Quine on Facts: A Case-Study in Projective Fallacies

Quine was famously skeptical about facts. As I said in the last post, Quine can be seen as resolutely maintaining something which Strawson seems to suggest at his most objectionable moments. This will enable us to give a sharp diagnosis of one particular skeptical confusion about facts.

What on the part of true sentences is meant to correspond to what on the part of reality? If we seek a correspondence word by word, we find ourselves eking reality out with a complement of abstract objects fabricated for the sake of the correspondence. Or perhaps we settle for a correspondence of whole sentences with facts: a sentence is true if it reports a fact. But here again we have fabricated substance for an empty doctrine. The world is full of things, variously related, but what, in addition to all that, are facts? They are projected from true sentences for the sake of correspondence.

But let us ponder this last maneuver for a moment. The truth of 'Snow is white' is due, we are told, to the fact that snow is white. The true sentence 'Snow is white' corresponds to the fact that snow is white. The sentence 'Snow is white' is true if and only if it is a fact that snow is white. Now we have worked the fact, factitious fiction that it is, into a corner where we can deal it the coup de grace. The combination 'it is a fact that' is vacuous and can be dropped; 'It is a fact that snow is white' reduces to 'Snow is white'. Our account of the truth of 'Snow is white' in terms of facts has now come down to this: 'Snow is white' is true if and only if snow is white.

This nicely illustrates the attitude about fact-talk we were arguing Strawson had, and which Quine shares. All but the thinnest, most eliminable uses of fact-talk, such as prefacing propositions with 'It is a fact that', are cast out as bad philosophy. But this doesn't at all follow from the explanatory failure, if such there be, of attempting to account for truth in terms of correspondence with facts; why would dubious theories of truth be the only other thing you can do with fact talk, besides these most eliminable uses? We haven't been given a shred of evidence to suggest that they are.

Consider the argument in the second paragraph. It can be resisted from the point of view of the correspondence theory. Furthermore, we can put the correspondence theory to one side and show that, in any case, it does not even begin to show facts to be 'fictions'.

First of all, consider the point of view of a fact-based correspondence theory: the truth of propositions can be explained in terms of a relation of correspondence and certain relata, facts. Quine's transformation, which he just blandly performs without a word of explanation or justification, of the 'corresponds to the fact that' formulation into the 'if and only if it is a fact that' formulation, from this point of view, could justly be said to rather obscure the explanation. And the next step, of declaring 'it is a fact that' to be vacuous and dropping it, is completely indefensible. One thing is the fact that you can drop that phrase in many ordinary contexts – it does not at all follow that you can further mutilate the philosophical explanation in question in the same way.

In Strawson's case, the “elimination” was of a different sort, effected by imagining a counterfactual scenario in which we speak a language consisting only of simple commands. In the present case, the "elimination" is effected by transforming sentences of our language so that reference to facts disappears. It fails triply:

Firstly, the transformations are unjustified from the point of view of the correspondence theory.

Secondly: no evidence has been given that there are not other occurrences of fact talk which Quine cannot eliminate.

Thirdly: even if fact-talk were always eliminable, that doesn't eliminate facts, doesn't show them not to exist – that would be a use-mention confusion. (This point was made by my former teacher Adrian Heathcote.)

(Quine, or a good Quinean, however, may object that this third objection misses the point, and that there is something lying behind this argument: Quine's conception of ontology. I will not get into that possibility here.)

These three problems with Quine's “elimination” aside, we still have the contention in the first paragraph that facts are 'projected from true sentences'. This suggestive idea, particularly in light of our considerations about the role of concepts (or internal meanings, or modes of presentation) in the individuation of facts, could give independent support to the idea that facts are fiction, so it requires separate treatment. To this end, we shall now consider the idea of a projective fallacy in general, and go on to show that it is Quine, not the person who speaks of facts, who is guilty of one here.

Projective Fallacies (or Confusions) in General

There is a general idea, which seems to me to be important and useful in philosophy, that we sometimes get led into error or confusion by reading features of our language or thought into the world – or alternatively, projecting them onto the world.

Before considering some (hopefully relatively uncontentious) examples of such confusions or errors, let us review some classic philosophical expressions of the general idea.

Hume, in A Treatise of Human Nature: “The mind has a great propensity to spread itself on objects.” [Book 1, Part 3, §XIV]

Russell, in his Logical Atomism lectures: 'There is a good deal of importance to philosophy in the theory of symbolism, a good deal more than one time I thought. I think the importance is almost entirely negative, i.e., the importance lies in the fact that unless you are fairly self-conscious about symbols, unless you are fairly aware of the relation of the symbol to what it symbolizes, you will find yourself attributing to the thing properties which only belong to the symbol. That, of course, is especially likely in very abstract studies such as philosophical logic, because the subject-matter that you are supposed to be thinking of is so exceedingly difficult and elusive that any person who has ever tried to think about it knows you do not think about it except perhaps once in six months for half a minute.'

Wittgenstein, in the Investigations 104: 'We predicate of the thing what lies in the method of representing it.'

I will speak of 'projective fallacies' to refer to instances of this sort of thing, with the caveat that 'confusion' may be more appropriate in many cases, since there need not be any definite fallacious inference drawn, in the sense of a transition from proposition to proposition forming part of a chain of reasoning.

Examples of Projective Fallacies

Here I will try to give some examples of projective fallacies which aren't very philosophically loaded, in order to give a better idea of what they are.

Bands in the rainbow: looking at rainbows in relative scientific ignorance, it would be natural to think that the bands of colour we perceive in them correspond to intrinsic structural features of them. We might expect that bits of the rainbow near the end (width-wise) of band are more intrinsically different from those near the same blurry boundary on the other side, than are two equally distant bits which fall within one band. But this would be a projective fallacy.

Illusory failures of homophony: Taking two words with the same pronunciation but different spellings in isolation, and saying them one after the other by themselves, we might persuade ourselves that we ordinarily pronounce them very slightly differently, when this is not in fact the case. A difference which lies only in our mode of representing speech has been projected into our speech.

