Beyond Necessity

Discussions of linguistic reference rarely define what reference is. An example is the SEP article here, which as far as I can see does not give any definition, merely stating that linguistic reference is ‘a relation that obtains between certain sorts of linguistic expressions and what speakers use those expressions to talk about’. And what relation is that? Slightly more helpfully it characterises it ‘metaphorically’ as a mechanism that enables us to talk about the world – say about George Bush – through referring terms which hook on to the world. But only slightly. What are these hooks?

Let’s try this. If Socrates is not running and Plato is running, ‘Socrates is running’ is false, and ‘Plato is running’ is true. But ‘a man is running’ is true, because Plato is running. The non-referring, i.e. indefinite, statement is true or false regardless of who is running. But the truth of falsity of the singular statements depends on who is running.

So a singular or referring statement is true when there is some particular person such that the predicate is satisfied by that person, and is false when that person fails to satisfy the predicate, even if the predicate is satisfied by other people. But a non-referring or existential statement is true when any individual, no matter who, satisfies the predicate.

Does that work?

According to Fred Sommers (The Logic of Natural Language, chapter 3) in traditional formal logic (TFL) as opposed to modern predicate logic (MPL), indefinite noun phrases do refer. “The distinctions crucial to MPL between subject expressions like ‘Socrates’ and ‘denoting phrases’ like ‘a senator’ are not crucial in TFL” (p.51).

Where he gets this idea I don’t know. The scholastic logicians followed Aristotle, and Aristotle says (Peri hermenias 17a38) ‘λέγω δὲ καθόλου μὲν ὃ ἐπὶ πλειόνων πέφυκε κατηγορεῖσθαι, καθ’ ἕκαστον δὲ ὃ μή’. ‘By universal I mean what is by nature disposed (πέφυκε) to be predicated of many, by singular what is not [thus disposed]’. He gives the example of ‘man’ as universal, and the proper name ‘Callias’ as singular. The Greek terms καθόλου and ἕκαστον were translated by the Latins as universale and singulare respectively, from which we get the corresponding Latin-English terms. Note the ‘by nature disposed’ bit – Greek πέφυκε, Latin natum est. I.e. it’s in the very nature of a common term like ‘man’ to be predicable of more than one individual. But this is not true of a genuinely singular term, i.e. its nature is such as to be predicable only of one.

Aristotle also says (Metaphysics 1040a28) that we cannot define singular terms, and that we should not be deceived by the fact that some individual objects have attributes that are unique, like ‘going round the earth’ (= the sun according to his geocentric theory). He points out that more than one thing could go round the earth, or none, so the definite description doesn’t really define ‘sun’ (ἥλιος). ‘But the sun was supposed to be an individual (ἕκαστα), like Cleon or Socrates’. So the ‘nature’ of a genuinely singular term is not just to be predicable of one thing alone, like a uniquely applying description, but to be predicable of that thing in virtue of its very meaning. Is Aristotle anticipating Kripke’s doctrine of the rigidity of reference?

Geach has a challenging objection to this. Suppose I say, referring to a meeting I attended ‘a man was shouting’. And suppose the indefinite noun phrase ‘a man’ refers to, i.e. picks out or identifies some man in the crowd, say Frank, or aims to do so. But suppose Frank wasn’t shouting, but Richard was. Then ‘a man was shouting’ is true, because Richard was shouting. Yet I meant to refer to Frank. I meant to say something which is actually false, but which is true because some other person than I meant satisfied the predicate.

The whole point of indefinite noun phrases is not to refer, at least if to refer means to identify or pick out, to tell you which individual I have in mind. In that sense, ‘a man was shouting’ doesn’t tell you which person you have in mind. It is true just so long as at least one man – it absolutely doesn’t matter which – was shouting. This contrasts with definite terms, which are true only when the person identified satisfies the predication.

I hold that all singular ‘reference’, i.e. telling the audience which individual is said to satisfy the predicate, is intralinguistic, and that there are chains of back-reference which originate in some indefinite noun phrase, e.g. ‘a certain young man’. This originating phrase does not refer in the sense that it ‘tells us which’. Clearly it can be satisfied, i.e. true of some man. But it doesn’t tell us which man it was. For example, some have thought that the man in Mark 14:51 was Mark himself, i.e. the author of the gospel. After all, all the other disciples had fled, so who knew about the man in the linen cloth, apart from the author himself? On the other hand, there were other witnesses present, and the story might have been passed around until Mark heard it, who put it in his account.

