Two Opposite Types of Granularity Difference

This is another post in my series on semantic granularity. The others so far, in chronological order, are:

Kripke's Puzzle and Semantic Granularity

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

John and Mary both use the word 'happiness', and understand each other perfectly in most conversations. They use it in propositions in such a way that we would say that they both attach the same meaning to the propositions used, are on the same page, etc. But in certain relatively peripheral regions of application, they differ systematically.

We want to be able to tie John's peripheral uses of 'happiness' together with his non-peripheral uses - we want to say he's using the word in the same sense in both cases, but we also want to bundle his non-peripheral uses with Mary's. However, we also want to be able to make a semantic distinction between Mary's peripheral use and John's.

The solution is two operate at two granularities. A relatively coarse-grained bundling can tie all John and Mary's uses together - roughly, by ignoring peripheral use features. But we can use a more fine-grained bundling to describe the linguistic difference between Mary and John - at this granularity, we say they mean slightly different things by 'happiness'.

But there is another sort of descriptive problem which we solve with granularity shifts. For example, consider the normal uses made of the word 'hard' in the phrases 'hard man' (meaning something like 'tough guy'), 'hard wood' and 'hard test' (meaning a difficult test). We can distinguish three different senses here - very roughly, (i) toughness, (ii) solidity and resistance, and (iii) difficulty. Or two, a literal sense ('hard wood') and a "metaphorical" sense ('hard man', 'hard test'). Or we can bundle all these together.

Visually, we can think of the first kind of fine-graining as a kind of broadening of considerations which go into bundling, and the second kind of fine-graining as a kind of narrowing.

This is perhaps one of the things which have made granularity considerations, although quite natural, seem difficult - or not even arise as a serious possibility - from the point of view of analytic philosophy. That two different, in a sense opposing, things can be going on in shifts toward finer granularity, can make the matter confusing. But once we see what is happening and master it, it just reveals the richness and power of the approach.

From these examples, it may look like the first, 'broadening' type of fine graining is concerned with intersystematic distinctions – distinctions between different sign systems (in the example above, John's and Mary's idiolects) – and that the 'narrowing' type is concerned with intrasystematic distinctions – between elements and uses of some given sign system.

But this doesn't generally hold. In the broadening case, for example, we may have spoken about two very similar but subtly distinguishable meanings of quite different words in, say, John's idiolect. 'Envy' and 'jealousy', perhaps. Or 'rage' and 'fury'. Likewise, in the narrowing case, where we, at finer grain, distinguish the meaning of 'hard wood' from 'hard test', we could instead make that distinction between these words as used by two different people, or two different words used by two different people.

One thing we can say, perhaps, is that the 'broadening' type of fine graining is about considering how more ground is covered, factoring in more stuff about 'the lay of the land', where the 'narrowing' type is more about marking off different regions. The first involves making more distincions among expression-uses based on how the expressions cover the ground they cover, the second involves making more distinctions among expression-uses based on what ground they are covering in that use.

The Principle of Compositionality and Semantic Granularity

This is another post in my series on semantic granularity. The others so far, in chronological order, are:

Kripke's Puzzle and Semantic Granularity

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

If meanings properly get carved up at different granularities, as I maintain, what are the implications for the 'the principle of compositionality'? I believe that granularity considerations can shed light on the status and application of this principle, and clear up much of the confusion surrounding it.

This confusion appears to be considerable. Witness Daniel Cohnitz ('Is Compositionality an A Priori Principle?'):

A superficial look at the literature on the principle of compositionality [...] could suggest that the discussion is as confused as a discussion can be.

I will now quote some classic and some typical formulations of the principle, and then indicate what we can say about it in light of granularity.

From the Tractatus:

I conceive the proposition—like Frege and Russell—as a function of the expressions contained in it. (3.318)

To understand a proposition means to know what is the case, if it is true.

(One can therefore understand it without knowing whether it is true or not.)

One understands it if one understands its constituent parts. (4.024)

It is essential to propositions, that they can communicate a new sense to us. (4.027)

Frege, in a letter to P.F. Jourdain, probably written in 1914:

The possibility of our understanding [my emphasis] propositions which we have never heard before rests evidently on this, that we construct the sense of a proposition out of the parts that correspond to the words.

Theo Janssen, 'Compositionality':

The principle of compositionality reads, in its best known formulation:

The meaning of a compound expression is a function of the meanings of its parts.

But this omits something. The way the parts are put together, not just their meaning, goes into determining the meaning of the whole. ('John loves Mary' means something different from 'Mary loves John'.)

This is the point made by 3.141 of the Tractatus:

The proposition is not a mixture of words (just as the musical theme is not a mixture of tones). 

