[Xmca-l] Re: Parts and wholes

[David Kellogg]

It turns out that the bridge at Zhaozhou was probably not the first open
spandrel bridge. Maybe Marco Polo was right to be a little arrogant--the
Romans, his immediate neighbors back in old Italy, built open spandrel
bridges, but they didn't really know what they were doing. They just used
wood, and with wood, open spandrels make manufacturing sense in a way they
don't with stone, because boards don't come in bricks, and they bend
themselves to arches better.

Li Chun's problem was similarly material at first: he wanted gaps in the
bridge that would keep the spring floods from washing it away. And the best
way to produce these gaps was to create "secondary rivers" above the main
arch and then "secondary arches" above the secondary rivers, ad infinitum.
The difference, I think, is that there is a mathematical insight that
arises from Li Chun's way of thinking about the problem that doesn't arise
if you just think about the problem in terms of what's easiest to do with
your material. That's the mathematical insight (as an indefinitely
repeatable function), which allows Li Chun to "re-ascend" to the concrete.
There are a number of similar bridges nearby, which are almost as old.

David Kellogg
Macquarie University

On Sat, Sep 3, 2016 at 1:27 PM, Martin John Packer <mpacker@uniandes.edu.co>
wrote:

> Okay, but I wasn’t exploring the issue of which one — substance or formula
> -- is basic. You suggested that the arch should be thought of as,
> ontologically speaking, an idea or a formula. It struck me that we could
> extend the vocabulary a little and say that the arch is a function.
>
> I don’t want to hijack the thread, it’s just that I’ve been reflecting
> recently on Lewin’s distinction between Aristotelian and Galilean science,
> and the difference between substantial concepts and functional concepts.
> Your remarks seemed to me to point to something similar.
>
> > On Sep 2, 2016, at 10:16 PM, Rein Raud <rein.raud@tlu.ee> wrote:
> >
> > Well, workable ontologies can be constructed out of both approaches -
> both the traditional way of thinking that self-identical continuous things
> are the basic constituents of what is, and that relations between them are
> contingent upon them, or that infinite division is possible unto the level
> of subatomic particles whose material self-identity and continuity cannot
> be determined, and that therefore we are safer with thinking of all
> existents as composites, in which case the formula-level is primary. RR
> >
> >> On 03 Sep 2016, at 06:09, Martin John Packer <mpacker@uniandes.edu.co>
> wrote:
> >>
> >> Which way we take to be basic?
> >>
> >> Martin
> >>
> >>> On Sep 2, 2016, at 10:03 PM, Rein Raud <rein.raud@tlu.ee> wrote:
> >>>
> >>> Well, this depends on which way of existence we take to be basic. RR
> >>>
> >>>> On 03 Sep 2016, at 05:56, Martin John Packer <mpacker@uniandes.edu.co>
> wrote:
> >>>>
> >>>> Interesting proposal, Rein. Might one also say, do you think, that we
> could say that the ontological status of the arch is a function? In the
> mathematical sense.
> >>>>
> >>>> Martin
> >>>>
> >>>>> On Sep 2, 2016, at 9:30 PM, Rein Raud <rein.raud@tlu.ee> wrote:
> >>>>>
> >>>>> Let me point out a basic ontological difference between the two
> levels of the arch and the stones. When we speak about stones, we refer to
> things the wholeness of which is closed and implicit, ie the molecular
> structure of the minerals that make these stones up is, for us, not really
> relevant in the context of their “stoneness”. However, when we speak about
> the arch (as intended in Calvino’s parable) we are not actually referring
> to a similar “thing”. The arch is nothing but the relation in which the
> stones are placed to each other. Its own ontological status is that of an
> idea, or a formula. (As soon as we begin to think of stones as molecular
> structures, the same difference is highlighted on a lower level, as it can
> be with molecules consisting of atoms etc.) When Li Chun is looking for a
> cleaner arch, from which superfluous stones are eliminated, he performs an
> analogical operation to what mathematicians do when they reduce 3/18 to
> 1/6. Thus, in order to formulate the
> >> pr
> >>>> oblem clearly, we need to distinguish between the characters of a
> formula and an entity (the being of which is not contingent of the formula,
> as the stones can easily make up also something other than a bridge).
> >>>>>
> >>>>> With best wishes,
> >>>>>
> >>>>> Rein Raud
> >>>>
> >>>>
> >>>
> >>>
> >>
> >>
> >
> >
>
>
>