[time 1123] Re: [time 1119] Monads (Re: [time 1105])

Koichiro Matsuno (kmatsuno@vos.nagaokaut.ac.jp)
Thu, 16 Dec 1999 12:57:24 +0900

Dear Hitoshi and All,

   At 22:58 on 15 Dec 1999, Hitoshi Kitada <hitoshi@kitada.com> wrote:

>Then may I ask what do you think a right way to realize consistency and the
>completeness simultaneously?

   A tough question, indeed. I don't know the answer.

   May I add a small footnote here? Most often, we do both syntactic
integration and semantic concretization when we try to say anything.
Consistency is for syntactic integration, and completeness for semantic
concretization. If both syntactic consistency and semantic completeness are
literally synchronized with each other, Leibniz' Monadology must be the best
buy. However, once it is legitimately noticed that semantic concretization
proceeds in the empirical or practical domain while syntactic integration
does in the abstract domain, the literal synchronization between the two
would come to get into trouble. The second best one could imagine might be
to let semantic concretization drive the subsequent syntactic integration
while being driven by the necessary failure in the preceding consistent
integration. An example of this endeavor is Karl Popper's falsification in
the practice of empirical sciences. Any sound model conceived for an
empirical phenomenon must be concrete enough to be falsified later. A
positive implication of the falsification business is seen in that
concretization persistently goes beyond syntactic integration since possible
concretizations constantly remain innumerable.

>I do not see your "model" of the update. Could you describe it more

   Just for the sake of argument, consider the law of action and reaction in
classical mechanics. The third law of mechanics is about syntactic
integration. However, implementing each action and reaction is about
semantic concretization. If there is no synchronization between the two, the
concretization process will have no model of making itself concrete enough
in advance. Despite that, one likelihood of having a model on the semantic
concretization might be to let the law in the abstract domain be fulfilled
if each concretization in the empirical domain is properly abstracted. One
advantage of this strategy is to enable one to say that movements in the
empirical domain proceed so as to fulfill the third law of mechanics,
instead of saying that movements already fulfilling the third law should
proceed. I have a few concrete examples of this sort.

   Our problem is this: Once measurement or observation as a concretization
process enters, contradictions or inconsistencies would become inevitable.
One way to live with these inconveniences is to let the abstraction of
syntactic integration also be part of empirical activities.

>So you set the basis on our existence?


>Completeness is implicitly assumed in our daily life: We always think we
>what we want to express fully well, but it is usually an illusion. This is
>case also in sciences, which is the cause that we need to make
>forever. If completeness had been realized, we need not exist.



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