The proposition is articulate.

The following instances do not omit this:

B.H. Partee, handout for Ling 310 The Structure of Meaning, Lecture 1, February 20, 2006 p.1:

The Principle of Compositionality: The meaning of an expression is a function of the meanings of its parts and of the way they are syntactically combined.

'Compositionality', The Stanford Encyclopedia of Philosophy:

[T]he meaning of a complex expression is fully determined by its structure and the meanings of its constituents.

We have now seen the principle of compositionality stated in various ways.

One idea I want to suggest is that, at a maximally fine granularity, the principle of compositionality can be thought of as guaranteed to hold – a blanket, a priori principle.

However, once we relax the granularity, compositionality can begin to fail in many cases.

This would give us an avenue by which to approach the confusion about whether the principle of compositionality is just a conceptual truth about how all languages – everything we would call a language – must work, or an ideal which is sometimes met and sometimes not, or just something which occurs sometimes (i.e. for some languages, or parts of languages) and not others, without necessarily being an ideal: from a fine-grained point of view, it can be construed as something which applies without exception, but from courser-grained points of view, we can make distinctions between cases where it holds and cases where it doesn't. (The stuff about being an ideal versus not being an ideal can then be considered using this as a basis.)

The proposal I just indicated – that at a maximally fine granularity, compositionality can be thought of as holding a priori and across the board – while it has a certain theoretical appeal, is problematic: it might seem straightforwardly false (in light of the existence of idioms, for example), but of course replies can be made to that (for example, that semantically, idiomatic phrases have less, or just different, parts or constituents than they would appear to have considered literalistically). I do not want to be dogmatic about this, and I suspect there is room for “having it both ways” by means of careful disambiguation.

Some of the points I want to make here can be made without any such strong principle (that is, without the proposal above – call it 'the blanket proposal'). I will therefore do that first, and then come back and reconsider the blanket proposal.

Compositionality Can Depend on Granularity

The proposal summed up in this heading is weaker than the blanket proposal (the proposal that granularity holds a priori across the board at maximally fine granularity but can fail in cases as the granularity is coarsened): all that is claimed is that some complex expressions are such that compositionality may be said to hold of them, given a certain granularity of individuation of their components' meanings, but also such that compositionality then fails to hold at a coarser granularity.

Consider this bit of dialogue from season 2 of Flight of the Conchords:

Murray: Now, we've known each other for quite some time in the professional realm. I'd like to push things forward in the friendship realm.

Jemaine: What's the friendship realm?

Murray: Well, you've heard of a realm?

Bret: Mm.

Murray: Yep?

Jemaine: Yes.

Murray: Well this is like a friendship one.

What makes this sequence is the way Murray's compositional "explanation" of 'the friendship realm' fails drastically. Is this, then, a “counterexample to compositionality”? Not really; or at least, to say that would not be to tell the whole story.

I think we can take two views of this case, and many others like it: a compositional/fine-grained view and a non-compositional/course-grained view.

On the first conception, we think: Murray means something here, he has put together a meaningful proposition. 'Friendship' and 'realm' here are clearly functioning in a way that is continuous with and related to a great many other occurrences of these words. Therefore, whatever this proposition means, that 'friendship' and 'realm' contribute in the way they do, or that they appear here in the way they do, in a proposition with this meaning, is part of – or an aspect of – the meaning, or the use, of these words (given fineness of grain).

Taking this viewpoint does not commit us to saying that these fine-grained component meanings were fully present before the phrase 'friendship realm' was ever used: depending on the details of the case, we could say that some people attached those meanings to the component terms already and some attached others (but that the difference never showed up, or slightly, but not in such a way as to prevent mutual understanding), or that no one used the words with exactly those meanings before the phrase was used, but that they were spontaneously arrived at when the phrase was coined (and understood, if we change the case and suppose it was understood by Jemaine and Brett, as would be more likely in real life) – that is, the meanings of 'friendship' and 'realm' were spontaneously and slightly extended.

On the second conception, by contrast, we think: 'friendship' and 'realm' are familiar words, and they were both presumably around for a long time before 'friendship realm' was ever used. Putting these two meaningful words together, however, doesn't all by itself yield one and only one possible meaning. There is room for going different ways here. ('The friendship realm', for instance, might be used differently from how Murray uses it, to mean some mythical realm in which everyone is friends.) Of course, when 'friendship realm' does end up meaning some particular thing, this will not be unrelated to 'friendship' and 'realm' – they guide the meaning, without determining it. The gap between what they provide and the meaning of 'friendship realm' must be filled by semantic developments pertaining to 'friendship realm'. But we needn't say that these developments affect the meanings of 'friendship' and 'realm' taken by themselves – we can maintain that they haven't taken on new meanings.