Taking an “operator” for a representative: An extra-terrestrial who had correctly concluded that road signs sometimes depict objects to be found in their vicinity (such as speed-bump signs, signs indicating the presence of wildlife, etc.), might see a sign disallowing dogs and mistakenly infer that there are creatures nearby with large crosses attached to their bodies.

Incidental features of models: A boy makes a model of a boat he admires, and uses a piece of wood in which he had made, at another time and for some other purpose, a regular series of indentations. Years later, as a grown man, he finds the model he made, notices and remembers deliberately making the indentations, and forms the erroneous idea that the boat he admired bore indentations in the corresponding place.

Projection-Based Skepticism about Facts

Let us return now to Quine's formulation of projection-based skepticism about facts. He said:

The world is full of things, variously related, but what, in addition to all that, are facts? They are projected from true sentences for the sake of correspondence.

In other words, the idea that there are facts involves a projective fallacy. In the following two sections I want to show that this is completely wrong, and ironically so: it is Quine who is guilty of a projective fallacy here, in thinking that the believer of facts is guilty of a projective fallacy.

Something Which Is True: A Genetic Point about Ideas of Facts

We talk of particular facts – we have concepts, or ideas, of particular facts. How do we arrive at these? I think it is plausible to say that we derive them, in some sense, from true propositions. Think of how we form our ideas of particular propositions: first we formulate the propositions, then we produce an idea of that proposition. We might say these ideas of propositions are projected from the propositions themselves. Likewise with ideas of facts, although the projection is different.

This may be called a genetic point about ideas of particular facts, since it is not a piece of semantics or analysis, but rather a hypothesis about how certain cognitive structures come about.

It seems plausible, does it not, that in order to have an idea of a particular fact, you need to have some true propositions under your belt? The reason for this, we may say, is that our ideas of particular facts are – in some, if not all cases – derived from our representations that such-and-such is the case, when it is the case – that is, from true propositions.

The Irony of Projection-Based Skepticism About Facts

We are now in a position to see that Quine, in painting the idea that there are facts as guilty of a projective fallacy, is himself guilty of a projective fallacy: he has projected a property of our ideas of facts – namely, their being derived, or projected, from our true propositions – onto facts themselves, and concluded that, since facts are also meant to be mind- and language-independent, the whole idea of facts is bankrupt; facts are impossible fictions. But that is a mistake.

Reference

Quine, W. V. (1987). Quiddities: An Intermittently Philosophical Dictionary. Belknap Press of Harvard University Press.

Skepticism About Facts: The Case of Strawson

So far in this series on facts, I have argued that the object-property-relation model of facts is untenable at its core. Lastly, I have offered a reason to think that granularity considerations apply to our carving up of facts as well as to our carving up of meanings, although not always in a way which yields a one-to-one correspondence between true proposition-meanings and facts.

All of this may give rise to worries about what facts are, and whether they can be held to be the real, mind-independent things we generally think of them as. Relatedly, there is the idea that facts are a fiction invented by thinkers caught in the grip of a “correspondence theory of truth” for the sake of having something for true propositions to correspond to.

The object-property-relation model may have some of its appeal in appearing to stave off these worries to some extent, by giving a uniform, extensional way of picturing things – but that's a desperate game when it comes to our ordinary conception of facts, as we have seen.

Surmounting these worries is no mere defensive exercise, but will afford us insight into the concept of facts, the use of 'fact'.

I will begin in this post by examining Strawson's discussion of facts in his famous article 'Truth', attempting to diagnose and avoid certain confusions (at his expense). (I got quite carried away with this, and my tone gets a bit harsh, especially considering that the poor bugger wrote his paper over 60 years ago. But I like Strawson very much. Much more than Quine.) I will then discuss, in a future post, a well-known and striking passage in Quine, purportedly showing facts to be 'fictions'.

Following that, I will try to sharpen up one aspect of the Strawson-Quine worries by taking the concept of 'projection' used by Quine (in his claim that facts are fictions projected from true sentences for the sake of the correspondence theory) and turning it against him (and Strawson); it is they, not the person who speaks of facts and declines to call them fictions (Quine) or pseudo-entities (Strawson), who are guilty (in a subtle way) of projecting features of language and thought onto reality. (This is a different use of the concept of projection than in the notion of 'external projective relations' used in the characterization of propositions.)

I will then conclude this series on facts with a brief look at residual worries about the 'shadowiness' of facts, and the idea (which comes through very clearly in Russell's Atomism Lectures) that there is something incredible about the idea that certain kinds of facts exist.

Strawson on Facts

Strawon's discussion of facts in his much-discussed paper 'Truth' (a reply to Austin's paper of the same name) seems to me to embody certain confusions which, at our present dialectical point, we are particularly liable to. We have examined the object-property-relation model of facts and found it wanting, and have noticed some striking features to do with the individuation of facts, namely: that concepts of modes of presentation come into their individuation in some way, that they can be individuated at different granularities, but that this does not go hand-in-hand with the individuation of true proposition-meanings.

Strawson's paper is positively tortured with scruples about 'fact' talk. One gets the feeling that, if he's right, then with fact talk, if you so much as blink, you might find yourself making up fictions and talking nonsense.

He is arguing against the correspondence theory of truth, particularly Austin's purportedly cleaned-up and clarified version.

Strawson's idea seems to be that fact-talk is assigned a role in the correspondence theory of truth which it is not fit to play – and that nothing else is fit to play the role either. He urges this in part by drawing our attention to the grammar of 'fact', and its close relationship with 'that'-clauses. That is, he has noticed, at least in part, what Wittgenstein was pointing out in the quotations from the 'Complex and Fact' given here.

