphere", as distinct from "prismatic solid". So "ball A
at t" is a 'determinate' that 'is an instance of' the 'determinable'
"sphere". Thus the 'individual' "sphere" 'is a subtype of' Q1, and the
same 'individual' "sphere" 'is an instance of' Q2.
> 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.
>
> 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.
>
> And here are some axioms:
>
> A1: Necessarily, if a Q1-instance (e.g., a spherical instance) then also a
> Q2-instance (shape instance).
>
>
No. This is not an axiom I mean. What I want is: (03)
(forall (x D)(if (and (Q2 D) (D x))
(Q1 x)
))
Every instance of Q2 is a subtype of Q1.
> 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.).
>
Again. I don't understand this axiom. What I mean is: (04)
(forall (x)(if (Q1 x)
(exists (D) (and (Q2 D) (D x)))
))
Every individual that is an instance of Q1 is also an instance of some
determinable D that is an instance of Q2.
> A3: Only quantified determinates of the same determinable can be added and
> subtraced (in a physically menaingful way).
>
>
The VIM term is "comparable" ("added and subtracted" is perhaps too
specialized a notion).
But the axiom is stronger than that: (05)
(forall (x y)(iff (exists (D) (and (Q2 D) (D x) (D y)))
(comparable x y) ))
x and y are comparable if and only if there is some determinable D in Q2
such that x and y are both instances of D. (06)
> A4 (for many but not all determinables): Two Q2-instances cannot possibly
> exist in the same spatiotemporal region.
>
I am going to assume I don't understand this, because what I understand
it might be intended to mean is false. (07)
Assuming the relation (st-location x r) means x has a spatiotemporal
existence in region r, then we probably do mean (although I am not sure): (08)
(forall (x)(if (Q1 x)
(exists (r) (st-location x r)) ))
Every instance of Q1 has some spatiotemporal location. Every measurable
instance is physical. (09)
What I think Ingvar means is: (010)
(forall (x y rx ry)(if (and (exists D)(and (Q2 D) (D x) (D y)))
(st-location x rx)
(st-location y ry))
(not (= rx ry)) )) (011)
If two 'determinates' (measurable instances) x and y are both instances
of a common 'determinable', their spatiotemporal locations cannot be the
same. (012)
But I don't think that is true, at least not of what I called Q2. For
example, the width of a given box and the height of the same box are
both instances of a Q2 (determinable) called "length". Do we really
mean that those properties are not coincident in space-time? That seems
to me to be an issue in philosphical geometry. ;-) (013)
-Ed (014)
--
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 (015)
"The opinions expressed above do not reflect consensus of NIST,
and have not been reviewed by any Government authority." (016)
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