(It may be that compositionality doesn't necessarily fail according to this second conception: perhaps the gap between what the pre-existing meanings of 'friendship' and 'realm' and a meaning for 'friendship realm' can be thought of as being filled by a structure or mode of composition, if we construe this as going beyond surface syntax.)

Now, what does this get us, i.e. what does it get us to see that there is all this room for manoeuvring here?

One thing it gets us is a way of explaining a large class of putative counterexamples to the principle of compositionality, without denying any natural point of view. In fact, we have before us two ways of accounting for the idea that this is a counterexample to compositionality. Rather than two equally good ways of accounting for exactly the same thing, I think they cover different sorts of cases, different instances of the idea that this is a counterexample to compositionality; compositionality can be said to fail here in two senses:

(1) While compositionality may be said to hold at a very fine granularity, it can be said not to hold at a coarser one. So, one thing that might be going on when we think we have a counterexample to compositionality is that we are operating at a granularity at which it is a counterexample – and if someone disagrees, we might be talking at crossed granularities.

(2) A dynamic, temporal sense. We make no bones about the fact that now we have some new complex expression, we can say that the meanings of its parts, plus its structure, determines the meaning of the whole. (Thus we are operating at the finer granularity.) But we insist that when it was introduced, its meaning wasn't so determined: rather, it induced spontaneous semantic development. So, we can call a use of language non-compositional in this sense if it involved such development – and we may relativize this to a thinker or speaker, a listener, etc. Something compositional for me might be non-compositional for you at first, but my saying it induces spontaneous semantic development on your side so that it becomes compositional after the fact. We might use 'dynamic compositionality' for this idea; when spontaneous semantic innovations occur involving complex expressions, we can say that those expression uses were dynamically non-compositional.

Neither sense conflicts with the claim that, at fine-grain and timelessly, 'friendship realm' and similar cases are perfectly compositional.

These considerations may also shed some light on the issue of whether, or in what circumstances, compositionality is to be regarded as an ideal to be striven towards, if not attained. In some cases, we may have as an ideal that no spontaneous semantic innovation – no guesswork, we might say, from an interpreter's perspective – be required for a certain language-game (use of language), for example in parts of science, certain personal encounters, or in parts of legislature. That is, dynamic compositionality may be desired. But it is just as clear that sometimes we want dynamic non-compositionality.

Or we might want a language, or a part of language, to be so simple that there is no room for granularity shifting: each expression has a couple of clear rules attached to it, and if you change any of them, it's just not natural to say that the meanings stayed the same. We might be able to ensure this by laying it down that compositionality must not fail. (If we're aware of granularity considerations, we might say 'must not fail at any reasonable granularity', but we need not be aware of them to pull off the trick.)

So, the above considerations get us a few things. What remains?

We have seen that many cases where compositionality seems to fail – such as Murray's use of 'friendship realm' – may be explained away by saying: if you individuate the components' meanings at a finer granularity, this is no longer a counterexample. But the question remains: can that be done in every case? That is, does the blanket proposal hold?

By getting clearer about the blanket proposal, we will get clearer about the nature or meaning of the principle of compositionality. In this connection, we should consider idioms, metaphors and similes, sarcasm and the like, and semantic “outgrowths” like 'Wednesday is fat' and 'The letter a is yellow'.

Such linguistic phenomena also suggest that there may be more to say about the notion of compositionality as an ideal.

The Blanket Proposal

A proponent of the blanket proposal might say that, when compositionality fails, we have decided to bundle together as having one meaning expressions, or possible occurrences of expressions, which on a more fine-grained conception would be regarded as having (perhaps only slightly) different meanings. But is this really plausible in every case?

Here are some difficult types of cases:

Idioms: Consider phrases like 'spitting image', 'dead ringer', 'nest egg', 'piece of cake', 'funny farm', 'loose cannon', 'no dice', 'from scratch', 'kick the bucket'.

Propositions like 'He is a loose cannon'

'Pull strings' a bit more flexible. Frozen metaphor.

Sarcasm and the like: A sarcastic utterance of 'That's just great' may seem to be a kind of counterexample to compositionality: what is meant is that something is terrible, but this depends not just on the meanings of the components and how they are put together, but also on the context: it might be meant non-sarcastically.

But we can invoke an intensional (internal semantic) analogue of Kripke's distinction between speaker's reference and semantic reference here, and insist that what this expression means, even in the sarcastic use, is that the thing in question is very good, even though what the speaker means by it is something else.

From the point of view of expression-meaning, then, sarcasm and the like do not threaten compositionality in the least. But there is nothing stopping us talking about compositionality in connection with speaker-meaning, and saying that it fails in this case ('That's just great').