So, correspondence theorists, in Strawson's view as I understand it, are trading on a misconstrual of facts, of the grammar of 'fact', in order to create (for themselves as much as for others) the appearance of a theory which accounts for the truth of propositions in terms of (to take, rather than Austin's difficult remarks, the full-blown early-analytic object-property-relation 'complex' view) a correspondence between elements of the proposition and elements of a fact. (Austin's view retains enough of this approach for Strawson to object that the correspondence theory requires 'not purification, but elimination'.)

There might be something in this as a criticism of the correspondence theory of truth qua explanatory theory. I will not pursue this here. What I want to do is vouchsafe the idea of facts from Strawson's attacks on it, and understand the pathology of these attacks – not for the sake, necessarily, of explaining what truth consists in, but for broader reasons: fact-talk is important in all kinds of connections besides philosophical theorizing about the nature of truth.

However, perhaps I should say a couple of things about (my view of) the proposition 'Truth is correspondence with the facts', in case this helps to avoid some possible misunderstandings. This proposition can be used legitimately, but it can be also be misunderstood and misused (in ways connected with the object-property-relation model of facts we considered above, but also in others, such as by making all truth look like it has to be empirical, through a narrow conception of 'correspondence with the facts'). You can say it, it is true as far as it goes, but some (who you might call 'correspondence theorists') have imagined it to go further than it does. It can be a useful consideration against certain confused views in the directions of coherentism, relativism and pragmatism (not to say that all views in those directions are confused), although by itself it cannot be expected to have any effect on seasoned theorists. More humbly, it might in some connections be able to assist someone to learn to speak correctly, and with more expressive power.

Correspondence theory of truth aside, Strawson's rejection of it so far leaves a proper understanding of the notion of facts as an open problem: how does fact-talk work, and what's it doing in our language and thought? This is where Strawson is weak. He doesn't seem prepared for what a subtle and difficult matter this may be. His view of the matter is formed in reaction to the correspondence theory of truth, and it leads him to say some strange things of his own about facts, things which could be said to be out of touch with the real grammar of 'fact' – and the grammars of the certain other words in the things he says – every bit as much as much as the explanatory or pseudo-explanatory use of 'fact' by the correspondence theorists. (This dogs Strawson's negative arguments about the correspondence theory, which more-or-less make up the whole paper, too – it is not a simple matter of a good negative story and a bad positive one).

He doesn't seem to realize what a subtle and difficult matter this may still be once you reject the correspondence theory. The correspondence theory is the root of all evil – get rid of that, and there is no difficulty. His view of the matter is reactionary, and it leads him to say some strange things of his own about facts, things which could be said to be every bit as out of touch with the real grammar of 'fact' – and the grammars of the certain other words in the things he says – as the explanatory or pseudo-explanatory use of 'fact' made by some correspondence theorists.

Strawson is probably not aptly characterized as a 'skeptic about facts' (a phrase Quine must wear), although many of the things he says sound like skepticism about facts. His position at the time of this paper was probably essentially confused and unstable. We can only describe as best we can the pickle he is in.

Strawson has, we might say, become paranoid about fact-talk: he sees the correspondence theory – with its attendant misuse of fact talk - everywhere he looks. He sees it in certain linguistic forms which in themselves need not be used in a correspondence-theoretic way at all: they admit of perfectly harmless use, and more than that, their use is important from our general point of view as speakers and thinking people, and their working is non-trivial from the point of view of the investigator of language and thought. This paranoia leads him to denials and counter-prescriptions of his own which are every bit as objectionable as correspondence-talk.
 
I will now briefly discuss some important passages from Strawson's paper, to illustrate the above charge. We will then move on to Quine on facts, who can be seen as resolutely maintaining something which Strawson seems to suggest at his most objectionable moments. The discussion of Strawson's we are focussing on presently is complex and ambiguous and many-sided – this makes it rich but difficult material to discuss. The passage from Quine we will look at, by contrast, is utterly forthright, and this will enable us in a later post to give a sharp diagnosis of one particular skeptical confusion about facts.

That (person, thing, etc.) to which the referring part of the statement refers, and which the describing part of the statement fits or fails to fit, is that which the statement is about. It is evident that there is nothing else in the world for the statement itself to be related to either in some further way of its own or in either of the different ways in which these different parts of the statement are related to what the statement is about. And it is evident that the demand that there should be such a relatum is logically absurd: a logically fundamental type-mistake. But the demand for something in the world which makes the statement true (Mr. Austin's phrase), or to which the statement corresponds when it is true, is just this demand.

The phrase 'in the world' is doing a good deal of work here, but what does it really mean? Are facts in the world or not in it? Isn't this precisely the sort of unclear, grammatically out-of-touch talk which Strawson is supposed to be so fastidious about? Having noticed fundamental grammatical differences between, e.g. 'fact' on the one hand and 'table' and 'complex' (and 'proposition' for that matter) on the other, he tries to mark them by saying there is nothing in the world which could be called a fact and which could be said to make propositions true, and which propositions could be said to fit or correspond to. But this is crude in the extreme. There is simply no reason to think there is a single, clear-enough idea of what it is for something to be 'in the world', which Strawson can use here. So the impressive-sounding phrase 'a logically fundamental type-mistake' is quite unjustified. That makes it sound almost as if this were an instance of some fallacy well-known to experts. It is nothing of the kind. I think it is fair to say that there is an element of hocus pocus here with this talk of a 'logically fundamental type-mistake'.

The only plausible candidate for the position of what (in the world) makes the statement true is the fact it states; but the fact it states is not something in the world. It is not an object: not even (as some have supposed) a complex object consisting of one or more particular elements (constituents, parts) and a universal element (constituent, part).

Here, after a rehearsal of the opaque 'in the world' line, we get a further heady-sounding claim – facts aren't objects! As if this too followed from the rejection of the correspondence theory, and the realization that 'fact' behaves very differently not just from 'proposition', but also from 'table' and 'complex'! But to me, this sounds like further unexplained metaphysics, or at best, hopelessly crude, hand-wavy grammar. (Are facts things, if not objects? May we say that, officer?) More to come.
 

