Monday 3 March 2014

Kripke's Puzzle and Semantic Granularity

(Added October 2016: my most up-to-date treatment of granularity can be found in Chapter 6 of my PhD thesis. This is an early, undeveloped attempt.)

This is the post where I first introduced my doctrine of semantic granularity. Follow-ups so far:

Facts and Granularity
Granularity and Quine
Metaphysical Realism and Conceptual Relativity: An Application of Granularity
Granularity and Relativism about Truth
Granularity and the Paradox of Analysis
The Principle of Compositionality and Semantic Granularity
Two Opposite Types of Granularity Difference

Meanings of expressions and belief-contents can be carved up at different granularities. That is, it can sometimes be the case that, when operating at one granularity it is correct to bundle two expressions or beliefs together as having the same meaning or content, while at another granularity it is correct to put them in separate bundles. I think this must be acknowledged in order to fully solve Kripke's puzzle about belief.

There are aspects of the puzzle which do not require this - i.e. the puzzle has some morals which do not involve this. But until semantic granularity is recognized there will be a remainder.

One aspect of Kripke's puzzle is like Frege's puzzle: we need difference-makers for 'Londres' and 'London' and the propositions they appear in, so that we can avoid the conclusion that Pierre here believes some proposition as well as the negation of that very proposition (i.e. we need to differentiate his 'Londres'-mediated beliefs from his 'London' ones). I do this with my accounts of names and propositions.

Another, closely related, aspect of the puzzle is that, once we have the required difference-makers, we need to put them to work somehow in distinguishing the sense in which Pierre has inconsistent beliefs from the sense in which he does not have inconsistent beliefs. Accordingly I distinguish internal and external inconsistency. Two beliefs are internally inconsistent iff no two beliefs with the same internal meaning could both be true. Two beliefs are externally inconsistent iff those very two beliefs, with their actual external projective relations to reality, could not both be true. Internal inconsistency implies external, but not the other way around. And one of the morals of Kripke's puzzle is that merely internal inconsistency does not constitute irrationality.

But there is a further aspect that remains puzzling even with the required difference-makers, and the distinction between internal and external consistency with its associated moral about rationality. And this comes out in Kripke's summing up of the puzzle: does Pierre, or does he not, believe that London is pretty?

And here, to see that this is still puzzling, it is very important that we take to heart Kripke's stipulation that he is using the language of belief reports not in a de re sense, but in a de dicto sense; that he is using forms like 'S believes that a is F' not in the sense of 'S believes, of a, that it is F' or 'S has a belief concerning a to the effect that it is F', but to actually specify belief-contents. Kripke gives a supplementary explanation of his meaning by saying that we could emphasize it by putting a colon in place of the that-clause: 'S believes: a is F'.

It is important to take this to heart because, if we stick to a de re sense, we can give an answer with what we already have; we can say, in answer to Kripke's puzzle question reproduced at the end of the second last paragraph, 'He does; Pierre believes, of London, via his "Londres" concept (or via his symbol "Londres" with its attendant use or internal meaning) that it is pretty. But he also believes, of London, that it is not pretty, but in that case his belief goes via his "London" concept (or via his symbol "London")'.

And this is just using the stuff we needed anyway to solve Frege's puzzle. And furthermore we can add that there is no irrationality on Pierre's part here, since his two conflicting beliefs, while externally inconsistent, are internally consistent, and he doesn't know that they concern the same object.

But this doesn't enable us to answer Kripke's puzzle-question as he intended it, namely in a belief-content specifying sense. Indeed, it can seem to be part of the problem. We wanted to allow that Pierre is not being irrational, and distinguish his 'London' concept from his 'Londres' concept. But then what was going on when, in the first part of the story, we felt the pull of saying that Pierre believes that London is pretty – i.e. that Pierre believes the same thing that we mean when we say 'London is pretty'?

The solution is to see that a shift in granularity has taken place, and that the answer to Kripke's question - indeed, the meaning of that question - depends on what granularity one is operating at. In the first part of the story, we naturally go for a granularity coarser than the one we will end up at, in order to capture in an efficient way what Pierre's and our contents have in common. Then, when the special “splitting” (mistaking one for two) situation arises, it becomes much more convenient to describe the situation using the same device of belief reports, but at a finer granularity. 