Or, we may say that what the speaker means by the whole is determined by what the speaker means by the parts, together with their mode of composition, by maintaining that by 'great' the speaker means 'terrible'.

But other cases seem different. Suppose someone takes something to be very obvious, but, by way of parody of some other group who may doubt it, might sarcastically say, 'Of course, empirical studies may prove me wrong' (let's suppose they're quite nerdy). Here, the meaning is something like 'Come on, we know this!', but the sarcasm cannot be located, so to speak, in any particular phrase. The whole construction is bound up with the sarcasm – what is literally meant cannot aptly be stated using the same syntactic form, only negated (e.g. 'Of course, it's not the case that empirical studies may prove me wrong', or some other placement of negation).

For now I remain agnostic.

A Final Observation about Wholes and Parts and Granularity

Observation: Two propositions - or more generally, complex expressions - can be identical in meaning at one granularity, while none of their parts have the same meaning at any reasonable granularity. Or less extremely, while few of their parts, or none of their "key words", have the same meaning at any reasonable granularity. Or again, while their overall structure and arrangement of parts is quite different.

For example: 'Get out!' and 'Leave at once!'.

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)

Metaphysical Realism and Conceptual Relativity: An Application of Granularity

Granularity introduced:

Kripke's Puzzle and Semantic Granularity

Also: 

Facts and Granularity

Granularity and Relativism about Truth

The doctrine of semantic granularity can, I think, shed considerable light on the meaning and motivation of relativism about truth. It may even help resolve debates surrounding it.

In this post I will try to briefly indicate how I think this is so. I had a post on granularity and the paradox of analysis lined up for this month, but I will postpone it and get this one out now, in response to this related post on the blog language goes on holiday.

This may not be very clear to others yet, although I think I have it fairly clear in my own mind. Reading the other posts on granularity here, including future ones, will certainly help. (Soon I will do a granularity "roundup" post, collecting them all in one place and sumarizing their contents, but for now see the bottom of this post.) I will try my best under present constraints, in the hope that some reader gets something clear out of this.

Why bother? Well, I think this may be a pretty powerful and important application of granularity, since relativism about truth is such a vexed and widely ramified issue in our intellectual culture. Anyway, here goes.

Granularity and Relativism about Truth

Once the doctrine of granularity is on the table in its basic form, questions of this sort arise (among others): OK, meanings and the like can be carved up at different granularities, but what is the range of possible carvings up?

Surely there are limits; it is far from being the case that, for every two instances of thought or talk, there is a granularity at which they are counted as meaning the same. And it seems quite probable, although this is more debatable, that it also isn't the case that, for every two instances of thought or talk, there is a granularity at which they are counted as differing in meaning.

And do these different possible carvings up fall on a continuum, or are there multiple dimensions of what may count and what may not count towards difference in meaning? (I think the answer is that there are multiple dimensions, and I will try to say something about this in future.)

Now, these sorts of questions suggest a basic constraint on possible or "admissible" granularities for carving up propositions: if two instances of propositions are to be counted as meaning the same, they had better not differ in truth-value.

And now we can see relativism about truth in a new light, namely as the rejection of this constraint.

Furthermore, it is not hard to see how, in certain areas, it may be tempting to reject the constraint. Between two instances, there may be so much of the sort of stuff which usually counts toward sameness of meaning in common that it is really tempting to count them - at some granularity - as meaning the same, while nevertheless certain other important stuff differs so as to make (it best to say that) the truth-values come out differently in the two instances.

This may be particularly likely to happen with the rich and complicated concepts in the moral and aesthetic domains. And perhaps others too. And so we get a new perspective on the motivation of relativism about truth as well.

Of course, in many areas this sort of thing just won't happen - the motivation won't be there. It has often been observed (most saliently in my memory by my former teacher Adrian Heathcote, in unpublished writings) that relativism about truth appeals to people in some domains, such as morality and aesthetics, where it would never seem appealing in others. And so the general, woolly-seeming doctrine that all truth is relative can be and often is condemned as being based on a far too narrow diet of examples: you may be tempted to say such a thing after considering some moral or aesthetic matter (for instance), but with other matters such as basic geography or facts about how many chairs there are in some easily observable room, the notion that something may be true for me, while something else is true for you, would never occur to anyone, and seems completely absurd.

But relativism about truth need not be maintained that way - it may be maintained that in some areas, or with some propositions, truth is relative. Call this moderate relativism.

And, as I have tried to indicate, granularity considerations can shed some light on what this may mean, and what may motivate it. This in itself is, I think, a good advertisement for the power of granularity considerations, as relativism about truth is a big deal, especially in the borderlands of philosophy.