Successful reference: You must not only hit something; you must hit the right thing. And what makes a thing the right thing is the intention of the one who refers.

I discussed this 'target practice' theory of reference a while ago. I am not impressed. The purpose of language is to communicate, and the role that reference plays is to communicate which individual the speaker is talking about. Or rather, when the speaker utters a sentence of subject-predicate form, with a referring term as subject, the purpose of reference is to communicate which individual the predicate is said to apply to.

So it's not just a matter of hitting the target on the bull's eye. The person you are communicating with has to understand too. How does he know you hit the target? Is it e.g. that he also has to have the target in his or her sights in some way?

We watched American Sniper over the weekend. At the target practice, there was a supervisor with binoculars who would check whether the trainee had hit the target successfully. If that is the analogy, how would it apply to reference? It implies the hearer has some privileged relationship with the target. What if the hearer is an atheist, and does not see, or refuses to see, the target? That implies an atheist cannot understand a Christian’s reference to God. But surely he can. I am sure there are a few atheists or agnostics following this discussion. Are they unable to follow it without binoculars? Surely not.

The Maverick Philosopher agrees that the Quran contains tokens of 'Moses' (or its Arabic equivalent). He is still not sure whether those tokens refer to Moses or not. I suggested the following questions.

1. Do the OT and NT also contain tokens of 'Moses' (or Hebrew or Greek or Latin equivalent)?

2. Do the OT tokens of ‘Moses’ refer to Moses?

3. Does a ‘yes’ answer to the question immediately above, where I use the name ‘Moses’ also answer the question of whether I can refer to Moses?

4. Do the NT tokens of ‘Moses’ refer to Moses?

5. Some passages in the Quran (not all) that use tokens of ‘Moses’ are clearly quotations from the OT. If we agree that the OT passages refer to Moses, do we also agree that the quoted passages in the Quran also refer to him?

6. If we don’t agree that the quoted passages using ‘Moses’ refer to Moses, what happens if a Muslim printer publishes a copy of the OT? Does the reference failure result from identity or religious beliefs of the person printing or copying all or part of the OT? What happens if a Muslim printer publishes an annotated edition of the Quran which copies (as footnotes) the OT passages verbatim? I.e. does the reference of ‘Moses’ in an OT passage depend on its printed location?

7. If we agree that the passages in the Quran which quote the OT ‘Moses’ passages do refer to Moses, what about the passages which are not obvious quotes. Do they also refer to Moses, or not?

8. If we answer ‘no’ to the question immediately above, what about such passages which are not quotations from OT, but which use pronouns such as ‘he’ to refer back to passages which are quotations? If we agree that in the quotation passages the tokens of ‘Moses’ refer to Moses, is any subsequent pronominal back-reference also a reference to Moses?

This Wikipedia article is useful in matching Biblical and Quranic texts. Note that it gives the Arabic as well as the Romanised names. Thus ‘Moses’ corresponds to the Arabic موسى. So in translating the Arabic name to the Romanised one, do we translate the reference as well? I.e. do we assume that ‘Moses’ always refers to one mentioned in the Old Testament, and that the translation of موسى as ‘Moses’ guarantees that the Quran refers to Moses? Imagine an Arabic-English dictionary which as well as translating nouns, adjectives and verbs, also translates proper names, so that ‘Moses’ is given as the meaning for موسى. Or has the translator violated the principal of exegetical neutrality in assuming sameness of reference?

In any case, Wikipedia appears to violate the principle. E.g. it says “Islam believes that God thoroughly forgave Adam and Eve their transgression when they begged His mercy”. Presumably the names have their standard reference?

Ed Feser has an interesting post about Christians, Muslims, and the reference of “God” .Nearly 300 comments, including some very bad philosophy. The issue is essentially a linguistic and semantical one, not theological. Ed correctly points out that a speaker’s erroneous beliefs don’t entail that he is not referring to the same thing that speakers with correct beliefs are referring to, mentioning the example made famous by Keith Donellan. He points out that it is “perfectly coherent to say that Muslims are “importantly” and “crucially” wrong precisely because they are referring to the very same thing Christians are when they use the word “God,” and that they go on to make erroneous claims about this referent.That the errors are “important” or “crucial” is not by itself sufficient to prevent successful reference.

