Indefinite reference

14:51 And there followed him [Jesus] a certain young man (νεανίσκος) , having a linen cloth (σινδόνα) cast about his naked body; and the young men laid hold on him. 14:52 And he left the linen cloth, and fled from them naked.

The pronouns ‘he’, ‘his’, ‘him’ etc. clearly refer back to ‘a certain young man’. On the theory of extralinguistic reference, they do not refer in themselves, but inherit their reference from the antecedent. But the antecedent is an indefinite noun phrase. Can that refer? Surely not. Mark says ‘νεανίσκος τις’. The article τις (Latin quidam) means ‘a certain’, often used to suggest that the writer either cannot or will not speak more particularly. Commentators have speculated that the man was Mark himself, the author of the gospel, which if true means that ‘a certain young man’ and the pronouns, could be replaced with ‘I’, salva veritate. But Mark deliberately does not tell us. So in what sense does it refer?

Or suppose it does refer. Then as Geach argues (Reference and Generality chapter 1), the sentence ‘some man was wearing a linen cloth’ is true if some man – any man – was wearing a linen cloth. Even if the speaker has some particular man in mind, say Frank, and he means to say that Frank was wearing a linen cloth, it could have been the case that Frank wasn’t wearing a linen cloth, but some other man was, say Dick. So Dick was wearing a linen cloth, and so what the speaker actually said, i.e. ‘some man was wearing a linen cloth’, is true. But what the speaker meant to say is false.

It gets more difficult. If it is true that some man was wearing a linen cloth, whoever he was, then it is true to say that he was wearing a linen cloth. Note I use the pronoun ‘he’. I wrote ‘he was wearing a linen cloth’. But the subject of that sentence is a definite noun phrase, and so the sentence is true if and only if that man, and no other, satisfied the predicate. E.g. if that man was Frank, then the pronominal sentence is true if Frank satisfied the predicate, and false if he didn’t, even if Dick was wearing a linen cloth. Furthermore:

(1) Some man was wearing a linen cloth
(2) Sentence (1) is true if and only he – that man – was wearing a linen cloth.

How weird. Didn’t I say that sentence (1) can be true so long as someone – anyone satisfied ‘was wearing a linen cloth’? Yes, that’s still correct, because he, that man, could be any of the men. He could be Frank, Dick or Raymond. The whole point is that sentence (1) has an indefinite subject, and so doesn’t tell us which person satisfies the predicate. We know that he satisfies it, if the sentence is true. But we don’t know who he is.

Linguistic Idealism?

Prior ("Oratio obliqua", Proceedings of the Aristotelian Society, Supp. Vol. 37 (1963) 115-26, reprinted in Papers in Logic and Ethics, London:Duckworth, 1976) writes

When we describe our ordinary historical belief as a belief that Julius Caesar crossed the Rubicon, the words "Julius Caesar" do not have reference but only cross-reference. Proper names may acquire intelligibility either through our being introduced in some way to their bearers, or by being incorporated into a story – "Once upon a time someone lived in Rome who was called "Julius Caesar", and this Julius Caesar conquered Gaul, crossed the Rubicon, and so forth".

We believe that Julius Caesar crossed the Rubicon in the sense that we believe the relevant part of this story; there is no one to whom we are related as believing the whole story of him, but we identify the subject of the later part of the story, ultimately, as simply the "someone" with whom the story begins. ... there is no one of whom I say that he crossed the Rubicon; but I do say that someone crossed the Rubicon, and I have previously said (among much else) that this same someone was called "Julius Caesar".

We have a mass of historical documentation concerning Caesar, and a further, even greater mass of documentation about other people of his era, with multiple cross-references between them. We can extend this documentation by writing a biography of Caesar, using the same method of cross-reference, i.e. reference to historical documentation, which makes the name meaningful. Taking all the historical documentation as a whole, including later speculations (including biographies and historical studies) which attempt to remove contradiction or inconsistency, then you have a massive indefinite description of reality. ‘Caesar crossed the Rubicon’ is definite, of course, but only because of this cross-reference.

Is this linguistic idealism? Surely not. For that historical documentation gives us information about the past. Think of cross-reference as a neat way of locating information. (Think of history as a massive set of old-fashioned metal filing cabinets, where you can make ‘singular reference’ to individual sections of a cabinet, and check for cross-references).

Contingent and necessary identity

Anthony asks what happens if we attach the sentence "Someone called Shakespeare wrote Macbeth" to a text containing a fragment such as

(*) There was [also] a man called ‘Shakespeare’ who lived in Stratford. Shakespeare was a shareholder of the Globe company

I argued in my previous post that indefinite terms act as ‘referential isolators’. They prevent back-reference to any term in an earlier sentence. What Anthony seems to be getting at here is that ‘wrote Macbeth’ seems to be a description that applies to the Shakespeare who was a shareholder of the Globe, and so we might infer an identity, and hence a reference, that is ruled out by the ‘isolator’ theory.

I don’t agree. Consider

(**) Someone called ‘Shakespeare’ wrote Macbeth. There was [also] a man called ‘Shakespeare’ who lived in Stratford. Shakespeare was a shareholder of the Globe company.