OK, good. But now a further question comes up: is it true? Are there, in some areas or with some kinds of propositions, admissible granularities on which two instances of propositions get counted as meaning the same but differing in truth-value?

I think that here we need to consider allowing the possibility of a kind of pluralism - slightly different sets of concepts such that, on one set, the issue gets decided one way, and on another set, the issue gets decided the other way. For instance, it could be that the maintainer of moderate relativism has a slightly broader or more flexible notion of meaning/proposition than the denier. And perhaps realizing that may enable them to resolve their dispute.

Still, it may give way to different disputes about how best to use certain words, and about which concepts to deploy where - but these may be more tractable.

(Here we get into the difficult and important topic of verbal disputes. Chalmers has recently had things to say on this topic, which was arguably being neglected before he did so. See his paper 'Verbal Disputes'.)

So, granularity considerations can be fruitfully applied to relativism about truth. They may help to (i) clarify its meaning, (ii) shed light on what motivates its adoption and (iii) help show the way to a resolution of debates over it.

Related Posts

Kripke's Puzzle and Semantic Granularity

Facts and Granularity

Granularity and Quine

Metaphysical Realism and Conceptual Relativity: An Application of Granularity

Metaphysical Realism and Conceptual Relativity: An Application of Granularity

This is another instalment in the 'Applications of Granularity' series I introduced in the last post. To learn what is going on here, have a look at the first paragraphs of that, and the original post on Kripke's puzzle and semantic granularity.

Let us characterize metaphysical realism as the view that there is exactly one true and complete description of the world, and let us characterize conceptual relativity as the denial of that claim.

These two opposing views, at least in name, come from Putnam's discussions in, among other places, the books cited at the end of this post, and have since been discussed by many philosophers. It is not clear to me whether Putnam ever took the characterizations I have given as full characterizations, but they have certainly been for him at least part of what is involved in the two views.

Putnam used different characterizations at different times, and plenty of people have worked at sorting that out a bit. I'm not getting into any of that. I just want to stipulate the above characterizations, and briefly indicate how the doctrine of semantic granularity can dissolve the appearance of a hard- or impossible-to-resolve philosophical disagreement here.

It can do this as follows. If a complete description of a domain D is a set of propositions such that every proposition which says something true about D means the same as one of the propositions in the set (or a conjunction of them), then whether we say a description of the world is complete depends on the granularity we are operating at. Conceptual relativity may hold at a certain granularity, but once you make the granularity finer, it may collapse into metaphysical realism.

Seen in this way, where one claim, conceptual relativism, holds at one granularity or set thereof and the other, metaphysical realism, holds at another (finer) one or set thereof, they are not inconsistent with each other, and each has its own point.

Conceptual relativity as it were emphasizes the possibility of attaining the same or similar goals by different cognitive and linguistic means. Metaphysical realism on the oher hand emphasizes what we might call the sovereignty, the special individuality, of the different ways of doing things.

Relevant Works

Putnam, Hilary (1978). Meaning and the Moral Sciences, Routledge & K. Paul.

Putnam, Hilary (1981). Reason, Truth and History, Cambridge: Cambridge University Press.

Putnam, Hilary (1985). Realism and Reason, volume 3 of Philosophical Papers, Cambridge: Cambridge University Press.

Putnam, Hilary (1990). Realism with a Human Face, Cambridge, MA: Harvard University Press.

Not to mention the innumerable writings by others dealing with Putnam's philosophy.

Granularity and Quine

In a former post I introduced the idea that meanings and the like can be carved up at different granularities. This was motivated using Kripke's famous puzzle about belief, and introduced as offering the key to a solution.

I plan to develop this doctrine of semantic granularity further, adding detail and removing certain possible misconceptions, in future posts. For the time being, however, I will defer that and outline a further application of the doctrine (the original one being to Kripke's puzzle). Several more applications have occurred to me since arriving at the doctrine, each time bringing great joy and encouragement, since they seem to suggest that it really is a good idea. Accordingly, this will in all probability be the first of a series of posts which as a whole may be called 'Applications of Granularity'.

The application I want to outline this time is to Quine's famous skepticism about meaning and propositions. Quine's position is not so much that there are no such things as meanings or propositions (where these latter are construed as sentence-meanings) - although he does sometimes seem committed to that too - but rather that semantic notions such as that of meaning are somehow second-rate, badly-behaved, and not worthy of serious thought.

(Quine's peculiar conception of serious thought, first-rate concepts, real scientificality and the like - which could be called a scientistic conception, but is, to be fair to science, really much narrower than that; what we really have is a bias in favour of notions which Quine for his own peculiar reasons thinks of as first-rate scientific ones - is a very interesting matter which I would like one day to scrutinize here at some length. But this will have to wait till another time.)

