Text: What is an explaining formal Theory?
This is a working paper which will probably be rewritten several times in the next months
AUTHOR: Dr. Gerd Döben-Henisch
FIRST DATE: December 27, 1995
DATE of LAST CHANGE: March-5, 96
Presuppositions
In the Introduction to KIP II Theory we have postulated a phenomenological point of view as our starting point. This point of view offers us the class of all phenomena D-PHEN, where we localized a several special subsets constituting the domain of different theories. There we gave also a first outline of the basic elements of a theory describing and explaining some properties of the domain under investigation.
Epistemology and Theory of Science
We consider epistemology to be that discipline which reflects about the general conditions and principles of our knowledge. And we consider Theory of Science as that discipline which as a branche of epistemology investigates the question, what are scientific theories
The Observer constitutes a domain and a measurement
Any explaining theory has to presuppose some domain of investigation, which is in the case of humans inevitably the set of phenomena which can be experienced by humans. In the general case this is D-PHEN. Possible special cases are e.g. D-OBJ and D-PHYS, where SUBSET(D-PHYS, D-OBJ), SUBSET(D-OBJ, D-PHEN).
The theory producent -until today usually a human person- has to select some such domain of investigation by pointing out those qualities he wants to consider as being characteristic for his domain of investigation.
The selection of a subset of D-PHEN is realized by the introduction of basic desriptive concepts which constitute what has to be seen as a datum in the intended theory.
The communication of descriptive concepts demands for some kind of a language to represent the data of the intended theory. We call such a language the data language LD. The text written with the data language is called a data protocol D-PROT. A single statement of D-PROT we call a datum [DAT].
Formal Theory
The data protocol reports only single events, eventually indexed by some space and time notation. To represent complex relations between those events and to state general laws one needs an additional text T written in some language LT which represents a theory
We assume that all expressions of LD are also expressions of LT, i.e. SUBSET(Expr(LD), Expr(LT)), and that LT and LD are subsets of a settheoretical language.
A formal theory is a theory with LT and LD as formal languages and organized as structure <O,R,A > containing sets of objects O, sets of relations R, and axioms A. The inference concept INF, which tells us what is a valid consequence of A, can be part of the presupposed set theory -which is assumed here-, or has to be individually introduced as part of the theory concept. The set of consequences C of a theory T is also called the set of theorems of T. It is assumed that the data DAT of a theory T are a subset of the axioms of T, i.e. SUBSET(T-DAT, T-A).
Classification of Sciences
According to the above mentioned criteria we can construct a simple classification of sciences.
If the set of data is empty, then we have a purely formal theory.
If the measured data are restricted to the domain D-OBJ, then we speak of empirical data and the resulting theory is called an empirical theory.
If the measured data are not restricted to certain subsets of D-PHEN, i.e. are open to the whole set D-PHEN, then we have pychological data and the resulting theory is called a psychological theory.
Because empirical data are subsets of psychological data can empirical theories be part of psychological theories. Within a psychological theory one can use empirical theories in a threefold way: (i)Consciously, i.e. they are considered as part of D-PHEN; (ii) uncorrelated, i.e. one looks to D-OBJ as empirical data and structures without any direct relationship to non-empirical phenomena. (iii) correlated, i.e. one uses two sets of data, empirical and non-empirical ones, and tries to correlated both sets. This can be done (iii.1) empirically via time intervalls, or (iii.2) psychologically on the basis of the subjective knowledge of both. In case of (iii.1) one has the special problem, that non-empirical phenomena are only given indirectly by some articulations of a human. The articulations, which represent the intended phenomena are not the phenomena themselves; they are only given by a presupposed representation-relation. Insofar this presupposed relation works and insofar the correlation is feasible allows this e.g. the encoding of purely subjective data by physiological or ethological data and vice versa. In the correlated case could then a psychological observer use empirical theories to explain the occurence and the behavior of subjective data with respect to empirically hypothesized physiological and physical mechanisms as responsible sources for the 'generation' of the psychological phenomena.
Example 1 of a simple theory (Nov-10 95)
Comments are welcome to doeb@inm.de
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