I say that the identity between the Stratford man and the Globe man follows from the truth of the second and third sentence, because we cannot understand the ‘Shakespeare’ of the third sentence without understanding that it refers back to the indefinite ‘a man called Shakespeare’. Hence the identity statement ‘The Stratford man was the shareholder of the Globe company’ is true in virtue of the meaning of the terms.

By contrast, the identity of the author of Macbeth and the Globe shareholder cannot be inferred as a logical consequence of the truth of discourse (**) above. It makes the identity highly probable, admittedly, but probability, even if almost absolutely certain, is not the same as logical certainty. This is because of the referential isolator of the second sentence. By contrast, if we change this to

(***) Someone called ‘Shakespeare’ wrote Macbeth. Shakespeare lived in Stratford. Shakespeare was a shareholder of the Globe company.

i.e. if we turn the isolator into a back-referring term, the statement ‘the author of Macbeth was the Globe shareholder' is now true in virtue of the meaning of the terms.

This resolves Wittgenstein's complaint about identity, Tractatus 5.5303 - "Roughly speaking, to say of two things that they are identical is nonsense, and to say of one thing that it is identical with itself is to say nothing at all.  To say that "X is identical with itself" is trivial, because 'itself' refers back to the subject of the sentence. Because of the grammar, we cannot place an isolator between 'itself' and 'X'.  When there is an isolator, as with (**) above, the identity ceases to be trivial. The identity sign therefore is an essential constituent of our language.

Referential isolators

The previous post gives the background. It is time to introduce the idea of ‘referential isolation’, which we can easily explicate by considering the difference between the following three sentences.

(1) There was a man called ‘Shakespeare’ who lived in Stratford. There was a man called ‘Shakespeare’ who was a shareholder of the Globe company.
(2) There was a man called ‘Shakespeare’ who lived in Stratford. Shakespeare was a shareholder of the Globe company.
(3) Shakespeare lived in Stratford. Shakespeare was a shareholder of the Globe company.

Discourse (1) is two separate and complete sentences. It is not part of the meaning of the two sentences that there was a person who lived in Stratford who was a shareholder of the Globe company, although it is part of their meaning that there was someone in Stratford, and that there was someone – possibly the same person, possibly a different person – who was part of the Globe company. Thus it is not part of the meaning of the second sentence that its subject, if there is one, is the same as or different from the subject of the first, nor that it is the same as or different from the subject of any previous sentence. The indefinite article is thus a referential isolator. It prohibits back-reference to any previous sentence.

By contrast discourse (2) is complete as a whole, but the second sentence is incomplete. That is because the definite article ‘the’ cannot be meaningful unless it identifies the subject of some preceding sentence – in this case, the immediately preceding sentence, the first. It forces us to look back in just the way that the indefinite article forces us not to look back, and so acts as the opposite of an isolator (a ‘conductor’, perhaps?). Yet the back reference comes to a halt at the first sentence, because the isolator (‘a man called Shakespeare’) is still in place. The two sentences are complete, and have the force of a single indefinite sentence. They tell us that some person lived in Stratford and belonged to the Globe, without telling us whether this person was the same as or different from the subject of any previous sentence.

Discourse (3) is incomplete both as single sentences and as a whole. That is because when attached to the larger text of which it is a fragment, it is capable of generating further implications that you won’t get from (2), or (1). If there is a preceding sentence saying ‘someone called Shakepeare wrote Macbeth’, then we can infer, when (3) follows it, that the author of Macbeth lived in Stratford, and was a shareholder of the Globe. The two sentences are a sort of live rail potentially connecting us an earlier part, or parts, of a larger discourse.

This all presumes two things, namely (a) that the discourse is ordered by prior and posterior sentence and (b) that all parts of the discourse are available ad audientem. This is true of any verbal discourse through the ordering of time of utterance. It is true of any written text where the order of reading is determined, and the text is securely bound together so that there are no missing pages, or worm-eaten parts, or any other form of corruption. It is true of hypertext containing fixed and ordered links. It is not true of corrupt texts such as manuscripts, or where the text is complete but with the pages wrongly bound. It is not true of a newspaper where the articles are not supposed to be read in any particular order. It is not true of news media in general, where even if there is ordering there is no guarantee that the audience has received all the elements of the ordering (for example, he or she has missed the 9 o’clock news).

The question of how reference operates in the case of disordered and incomplete texts will be the next topic for discussion.

Semantic completeness and singular terms

In my last post I distinguished between terms of which you would learn as part of a general requirement to communicate with others, and terms that you would need for specialist communication.  The former you would find in any standard or pocket dictionary,  the latter in a specialist work according to subject (a medical dictionary, a glossary of advanced mathematical terms etc).

The purpose of doing this was to avoid making any philosophical distinction such as between general terms (man') and singular terms ('Socrates').  General terms can occur in generalist ('man') and specialist ('acrocanthosaurus') reference books, and similarly for singular terms: the proper name 'London' is in my general dictionary, the name of individual Londoners in the London telephone book (think of a telephone book as a specialist dictionary of proper names), and the names of individual streets in the specialist 'A-Z of London' street directory.