Mr. Austin seems to ignore the complete difference of type between, e.g., "fact" and "thing"; to talk as if "fact" were just a very general word (with, unfortunately, some misleading features) for “event,” “thing,” etc., instead of being (as it is) both wholly different from these, and yet the only possible candidate for the desired non-linguistic correlate of “statement.” 

This passage is shot through with use-mention confusion. What would it mean for 'fact' to be a word for other words ('event', 'thing')? (None of 'fact', 'event' and 'thing' is synonymous with another, and Austin never implies otherwise, as far as I've been able to tell.) Secondly, how could the word 'fact' be a candidate for a non-linguistic correlate of anything? And why would the word 'statement' have a non-linguistic correlate?

'Thing' is indeed very different from 'fact' – it is a lot more general, and often functions like a variable. But does that mean we can't speak of facts, that we can't use the word 'thing' in connection with them (as in 'Facts are her favourite things', 'Something I didn't appreciate was the fact that …')? (But why not, officer, when there's no harm in it?)
 

These points are, of course, reflected in the behaviour of the word "fact" in ordinary language; behaviour which Mr. Austin notes, but by which he is insufficiently warned. "Fact," like "true," "states" and "statement" is wedded to "that"-clauses; and there is nothing unholy about this union.

It is interesting to note that Strawson says 'there is nothing unholy about this union'. It is easy enough to comprehend, because we know Strawson allows that fact-talk is not always entirely spurious, with the caveat its use is quite specific and narrow, and cannot be exploited for a correspondence theory of truth. Compare what is said in this description of a form of skeptical position about facts, given the Stanford Encyclopedia of Philosophy entry for 'Facts':

3.F2: All facts, even the most simple ones, are disreputable. Fact-talk, being wedded to that-clauses, is entirely parasitic on truth-talk. Facts are too much like truthbearers. Facts are fictions, spurious sentence-like slices of reality, “projected from true sentences for the sake of correspondence” (Quine 1987, p. 213; cf. Strawson 1950)

The second citation is to the paper we are now considering! (The first is to the passage in Quine which we will discuss in the next post, and that is where the quoted phrase 'projected from true sentences for the sake of correspondence' is taken from.) Contrast 'disreputable' with Strawson's 'there is nothing unholy about this union'. This is a testament to how ambiguous and difficult Strawson's position is.

This citation may seem from the narrow point of view of this passage to betray an incompetent misreading, but that would be completely unfair to its author. Recall Strawson above saying that the 'demand' for facts as things 'in the world' for truths to correspond to rests on a mistake, and his curious claim that facts are not 'objects'. And furthermore, following the above-quoted talk about the not-unholy union, as a continuation of this theme of the close relationship between 'fact', 'statement' and 'that'-clauses, we find:
 

Of course, statements and facts fit. They were made for each other. If you prise the statements off the world you prise the facts off it too; but the world would be none the poorer. (You don't also prise off the world what the statements are about – for this you would need a different kind of lever.)

What? (Is that you, officer?) Strawson has been having such a good time that his ordinary-language hat has fallen off entirely, indeed out the window. He is now heading for the stratosphere, where Kant sits waiting; he'll probably exit via the same window.
 
There is obviously a double-standard at work here. We mustn't say that true propositions correspond to facts, and we mustn't say that facts make true propositions true. But it's perfectly legitimate to say something like: facts are made for statements. It's fine to talk about prising facts off the world.
 
We can explain this as follows: Strawson has got it into his head that the correspondence theory is the root of all evil when it comes to our understanding of fact-talk, and of language and its connections to the world. As long as we don't say correspondence-theoretic things, we'll be alright. So we can forget all our scruples and say all sorts of colourful, deeply-philosophical sounding things, as long as they aren't correspondence-theoretic in spirit – and if these things might work as propaganda against the correspondence theory, we positively ought to say them.
 
The question remains: what on Earth is going on in this passage? When we consider Quine on facts in the next post, we will suggest that Quine is, ironically, guilty of a subtle 'projection fallacy' (a term which will be explained) in his contention that facts are 'projected from true sentences for the sake of correspondence'. We should then be able to see clearly that this is also what is going on in this astounding passage of Strawson's. And so the SEP citation of Strawson in connection with the idea that facts are 'disreputable' 'projections' is justifiable.

Here is a passage which shows that, not only are facts not objects, they are not even things.

the whole charm of talking of situations, states of affairs or facts as included in, or parts of, the world, consists in thinking of them as things, and groups of things; [...] the temptation to talk of situations, etc., in the idiom appropriate to talking of things and events is, once this first step is taken, overwhelming. Mr. Austin does not withstand it.

What does he mean by this? What does it mean to think of something as a thing, anyway?
 
The reader will probably agree whole-heartedly that I have protested sufficiently now about the meaningfulness and clarity of what Strawson is saying. I will leave off that now, and conclude this post with a word about a curious argument involving imperatives, which occurs near the end of Strawson's section on facts:

Orders, as well as information, are conventionally communicated. Suppose "orange" always meant what we mean by “Bring me an orange" and "that orange" always meant what we mean by "Bring me that orange," and, in general, our language contained only sentences in some such way imperative. There would be no less need for a conventional correlation between the word and the world. Nor would there be any less to be found in the world. But those pseudo-entities which make statements true would not figure among the non-linguistic correlates. They would no more be found; (they never were found, and never did figure among the non-linguistic correlates).

The argument seems to be, in essence: if our language consisted only of simple commands, these would have to be correlated with the world, but we wouldn't correlate them or any of their constituents with facts, and so facts would 'no more be found'. But why does that entitle Strawson to call facts 'pseudo-entities'? And how can he say, on the basis of considering this primitive sort of language, say that 'they [the relevant “pseudo-entities”, facts] never were found'? He can't – that's a completely different, and completely unsupported, claim.

