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.