# How do the different fields of core scientific methods - like statistics - fit into a deductive vs inductive classification?

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
• analysis
• statistics with frequentist probability (confirmatory)
• data mining (exploratory)

Deductive fields of science:

• axiom definition
• ontology engineering
• logic

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?

## 1 Answer

Science is inherently inductive: you collect data about things and try to reason from it, and you cannot (except in very rare cases) collect all possible data.

Bayesian analysis just provides a formal structure around your inductions that is different than the frequentist structure. It's still inductive at its heart in that you will conclude that X is true (p < whatever) on the basis of N examples. Regression, classification, and data mining as typically used all fall into this camp also--extrapolating or interpolating general patterns on the basis of a non-exhaustive set of samples. The cases where you have all examples and don't want to think about any more are pretty limited (but those could be deductive, strictly speaking).

Modeling is another area which may seem ambiguous. Most modeling is essentially deductive--given that we think we know X, Y follows in a non-obvious and perhaps computationally intensive way. But once you use your model to fill in for missing data, you're taking an inductive step.

However, I don't think that in actual practice scientists spend a lot of time worrying about the distinction between inductive and deductive modes of inquiry. A lot of the interesting questions involve both mixed in tremendously complicated ways (e.g. nonlinear systems research, with complex mathematics telling you the consequences of rules that you've derived inductively, etc.). Indeed, the whole idea of "propagation of error" highlights how induction (on data) and deduction (giving mathematical formulae) are frequently and deeply mixed. A scientist ought to spend his or her time considering estimates of errors rather than which steps are inductive and which deductive.

• I'm not really trying to be descriptive in trying to see when scientists use deductive vs inductive steps. I'm trying to be prescriptive for content organization purposes. A "metaphysical" +1 for the observation on modeling (I don't have vote-up privilege yet). – user1202664 Sep 28 '12 at 14:26
• "Science is inherently inductive"? I know it's common since the turn early 1900s for inductivists to hide behind the "difficulty" of defining induction or "modern definitions" of induction. But induction is induction (we all know what it means in contrast to deduction and guessing) and its not ever what scientists do if they want their explanations to rest on a firm footing. – orome Mar 29 '17 at 11:02
• @raxacoricofallapatorius - Given the nature of data, one has no choice but to reason inductively (setting aside precisely what that means, but contrasting it from both deduction and guessing). Just because something's inductive doesn't mean it's unreliable in practice. – Rex Kerr Mar 30 '17 at 16:36