I say that a discourse is 'semantically complete' in respect of any particular reference dictionary when it is syntactically well-formed, and when its meaning is clear to any person who has learned the meaning of terms found in the dictionary. 

I shall show that a discourse consisting of more than one sentence can be semantically complete, even when some of its component sentences are semantically incomplete. For example:

(1) A man and a boy were standing by a fountain.  The man had a drink.

Clearly the two sentences taken together are semantically complete. Any compact dictionary of English contains words such as 'a', 'man', 'boy' etc, and anyone who has learned the meaning of those words and understands basic English syntax will understand what the two sentences mean together.  So also the first sentence is complete.  Everyone who understands basic English understands "A man and a boy were standing by a fountain".  But the second sentence is not complete, at least not on its own.  You don't understand "the man had a drink" without reference to the first sentence, because without it, you don't understand that the two sentences together imply that a man who was standing by a fountain had a drink.  To understand the second sentence, you have to understand that 'the man' refers back to the man mentioned in the first sentence.  So it is not semantically complete, even though it is part of a discourse which is.

It is the same when we use proper names.

(2) A man called 'Dudley' and a boy were standing by a fountain. Dudley had a drink.

Even though the name 'Dudley', as it is used here, is not contained in any directory or dictionary of proper names, the meaning of the two sentences together is available to any competent speaker of English. For the name 'Dudley' is defined in the first sentence, and for that reason the second sentence is semantically incomplete.  It depends on the definition of the name given in the first sentence, and is not properly understandable without it.  Thus the 'reference' of the proper name 'Dudley' is really back-reference to a previous part of the text.

This conception of reference contrasts with the Kripkean conception of reference where the incomplete sense of a singular sentence must be completed by reference to the external world (not some prior text), and where the sense of a singular term must somehow be 'passed on' from speaker to hearer.  There is no need for reference to the external world, and there is no need for 'passing on' reference.  The reference of the name 'Dudley' in the second sentence is clear because of the semantic completeness of the two sentences together.  It is objectively clear, and does not need to be 'handed' from one person to another except in the sense that the speaker is able to construct a discourse that is clear to any competent hearer, and when the hearer is competent enough to understand it.

Context and content

Anthony has commented a couple of times that we require context in order to resolve the ambiguities inherent in language.  True, but the requirement is strictly limited, as the following argument shows. 

We can divide sentences which require context into those which contain indexicals, and which therefore require a perceptual context, and those which require a linguistic context (or those which require both, but this is not an important or separate case). An indexical is a term which requires a perceptual background in order to be intelligible.  The background will determine which object is pointed to, or which place is 'here' or which time or date is 'now', and so on.  The context requirement for indexicals is therefore limited. 

The requirement for linguistic context must also be limited, for if the context-supplying language A itself required a linguistic context B, and if B required yet another context C, there would be an infinite regress, and nothing would be intelligible.  But language is intelligible, therefore the requirement for linguistic context must be limited.

As an example of the limitation of linguistic context, consider:

A man and a boy were standing by a fountain.  The man had a drink.

The sentence 'the man had a drink' requires a context in order for its meaning to be properly understood, for the description 'the man' tells us which of the two individuals standing by the fountain had a drink.  The context is supplied by the preceding sentence 'A man and a boy were standing by a fountain', which requires no further context.  We understand the first sentence simply by understanding the meanings of 'a', 'man', 'and', 'boy' and so on, and this understanding should be available to any competent speaker of the language.  As a result, the two sentences together require no further context at all.  Any competent user of the language can understand them, as long as they are available together, and as long as their correct sequence is determined by the physical nature of the text (or by some other method of determinate ordering).

The narrative conception of reference

Sentences like “I noticed the dark-haired girl I had met the other night” drive me to frustration. I read fiction in a slapdash way, and have a poor memory for detail. So I leaf through the pages, trying to find when ‘the other night’ was, and when I have, try to find the dark-haired girl. But who or what am I really trying to find here? It’s a piece of fiction, there was no such girl. And what do I mean ‘no such girl’? There are billions of dark-haired girls, and thousands of ‘other nights’.

However, frustration aside, the example throws light on an idea I have discussed earlier, namely that the semantics of a definite description are ‘external’ to the proposition that contains it. According to the classic theory of descriptions, the semantics of the description is ‘internal’ to the proposition. We understand the meaning of ‘the first dog born at sea’ by understanding the dictionary meanings of ‘first’, ‘dog’, ‘sea’ etc. But we don’t understand ‘the dark-haired girl I had met the other night’ simply by understanding a dictionary. I have to locate a passage from a previous part of the narrative in order to understand it. The description is incomplete, and we require information external to its proposition in order to understand its meaning.

It also illuminates the conception of reference that I have defended in many posts here, the conception of reference as essentially embedded in a narrative. When the author used that description, he or she was doing so in the knowledge that information provided earlier would be available to me. They knew that because they had written the narrative that included the information, and they knew it would be available in a text presented (either in print or in hypertext) in an ordered sequence. They knew that I would be reading ‘the dark-haired girl’ on p. 46 after I had read ‘a dark-haired girl’ on p.15.