But then Ed claims (in a comment on his own post) that Jews, Christians and Muslims also use “God” to mean “the uncaused cause of everything other than himself, who is omnipotent, omniscient, perfectly good, etc.”“

Why? By ‘God’ don’t they all just mean the being referred to at the beginning of Genesis “In the beginning GOD created the heavens and the earth”, and who is referred to continuously throughout the old Testament?When any of them uses the name used in the Bible, they are using it with the same reference as the Bible, the text from which they learned the name.

So it is perfectly rational for a Christian to deny that God (i.e. the being referred to in Genesis et al) is the uncaused cause of everything other than himself. I.e. the proposition ‘God is the uncaused cause of everything other than himself’ is synthetic rather than analytic. But it is contradictory to say that God is not the being referred to at the beginning of Genesis, at least if the use of ‘God’ is intended to continue the chain of reference begun in Genesis and which extends throughout the Bible.

I mentioned Frege's distinction between concept and object earlier, and said I was taking a feature of that distinction as fundamental, namely that the distinction between predicate and sentential negation only applies to concept words (or rather, quantified concept words), and not to object words ('logical subjects').

David Brightly wasn't so sure it was a feature of that distinction, as opposed to a mere accident. Well, two further reasons. First, it is build into the predicate calculus that simple singular propositions have only one form of negation. We write '~Fa'. The syntax of the calculus is designed so that we cannot even represent the difference between 'Socrates is not running' and 'it is not the case that Socrates is running'.

Second, Frege begins his discourse by saying that a concept is predicative, whereas the name of an object, a proper name, is quite incapable of being used as a grammatical predicate. Now, we can say that someone is Alexander the Great, or is the planet Venus, but this is not predicating the object itself. For the predicate 'is the planet Venus' is predication not of Venus itself but of the concept of being identical with Venus. The verb 'is' is not a mere copula, its content is an essential part of the predicate.

Thus for an object-word to signify, it has to signify an object. It is essential to an object word like 'Venus' that it has to be satisfied, whereas it is essential to a concept word like 'planet' that it can be satisfied, or not. "An equation is reversible; an object's falling under a concept is an irreversible relation.

Thus "‘Venus exists’ is true in virtue of the meaning of the proper name ‘Venus’. Maverick says that this has it precisely backwards. What I should say is that 'Venus' has meaning in virtue of the truth of 'Venus exists'. Not at all. 'Venus' has meaning in virtue of its meaning something, just as you are an employer in virtue of your employing someone.

Here I mentioned Frege's distinction between concept and object, and Anthony is rightly asking questions about it. How does direct reference relate to the distinction?

So I go back to Frege, and his famous essay. It's rather hard to get anything out of it, because he never properly defines the distinction. He says that his explanation is not meant as a proper definition. "One cannot require that everything shall be defined, any more than one can require that a chemist shall decompose every substance". What is logically simple cannot have a proper definition (as Aristotle also noticed).

But he does give the famous example of "all mammals are land dwellers", which will do for my purpose. He says that if 'all mammals' were the logical subject of 'are land dwellers', then to negate the whole sentence we should have to negate the predicate, giving "all mammals are not land-dwellers". That is obviously wrong, for this predicate negation gives the contrary of the sentence it negates, not the contradictory. Thus we must put the 'not' in front of the 'all', to give sentence negation. But no such distinction applies to genuinely singular subjects, i.e. object words. Indeed, he proves this by re-writing the original sentence as "the concept mammal is subordinate to the concept land-dweller". By negating the predicate we get "the concept mammal is not subordinate to the concept land-dweller", which is the contradictory of the original sentence. And so a useful criterion for determining whether an expression is a concept expression (a logical predicate) or an object expression (a logical subject) is to determine whether predicate negation is equivalent to sentence negation or not. If it is, then the grammatical subject is a logical subject as well. Otherwise it is a logical predicate.

With that test in mind, and on the assumption that proper names are logical subjects, direct reference immediately follows, as I shall show tomorrow.

