Pat and Ingvar, (01)
I agree with your recent comments, which are compatible with
my suggestions about limiting the number of axioms and
definitions we propose. (02)
PH> Our ontology does not need to *define* mass or length; indeed,
> it had better not try, since nobody knows how to define mass. (03)
Indeed. The kilogram is one of the few units that is still defined
by a specific artifact -- a lump of platinum in a vault in Paris. (04)
There are more recent proposals, which may be adopted soon, that
define a kilogram as the mass of a certain number of atoms. But
that definition also accepts the notion of mass as a primitive.
It just uses a collection of smaller objects as the standard. (05)
There are some still unconfirmed theories of physics that propose
more fundamental definitions of mass. But none of those theories,
even if confirmed, would make the slightest difference in either
of the above ways of defining the kilogram. (06)
PH> What it can do, however, is refer to mass as a property and say
> a few uncontroversial things about it, eg that its values are
> additive and hence can be multiplied by real numbers, that it has
> a zero, etc.. This is not to *specify* it or to *define* it, but
> it is also not to completely ignore it or exclude all mention of
> it from our ontology, or to refuse to even think about how
> discussions of mass units can be related to statements about
> actual physical things. (07)
I agree. (08)
PH> ... but we ought to provide some axioms relating our notions
> to appropriate higher-level categories, if only in order to provide
> a guide to those whose task it is to write such axioms. Can people
> use 'mass' as a function on physical objects, for example? (09)
I agree. The VIM document does provide such guidelines, and we
could formalize them by statements in our versions of logic. (010)
IJ> I think the following classification and definition proposals are
> compatible with VIM and the SI system:
>
> 1. Divide a primitive 'Dimension' into 'Not-quantified dimension' (shape
> would be an example) and 'Quantified dimension' (= what is called just
> 'dimension' in VIM aand the SI-system).
>
> 2. Define 'Quantity' as a quantified dimension with a standard unit.
>
> 3. Divide 'Quantity' into 'Kind-of-quantity' and 'Quantity that is not a
> kind-of-quantity'; the latter might be called 'Nominal quantity'.
>
> 4. Define 'Kind-of-quantity' as a quantity where all the instances of all
> the values are in principle physical-chemically comparable. (011)
I would agree with the assumption of "primitives" and definitions along
those lines. (012)
John (013)
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