Wednesday, 12 November 2014

Granularity and the Paradox of Analysis

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)

Granularity introduced:



  1. I am reminded of the poet's dictum that there are no synonyms in the English language. There's a sense in which that's true and a sense in which it's not. It's plausible that some notion of SG could help with that.

    Does a granularity thesis make experiential identities like "water is H2O" no longer easily distinguishable from analytic identities? Is that a problem if so?

    - S

    1. Re. your first paragraph: totally! I think SG can straightforwardly explain a sense in which that is the literal truth.

      Re. your second paragraph, I don't see any problem. Perhaps at some coarse granularity, some experiential identity will come out meaning the same as an analytic one, but that will be a very coarse one for many purposes, and there will always be a finer one at which they come out different.

      For my part, I think the analytic truths are a subset of the a priori truths, and that there is an important distinction between the latter and empirical truths. I am developing an account of the a priori / a posteriori distinction and my granularity stuff doesn't seem to be in tension with it. (There's a little on the account I allude to in this post but more coming.)

      Another question your question raises, since it seems like it may be an assumption in the background (although maybe I'm wrong about that, as I'm not sure I understand where your question comes from), is: are the left hand and right hand sides of analytic identity statements always synonymous (at some granularity, perhaps, if you want to bring that into it)? I think the answer is probably No: semantically ascending to make the point, it can be analytic that the extension of two terms is the same without them having the same intension at all.

      Thanks for commenting.

  2. Please find some related references on the nature of (Quantum) Reality before our dualistic language games slice IT up into seemingly separate bits-and-pieces (just like Humpty Dumpty)

  3. I don't think that would be relevant. It seems to me like you've just picked up on a couple of words I've used and hallucinated a connection with your pet concerns. I might be wrong, but I don't know what else to think, given what you've said here.

  4. Hi Tristan,

    I didn't read your whole granularity series, but I have a question. Besides the person-relative notion of informativeness (where the language of the person is crucial, as is her background knowledge), there is an 'objective' notion of informativeness. In the latter case, the analysans and the analysandum, despite always having the same extension, express different senses. I think it is the latter notion that is used in the formulation of the Paradox of Analysis. For the puzzle seems to be that an analysis cannot be informative and express a synonymy relation at the same time (if synonymy is idendity of sense): informativeness entails non-synonymy.

    Wouldn't that objective interpretation of informativeness pose a problem for your solution?

    1. Hi Luis,

      Thanks for the commend and pardon the late reply. I don't see a problem here - the appearance of one, I think, should be resolved by saying that perhaps informativeness entails non-synonymy at some granularity. Given that, and given some informative analysis, two options arise: it is still one that can be counted as a meaning-giving analysis, in which case the LHS and RHS will be synonymous at some coarser granularity, or it is a sort of analysis (put scare quotes around that if you prefer to use 'analysis' only for things which purport to me meaning-giving) which isn't meaning-giving, but which shows or purports to show a connection. I invite you to check out some other members of this series of posts!