Tanja Hötte - A formal model for theories of concepts

In my talk I will present a formal basis for the presentation of theories of concepts.
The formal model is useful in two respects:

(1) It gives a frame for the comparison of theories of concepts and for clarifying their formal implications.

(2) By rendering all desiderata on theories of concepts formally, we are able to decide whether there can be a perfect theory of oncepts in the sense of a theory that fulfills all the conditions or whether such a theory would have to be contradictory.

   Each theory of concepts deals with a set of concepts, a set of extensions, a set of intensions and the relations between them. That is, we have a function f_e from the set of concepts to the set of extensions, a function f_i from the set of concepts to the powerset of the set of intensions, and a function g_i from the set of intensions to the set of extensions. If a theory of concepts is made in order to discuss the possession of concepts, all three sets might occur for every epistemic subject, again with relations between them and possibly between the non-subjective sets.   For example, formal concept analysis just deals with the latter kind of sets. Their sets of concepts actually is a set of pairs of intensions (in their case: attributes) and extensions that fulfills certain constrains.   In contrast, Fodor sees concepts as a mind-world relation. Thus there can only be subjective sets of concepts for him; each concept has to be bound to an epistemic subject.   Each theory of concepts is geared towards some special desiderata. These desiderata can be stated as formal conditions. For example, Freges condition that each concept has exactly one intension is expressed in this framework by the condition that the range of f_i just contains singleton sets.    Modern modal logic takes it that one concept can have different intensions depending on the context it is used in. These intensions can have different extensions as well. To illustrate this, regard the concept “mother of”. In perception-based context a mother would be the female caring for and raising a child. Switching over to a theoretical concept, the mother is the female who has born the child. Both women can of course be identical, but there are cases like a foster-mother where the extensions differ.