I would argue that all descriptions are presented to us in essentially the same way. The author of the description uses it with the expectation that the background information necessary to understand it are available to his audience. A work of history, for example, is no different from a work of fiction. Gibbon’s monumental Decline and Fall is written as a single work covering more than a thousand years of history. But if he wrote it correctly, i.e. such that his intended meaning was available to any diligent person reading it, recurring descriptions, even when incomplete in the sense above, should be intelligible to the reader. In writing his history, Gibbon knew, or intended, that the persons reading it would have the whole work available, and that proper understanding of it requires reading it in the intended order.

It may seem to be different in the case of narratives which do not have a definite order, but I will discuss these cases later.

Reprise (reference)

A number of new readers have joined since I started the topics on 'reference' more than a year ago. To avoid going over the same ground again, I will link to some earlier posts for background. Of course, this is all work in progress, and anything may change.

For example, Anthony objects that I am attempting "to develop a theory of reference based on fictional stories". Correct, and that is the whole point. As I argued earlier, the semantics of empty proper names do not obviously differ from that of non-empty names, and it seems that the names of historical characters individuate in just the same way as fictional ones. See also this post about the reference of 'God' and 'Allah'.

I have argued further here that there cannot be such a thing as reference failure. To understand a proper name is to understand which person its sentence is about.

This means (I have argued) that reference cannot be relation between a term – a linguistic item - and an item in non-linguistic reality. The verb 'refers to' is therefore logically intransitive. I explain the notion of logical intransitivity here, and its application to reference here. This leads to the "'Frodo'-Frodo" theory of reference.

More on predicate logic and direct reference

David Brightly asks here whether modern predicate logic (MPL) in fact rests on ‘weak’ (relativistic) reference, not strong (direct) reference. He appeals to the way that singular sentences in MPL seem to have a meaning even when the singular term is empty.

There are a number of connected reasons why this won’t work. Here are the main characteristics of the relativistic logic (RL) I have defended here.

• In RL there are two forms of negation for singular sentences. There is a narrow form ‘nonF(a)’, which is true when a exists and it is not the case that Fa, i.e. a is a nonF; and a wide form, which is true when either nonF(a), or when a does not exist. Excluded middle applies only to the wide form, naturally. By contrast, MPL has no such feature.
• In RL, a sentence of the form ‘An S is P’ has a narrow existential sense: it is convertible with ‘An S-P exists’. There is no distinction between a wide sense conveyed by ‘some’, and the narrow sense conveyed by ‘exist’. RL is not Meinongian. By contrast, it is open to MPL to invent an existence predicate ‘E()’, which may satisfied by some members of the domain, but not by others.
• As a direct consequence, in RL, the wide negation ‘it is not the case that Fa’ never implies the existential form ‘some x is non-F’. By contrast, in MPL a singular sentence is existential, at least in the wide sense: ‘~Fa’ implies ‘Ex ~Fx’.
• A further difference, though probably not relevant here, is that some relational statements in RL are not existential. ‘aRb’ does not always imply ‘Ex aRx’, namely in the case where ‘R’ is not logically transitive. This is how RL avoids the problem of intentionality without invoking Meinongian non-existent objects.

The net result is that if a singular sentence in MPL cannot be empty in the sense required by RL. Let ‘v’ be a term that purports to denote Vulcan (a non-existent planet). Then either Vulcan lies within the orbit of Mercury - OM(v), or not - ~OM(v). The problem is the negation. If ~OM(v), standard predicate logic implies Ex ~Fx. But that leads to Meinongianism, i.e. positing objects that do not exist, and this, as I have argued, is a form of direct reference. Direct reference is the thesis that if ‘Fa’ is meaningful, then ‘a’ refers to something - possibly a non-existent something.

Another argument: how can we even say in MPL that Vulcan does not exist? The sentence ‘~Ex x=v’ will not do, for it asserts of something in the domain that it is not in the domain; ‘~E(v)’ will do, where ‘E’ means ‘exists’, but this comes at the price of Meinong’s junkyard. For ‘~E(v)’ implies ‘Ex ~E(x)’, which is precisely Meinongianism. Or it can be denied that ‘OM(v)’ means anything at all, which is strong Direct Reference of the familiar variety. There is no escape. Either we adopt a radically different semantics and inference schemata, on the lines of RL above, or we are left with Direct Reference.

Wittgenstein on relativity

William has given us an interesting link here.

Meeting a friend in the corridor, Ludwig Wittgenstein (1889-1951) said: "Tell me, why do people always say that it was natural for men to assume that the sun went around the earth rather than the earth was rotating?"

His friend said: "Well, obviously, because it just looks as if the sun is going around the earth."

To which the philosopher replied: "Well, what would it look like if it had looked as if the earth were rotating?"

How clever of Wittgenstein. He is not asking what it would have looked like if the earth were rotating, but what it would have looked like if it had looked as if the earth were rotating. Implying that to look as though the observer is moving with respect to their environment is the same as looking as though the environment is moving with respect to the observer.

