This is another instalment in the 'Applications of Granularity' series, the earlier members of which are listed at the bottom.
The doctrine of semantic granularity offers us a way of resolving the paradox of analysis: if the expression on the right-hand side of an analysis gives the meaning of the expression on the left-hand side - the expression (for the notion) to be analyzed - then, if the analysis is correct, both sides mean the same. But in that case, how can an analysis be informative?
Now, it might be that some things worth being called analyses - even if they take the classical form of a biconditional - do not, and do not purport to, 'give the meaning' of the left-hand side. They may merely be intended to shed light on the meaning of the left-hand side by exhibiting a connextion between it and the right-hand side.
For such cases, there is no paradox of analysis. But it seems to me, and evidently many others, that there are indeed analyses which go beyond this exhibiting-a-connection, and really do purport to 'give the meaning', in some sense, of the left-hand side.
I propose that considerations of semantic granularity can resolve the paradox here. All such cases, of true, meaning-giving, non-trivial (i.e. informative) analyses - but note that whether an analysis is trivial may depend on its precise meaning in the idiolect of the subject considering it - are such that, at some reasonably granularity, the LHS and the RHS mean the same, but at another, finer granularity, they do not.
The RHS's of many good meaning-giving analyses, for instance, will have more structure than what they are analyses of. And this itself may make it the case, at a certain granularity, they have different meanings. In general, there will be differences between the LHS and RHS - where they occur, the effects they have on thinkers and speakers, and so on - which may be counted as meaning-constitutive, in which case we are operating at a granularity on which they should be said to be non-synonymous. But nevertheless, if they are good meaning-giving analyses, there will be another granularity at which these differences are not made to count, and at that granularity the LHS and RHS may be said to mean the same.
Earlier posts in the series:
Granularity and Quine (in which the series is introduced)