The following analogy, though rough, seems to bring out the unsoundness of Strawson's semi-implicit reasoning here. Suppose we spoke a language with no word for acceleration. In a sense, acceleration would then no longer be a correlate of our language. And perhaps, in a sense, acceleration would not be 'found', by us. But that doesn't mean there is no acceleration, and that we do not 'find' it as a correlate of something in the language we actually speak. To conlude that would be to perpetrate a use-mention confusion: eliminate the signs, and you haven't thereby eliminated what they represent. (We will have occasion to note a similar confusion in Quine in the next post. The point is due to my former teacher Adrian Heathcote, who applied it to Quine.) We can also see it as a projection fallacy: what is gotten rid of in Strawson's imagined case is language, concepts, but this absence is projected onto reality, i.e. onto what the language and concepts were about.

Reference

J. L. Austin , P. F. Strawson & D. R. Cousin (1950). Symposium: Truth. Aristotelian Society Supplementary Volume 24:111 - 172. 

Further background:

- A video of Strawson and Gareth Evans discussing truth in the early 1970s.
- Section 3 of the SEP article on Strawson.

Facts and Granularity

We have already noted that (it is natural to say that) the fact that Clark Kent is Superman is distinct from the fact that Clark Kent is Clark Kent. And this seems to reflect, in some way, the fact that our proposition 'Clark Kent is Superman' involves two different concepts, modes of presentation, name-uses or internal meanings, whereas 'Clark Kent is Clark Kent' just involves the one.

As we have argued, these things (let's call them concepts for now) can be individuated at different granularities. This raises the question: should we say that facts can be individuated at different granularities as well?

We will now consider a case which strongly suggests an affirmative answer. We will then consider the further question: does the individuation of facts go hand-in-hand with that of propositions? Consideration of a familiar case will be seen to suggest that it does not: there are contexts where we can naturally distinguish two true propositions which we might count as the same at a coarser granularity, but where it is unnatural to distinguish two facts corresponding to the propositions so distinguished.

Here is the case which suggests that facts can be individuated at different granularities. An untravelled German called Pieter who is, like Kripke's Pierre in France, ignorant of English, uses the name 'Uebermensch' for the hero we know as 'Superman'. He has never heard the term 'Superman', but is privy to the fact that the hero has two guises, and knows that he is called 'Clark Kent' in the non-hero guise. So he assents to 'Clark Kent ist Uebermensch'. He knows, from reading and testimony, quite a bit about the hero, but doesn't know much about his appearance in his hero guise – has never seen a picture, heard or read a detailed description, etc. Let us suppose further that he assumes correctly there must be some name, unknown to him, which is used for the hero in his hero guise, but has no idea what this might be.

In a Pierre-like development, Pieter comes to America and comes into regular contact with Superman. He learns the name 'Superman', and uses it to refer to Superman. But he doesn't realize that this is the hero with two guises, the hero he already knew about in Germany. He just assumes this hero whom he knows as 'Superman' only appears as a hero. He has learnt some English, including the words 'super' and 'man', but just hasn't put two-and-two together.

When Pieter is talking one day with someone privy to the business of Superman having two guises, this person makes some remark, intended to be quite trivial, beginning: 'Even though I realize that Clark Kent is Superman, when ever he wears that suit, I…'. The penny drops. Pieter bursts out with 'Clark Kent is Superman?!', and thinks to himself ('Superman ist Uebermensch!'). The person looks at him, and says 'I didn't realize you weren't aware of that fact'.

I will now explain why I think this case shows that it is natural to individuate facts at different granularities, given different descriptive needs. Before the Pierre-like development, when Pieter was in Germany, we would, on the basis of what we have supposed about him, find it natural to say that he knows who Superman is (although he doesn't know the name he is called by in America, and doesn't know what he looks like), and that he is aware of the fact that Clark Kent is Superman. Nevertheless, as the story develops above, someone has the opportunity to, apparently quite properly, say 'I didn't realize you weren't aware of that fact' right after his outburst, which was 'Clark Kent is Superman?!'. Here, it is natural to say that he became aware of the fact that Clark Kent is Superman, and also of the fact that Superman is the hero he knew as 'Uebermensch'. In this latter connection, he might say: 'I am very surprised at the fact that Superman is Uebermensch – I never even considered the possibility, although I should have worked it out!'.

I submit that the best way of making sense of this situation is to embrace the idea that we carve up facts at different granularities. If we consider Pieter in Germany, without any inkling of what is to take place later, we find it expedient to use a granularity coarser than the one we will end up at, and we take Pieter's sentence 'Clark Kent ist Uebermensch' to state the same fact we state with 'Clark Kent is Superman'. (Although, if we so much as consider speaking of 'the fact that Uebermensch is Superman', we will begin to want to shift to a finer granularity.) Then, once Pieter goes to America, it becomes expedient to shift to a finer granularity and distinguish more facts: there is the fact that Pieter stated in Germany with 'Clark Kent ist Uebermensch', which we might call the fact that Clark Kent is Uebermensch, and there is the fact which now surprises Pieter in America, which we might call the fact that Clark Kent is Superman. It also seems natural to say that Pieter puts knowledge of these two facts together and immediately comes to know a third, which we might call the fact that Superman is Uebermensch.

If we do individuate facts at different granularities, the question arises whether this goes hand-in-hand with the individuation of proposition-meanings. There are really two questions here. It is expedient to operate at different granularities under different circumstances. One thing we can ask is: is it the case that, in any given circumstance, if it is expedient to distinguish two true proposition-meanings, is it also expedient to distinguish two facts, and vice versa? Another thing we can ask is: is it the case that, if it is expedient in some circumstance to distinguish two true propositions meanings, it is expedient in some (possibly distinct) circumstance to distinguish two facts, and vice versa?

It seems to me that the answer to the first question is 'no'. I do not know what to think about the second question, and remain agnostic. I think the 'vice versa' parts hold in both cases; if ever it is expedient in some situation to distinguish two facts (and provided these facts are expressible by propositions at all), it will be expedient to distinguish two corresponding true propositions, and expedient in the very same circumstance at that.