But is that true? As a postgraduate I house-shared with a research assistant who was working on the neurophysiology of perception. Some of his work showed that the world actually looks different dependent on whether the observer is moving with respect to a stationary environment, or the other way round. There are a number of kinaesthetic sensors in the body which respond to bodily motion or rotation, and these interact with the visual sense in various ways. You can fool these sensors in all sorts of ways – for example you can create the illusion of acceleration by tilting their seat backwards, which is how flight simulators like this work. The answer to Wittgenstein’s question could well be “well, it would look exactly like that” – namely, looking as if the earth were moving, rather than the sun.

Ad secundum

I reply to the second argument of the four arguments for direct reference. The argument was that a name cannot be significant or intelligible to another unless the idea of what the name applies to is in the other person’s mind. Thus the meaning of most proper names is unknown to nearly all people in the world; they have no corresponding words in other languages. We can only have the idea of a particular thing by being acquainted with that thing, which is only possible if that thing actually exists. It follows that the meaning of a proper name involves direct acquaintance with the individual for which it is a name.

There a number of things to criticise in the argument. For example, the assumption that we use language as it were to evoke the ‘same idea’ in someone else’s mind. This goes back at least to Aristotle – “Just as all men have not the same writing, so all men have not the same speech sounds, but the mental experiences, which these directly symbolize, are the same for all, as also are those things of which our experiences are the images” (On Interpretation, ch. 1). This is questionable – as Frege argued, the distinction between things, meanings and ideas is analogous to that between the moon, which is publicly observable, the image of the moon in a camera or telescope, which is publicly observable, and the retinal image, which is not.

The reference of a proper name is the object itself which we designate by its means; the idea, which we have in that case, is wholly subjective; in between lies the sense, which is indeed no longer subjective like the idea, but is yet not the object itself. The following analogy will perhaps clarify these relationships. Somebody observes the Moon through a telescope. I compare the Moon itself to the reference; it is the object of the observation, mediated by the real image projected by the object glass in the interior of the telescope, and by the retinal image of the observer. The former I compare to the sense, the latter is like the idea or experience. The optical image in the telescope is indeed one-sided and dependent upon the standpoint of observation; but it is still objective, inasmuch as it can be used by several observers. At any rate it could be arranged for several to use it simultaneously. But each one would have his own retinal image [On Sense and Reference].

But that would take us too far afield. The objection errs in assuming that the meaning of a proper name cannot be communicated to another person, other than by direct acquaintance with the object that it names. But of course it can. As I commented here, the first time we encounter a proper name in a particular context, it signifies (for us) no more than a general idea - “Some Trojan warrior called ‘Aeneas’” perhaps. But every subsequent time we encounter the name, it has a definite and singular sense: the very same person as that Trojan warrior. It signifies merely that every sentence containing it is true – if true at all – of a single person. It signifies no more than that. And we easily learn this signification without being ‘acquainted’ – whatever that means – with the person who is named. That is how we learned the signification of the name ‘Jesus’, as I argued here and elsewhere.

On the fact that the meaning of most proper names is unknown to most people in the world, this is no more significant than the fact (assuming it is a fact) that eskimos have many different words for types of snow. And proper names are a part of a language if they are a significant part of the literature of that language. My Latin dictionary contains the Latinised form of all the main characters in Latin literature. Many of these are fictional, of course. All reference, I claim, is story relative reference.

Reference and intention

In my last post I asked which towers Tolkien was referring to in his title 'The Two Towers'.  I should have said intending to refer to.  For (as I am using the term), we cannot fail to refer.  I argued this here, but there is more to say.  Consider:

"Tales out of the South", Gollum went on again, "about the tall Men with the shining eyes, and their houses like hills of stone, and the silver crown of their King and his White Tree: wonderful tales. They built very tall towers, and one they raised was silver-white, and in it there was a stone like the Moon, and round it were great white walls. O yes, there were many tales about  the Tower of the Moon."

"That would be Minas Ithil that Isildur the son of Elendil built," said Frodo. "It was Isildur who cut off the finger of the Enemy."

"Yes, He has only four on the Black Hand, but they are enough," said Gollum shuddering. "And He hated Isildur's city."

"What does he not hate?" said Frodo. "But what has the Tower of the Moon to do with us?"

I have emphasised the co-referring expressions.  There are actually two sets.  The first begins with an indefinite noun phrase 'one', and continues with the terms 'it', 'it', 'the Tower of the Moon' as uttered by Gollum, the relative pronoun 'that' uttered by Frodo, and 'the Tower of the Moon' as uttered by Frodo at the end.  The reason for the co-reference is entirely due to rules of use for singular terms.  Even if Tolkien had intended to refer to different things, he would have failed, because of rules like these.  His intention is realised only by the instruments - the signs - he is using, which give a fixed and determinate reference. The other set has one member in this passage: 'Minas Ithil'.  This set was begun much earlier in the book, and each member has likewise a determinate reference back to the previous ones.  Tolkien joins them at the point where Frodo says "That would be Minas Ithil".  Now we know (as long as we know the identity statement uttered at this point) that the two chains are co-referring.  But this identity is not a grammatical rule or some other 'rule of narrative', but is contingent upon a statement made within the narrative - the identity statement "A (that tower) = B (Minas Ithil)".

