1) If a distinction is made between scientific inquiry that proceeds via induction and scientific inquiry that proceeds via deduction, what are the core activities and disciplines of each?
My attempt, which may serve as guide to what I'm after, is below.
Inductive fields of science:
- data collection
- database management
- statistics with frequentist probability (confirmatory)
- data mining (exploratory)
Deductive fields of science:
- axiom definition
- ontology engineering
2) If a mixture of deductive and inductive methods are used, what are the different disciplies for using axioms and data in analysis? To me, the obvious one that springs to mind is statistics with Bayesian probability as the inference paradigm. How do regression, classification and data mining fit into this division?