The answer to the first question is 'no', I argue, because, while the vice versa part holds (granted the expressibility of the facts), the first condition doesn't – i.e. it is not the case that, in any given circumstance where it is expedient to distinguish two true propositions, it is expedient to distinguish two corresponding facts. Kripke's original Pierre case gives us an opportunity to see this.

Suppose that London is pretty. (Worries about the subjectivity or indeterminacy of London's prettiness – in short, about there being no fact of the matter, can be easily avoided with a simple alteration of the case.) Now, as we saw in 'Kripke's Puzzle and Semantic Granularity', once Pierre comes to London and forms a second, unconnected conception of it, it becomes expedient to distinguish the proposition he expresses with 'Londres est jolie' from the proposition he would understand by 'London is pretty' – he believes the first, and disbelieves the second. But in this case, as it stands, there is no pressure to distinguish two facts – on the contrary, this is not natural at all. There is just one fact which makes these two propositions true: the fact that London is pretty. Pierre, we might say, is aware of this fact via one mode of presentation (or concept), via one belief-content, but also has another belief-content, involving another mode of presentation, which directly contradicts (or is made false by) this fact.

So, to sum up the preceding discussion: we have reason to think that facts can be carved up at different granularities (the Pieter case), but that their carving up does not go hand-in-hand with that of true propositions (the Pierre case).

In future posts I will discuss skeptical worries about facts, beginning with Strawson's pronouncements on the matter in his famous article 'Truth'.

Facts: The Object-Property-Relation Model

While the notion of a fact is not itself central to the main accounts I have been developing (e.g. of names, of necessity, analyticity and a priority, and of propositions), it is intimately connected with notions which are central, e.g. that of a proposition. In this series of posts, I want to consider what might be said about facts in certain connections in light of those ideas.

The Object-Property-Relation Model

An idea that has been very influential in analytic philosophy is that facts, or a certain class of basic facts at least, are complexes of objects, properties and relations – or objects, properties and relations arranged in a certain way.

There are many familiar issues with this sort of conception. Some of these are:

- How are the elements of a fact glued together? (The problem of the unity of the proposition, but for facts.)

- Are there negative facts? What are they like?

- Are there general (quantificational) facts? What are they like? (Generality can not be reduced to truth-functions.)

- What other forms of facts are there, and how are they related to basic facts? (E.g. propositional attitude facts, conditional facts.)

The first item on this rough list, and related worries, may be avoided in large part without thereby avoiding the rest, and the further ones I will raise. I will not attempt a comprehensive discussion of this problem, but I will reproduce a brief selection of remarks from a Wittgenstein typescript, 'Complex and Fact', which seem to me to contain considerations which break the grip of it, and try to explain how they do so. These will not be the only considerations relevant to the problem, since the other problems remain and will require separate treatment which independently tells against the basic model of facts at work in the first problem. Here are the quotations:

Complex is not like fact. For I can, e.g., say of a complex that it moves from one place to another, but not of a fact.

But that this complex is now situated here is a fact.
…

A complex is composed of its parts, the things of a kind which go to make it up. (This is of course a grammatical proposition concerning the words 'complex', 'part' and 'composite'.)

To say that a red circle is composed of redness and circularity, or is a complex with these component parts, is a misuse of these words and is misleading. (Frege was aware of this and told me.)

It is just as misleading to say that the fact that this circle is red (that I am tired) is a complex whose component parts are a circle and redness (myself and tiredness).
…

'To describe a fact', or 'the description of a fact', is also a misleading expression for the assertion stating that the fact obtains, since it sounds like: 'describing the animal that I saw'.

Of course we also say: 'to point out a fact', but that always means; 'to point out the fact that …'.
…

A chain, too, is composed of its links, not of these and their spatial relations.

The fact that these links are so concatenated, isn't 'composed' of anything at all.

What do these considerations achieve? By drawing attention to the actual grammar of 'fact', and showing how it differs from that of 'complex' (and 'animal', and 'chain') they can break the grip of the worry about how the components of facts are glued together; this rests on a false grammatical assimilation.

The same grammatical points may also help rid us of 'shadowiness' worries: worries about what queer sort of things facts could be. (I will discuss worries of this sort at greater length in future posts.)

However, it seems to me that a certain core of the object-property-relation view can survive considerations such as those above – or at least, such considerations do not effectively neutralize this core. Also, once the core is finally neutralized, shadowiness worries will arise again, and will have to be dealt with.

The plan for this series of posts is as follows. Firstly, to identify the core of the object-property-relation view. Secondly, to neutralize it – to show that it doesn't work, and give due weight and care to the observations which tell against it. I will do this firstly by considering the remaining worries on the list above, and secondly by means of the examples of facts about identity and singular existence. These are the tasks of the present post.

In one subsequent post, I will discuss facts in connection with granularity. In others, I will discuss the worries which arise in the wake of the demolition of the object-property relation model. Broadly, these could be called shadowiness worries – but I will distinguish and separately discredit a special form of worry - roughly, the worry that facts are fictions arising from an illicit projection of features of language and thought onto the world.

This series of posts should not be seen as being all about the object-property-relation model of facts. Although it begins with that, it is just as much a discussion of skepticism about facts – since it deals with the problem of what facts could be, if the object-property-relation model doesn't work (which it doesn't). The skeptic can be thought of as someone who sees that that model doesn't work, but can't see any acceptable way of thinking about facts either.

The Remaining Core

I will now try to characterize the remaining core of the object-property-relation model of facts, explicitly abstracting away from differences between different views which share it.

There are basic or atomic facts, and these are what make the most basic true propositions true. This is part of the core. Views incorporating this core may differ on the following points (1) whether these basic facts include negative facts, and (2) whether there are complex facts, built out of basic facts, or whether complex true propositions are just made true by the atomic facts somehow (in which case 'basic' or 'atomic' is actually superfluous, or even misleading, in relation to facts; they're all basic).