Frege famously classified the semantic function of a proper name into sense (Sinn) and reference (Bedeutung). But this conceals a difficulty. The sense of a proper name is clearly part of its meaning, and Frege even says this in a letter to Bertrand Russell written in November 1904. My father would have been alive then, although only eight months old. Frege writes

Mont Blanc with its snowfields is not itself a component part of the thought that Mont Blanc is more than 4,000 metres high ... The sense of the word 'Moon' is a component part of the thought that the moon is smaller than the earth. The moon itself (i.e. the Bedeutung of the word 'Moon' is not part of the sense of the word 'Moon'; for then it would also be a component part of a thought. We can nevertheless say: 'The Moon is idential with the heavenly body closest to the earth'. What is identical, however, is not a component part but the Bedeutung of the expression 'the Moon' and 'the heavenly body closest to the earth'. We can say that 3+4 is identical with 8-1; i.e. that the Bedeutung of '3+4' coincides with the Bedeutung of '8-1'. But this Bedeutung, namely the number 7, is not a component part of the sense of '3+4'. The identity is not an identity of sense, nor of part of the sense, but of Bedeutung ...

But if so, in what sense is the 'Bedeutung' a meaning at all? Bedeuten: the German for 'mean' or 'signify'. Frege is clearly disturbed by the idea that Mont Blanc, with its massive snowfields, could be part of a thought. But if it isn't, how could it still be part of the meaning? If Mont Blanc is destroyed in an enormous eruption (here Frege's other analogy to Etna would have been more appropriate), does the meaning of 'Mont Blanc', or some part of it, remain?

And if Mont Blanc itself isn't part of the meaning of its name, there is a further difficulty for Frege's theory that I commented on yesterday. If the name retains its sense after the Bedeutung, the referent, is destroyed, then we must suppose the sense of a name is something permanent to which its referent bears an impermanent and external relation. Let's say the sense is 'satisfied' when the referent exists. So, the sense of 'Mont Blanc' was not satisfied before the enormous geological upheaval created its referent, but is satisfied now, although it would once again not be satisfied if Mont Blanc exploded into nothingness. The difficulty is that his theory depends on the concept-object distinction. According to that distinction, concept words or predicates are fundamentally different from object words or singular terms, in that concept words are sensitive to the scope of negation, whereas singular terms are not. Take 'a man is not running' and 'it is not the case that a man is running'. The predicate negation is true when there is at least one man, and he is not running. The sentential negation is true only when no man runs. But there is no such distinction with singular propositions, at least as the object-concept distinction requires it. 'Socrates is not running' and 'It is not the case that Socrates is running' is true only when Socrates exists, and he is not running. There appears to be no room for the possibility of Socrates not existing. Yet if the meaning of a proper name is its sense, and if the sense exists even when the referent does not, 'Socrates is running' is false when Socrates does not exist, yet 'Socrates is not running' is false as well.

Russell replied, a month later in the days before email, that Mont Blanc really is a part of what is asserted by 'Mont Blanc is more than 4,000 metres high'. I think he changed his mind shortly later, but then Russell often changed his mind (which is a good thing).

As I noted in the page linked above, I could not then find where Russell was writing from. He moved there in 1904 in order to work out a theory of denoting that could be used in Principia Mathematica, but which would avoid the Paradox (now known as Russell's paradox) that he had discovered while working on the Principles of Mathematics. He took his first wife Alys there, but this was a disastrous part of a disastrous marriage, and he was probably not very happy there. Nor actually was she, as Russell seems to have been a beast towards her. Thanks to Google maps I think I have located the place. It certainly is secluded, a short distance from Lower Frensham pond in a fairly exclusive part of the Surrey stockbroker belt. I don't like Surrey. Mostly places like that. Small roads in the English countryside, looking as they might have looked two hundred years ago, then suddenly there appears a large, usually Edwardian mansion at the end of a long gated drive. Inside, they still drink gin and tonic. But nothing wrong with that, I suppose.

I made a start here on an account of medieval 'supposition theory', although there is a lot more to do. I was getting irritated with the Wikipedia article, although it is not bad by Wikipedia standards, having been written in 2006 by someone who is actually a professor of philosophy. Brian is not an expert though (few people are in this arcane branch of logic) and the article has a few problems. It's sad too that he could not continue his work on Wikipedia because work for inaccessible peer-reviewed journals was more important, according to his Dean of studies. (I know him from the days I was naively trying to recruit academics to Wikipedia).