The possibility of there being separate 'referential chains' within a narrative which are identified as co-referring at some later point provides a device that writers have used for dramatic purposes. In Dumas' The Vicomte de Bragellone, we are introduced to a traveller at a hostelry in Blois, 'a man of scarcely 30 years, handsome, tall, austere, or rather melancholy, in all his gestures and looks'. In the story that follows, this person is referred to as 'the gentleman', 'the traveller' and, intriguingly, as 'the unknown'. Intriguingly, because the expression 'the unknown' identifies the stranger perfectly well within the story, where he is actually 'known' or identifiable, but not outside the story, even though the expression signals that he is known or identifiable under another name or description. Later we learn that he is Charles II, King of England.

Sometimes, as with 'The Two Towers', an author may fail to disclose a fictional identity. In this case, we can ask what he may have intended to refer to. The point is that reference is always fixed and determinate, and depends on meaning and convention. Intended reference is not.

What are "The Two Towers"?

David Brightly asks "how sometimes my mental file [corresponding to a singular term] coheres with yours sufficiently to give rise to the sense of reference to a single external object". 

That's a good question which I can't answer right now. But let's begin with a valid question about reference in fiction.  As I have argued in earlier posts (e.g. here) there is a perfectly valid sense of 'refer to' where it takes an fictional accusative.  For example, we can ask who the phrase "The Lord of the Rings" refers to.  And the Wikipedia page on The Lord of the Rings even gives us an answer, saying that "the title of the novel refers to the story's main antagonist, the Dark Lord Sauron". 

Equally, we can ask what the ‘Two Towers’ in the Lord of the Rings are, since there are so many towers in the book.  Some of these are:

• Orthanc, the black tower of Isengard in the West, the stronghold of the wizard Saruman.
• Barad-dûr, the fortress of Sauron in the heart of Mordor in the East
• The Tower of Ecthelion, the White Tower of the city of Minas Tirith, on the Western border of Mordor
• The Tower of Black Sorcery in Minas Morgul Vale, on the other side of the border from Minas Tirith
• The Tower of Cirith Ungol above the Morgul Pass on the northern side of the Morgul Vale.

Which two, if any, are the Two Towers? In Peter Jackson’s film of the book, they are depicted as Barad-Dur and Orthanc, perhaps because of the troubled relationship between the two palantirs in each tower, easy to represent on film. But they may be Minas Tirith and Minas Morgul, as the one was made to guard the East and the other the West, and were also built at the same time, making them twins. Or they may be Orthanc and Minas Morgul, since that is where all the action takes place in books three and four. (In book three, the main tower is Orthanc. In book four, Minas Morgul). In a letter to Rayner Unwin, Tolkien states that they are 'Orthanc and the Tower of Cirith Ungol'. 

22 January 1954: It must if there is any real reference to volume II refer to Orthanc and The Tower of Cirith Ungol . But since there is so much made of the basic opposition of the Dark Tower and Minas Tirith, that seems very misleading. There is, of course, actually no real connecting link between Books III and IV, when cut off and presented separately as a volume*.

This is because the first book of the Volume deals with Saruman and the second book of the Volume deals with Frodo and Sam's passage into Mordor and his capture in the Tower of Cirith Ungol. Note his use of the term ‘refers to’. On the other hand, in his original design for the jacket of ''The Two Towers'' the Towers are certainly Orthanc and Minas Morgul (Orthanc is shown as a black tower, three-horned, with the sign of the White Hand beside it; Minas Morgul is a white tower, with a thin waning moon above it, an allusion to its original name, Minas Ithil, the Tower of the Rising Moon). In yet another letter Tolkien says the question can be left undecided, and “The Two Towers” could refer to three possible pairs: Isengard/Barad dur; Minas tirith/Barad dur; or Isengard/Cirith Ungol.

More later, but clearly the question of which character is being referred to involves authorial intention. There is a lovely discussion on a Tolkien fansite here. Here also is a link to The Battle of Evermore, a Tolkien-inspired number by the English rock group Led Zeppelin.  Some people think that the song may be referring to the Battle of Pelennor Fields.

* From Hammond, Wayne G, Douglas A. Anderson, JRR Tolkien: A Descriptive Bibliography, New Castle, Delaware and Winchester : Oak Knoll Books and St Paul's Bibliographies 2002

Crane on singularity

In an earlier post I looked approvingly at Tim Crane's views on singularity, and promised to follow up with some things I don't like so much.  Now what I don't like so much is Crane's characterisation of failed reference.  He says that "a thinker can think about a particular object and yet fail to refer to that object in thought", and that “There are many cases where thinkers appear to be having singular thoughts in this sense even though the object of the thought does not exist: aiming to refer to a specific object in this case fails to ‘hit’ the target object" (my emphasis).


