# Re “Function”, “Implicit Definition”, “The Objective of the Analysis”, and “Scientific Significance”

“Functional” is for Lonergan a technical term pertaining to the realm of explanation, analysis, theory; it does not mean “who does what” in some (descriptive) realm of activity.  ¶ Lonergan illustrates his basic meaning of ‘explanation’ by referring to D. Hilbert’s method of implicit definition: ‘Let us say, then, that for every basic insight there is a circle of terms and relations, such that the terms fix the relations, the relations fix the terms, and the insight fixes both.’  … ‘Thus the meaning of both point and straight line is fixed by the relation that two and only two points determine a straight line. ‘In terms of the foregoing analysis, one may say that implicit definition consists in explanatory definition without nominal definition.’ (See CWL 3 Insight 12/ 36-37)  Lonergan went on to identify the contemporary notion of a “function” as one of the most basic kinds of explanatory, implicit definition – one that specifies “things in their relations to one another” (CWL 3, 37-38/61-62)…In Lonergan’s circulation analysis, the basic terms are rates – rates of productive activities and rates of payments.  The objective of the analysis is to discover the underlying intelligible and dynamic network of functional, mutually conditioning, and interdependent relationships of these rates to one another.  [CWL 15, 26-27  ftnt 27]

Hilbert has worked out Foundations of Geometry that satisfy contemporary logicians. One of his important devices is known as implicit definition. Thus the meaning of both point and straight line is fixed by the relation that two and only two points determine a straight line.  ¶In terms of the foregoing analysis, one may say that implicit definition consists in explanatory definition without nominal definition.  It consists in explanatory definition, for the relation … is a postulational element such as the equality of all radii in a circle.  (Implicit definition) omits nominal definition, for one cannot restrict Hilbert’s point to the Euclidean meaning of position without magnitude. … The significance of implicit definition is its complete generality (and potential applicability).  The omission of nominal definition is the omission of a restriction to objects which, in the first instance, one happens to be merely thinking about.  The exclusive use of explanatory or postulational elements concentrates attention upon the set of pure relationships in which the whole scientific significance is contained. [CWL 3, 12/36]