Anyway, one of the problems with the article is the way it compares supposition theory to modern theories of reference. That's actually not a problem for Wikipedia – most standard reference works say exactly the same. But Catarina Dutilh Novaes has objected, in a number of published works including her Ph.D. thesis, that this is an anachronism. She doesn't think the concepts of supposition and reference are comparable at all, and part of the problem, she says, is that modern philosophical logicians do not understand medieval theories of supposition, and medieval scholars do not understand the concepts of modern philosophical logic such as reference. Each is comparing something they do understand to something they don't understand, and it's all wrong.

I used to think she was right about this, but now I don't. The problem is that modern philosophical logicians don't really agree on what 'reference' is, and the definitions they give are extremely vague. Consider the definition from the much-better-than-Wikipedia SEP:

Reference is a relation that obtains between expressions and what speakers use expressions to talk about. When I assert ‘George W. Bush is a Republican’, I use the proper name ‘George W. Bush’ to refer to a particular individual, an individual about whom I go on to speak. [...] More picturesquely, we are able to use language to talk about the world because words, at least certain types of words, somehow ‘hook on to’ things in the world — things like George W. Bush. Proper names — expressions like ‘George W. Bush’ — are widely regarded as paradigmatic referring expressions.

What does all that mean? One of Catarina's objections to comparing supposition to reference is that in classical supposition theory, common terms as well as proper names have supposition. 'Man' supposits for all men, 'Socrates' supposits for just Socrates. But according to the SEP definition above, it seems like common terms can refer. If reference is 'talking about', then we can use the expression 'every man' to talk about every man, and when we assert 'every man is an animal' we use the quantified expression 'every man' to talk about a particular group of individuals, individuals about whom we go on to speak.

Now Frege had an objection to this (and Frege is the source of all our modern ideas about reference).

If I utter a sentence with the grammatical subject 'all men', I do not wish to say something about some Central African chief wholly unknown to me. It is thus utterly false that I am in any way designating [my emphasis] this chief when I use the word 'man', or that this chief belongs in any way to what the word 'man' means.

Which is not correct at all. When you use the expression 'every man' or 'all men', you certainly are saying something about this individual, even though he is unknown to you. And why is it false that you are designating him? It depends what mean by designation, but then you are back to the problem of defining 'reference'. And the chief does belong in some way to what the name means. If it meant something different, e.g. if the English word 'man' meant only European men, then the sentence wouldn't be about this chief, would it?

In summary, there is nothing about the definition of reference as given by at least two authoritative sources (the SEP and Frege) that distinguishes it from the medieval concept of supposition. More later.

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.

This morning I had the idea for the following loose definition. A discourse* 'semantically complete' when any competent user of the language can understand it, simply in virtue of understanding the language.

But this of course won't do. I had meant to eliminate proper names, because understanding the language is not a requirement for understanding them. But who is to say that the process of learning new proper names (or new meanings for the same proper name) is not also a process of understanding the language? I need a criterion for 'understanding the language' that rules out proper names, but I don't have one.

Is it that a certain perceptual acquaintance, or some relation with the external world is necessary in order to learn a proper name? Well perhaps, but that doesn't distinguish them from common names, because to learn the meaning of certain basic terms like 'red', 'round' and so on, we have to be acquainted with external reality.

*Discourse - a sentences or any group of sentences.

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.

Tristan Haze pointed me to this paper by Saul Kripke, which mentions the distinction between speakers reference and semantic reference. "I'd be interested to hear whether you think this answers your objection".

Having read Kripke's paper, which has a lot about another famous distinction, made by Keith Donnellan (I have discussed this somewhere here, some time ago), I don't think it does. My view is that all 'reference' whatsoever is semantic reference, so I don't make the distinction between different kinds of reference.

Furthermore, I don't think that what Kripke calls 'semantic reference' is the same as what I mean by it. I claim that all reference has the same semantic model as 'story relative reference'. Story relative reference is the mechanism that allows us to say which character is which, in a narrative that can be true (as with history) or false (as with fiction). This kind of reference cannot involve any semantic relation between language and the world, because it has the same semantic properties whether or not the information was caused by real people or events, or not. I argue this cogently against Tim Crane's view of reference here.

If I am right (i.e. reference is not a language-world relation) then my 'semantic reference' cannot be Kripke's semantic reference. For Kripke, a definite description signifies semantically by allowing us to identify a unique individual in the world that satisfies that description. Just by knowing the semantics of the terms 'queen', 'England' and '2012', we can determine which individual in reality is satisfied by 'Queen of England in 2012', and so can grasp the truth conditions of 'the Queen of England in 2012 lives in London'. By contrast, I reject entirely the view that the semantics of anything involves a word-world relation. This is true of definite descriptions as well as proper names. So what I mean by 'semantic reference' is different from what is meant by Kripke, and by most other contemporary philosophers of language.

