Lonergan sets up three steps in generalizing the
example from algebra (re: the clues).

Name the unknown: “The
nature of ….” (2.2)

Similars are similarily
understood (abstraction to universals)

Anticipates that similar same
data will have the same insight. True whether

data in relation to senses
(known before one has turned to a search for, or an anticipation
of “nature of…” something)

hence the nature of X (where X
is understood in the same way no matter place or time)

or data in relation to each
other (become the proximate materials for understanding the
“nature of…”) Hence, one turns to organizing
this data only if one is on the search for the “nature
of….”, however seeking insights into this nature in
terms of coorelations/functions.

"Indeterminate correlation
to be determined/indeterminate function to be determined”

Anticipates similar data will be
understood in the same way, and that understanding is formulated
in a universal definition which is a determinate function or
correlation.

Notice how we heuristically
anticipate something at each step:

Anticipate the nature

Anticipate the
universality of the insight

Anticipate the correlation/function.

One general summary of the
emergence of modern scientific insights and definitions.

Merely Descriptive

Descriptive insights leading to the
identification of the “nature of…”

The “nature of…”
leading to more refined descriptive categorizations.

The descriptive categorizations
leading to possibilities of relating the data

The emergence of the
"indeterminate
correlation to be determined/the indeterminate function to be
determined". (In calculus, differentiation equations are ways of
finding functions, hence it leads to an extremely powerful way for
anticipating the answer).

Analogy: just as the discover
of patterns in arithmetic is algebra, and such patterns are
formulated in algebraic rules/laws (eg. a + b = b + a), and then
these algebraic laws can then be used to solve problems; so the
discovery of patterns in algebra is calculus, and such patterns
are formulated in the laws/rules of calculus (eg. power rule), and
then these laws/rules can be used to solve problems. In the case
of Algebra, the solution is an arithmetic number. In the case of
calculus, the solution is an algebraic function.

This anticipation then leads to a
series of more precise collections of data in their relations to
each other, which in turn provides the “image” into
which this highly potent anticipation of a function can become
determined.

Once determined, then the
definition in a functional equation emerges.