Structure and Dynamics

I am concerned with the distinction between data processing, modeling and actual theory formation, with the generating of empirically interpretable additional theorems, and in particular how formalization, far from abstracting away from data, makes one look at levels of detail one never before even noticed.

I shall begin by examining a conjecture (due to my pupil Zhang Wenyi) about the formalism for distinguishing crowds and ‘groups’ from corporations/corporateness: the former are what I may call event-theoretical topologies (neighborhoods) event theory having to do with temporal-aspectual-modal categories, on which I have written elsewhere. In turn, this has everything to do with the whole controversial question of fuzziness, which I shall go into here. I shall argue that so-called fuzzy sets are topologies, particularly having to do with the saliency of the ‘extent’ of a field, such that, as Zadeh, the originator of Fuzzy Set theory, himself long since pointed out, fuzziness is essentially a matter of Decision Theory rather than a theory defining a species of conceptual categories as such. This, in turn, leads me into a brief consideration of set topology, namely the distinction between open and closed sets and so on with regard in particular to events. This is all about inclusion, exclusion and well-boundedness.

The foregoing will take me into a consideration of a certain problem in kinship-group theory, namely, whether one can properly talk of cognatic (‘non-unilineal’) ‘descent groups’. The solution, again, depends upon reconsideration of the role of ‘choice’ (decision-theoretically understood) in the theory of kin-groupings and thus the matter of defining ‘modes of lineation’ in the space of genealogical reckoning, and thus in turn the whole theory of ‘descent’ itself. Here my foil is the work of Fortes, of course.

Finally, I want to adduce a specific example of the way a formal theory of the map from Primary Genealogical Space (PGS) to a particular system of kin-categorization (and terminology) has led directly to a theorem that clarifies a hitherto controversial idea, namely Fortes’s notion of ‘complimentary filiation’ in the context of his argument against ‘alliance theory’ in the sense of Leach. It turns out that this matter is resolved by a theorem of the formal account of an asymmetric-alliance terminology.