On the contrary.  As I have argued here, a proper name individuates: it tells us which individual a proposition is about.  It is easy to show (a) that it cannot fail to do this, once understood, and (b) that it has no other function.

Proof:

(a) A proper name individuates by telling us which sentences are verified by a single subject.  The sentences "Frodo is a hobbit ... Frodo has large feet" together say that some hobbit has large feet, i.e. a single thing is both a hobbit and has large feet, and not that some thing is a hobbit and that some thing (possibly a different thing) has large feet.  You simply haven't understood how the proper name works if you think that both sentences could be true without being true of a single thing.  I say a bit more about this here.

(b) This is all that proper names do.  (i) They have no descriptive sense.  They tell us which individual a sentence is about by telling us which individual it is the same as.  The 'Frodo' of the second sentence above tells us that if the second sentence is true, it is true of the same thing as the first sentence, if true, is true of, and no more.  This is exactly how proper names individuate in stories, and it is clear they can do no more than this.  Nor can they do any more even if the story is true, and all the names 'refer'.  (ii) They have no 'extra-linguistic' sense. As I argued here, if any piece of language has an important communication function, we should be able to tell whether it has an important communication function. One of the most important features of communicating with someone is that they should know they are being communicated to. Therefore, if non-empty proper names communicate information that empty proper names don’t, we should know this, and we should be able to tell whether a name was empty or not.  But we can't do this.  We do not know for certain whether the Christ Myth theory is true or not, and thus we don't know whether the name 'Jesus' is empty or not.

There is nothing that a proper name could try to do, that it does not do.  A proper name tells us which character is being written about, and it does this successfully whether in a story ('King Arthur found a sword') or in a piece of history ('King Albert burned the cakes').  Thus Crane's idea that it could possibly fail to accomplish anything is a mistake.

Reference and chess

How can sentences containing descriptive and singular terms come to represent the world, without any word-world semantic relation?  "If reference is not a relation between a word and some object in the world, then it is completely mysterious how can the use of a name help us pick out anything in the world" says Peter Lupu.

Perhaps it is like chess, and the notation that we use to represent the pieces and the moves. Here is one well-known and simple game:

e4 e5
Qh5?! Nc6
Bc4 Nf6??
Qxf7# 1–0
 
The major pieces get proper names (K for king, Q for queen).  The minor pieces get descriptions ('Nc6' means that the only knight which is available to be moved to c6, is moved there).  Play this game at your place, and leave the pieces where they are.  I will then play the same game at my place.  Then (if we have understood the language of chess correctly), the layout of pieces on my board will represent the layout on yours.  So, if your board were the world, and mine was the mental representation, the one would match the other.

The 'Frodo'-Frodo theory of reference

I have argued here for a theory of reference that I have called the 'relativity theory' of reference.  All reference is semantically indistinguishable from story-relative reference. Just as we can be told which hobbit carried the ring to Mount Doom (Frodo), so we can be told which US President's dog was killed by an assassin (Fido, Abraham Lincoln's dog).  History, like stories about hobbits, is just a story (although history, unlike stories about hobbits, is true).

But we could equally call it the 'Frodo'-Frodo theory of reference, after the well-known 'Fido'-Fido theory of meaning. According to 'Fido'-Fido theory, the most economical explanation of the meaning of the proper name 'Fido' is to say that it means, well, Fido.  Similarly, according to the 'Frodo'-Frodo theory, the simplest and the most economical explanation of the meaning of the proper name 'Frodo' is to say that it means, well, Frodo. You know, that hobbit. The one who carried the accursed Ring to Mordor.

All philosophical theories come with a curse, of course, just as the Ring did. If there were any simple explanation of a philosophical problem, the problem would have been resolved thousands of years ago.  The curse of the 'Frodo'-Frodo theory is Meinong.  It seems - though it actually doesn't - to commit us to the existence of non-existent objects. 

It doesn't, as I say. "'Frodo' means Frodo" is true, as is "'Frodo' means someone".  But this does not entail "someone is such that 'Frodo' means that person".  The verb 'means' is logically intransitive.  But by this time, you will have said Too long, didn't read.  Oh well.

Too long, didn't read

There is no greater enemy of theory that 'tl;dr' (Internet slang for 'too long: didn't read'). Schopenhauer wrote (I can't remember where) that the whole of his enormous work The World as Will and Representation was expressing a single proposition, presumably one that could not be expressed by any shorter proposition. That is bad. You should always have some shorter proposition up your sleeve for the day you are caught on a desert island and some brutish fellow requires you to defend your theory. What would Schopenhauer have done if marooned without his innumerable tomes?

So here is my 'short', three-part defence of the story-relative theory of reference which I have been discussing throughout this year in this blog (one day I will put all this into a book, but not yet).

(1) We can tell 'which' character is being talked about in a story. War and Peace has many hundreds of minor characters but we can always (assuming we have paid attention) tell which character the author is talking about or 'referring to'.

(2) There is no obvious difference between the semantics of a made-up story, and the semantics of a historical account which is perfectly true. E.g. we cannot tell from what is said in the Old Testament whether any of the characters really existed or not. Yet we can tell Adam from Eve, Cain from Abel, Moses from Isaiah and so on. Whatever explains reference in a story, also explains reference-in-history.

