On the very idea of non-explicit analysis
Dave Chalmers told me to read some of his papers. I have, and I'll probably say more on the deducibility problem soon. Here is just a little thought on conceptual analysis.
Chalmers suggests that we don't need explicit necessary and sufficient conditions to analyse a concept. Rather, we can analyze it just by considering its extension in hypothetical scenarios. What is it to consider a hypothetical scenario? The result seems to depends on how the scenario is presented. For example, 'the actual scenario' denotes the same scenario as 'the closest scenario to the actual one in which water is H2O'. But the difference in description could make a difference for judgements about extensions. Chalmers avoids such problems by explaining (§3.2, §3.5) that to consider a scenario is to pretend that a certain canonical description is true. Hence to analyze a concept, we evaluate material conditionals of the form 'if D then the extension of C is E', where D is a canonical description. (Are there only denumerably many epistemic possibilities or can D be infinite?) Now fix on a particular concept C and let K be the (possibly infinite) conjunction of all those 'application conditionals' (§3) that get evaluated as true. Replace every occurrence of 'C' in K by a variable x. Then 'something x is C iff K' is an explicit analysis giving necessary and sufficient conditions for being C.
There may not always be a simple, obvious, or finite explicit analysis, but at least there always is some explicit analysis. If moreover satisficing is allowed, it is very likely that we can settle with something much less than infinite.