Now, the application of the idea of semantic granularity I want to outline here is not to the refutation of Quine's position, although it may go some way toward breaking its grip. Rather, my focus is the explanation of Quine's position; what was going on with him when he came to it, and secondly, what is going on when other thinkers feel his arguments to have force.

Quine's skepticism focuses on the, to him, confusing individuation-behaviour of intuitive notions of meaning. To give a sense of his position, I will first quote from a section of McGrath's Stanford Encyclopedia of Philosophy entry on propositions, a section called 'The Individuation of Propositions', and then give a couple of illustrative quotes from Quine himself.

Some Quotes Illustrating Quine's Position

This section can be skipped or skimmed depending on how much of a sense one wants to get of Quine's position, or how much reminding one needs. To skip it, just scroll down to 'The Diagnosis'.

Probably needless to say, these quotations by themselves, to a reader unfamiliar with Quine's writings on the subject, will not give the full picture of what he had to say; it was an issue he picked up again and again and said a lot about.

Here is McGrath in the SEP:

Some philosophers, notably W.V.O. Quine, recognize the existence of certain sorts of abstract entities but not others at least partly on the basis of concerns about identity conditions. Quine granted the existence of sets, in part because they obey the extensionality axiom: sets are identical iff they have the same members. When it came to properties, relations and propositions, however, he found no such clear criterion of identity. The property of being a creature with a heart, he noted, is distinct from the property of being a creature with a kidney, even if all the same things exemplify the two properties. 

It is a controversial matter whether Quine was right to demand such rigorous criteria of identity as a condition for acceptance of a class of entities. However, even if Quine asks too much, any good theory of propositions ought to have something to say about when propositions are identical and when they are distinct. Developing theories which give such accounts in a way that fits well with intuitive data concerning propositional attitude ascriptions would enhance our reasons to accept propositions.

Now a few illustrative Quine quotes.

From 'Two Dogmas of Empiricism' (1951 edition):

For the theory of meaning the most conspicuous question is as to the nature of its objects: what sort of things are meanings? They are evidently intended to be ideas, somehow -- mental ideas for some semanticists, Platonic ideas for others. Objects of either sort are so elusive, not to say debatable, that there seems little hope of erecting a fruitful science about them. It is not even clear, granted meanings, when we have two and when we have one; it is not clear when linguistic forms should be regarded as synonymous, or alike in meaning, and when they should not.

This paragraph from a section of Philosophy of Logic boldly entitled 'Propositions Dismissed':

The uncritical acceptance of propositions as meanings of sentences is one manifestation of a widespread myth of meaning. It is as if there were a gallery of ideas, and each idea were tagged with the expression that means it; each proposition, in particular, with an appropriate sentence. In criticism of this attitude I have been airing the problem of individuation of propositions.

This passage from the 'Meaning' entry in the playful Quiddities:

[...] what is it for two expressions to have the same meaning? They cannot have exactly the same use, for when we use one we are not using the other. One wants to say rather that they have the same meaning if use of the one in place of the other does not make any relevant difference. The question of sameness of meaning, then, comes down to the question what to count as relevant difference.

I see no prospect of a precise answer, nor any need of one. Everything real and objective having to do with our use of expressions, and hence with their meaning, can be said without positing any relation of full synonymy ofexpressions, or sameness of meaning. In describing ways in which an expression is used we may be said still to be explaining its meaning, but there is no lingering trace of a museum of labeled ideas nor of any clear and simple relation of paraphrase or translation.
[...]
I urged at the end of the entry on IDEAS that there is no place in science for ideas, and under KNOWLEDGE that there is no place in the theory of knowledge for knowledge. Now we find me urging that there is no place in the theory of meaning for meanings, commonly so called.

Finally, if a bit more detail is wanted, here are selections (kept in order) from a more nuanced discussion in section 42 of Word and Object, 'Propositions as Meanings':