I will say some more about definite descriptions in the next post.

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.

I start my discussion of Kripke’s theory of reference by questioning whether it is necessary that we intend to use a name with the same reference as the person we learned the name from. In at least one simple example, this is neither necessary nor sufficient. Imagine a game were a group of people make up a story by successive members of the group uttering successive sentences of the story. So the first member starts:

(1) A soldier called ‘Alex’ returned from the war.

And the second member goes on

(2) Alex was looking forward to seeing his wife, Jenny, and his daughter Lucy.

And the third continues

(3) Jenny was only eight years old.

Now clearly the third speaker got it wrong. She probably meant to say ‘Lucy’; she meant the daughter, since it is a matter of biology that the wife cannot be eight years old. But her meaning or intentions are irrelevant in any case. For she has successfully used the name ‘Jenny’ with the same reference as the second speaker, and has successfully communicated the proposition that the soldier’s wife was only eight years old, even though she did not intend to use the name that way. What is relevant is not the intention of the speaker, but rather the rules of use of proper names (or other referring terms like pronouns or descriptions), plus an informational background available to both speaker and audience*.

Causation and intention are irrelevant, at least in this particular case. I shall argue in subsequent posts that all the different ways of passing on a reference are reducible to examples such as this one.

*Or an assumed background, which I shall discuss later.

My next series of posts are going to be about the causal theory of reference. As a preliminary, here is how the Stanford Encyclopedia of Philosophy characterises the theory.

The causal theory was adumbrated by Kripke[9] (1980) as an alternative to the description theory of nominal reference. The central idea underpinning this sort of theory is that (the use of) a name refers to whatever is linked to it in the appropriate way, a way that does not require speakers to associate any identifying descriptive content with the name.

The causal theory is generally presented as having two components: one dealing with reference fixing, the other dealing with reference borrowing. Reference is initially fixed at a dubbing, usually by perception, though sometimes by description. Reference-fixing is by perception when a speaker says, in effect, of a perceived object: “You're to be called ‘N’.” Reference-fixing is by description when a speaker stipulates, in effect: “Whatever is the unique such-and-such is to be called ‘N’.” (As noted by Kripke (1980), the name ‘Neptune’ was fixed by description, stipulated by the astronomer Leverrier to refer to whatever was the planetary cause of observed perturbations in the orbit of Uranus.)

After the reference-fixing, the name is passed on from speaker to speaker through communicative exchanges. Speakers succeed in referring to something by means of its name because underlying their uses of the name are links in a causal chain stretching back to the dubbing of the object with that name. Speakers thus effectively ‘borrow’ their reference from speakers earlier in the chain but borrowers do not have to be able to identify lenders; all that is required is that borrowers are appropriately linked to their lenders through communication. However, as Kripke points out, in order for a speaker (qua reference borrower) to succeed in using a proper name to refer to the object/individual the lender was using the name to refer to, he must intend to do so. Thus, I may use the name ‘Napoleon’ to refer to my pet cat, even if the lender of the name used it to refer to the famous French general. For in such a case, I do not intend “to use the name to refer to the individual the lender used it to refer to.”

From the article “Reference”, section “Causal Theory of Reference”, Stanford Encyclopedia of Philosophy.

Kripke writes:

A rough statement of a theory [of reference] might be the following: An initial 'baptism' takes place. Here the object may be named by ostension, or the reference of the name may be fixed by a description. When then name is 'passed from link to link', the receiver of the name must, I think, intend when he learns it to use it with the same reference as the man from whom he heard it. If I hear the name 'Napoleon' and decide it would be a nice name for my pet aardvark, I do not satisfy this condition. (Perhaps it is some such failure to keep the reference fixed which accounts for the divergence of present uses of 'Santa Claus' from the alleged original use.

Is that right? How do we intend to use a name with the same reference as the person from whom we heard the name from?

Anthony comments here about the difficulty of making sense of 'reference fixing'. Let's see what Gareth Evans and Saul Kripke say about it. In section 1.7 of The Varieties of Reference, Evans gives what he calls a 'particularly clear example' of the phenomenon.