While views incorporating the core may differ on the point of (2), it is essential that they are committed to one of those two alternatives (or at least something very like one of them). Views on which there are quite other facts, which are not in any way built out of these basic facts (whose characterization we are still at work on), do not count as incorporating the core. Incorporating the core involves, loosely speaking, seeing all facts as being ultimately a matter of objects, properties and relations – or objects possessing or standing in properties or relations, or not possessing or standing in them. (The view I advocate is that this is a good way of thinking of some facts, but that it doesn't work at all for others.)

An important part of the core, regarding its conception of the basic facts themselves, is the way they are individuated. This can be brought out quite precisely in the following terms. According to the core of the object-property-relation model, each basic fact maps onto one of a set of n-tuples whose elements are objects, properties and relations arranged according to a certain scheme, in such a way that two distinct facts never get mapped to the same n-tuple.

For example, we may use the set of n-tuples whose first element is an property or relation, and whose remaining elements are objects. (There need be no assumption that properties and relations cannot be construed as objects.)

Then, the fact that Socrates is mortal (assuming Socrates and the property of mortality to be basic enough) is a basic fact, and gets mapped to <mortality, Socrates>. The fact that John loves Mary gets mapped to <love, John, Mary>, etc. Negative facts, if they are posited as basic facts, pose no problem here: the fact that Mary does not love John gets mapped to <love, Mary, John>; if that's a fact, then there's no fact that Mary loves John around requiring mapping to the same tuple, so uniqueness of mapping remains. (These n-tuples, it must be remembered, are not supposed to be representations of basic facts, but are being used to make a point about individuation. If negative facts are not posited, they could serve as such representations. Otherwise, they could be conceived of as partial representations. But that is not necessary for the present point.)

The Remaining Familiar Worries

These are:

- Are there negative facts? What are they like?

- Are there general (quantificational) facts? What are they like? (Generality can not be reduced to truth-functions.)

- What other forms of facts are there, and how are they related to basic facts? (E.g. propositional attitude facts, conditionals.)

Of these remaining issues, the consideration of generality seems particularly telling against the object-property-relation model. Negative facts seem to require less of a departure from the ingredients of basic atomic facts. We might imagine that the arrangement of these ingredients in the fact is a “negative arrangement”, or some such thing.

As for truth-functions, there are prospects (which, in a later post, we will see Russell appealing to) for saying that they are made true by atomic facts. Alternatively, molecular, truth-functional facts may be posited. (It may be argued that the core-incorporating theorist who makes this latter moves owes us an account of how these facts are composed, or constituted, but it is clear that they can be regarded as in some sense being made up of non-truth-functional facts, so we will not attack the core of the object-property-relational model on the point of truth-functions.)

As for conditionals, there are prospects for analyzing these in terms of truth-functions and quantification over worlds or scenarios.

However, there seems no getting away from general, quantificational propositions which cannot be analyzed as truth-functions. It seems overwhelmingly plausible that these are genuine, fact-stating propositions. (Contra Ramsey.) But the facts they state just can't be represented with the object-property-relation model.

The Last Straw: Identity and Existence

There is another class of facts, however, which are very telling against the object-property-relation model, and in a particularly worrying way not shared with general facts: facts about identity.

It is a fact (assuming, as I am whenever I use examples such as the following, that the story of Superman is true) that Clark Kent is Superman. We can also say that it's a fact that Clark Kent is Clark Kent, but this is not the same fact. At least, that's a very natural thing to say. It is very natural to say that, if Lois Lane learned that Clark Kent is Superman, she would have learned a new fact which she didn't know before, namely the fact that Clark Kent is Superman.

What makes this 'particularly worrying' from the point of view of the object-property-relation model is, I believe, this: that here, the individuation of facts in some sense involves concepts, senses, meanings, modes of presentation or something of that sort. And not just in the sense that we need concepts or etc. to grasp objects, properties and relations which we then individuate by. Rather, we bring concepts or etc. to bear on the individuation itself; we count the fact that Clark Kent is Clark Kent as distinct from the fact that Clark Kent is Superman. (No such thing is suggested by the problem of general facts.)

As clear as it is that the fact that Clark Kent is Clark Kent is not the same as the fact that Clark Kent is Superman, this peculiar involvement of concepts (or whatever) in the individuation of facts which aren't about concepts, but other things like people, planets or numbers, appears outrageous from a certain confused point of view. Since (as I hope to make clear) it is a confused point of view, there is probably no such thing as a genuinely clear statement of what the problem is supposed to be with this involvement, but only more or less apt and characteristic evocations of the worry. The worry, then, is something like: facts are supposed to be objective, “out there”, and mind- and language-independent (at least when they are not facts about mental or linguistic things, or things which depend on them), but if their individuation can involve concepts or modes of presentation or whatever, how could they be? What are these strange, shadowy things, which seem to multiply before us when we bring new concepts on board? Are we not guilty of some confused reading of features of our language and thought into reality?

These are worries we will be dealing with in later posts. But for now, we will observe that there is a further class of facts upon which the core breaks down. Namely, the class of singular negative existential facts, such as the fact that Santa Claus doesn't exist, and the fact that Peter Pan doesn't exist. These are different facts, but they can't be sensibly mapped to any n-tuple which accords to the scheme considered above, let alone a distinct one each, because there are no (real, existing) objects which they are about.

So, facts about identity and existence destroy the core – the only way out, short of an unnatural and counterintuitive account of facts, would be to try to analyze propositions about identity and singular existence so that the problem disappears. I plan to argue in future that any such attempt will be futile. (Furthermore, any half-way plausible analysis of singular existence propositions would surely involve quantification, and quantification conflicts with the core, albeit perhaps in a less worrying way than identity and existence do.)