A large part of learning 'apple' or 'river' was learning what counts as the same apple or river reexposed and what counts as another. Similarly for 'proposition': little sense has been made of the term until we have before us some standard of when to speak of propositions as identical and when as distinct.
[...]
If we are content to define identity of propositions by synonymy of sentences, there is no evident objection to calling propositions meanings of eternal sentences. Misgivings as to what sort of object such a meaning might be could be allayed, if one pleases, by identifying it with the very class of all those mutually synonymous sentences that are said to have it. The worry that remains is the worry over a suitable notion of synonymy of eternal sentences. If propositions are to serve as objects of the propositional attitudes, then the broad sort of sentence synonymy talked of in § 14 [Details of that don't matter here - TH] would be unsatisfactory as a standard of identity of propositions even if adequately formulated. It would be too broad. For it would reckon all analytic sentences as meaning an identical proposition; yet surely one would not want to regard all analytic sentences as interchangeable in contexts of belief or indirect quotation, especially if all mathematical truths are regarded an analytic. Hence Lewis and Carnap have resorted to narrowed derivative relations of synonymy, or intensional isomorphism in Carnap's phrase, as better suited to interchange in contexts of propositional attitude.
[...]
Mates, Church, and Scheffler have argued that Carnap's intensional isomorphism (and Lewis's earlier construction of similar character) is still too broad for interchange in contexts of propositional attitude. Putnam and Church have responded with proposals for further tightening the relation. Scheffler still finds loopholes, but part of his criticism can be annulled [...]
We do have our analyticity intuition, but it grades off. [...] Now there is no objection to a graded notion of synonymy or of analyticity, supposing it made reasonably clear; but it is unlikely to contribute directly or indirectly to a standard of identity of propositions. For propositions have to be the same or distinct absolutely; identity, properly so-called, knows no gradations.
These reflections count only against hoping to base identity of propositions on some sort of intensional isomorphism derived from the broad sort of sentence synonymy which is interdefinable with analyticity. We might still hope to construct some approximation to intensional isomorphism suitable for identity of propositions, in some other way than from the elusive broad notion of sentence synonymy.
[...]
This last point [No need to worry about what that was - TH] has the germs of an argument not only against our specific plan of a structural synonymy concept as a standard of propositional identity, but against the whole idea of positing propositions. For, insofar as we take such a posit seriously, we thereby concede meaning, however inscrutable, to a synonymy relation that can be defined in general for eternal sentences of distinct languages as follows: sentences are synonymous that mean the same proposition. We would then have to suppose that among all the alternative systems of analytical hypotheses of translation (§§ 15, 16) which are compatible with the totality of dispositions to verbal behavior on the part of the speakers of two languages, some are "really" right and others wrong on behaviorally inscrutable grounds of propositional identity. Thus the conclusions reached in § 16 may of themselves be said implicitly to scout the whole notion of proposition, granted a generally scientific outlook. The difficulties cited earlier in the present section are merely by the way. The very question of conditions for identity of propositions presents not so much an unsolved problem as a mistaken ideal.

The Diagnosis

As we can see, Quine's objection to meanings, propositions, etc. was based on the idea that there is no single, clear criterion of identity for them. Given the doctrine of semantic granularity, this is no surprise and no objection. The individuation of these things differs at different granularities. In the grip of preconceptions about how language must properly work, Quine mistook a feature for a bug.

(I say that 'the individuation of these things differs at different granularities', but that form of expressing the point could be misleading and sound like some kind of antirealism - I will address that at length in a future post. For now: the point could be more carefully put in terms of the truth-values of synonymy or non-synonymy sentences, or of identity or distinctness statements about meanings, propositions etc.

This is connected with Quine's point in the Word and Object selection above, 'For propositions have to be the same or distinct absolutely; identity, properly so-called, knows no gradations.' On my approach, it is not that identity needs to have gradations, rather that identity statements with meaning- or proposition-designating phrases come out with different truth-values when operating at different granularities.)

It is instructive here to see how I, with my doctrine of granularity, can and indeed must agree with a lot of the things Quine says on the way to his hostile position, and how with the doctrine of semantic granularity on board, we can see that the hostile position doesn't follow.

For example: 'The very question of conditions for identity of propositions presents not so much an unsolved problem as a mistaken ideal' from the Word and Object selection. Indeed, if the question is construed as asking for a single, all-purpose set of conditions, it does present a mistaken ideal. What the doctrine of granularity says is that the conditions are different at different granularities, and that is part and parcel of the power and flexibility of semantic notions as bundlers and separators of linguistic items and occurrences.

And from Quiddities, 'The question of sameness of meaning, then, comes down to the question what to count as relevant difference. I see no prospect of a precise answer, nor any need of one.' Note the 'one'; the whole point of the doctrine of granularity is that there is no one answer here.

I hope I have conveyed in outline how the doctrine of semantic granularity can explain and perhaps help break the grip of Quine's hostility towards meanings, propositions and the like. This application will, if I am right, only become clearer and seem stronger with the development of the doctrine I intend to pursue in future posts.

Note finally that despite the focus here (especially in the Quine quotes) mostly being on propositions construed as sentence-meanings, all this applies just as much to sub- and super-sentential meanings as well, for instance with names and the individuation of their "meanings", which I construe as name-uses or individual concepts, or with the meanings of larger things like arguments or speeches or books.

References

McGrath, Matthew (2008). Propositions. Stanford Encyclopedia of Philosophy.

