An Analogical Approach

In an atomistic, analogical approach to description, our task is to select specific occurrences to model behavior after. In this kind of approach we always predict behavior in terms of positive contexts. Given a positive context x = a l a 2...a k (where the a i are each primitive unanalyzable elements), we first determine all the positive supracontexts of x; that is, all the positive contexts that contain x as a subcontext. For instance, if x = abc, then the positive supracontexts of x, in addition to abc itself, are ab—, a—c, —bc, a—, —b—, ——c, and ---. In order to list the positive supracontexts of any given positive context x, we systematically remove the primitive elements from x. In general, if x contains k primitive elements, then there will be 2 k positive supracontexts for x. With no primitive elements removed we have the given primitive context x = a l a 2...a k . Removing one primitive element, we have k possible supracontexts: $$- {{a}_{2}} \cdots {{a}_{k}}{{a}_{1}} - {{a}_{3}} \cdots {{a}_{k}} \ldots {{a}_{1}}{{a}_{2}} \cdots {{a}_{{k - 1}}} -$$ The next step is to remove two primitive elements, which will give us k(k—1)/2 supracontexts: $$- - {{a}_{3}} \cdots {{a}_{k}} - {{a}_{2}} - {{a}_{4}} \cdots {{a}_{k}} \ldots {{a}_{1}}{{a}_{2}} \cdots {{a}_{{k - 2}}} - -$$ Continuing in this fashion, we keep eliminating more primitive elements. Eventually we arrive at a stage when only one primitive element remains in each supracontext. At this stage there will be k supracontexts: $${{a}_{1}} - \cdots - - {{a}_{2}} - \cdots - \ldots - - \cdots - {{a}_{k}}$$ Finally, we get the null supracontext υ, for which all the k primitive elements have been removed: ——... —.