Knowing a Concept and Concept Indistinguishability

     What does it mean to say that someone knows a concept? What kinds of capabilities do we expect from someone that knows a concept? There are a variety of ways to answer this question. The figure below lists a set of capabilities that one might expect to be available to a person who knows a concept. The first is the abilitiy to correctly recognize whether a particular example is or is not an example of the concept in question. I have referred to this procedure as Identify. A second is the ability to Generate positive and/or negative examples of a concept. And, finally, there is the ability to explicitly State the definition of the concept.
   
     This provides a characterization of what it might mean to "know" a concept; and it also provides a basis for deciding when two different entities...say a "teacher" and a "learner" have the same concept. This is indicated in the lower section of the above figure. Notice that I have not tried to define the notion of identity between C and C'. Rather I have been content to focus on the conditions under which we might characterize C and C' as indistinguishable. And, as you can see, the definition depends on seeing whether or not the answers of the two concept holders are or are not the same.

Induction,Concepts, Uncertainty

© Charles F. Schmidt