In this chapter Lonergan analyzes the role of insight in the first two types of inquiry. The first two are classical and statistical methods of empirical science. The other two are the dialectical method of philosophy and the genetic method used to understand development. These forms of inquiries are heuristics structures for discovering knowledge. "All methodical investigations employ heuristic structures." Lonergan's worldview of the universe is emergent probability. "The notion of scheme of recurrence with its probabilities of emergence and survival" is crucial in understanding Lonergan's view.
Classical Heuristic Structures
"In every empirical inquiry there are knowns and unknowns. But the knowns are apprehended whether or not one understands: they are the data of sense" (77). The unknown to be known is to be known as the nature of .... Uses the unknown number x like in algebra. So in this chapter Lonergan is giving examples from empirical science on how insight emerges. The inquirer "follows up he seeks the 'nature of ...' by noting that the 'nature of ...' must be the same for all similar sets of data" (78). Similarities in their relations to us and to each other. The third step says let some "indeterminate function be the required function" (79).
Scientists achieve understanding at the end of the inquiry. The inquiry is methodical and method consists in ordering means to an end. They can order the means to an unknown end through the heuristic structure. The structure is classical because it is named for the work of Galileo, Newton, and Einstein.
Statistical Heuristic Structures
First, whereas classical investigation "heads towards the determinations of functions and their systematization, statistical investigation clings to concrete situations" (81).
Second, statistical inquiry attends not to the process but the results.
Third its attention is focused on "frequencies."
Fourth, they attempt to arrive at "exact numbers;" they do not make the same effort in "exact explanation."
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