Even if we follow Russell, and hive off definite descriptions for separate treatment as quantifiers, there still remain terms which would intuitively be regarded as singular terms, but for which the 'no referent - no thought (sense) position seems quite incorrect. A particularly clear example can be produced by introducing a name into the language by some such 'reference fixing' stipulation as* "Let us call who invented the zip 'Julius'". I call such names, whose reference is fixed by description, 'descriptive names'. Here, as with definite descriptions, it seems impossible to deny that someone speaking, and known to be speaking, 'within the scope of' this stipulation could express a thought, and convey that thought to another person, by uttering "Julius was an Englishman", even if the name is empty.

I'm not sure it is altogether clear, for the reasons that Kripke mentions in lecture III of Naming and Necessity. He asks whether the referent of 'Godel' could be fixed as 'the person who discovered the incompleteness of arithmetic', then imagines a situation where a man called 'Schmidt' was actually the author of the theorem. His body was found in Vienna in mysterious circumstances many years ago, and his friend Godel got hold of the manuscript, and published it as his own.

On the view in question, then, when our ordinary man uses the name 'Godel', he really means to refer to Schmidt, because Schmidt is the unique person satisfying the description 'the man who discovered the incompleteness of arithmetic' ... So, since the man who discovered the incompleteness of arithmetic is in fact Schnidt, we, when we talk about 'Godel', are in fact always referring to Schmidt. But it seems to me that we are not.

Perhaps a similar problem attaches to our Shakespeare example? If the name 'Shakespeare' simply means 'whoever wrote the plays such as Hamlet, Macbeth, Romeo and Juliet', and if Edward de Vere did in fact write those plays, then when we are talking about and referring to Shakespeare, we are in fact talking about and referring to De Vere. But it seems we are not, as Kripke puts it.

*I have modifed Evans' wording to avoid indent problems

Biblioarchy and Anthony have commented on ‘reference fixing’ by description. Anthony objects that in order to fix the referent of 'Shakespeare' as 'the man who wrote the plays and poems traditionally attributed to William Shakespeare of Stratford-upon-Avon", we need to agree on who that was.

If we just leave it floating out there as possibly being one person, and possibly being another person, and possibly being several people, and possibly not being a person at all (maybe aliens wrote the plays), then we haven't fixed it.

Biblioarchy makes a similar point, saying

Some Oxfordians and many Stratfordians believe that more than one hand was at play on many of the texts. Also that they appear to be palimpsests of sorts, revised and rewritten over the years by 'The Author', Shakespeare, whomEver he was, and perhaps, a cadre of University Wits in the Fisher's Folly Days Mid 1580's. This would of course, completely demolish the Stratfordian time-line, setting it back a decade, and disqualify the Stratford man.

Well, the idea of ‘reference fixing’ is not mine. Kripke introduced it in Naming and Necessity, and Gareth Evans discusses it in The Varieties of Reference. Kripke’s point – there is an excellent summary of it in the SEP article on Reference - is that while we can determine the reference of a proper name by some uniquely satisfied description – for example, we can fix the reference of ‘Aristotle’ as ‘the last great philosopher of antiquity’, the semantics of the name cannot be identical with the semantics of the description. For ‘the last great philosopher of antiquity’ might well apply to Plato in a possible world where Aristotle died in infancy.

But these comments do suggest a deeper problem with the whole idea of fixing reference by description, given that primary sources do not give us a single description of a putative historical character, but rather a series of descriptions. What if there wasn’t a single author of the Shakespeare plays? What if one person wrote Hamlet, another person wrote the Tempest? Indeed, I believe Oxfordians have to insist that the authors are different, given a fairly certain dating for the latter play of after 1604, when De Vere died*. What if there wasn’t even a single author of any of the plays? All mathematicians know about Nicholas Bourbaki, who is not a person at all – the name is a pseudonym under which a collective of French mathematicians wrote a series of books about advanced set theory and algebra.

My own subject is Duns Scotus. Who was he? A hundred years ago, we might have fixed the reference of his name by the description ‘the author of De Modis Significandi’. But that would have been wrong, as Grabmann demonstrated in 1922 that this work was by Thomas of Erfurt, a fourteenth century logician belong in to the Parisian ‘modist’ school. The authenticity of the Questions on the Prior Analytics, once attributed to him, is also doubtful. And though his books on the Categories, and on the Sophisticis Elenchis, and of course the monumental Ordinatio are almost certainly authentic, it is clear that we have a series of different descriptions – ‘the author of the Ordinatio’, the author of the Lectura, and so on – rather than a single description.

