Anticipation as Prediction in the Predication of Data Types
Symposium 5: Computational Intelligence and Experimental Design within Dynamical Anticipatory Systems and Networks
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.