Is conceptual analysis recursive?

Question

For example given the explanandum "the kettle has the ability to boil water" analyzed into a set of explananas:

1. "the kettle has the ability to store water"
2. "the kettle has the ability to heat the water"
3. "the kettle has the ability to draw electricity" (not a great analysis but just as an example). 

And further analysis of "the kettle has the ability to store water" into:

1.1. "the kettle has the ability to be water tight"
1.2. "the kettle has the ability to provide water"

Would all of the statements be explanas of the same analysis of the original explanadum?

Because It seems as though there are 2 explanadums "the kettle has the ability to boil water" and "the kettle has the ability to store water"?

Thank you

Answer 1

Here are some cursory thoughts. I will add more given time.

(a): Is all conceptual analysis recursive? A: Maybe, but that may not be a bad thing.

(i) Let's say that we have a base language L1 and we extend this language finitely many times. Then we consider one (quite strong!) model of conceptual analysis. Let a conceptual analysis step (CAS) take a concept C and return an analysis of C- an ordered tuple {D1,....,Dn} with each Di coming from an extension of L1 strictly less than C's. Then there should be no circularity involved.

(ii) The general intuition here is that we don't give an analysis of a concept in terms (ie "less" primitive concepts) that we don't already understand (in principle, if not in practice!).

(iii) Given some reduction relation, this process terminates in a finite number of steps, however concepts in the base language admit of no analysis. This creates a process entirely akin to foundationalism in epistemology, its likely that we can transpose arguments for and against. In general, I doubt this is a problem, a language ultimately must have some primitive concepts.

(iv): So we have a least one way in which conceptual analysis is recursive: we apply a routine and iterate the same routine on its own output- but not circular. Or no more circular than it is to have a base language, anyhow.

However, it seems to me that your main question is regarding explanation. That is a far broader topic ( I think) then conceptual analysis. (b): Would all the statements be explanatia of [the analysis of the original explanandum? A: Possibly.

(i) Let <e1,e2> be the explanatory relation, it is a simplified model but it will do for illustration. e1 is the explanans, e2 the explanandum. You are considering e's as propositions in general ( a good choice, I think) or as sets thereof (more risky, see below). You are asking if given e2 -> e3, and e1 -> e2', where e2' is somehow contained in e2, whether e1 is also contained in e2. Its clear that the answer to this will depend on what you mean by the containment relation.

(ii) If set theoretical containment, then no. Supposing that e2 is indeed a full explanation, then e2 clearly need not contain e1. For e2 is already a full explanation and adding things to a full explanation results in a false explanation (see Salmon for this argument, the general intuition is that eplanatia make explanandum more likely (perhaps epistemically), to add some additional a1 to a full explanans e2 is thus to claim that a1 is part of that explanation when it is not. But that is clearly false).

(iii) Perhaps you mean informationally (whatever that means). Again supposing that your analysis of the first statement in the original analysis is correct, it follows that the two are interchangeable - they are in some sense translations (this is what we mean by conceptual analysis in the first place). Given this and in your example, e2 (or part of it) is equivalent (under information) to e1 and thus in some sense contains e1's information.

(iii) Sidenote: we ought to be suspicious about allowing our explanatia to be conjuncts,sets,etc of statements. The general intuition should be that logical implication, set membership are different from the explanatory relation, and we would have to show that they always carry or are compatible with explanation- I believe I got this from Ruben's explaining explanation.