Scotus' biographical details are even more problematic. We have a handful of details about his life. Records show that someone of that name was ordained at St Andrew's Priory, Northampton on 17th March 1291, from which we infer a probable date of birth of about 1265, given the minimum age of 25 for ordination. So we have the description “person named ‘John Duns Scotus’, ordained in 1265 etc’. We believe he was in Oxford in 1300, based on a single passage in the Ordinatio that I discuss here. His name is on a list of those who opposed King Philip’s attempt to depose Pope Boniface around 1303. We have a few other bits of information. But whether these different descriptions are all satisfied by the same person is little more than conjecture and probable inference. We don’t know for absolutely certain whether there was a single author of his individual works. His Questions on the Perihermenias comes down to us in two separate versions, one of which (Opus I) contains a fragment of what may be another work. It is not certain how much of this was edited or rewritten by his disciple Antonius Andreas. So even a single work has a series of descriptions corresponding to the differing codices or primary sources which have come down to us.

*Shakespeare made extensive use of narratives describing the wreck and redemption of the ship the "Sea-Venture" in Bermuda in 1609, and the events which ensued when the crew made it safely ashore.

Is the following argument valid?

The UK Prime Minister is a man
The UK Prime Minister used to be a woman
Some man used to be a woman

You will probably say not. The first is true because David Cameron (who at the time of writing is Prime Minister) is a man. The second is true because Margaret Thatcher (who used to be the Prime Minister until the 1990s) is a woman, and always has been. But the implication is clearly invalid, since the premisses could be true and the conclusion false if no man had ever undergone a sex change.

Kripke's take on this is famous: definite descriptions such as 'The UK Prime Minister' are not rigid. They have different referents in different possible worlds, and so the inference is not valid, because of the non-ridigity of reference. By contrast, proper names are rigid designators. Understood in the same sense, they always refer to the same individual. Thus, if you substitute 'David Cameron' into the inference above, you get something that is valid (although not sound, of course, for the second premiss is false - as far as we know, David Cameron never used to be a woman).

But how about this?

The leader of Cambridge City Council is a woman
The leader of Cambridge City Council used to be a man
Some woman used to be a man

As it happens, the (current) leader of Cambridge City Council is Jenny Bailey, who underwent a sex change operation to become a woman. So Jenny Bailey is now a woman, but used to be a man, and so some woman used to be a man. The premisses can't be true (assuming "The leader of Cambridge City Council" has the same referent in both premisses) and the conclusion false, so the inference is valid.

How do we explain this? Are definite descriptions rigid or not?

Ockham has a quite different take on this, distinguishing between 'sense of composition' and 'sense of division'. He explains it in Book III of his great Summa Logicae here. In the sense of composition it is signified that a mode (such as 'is possible' or 'was the case that') is predicated of the whole proposition. In the sense of division it is denoted that the predicate is predicated of the subject by a verb determined by such a mode. Thus we must distinguish between 'it was the case that the (then) PM was a woman' and 'it is the case that the (current) PM was a woman'. Clearly, read in the sense of composition, the subject term may have a different sense in the different premisses. In 'The UK Prime Minister used to be a woman', the subject term means Margaret Thatcher. In 'The UK Prime Minister is a man' it means David Cameron. Hence (read in the sense of composition) the inference is not valid because of equivocation, just as any syllogism is invalid because of equivocation. But read in the sense of division it is valid. If by 'The UK Prime Minister used to be a woman' I mean that David Cameron used to be a woman, the first inference is valid, just as the second is (where 'The leader of Cambridge City Council' refers in both premisses to Jenny Bailey).

Hence we do not have to accept any fundamental distinction between definite descriptions and proper names. Rather, it is easier to read definite descriptions in an ambiguous way. When we say 'The UK Prime Minister used to be a woman', we can read it either as saying that the present PM used to be a woman, or that some former PM used to be a woman. And this ambiguity is not fundamentally different from the one we find here.

William Pitt was the youngest Prime Minister
William Pitt was not the youngest Prime Minister
the youngest Prime Minister was not the youngest Prime Minister

For there was more than one person called 'William Pitt', just as there was more than one person called 'Prime Minister of the UK'.