Propositions involving other constructions, such as propositional attitudes, or adverbs, may also be argued to conflict with the core, but this will not have the simple and dramatic effect that considerations of generality, and, especially, identity and existence, have. But the damage is already done; the object-property-relation model, at its core, just doesn't work as a general model of facts (or even just of facts not built out of further facts).

In the next post, we will consider the extent to which granularity considerations can come into the individuation of facts. In later posts, we will try to deal with some of the philosophical worries which arise in connection with facts once they are seen not to conform in general to the object-property-relation model.

Empty Names and Negative Existentials

Singular negative existential propositions such as 'Santa Claus does not exist' can be made to look puzzling without any explicit theoretical view on board, with Socrates-style questions such as: how can anything not exist? How can one ever truly say that something doesn't exist? For if one is right, there is no such thing as what one is talking about, and therefore one is talking about nothing.

Or: 'Santa Claus doesn't exist' – what is this thing which doesn't exist? How could there be such a thing?

For those who have a Millian conception of naming (and associated views of propositions), the problem of negative existentials assumes a particularly acute form. If all there is to the meaning of a name is its bearer, and if substituting co-referring names does not affect the 'proposition' (not my usage) expressed by the sentence, then how can a statement like 'Santa Claus does not exist' mean anything at all? Furthermore, how can it be true? And how can different true negative existentials have different meanings, as they seem to do?

All these questions push the Millian toward analysing existence statements – giving an account of what they really mean. (Witness for example Kripke's tortured discussion in Reference and Existence. Of course, he never officially and unequivocally endorses Millianism, but he's flirted outrageously with it in public and finds it intuitive.)
 
Having a non-Millian conception of naming such as the one I propose, on which names are recognized as being tied to individual concepts (or having uses - roles in the systems of language they occupy - which are semantically relevant), makes it a lot easier to answer these questions. But this does not mean that we are using individual concepts (or name-uses) as elements in an analysis of existence statements.

'N does not exist' does not, for instance, mean exactly the same thing as'“N” has no bearer' or 'The “N”-concept has empty extension' (that is, on a natural and sufficiently fine-grained conception of proposition-meanings): the existential proposition is not about a name or a concept.

We can say it is about N, if we understand 'about' as not having existential import, or we can say that it is not about any real thing, but it would muddy the waters intolerably to say that it is about a name or a concept.

And yet we can see what would make a person want to say that it is about a name or a concept. What we can truly and properly say is that, in 'N does not exist', the function of the name 'N' is not to pick out an object – rather, this name (rather than some other name) is used in order to bring a particular individual concept (or name-use) into the act (though I would not want to say 'under consideration', for it need not become an object of thought).

But then what do we say about the function of a name in a proposition like 'John is tall'? It is no less true to say that 'John' functions to bring a particular individual concept or name-use into the act, but here we can also say that it functions to pick out an object. But some have found it intuitive to say that a name functions purely to pick out an object. Given a certain very narrow concept of 'function', this is fine too, although it could be misleading – it could lead to the troubles of Millianism.

Let us now take a representative selection of the questions raised at the beginning of this section, showing how they can be answered with the conceptions of propositions and naming I favour. This is done without giving an analysis of existence statements (in the classical sense of giving something else which they are then said to mean). As with identity statements, the trick is to treat existence statements on their own terms, and to recognize that they occupy a special role for us, and work in a quite particular way.

How can anything not exist?

Just as we sometimes use names in a way which carries existential import, as in 'John is tall', and sometimes use them in a way which does not, as in 'Santa Claus does not exist', 'Some children believe in Santa Claus', we use terms like 'there is', 'something' and 'anything' in two different ways: with or without existential import. A clear example of the latter sort of use would be a kid saying 'I don't believe in Santa Claus, the Easter Bunny, or anything like that'.

The difficulty and puzzlingness of the above question derives from this ambiguity. The thorough answer is: in the sense of 'anything' etc. in which they carry existential import, nothing can fail to exist – i.e. it is not the case that it is possible for anything to not exist, but in the sense of 'anything' etc. in which they do not carry existential import, there are indeed things which do not exist.

At this point, individual concepts (notions of things), or name-uses can be brought into consideration, to help us make sense of the fact that we talk like this. What gives rise to it is that we sometimes have individual concepts without objects, name uses where the name lacks a bearer. We then formulate propositions which, if we treat them by analogy with propositions like 'John is tall' and 'Someone is in this room', look as though they would have to involve (existing) things in order to be true, in the way that these propositions would have to involve John and a person in the room – but in fact they face no such requirement. We use them in connection with objectless concepts, bearerless names etc. (and this connection is quite different from that which holds between 'John is tall' and John himself).

How can one ever truly say that something doesn't exist? For if one is right, there is no such thing as what one is talking about, and therefore one is talking about nothing.

In light of the above, this question can be disposed of quickly. We can truly say that something doesn't exist by using 'something' in the sense in which it doesn't carry existential import, and in virtue of the fact that we have objectless individual concepts and involve them in our talk. In the sentence after the question ('For if one ...'), 'there is no such thing as' and 'nothing' are used in their existential-import-having senses, and so there is no real conflict in what is being said here. It is just being said in a potentially misleading way.

How can a statement like 'Santa Claus does not exist' mean anything at all?

The proposition works by means of the fact that the name 'Santa Claus' brings an individual concept (or a way of using a name) into the act – not by referring to it, but because that is the concept tied to that name (or that is the way that name is used). The proposition is true iff the concept (or name-use) of 'Santa Claus' has an object.

This is not to say that the proposition means the same as any proposition about concepts or name-uses, or that the proposition holds of just the same possible situations as those of which what is said on the right hand side of the 'iff' holds. We are using the biconditional here not to give an analysis but to give a necessary and sufficient condition for the proposition in question, which we have before us, actually being true.

How can different true negative existentials have different meanings, as they seem to do? 
 
By bringing different individual concepts (or name-uses) into the act. 

Reference

Kripke, Saul A. (2013). Reference and Existence. The John Locke Lectures. Oxford University Press. 

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.]

Reference

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.]