Quine, W.V.O. (1986). Philosophy of Logic. Harvard University Press.

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

Quine, W.V.O. (1951). Two Dogmas of Empiricism. Philosophical Review 60 (1):20–43.

Quine, W.V.O. (1960). Word and Object. The MIT Press.

Names and the Publicity of Meaning

One sort of consideration which may seem to augur for Millianism, and against both descriptivism and my view of names, comes from the idea that meanings must be public items, shared by communicators. If the subject matter of semantics is supposed to be the public meanings of linguistic expressions - where this might be conceived as the stuff we must have implicit knowledge of in order to be competent speakers - then it is hard to see what, in any given case, could be essential to using a name correctly, except for using it to denote the right bearer. On the other hand, there does seem to be a technique of using certain empty names like 'Santa Claus' which is more specific than: using it such that it has no bearer. But perhaps we want a minimal conception of semantics on which such specific techniques are regarded as extra-semantic.

Given such a minimal conception of semantics, it will be hard to avoid the conclusion that belief-contents, proposition-meanings and propositions and have more to their identity than their structures and the semantics of their components. (That is, unless we are prepared to bite bullets like: '”Hesperus is Hesperus” means the same as “Hesperus is Phosphorus”'.) And if we accept this, then we must deny that the identity of a proposition can always be reckoned as being determined by its structure plus the meanings of its parts, in the relevant minimal sense of 'meaning'.

We can reinstate compositionality either by moving to a very coarse-grained notion of belief-contents or propositions (and so biting the bullet on 'Hesperus is Hesperus' and 'Hesperus is Phosphorus'), or by moving to a finer-grained conception of the meanings of parts such as names, a conception which will include things beyond public meanings and minimal competence conditions. This latter is, in effect, what I advocate in my view of names as having uses, or being tied to individual concepts, which can differ even though the names do not differ as regards extension.

'Hesperus and Phosphorus' seems to be a different proposition – seems to mean something different from – 'Hesperus is Hesperus'. And, quite apart from any general thesis about meaning-determination, this difference seems like it has to be laid at the door of the names 'Hesperus' and 'Phosphorus'. And that is what my view of names enables us to do, while remaining invulnerable to Kripkean anti-descriptivist arguments.

Why can't we all go home, then? Well, this kind of solution seems to worry people. It seems like they can see what its virtues would be, but don't feel they can help themselves to it. I suspect that one of the major causes of this reluctance is some kind of conceptual intuition to the effect that meanings – anything worth calling 'a meaning' – have, by definition, to be public and shared by competent communicators. I suspect that another major cause, perhaps even more active, is that people have sensed that on this way of going, there won't be any general story to tell about how to count meanings – i.e. about how to determine whether to say that two expressions, or instances thereof, are synonymous or not.
 
We can appease the first worry to some degree, I think, by allowing that there is a natural conception, which it is not improper to use the word 'meaning' in connection with, according to which meanings, in order to be meanings, must be public and shared. But we can also have a richer, more idiolectic conception, and maintain that this is what we're talking about in connection with names, and the semantic difference between 'Hesperus and Hesperus' and 'Hesperus is Phosphorus'.

Furthermore, these two sorts of conceptions need not be seen as two utterly different things, but as continuous. Both deal with systematic use-patterns of signs, or roles of signs in systems. Taking the 'public and shared' conception as our starting point, we may yet ask: how public and how shared must these use-patterns or system-roles be to count as meanings? We could have a conception on which the patterns or roles must be shared by all who competently speak the language. But how do we individuate languages? Peter Ludlow's recent work on 'the dynamic lexicon' can help prepare the ground for what I am saying here, being consonant with it in important ways.

This appearance of continuity and fluidity is not some nasty imprecision in our philosophy, but a faithful capturing of the facts. People differ from each other – and from themselves over time – in their use of symbols and the way their understandings work, and in most cases, the question whether two symbol-instances align in meaning can be given different answers for different purposes. When we're talking about something we're both familiar with, and our ideas of that thing are similar enough, our talk can be said to align in meaning. But notice that, in speaking just then of ideas being similar enough, I have already hinted that there might be a finer granularity at which our ideas are not type-identical – a finer granularity at which it may be said that we don't mean exactly the same thing. This seems realistic.

Regarding the second worry, my answer is already implicit in the above; I think the most fruitful response is not to try to explain it away, but to embrace it. There is no single way of counting meanings, since we can individuate them and count them differently at different granularities. We are already pushed toward this by considering Kripke's puzzle, and its character as a solution there is only strengthened when we see it has further applications, such as here to this worry about the very idea that names have internal meanings, to questions about the individuation of facts, and elsewhere.

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.