(3) All the objections which argue against proper names being concealed descriptions, also apply against proper names that are used in a story. Whatever features or accidents we ascribe to a character in a story, we can deny of that character using the proper name for that character, for example.

Which of these are you going to deny? Can Tolkien not tell us which hobbit threw the ring into Mount Doom? Is there any obvious semantic difference between a narrative which might be true (the Old Testament) and one which obviously isn't true (The Aeneid)? Is there any property signified by a fictional name except: being that very character?

There is more you could overlay on the theory. You would want to distinguish it from a Meinongian theory of reference, and thus defend it against objections to such theories. We would do this by the concept of the 'logically intransitive verb' which I described elsewhere. You would want to develop some account of the 'true logical form' of logical intransitivity. You would want to develop a deeper account of the distinction between singular and general terms. All this can be done, but it take time. And also may be just too long to read. We live in the barbaric world of the internet.

On the reference of 'Sherlock Holmes'

Bill asks here "What makes my utterance of 'Socrates' denote Socrates rather than someone or something else?"

And I ask "What makes my utterance of 'Sherlock Holmes' refer to Holmes rather than someone or something else?"  It's not simple.  There actually is a person called 'Sherlock Holmes' who is a minister of the church living in Massachusetts.  There is an article about him in the Sherlock Holmes society journal here.  So I could use the name to refer to him, as that article does.  Yet a character of the same name appears in the novel The Seven-Per-Cent Solution by Nicholas Meyer, but in this case it is made clear that the character is the same person as the one Conan Doyle wrote about. Meyer's book is an extension of the 'Holmes mythos'.  And also of the Ruritania mythos - in the book, Holmes meets Rudolf Rassendyll, hero of Prisoner of Zenda.

So we can use the name of a fictional character either (i) to refer to the character in a 'textual criticism' context (ii) to write more fiction in the same genre or mythos, (iii) to refer to a real person who happens to share the same name.  What a tangled net, no wonder so many clever people have been ensnared by it.

Obscure objects: Bouquet and Molina

Here is another scene from the film I discussed earlier. Mathieu and Conchita [Carole Bouquet] are sitting at a table in the garden. Conchita says "I have something to say, but not here". Mathieu gets up, and she follows him up a short flight of stairs, into the house. Mathieu shows her through the door. [Cut to interior of house] Mathieu accompanies Conchita [Angelina Molina] into the living room, where she says "Mathieu, I'll explain what happened last night".

Thus the identity is expressed by the context. We see a woman walk through a door in the exterior.  We cut to a woman walking through a door into the interior.  Therefore we assume it is the same door, and the same woman.  It is all fiction - there is no woman, and no identity.  But the film is telling us there is a woman, and it is telling us there is an identity.

Individuation in perception

I argued earlier, e.g. here and here, that 'verbal' individuation, where we have only linguistic information about a set of characters, and where we use proper names or pronouns to learn which character is being talked about, is object independent.  No F actually has to exist, for us to be told which thing is F.  There are no hobbits, yet Tolkien can tell us which hobbit carried the ring into Mordor, which hobbit was his gardener, and so on.  Is the same true about 'perceptual individuation'? This is where we tell which individual is being pointed to, or who is the reference of a demonstrative proposition, or simply which person we are seeing or hearing.  Can we understand the demonstrative 'this rose' without there being an actual rose that is pointed to? Can you draw my attention to something, if there isn't a something?

Let's begin with films.  We can tell a story in a film, and usually the story begins in a verbal format, a screenplay.  Here, as I have argued, individuation is object-independent.  In That Obscure Object of Desire, (Luis Bunuel, 1977), the two main characters are Mathieu, a middle-aged wealthy Frenchman, and Conchita, a beautiful Spanish dancer, who ensnares Mathieu.  You can read the synopsis in Wikipeda, where the proper names 'Mathieu' and 'Conchita' tell us which character is the subject of each proposition in the synopsis.

The same story is told, in somewhat more detail, in the film itself. This scene here, for example, visually expresses the proposition "Mathieu is talking to Conchita, dressed in a maid's uniform, against the background of a flowers on a table etc.".  But we don't use proper names to individuate.  Rather, we use the images projected on the computer screen.  One image resembles a man with certain features, the other a woman with certain features.  These images are what some philosophers (such as Reid, although the medieval philosophers had the same idea) called natural signs.  We individuate each character in the film by a combination of facial features and (particularly in this film) by the context in which the features occur.  Bunuel's film is peculiar in that the same character is played by two different actresses.  Carole Bouquet (above left) plays Conchita in the scene linked to above.  In a scene shortly afterwards,  Angela Molina plays her.  Even though the actresses do not actually look that similar, the context - the uniform, the action and the logic of the scene - express the identity.  Famously, many people sat through the film without realising there were different actresses (I plead guilty).

So, a film can express a complex proposition involving many different characters. We can tell which characters is which by visual, verbal and contextual cues.  But no such character has to exist, for the story to tell us this.  At least some demonstrative reference is object-independent.