Kripke's puzzle is puzzling because one part of the story induces one granularity, and another part induces another. With granularity kept in the background as an unarticulated and untheorized contextually variable aspect of the sense of belief reports, the results seem to contradict each other. Once we realize what is going on, the results can be seen to be no more contradictory than 'All the beer is in the fridge over there', under a certain natural contextual restriction of quantifiers, is of 'There is beer at the pub'.

Philosophers already talk about different granularities, but generally the distinction is made between two quite different notions: for example, the set-of-worlds conception of propositions is said to be more coarse grained than the Russellian. Here, I am keeping to one conception (which, in comparison with those just mentioned, is left more intuitive), but saying that we can operate at different granularities in individuating meanings, roles in language systems, and the contents of beliefs. The idea is that semantic notions such as that of synonymy and belief content are flexible devices, in that they can be used to bundle expressions and representations together in multiple ways.

The underlying idea here, analogues of which appear in connection with other things besides linguistic meaning and the content of belief, is quite commonsensical. For example, consider someone who takes a board game and alters some rules, inaugurating a social institution of playing to the altered rules which goes on along side the practice of playing the original game. Are we to say there are two different games here, or two different versions of the one game? It seems like common sense to say that one can say either. It's not as though there's some answer here which we haven't yet managed to find out. So, we individuate games at different granularities. And this is part and parcel of the usefulness and flexibility of our concept of a game. I think the same holds for the concept of meaning.

While this idea is quite commonsensical, the idea that it should be taken seriously in analytic philosophy of language appears quite radical. (It is as though, without really thinking it over, people have rejected any such move as inherently inimical to analytic conceptions and methods. A bit like vagueness before analytic philosophers began taking that seriously.)

Interestingly, after I had independently started applying the terminology of granularity and bundling to the matters of Kripke's puzzle and internal meaning, I found that AI researchers working on word sense disambiguation have been talking the same way (without apparently reflecting much on it philosophically, let alone from the point of view of the problems of analytic philosophy of language).

In this post I have tried to introduce the doctrine of semantic granularity, a doctrine which has come to assume an important role in my thinking. I have motivated it in the first instance using Kripke's famous puzzle about belief, which is also how I arrived at it. In subsequent posts I will develop the idea further and outline further applications of it.

[Here is one further application. - TH 25/8/14.]


Kripke, Saul A. (1979). A puzzle about belief. In A. Margalit (ed.), Meaning and Use. Reidel. 239--83. [Online here and here as of 4/3/14.]


  1. Hi Tristan

    It seems to me that we don’t have a problem if we stick the Russell/Frege theory of meaning. It’s when we try to speak of London (and Londres) and statements referring to it/them that we get a problem.

    Isn’t that just too bad for reference?

    we need difference-makers for 'Londres' and 'London'
    I think that if we go a little further and split sign, sense and the world it all becomes pretty straightforward. Let’s use punctuation: *London* is a sign, /London/ is a sense/concept and [London] is a big city that I live in.
    We don’t need a difference-maker for the signs *London* and *Londres*, they’re different signs.

    Nor do we need difference-makers for our senses of /London/ and /Londres/, because they’re both the same. In fact, it’s gets a bit confusing having /London/ and /Londres/; let’s use /L/. *London* and *Londres* both signify /L/.

    Unless, Pierre uses them. When Pierre uses *Londres* he signifies /LP1/, which includes the idea of “is pretty” and when Pierre uses *London* he signifies /LP2/, which includes the idea “is a dump”. /LP1/ is different from /LP2/ and we don’t need to search for difference makers.

    And this comes out in Kripke's summing up of the puzzle: does Pierre, or does he not, believe that London is pretty?

    Which London? We have a problem if we think that Pierre thinks [London] is pretty, because he also seems to think that [London] is a dump. But does Pierre's "pretty" refer to [London]?

    It seems to me that “Pierre believes that London is pretty” misses an awful lot of the sign/sense/world distinction out and (if taken a certain way) just misrepresents the situation. Pierre uses *London* to refer to /LP2/ that he believes corresponds to [a part of the world]. He doesn’t believe [London] is pretty at all he believes that [a part of the world and /LP2/ correspond: his belief does not refer to the world but to the correspondence of a concept and the world.

    1. I don't find what you're saying very clear but thanks for reading and commenting.