Anticipation as Prediction in the Predication of Data Types

Symposium 5: Computational Intelligence and Experimental Design within Dynamical Anticipatory Systems and Networks

Michael
Heather and

CEIS,

http://computing.unn.ac.uk/staff/cgnr1/

Typing is an essential feature of modern
systems theory. It is even at the essence of anticipation in anticipatory
systems. Yet typing appears in many different guises. From the quest of ancient
philosophers seeking the basic type of matter that makes up the world to the
current theory of the Standard Model of the fundamental particles of this
universe, and experiments to find them with CERN's hadron collider -- typing
still remains the burning question. Modern interest in information systems,
where typing has proved to be important, has confirmed recognition that
physical systems and information systems are not independent of one another.
However, there is a vast unknown chasm of understanding between fundamental
particle types and the operational information of genome types that are needed
in current biology and medicine.

That information is concerned with
language and logic was fully realised by Aristotle who it seems was the first
to apply to a system of types the word *categories * which in Greek originally referred to a legal
indictment, that is a statement that had to be drafted with a full formal
specification to stand up to rigorous argument in court. Translated into Latin,
the equivalent word for a legal indictment is *predicamentum*. Thus the
words *categories* and *predicates* have continued to the present day
in this sense in English. The predicate is usually language-oriented and the
category logic-related.

Typing can be traced back to Sanskrit
literature and did not begin with Aristotle but the only pre-socratic attempts
at classification relevant to anticipatory systems are perhaps the well known
fundamental types of Parmenides (*everything stays the same*)
and Heraclitus (*all is flux*)
which still continue today to receive considerable attention in philosophy. At
first sight the constancy of Parmenides
may seem to have little relevance to anticipatory systems if their prime
significance is to predict their own future states. However this is to presuppose
a simple linear time scale as an independent variable where an anticipatory system
embodies a model of itself, which is but weak anticipation. However the
Parmedian aspect of anticipatory systems is their intensional form where the
prediction can be ascertained from the typing of the system independently of
time. The extensional form of the anticipatory system is that of Heraclitus
where the anticipation lies in the semantics. The extension may well include
time but again if time is an independent variable it is still only weak
anticipation. In strong anticipation time is part of the data and may therefore
consist of a variety of forms of time.

Most of the theoretical work to date on
anticipatory systems relates to weak anticipation but the twenty first century
has moved from local dynamical systems in physics where these methods may be
quite adequate on to problems of globalisation and to very complex subject
areas like biology and medicine which call for solutions with strong
anticipation. As already implied, the troubles arise in the typing when there
is a lack of tools powerful enough to produce results with strong
anticipation. Twentieth century
mathematics has been dominated by a logic which is Parmedian in extension as
well as in its intension. The problems may be examined from the view points of
the three eminent mathematicians.

● the
undecidability of Gödel

● the paradox of
Russell

● the
impredication of Poincaré

Gödel has famously shown that both for
intension and extension it is not possible to determine whether any system
based on number and relying on axioms is true or false. This gives a general result that makes the
goal of ultimate consistency within set theory unattainable. Russell's paradox
and Poincaré's impredication are particular manifestations of Gödel's
undecidability.

As is well known Russell was acutely
aware of the inadequacy of set membership because the set of all sets could not
be a member of itself and from his study
of denotational predication explored a number of advanced theories of typing
to overcome the problems but on his own
admission these did not succeed. Poincaré had already pointed out that the crux
of the problem lies in the scoping of the predicate. This also has three
relevant strands to it:

● the logical
system of Whitehead & Russell's *Principia Mathematica *allows solely for a simple
predicate giving rise only to weak anticipation

● a predicate has
to be coextensive with its subject to give certainty

● a predicate
needs to be variable to allow for a varying context

Real problems that arise in closed
worlds of information systems provide very striking examples of the
difficulties that result from simplification and normalisation of predicates.
There is a demand for strong anticipation if information is to be reliably
exchanged through open interoperable systems. This will only be realisable from
the implementation of formal systems that can avoid the undecidability of
Gödel.