>Hi Pat...
>
>Wow.. That was a lot of writing. Forgive me if I fail to generate
>so long a discussion -- it is simply outside my ability. A couple
>of comments, though. And a pre-apology for top-posting, but it's
>simpler to say what I want as systemic comments on your post rather
>than a point-for-point response. (01)
OK, this is a second response to your message, partly to assuage that
rather exasperated tone of the previous one (concerning metaphysics).
Only relevant parts included. (02)
>4) Again, following Quine's doctrine, what are these things for
>which the continuant/occurrent distinction is incoherent?
>Presumably, you'd want to be quantifying over some class of objects
>for which you'd like to state some axioms governing, e.g., property
>change over time, however that comes out in your favorite formalism.
>Then, by Quine's doctrine you're committing to the existence of
>those things. Let's call them Continuoccurrents. Now you have to
>elaborate your theory of Continuoccurrents and distinguish them from
>temperatures, numbers, properties, propositions and all the kinds of
>other things you have in your ontology. Doesn't sound to me like
>that project is any less problematic than the defense of either
>bicategorialism, 4D, or any other metaphysical framework. By this I
>mean on a practical, engineering level. (03)
So, here is a sketch of the metaphysics. First, distinguish
spatiotemporal entities from others. (There might be many kinds of
others, but those distinctions are outside this thread's topic.)
Something is a spatiotemporal entity if it lasts for some time and
can be said to be in a place at every time it exists. That is, if it
occupies time and space. (The time and place might be a 'loose fit'
in that one has no idea exactly where the boundaries are: the Outback
is somewhere in Australia, but nobody knows exactly where it starts.
Which is fine.) This includes physical objects, events, many physical
processes, etc., but it does not include for example categories of
stuff (water, air), numbers or symbols. Does it include properties of
physical things, such as color? Well, you can have it either way. If
you are happy saying that a color is located in a place, then sure. I
myself would prefer not to say that, I find it confusing.) This is
the primary category, which can (will) be divided into many
subcategories: but the current point is that all spatiotemporal
entities are fitted into time and space in the same way, and can be
discussed using the same terminology and linguistic conventions. They
all can have spatial or temporal parts, they all can be described as
having properties which change with time, etc.. There are not two
fundamentally different kinds of spatiotemporal entity with
incommensurate ontologies and incompatible metaphysics. These things
have start and end times, may have tops and bottoms, may have widths,
volumes, etc.. They may contain, or be filled with, certain kinds of
stuff. They typically have edges and surfaces of various kinds, and
sometimes these have important properties in their own right. The
general theory of the spatial and temporal relationships between all
these spatiotemporal entities is well worked out and thoroughly
understood; it amounts to applied topology. (04)
Now, since these things have (usually) three spatial dimensions and
one temporal one, they are often described as '4-d', but that
terminology should not be taken to imply that they are some kind of
mathematical exotica. It means only that they are 3-d (or less) at
each moment and that they last for a while. Like most everyday
things, in fact. So a full description of their spatiotemporal
envelope - of where and when they exist - involves four dimensions.
This is also true for both continuants and occurrents, of course, but
with the difference that the in the first of these, the temporal
extent can't be described as a real extent in the same way. (05)
Just as 3-d entities have 2-d surface and sections, these things have
3-d 'surfaces' and 'sections'. A 3-d section of one of them is an
instantaneous snapshot of it, a freezing of it at a moment in time.
(If that moment is understood to be 'the present', then at that
present time, this section is very similar to a continuant, although
it cannot actually be the continuant for essentially logical
reasons.) But you can also 'slice' one of them along 2 spatial and
one temporal dimension. For example, a tomato is a spatiotemporal
entity, and the surface of the tomato is a 2+1-dimensional surface of
it: two spatial and one temporal. That is what you would see if you
were to watch a movie of the tomato's growth. Slicing that gives one
the surface of the tomato at a particular time-instant. All of these
are what one might call things which are related to the tomato itself
by spatiotemporal geometry. Events have exactly similar aspects. A
photo taken during a football match shows a temporal slice of it; the
lower boundary of the match is the surface of the playing field
(2-spatial-d) during the match (1-temporal-d), 2+1=3-dimensional in
total. In biology, many processes occur at such dynamic boundaries. A
cell membrane is a nice example of a 2+1-dimensional spatiotemporal
surface. It can have spatiotemporal properties, such as maintaining
an average osmotic gradient during an period of time. (06)
Hope this helps to understand what I was talking about. (07)
Pat (08)
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