As you embed, so Ködel must lie … 

ABSTRACT

Machery et al.’s 2004 x-phi project has been widely criticised for ambiguities contained in the expression ‘talk about’. Interestingly, although ‘about’ plays a prominent part in the debate, aboutness has not been a topic. This paper discusses this aspect. Alas, it must thereby add a further ambiguity to the list, the ambiguity between aboutness and reference, and thus also between subject matter and referent. It explains the distinction between intra-categorical aboutness which makes no ontological demands, and cross-categorical reference which requires the referent to exist. It then analyses the 4-fold embedding contained in Machery et al.’s study and shows how the aboutness-reference distinction bears on it.

KEYWORDS:

• Aboutness
• reference
• subject matter
• semantic intuitions
• proper names
• fiction

1. Introduction

1.1. The background

Imagine that John is mistaken in thinking of Gödel as the author of the Incompleteness Theorem (henceforth ‘IT’); instead, as Kripke once fantasised, the IT’s real author was Schmidt. When John uses the name ‘Gödel’, is he talking about Gödel or Schmidt? This is the question Machery et al. investigated in their much debated 2004 x-phi project. A recent paper, Heck (2018), continues the discussion, showing that Machery et al.’s probe contains further ambiguities. But this does still not complete the list. We will here pick up Heck’s thread and show that in addition to theirs, there is an ambiguity between aboutness and reference to be considered. But let us start from the beginning.

In their 2004 x-phi project, Machery et al. took issue with the fact that much of the reference debate in the philosophy of language relies on intuitions, specifically those of the respective authors. They suspected that intuitions may vary across cultures and therefore not be good guidance in reference theory. To prove their point, they ran an experiment to show that Asians respond differently from Westerners to some ‘intuition pumps’ about reference. The experiment was based on two of Kripke’s examples, the Gödel-Schmidt and the Jonah stories, which Kripke had used aiming to show that the causal-history theory of proper names was right and the description view (largely) mistaken.¹ Machery et al.’s paper has been criticised for numerous aspects, and Heck, too, raises important meta-philosophical concerns before addressing their experiments. In this paper, we will only discuss the latter, leaving meta-philosophy for another day.

Heck focuses on the authors’ Gödel-Schmidt intuition test (and so will we). Agreeing with Ludwig (2007) and Deutsch (2009), Heck, too, argues that the way the question was posed, and, in particular, the phrase ‘talking about’, is ambiguous between speaker reference and semantic reference, i.e. between the referent intended by the speaker and the ‘literal’ (as it were) referent of the name under both theories. But when ‘talking about’ someone or something, this need not be a referent; it can be a subject matter instead. As it happens, Heck’s paper coincides with a surge in aboutness research in the philosophy of logic and language, and we will use aboutness theory to help explain what the little word ‘about’ can mean in this context. In doing so, the ambiguity between aboutness and reference will be added to Heck’s list of distinctions relevant for the evaluation of Machery et al.’s test. In explaining this further distinction, the paper will build on an account of reference to fictional objects offered by de Ponte, Korta, and Perry (2020). The aim is to shed new light on both the study and the problem.

1.2. The issue

Let us begin by looking at Machery et al.’s probe as submitted to the test persons, which will also serve to remind ourselves of Kripke’s story:

Suppose that John has learned in college that Gödel is the man who proved an important mathematical theorem, called the incompleteness of arithmetic. John is quite good at mathematics and he can give an accurate statement of the incompleteness theorem, which he attributes to Gödel as the discoverer. But this is the only thing that he has heard about Gödel. Now suppose that Gödel was not the author of this theorem. A man called “Schmidt”, whose body was found in Vienna under mysterious circumstances many years ago, actually did the work in question. His friend Gödel somehow got hold of the manuscript and claimed credit for the work, which was thereafter attributed to Gödel. Thus, he has been known as the man who proved the incompleteness of arithmetic. Most people who have heard the name “Gödel” are like John; the claim that Gödel discovered the incompleteness theorem is the only thing they have ever heard about Gödel. When John uses the name “Gödel”, is he talking about:

(A) the person who really discovered the incompleteness of arithmetic? or

(B) the person who got hold of the manuscript and claimed credit for the work? (Machery et al. 2004:B6)

Machery et al. introduced a new character, John, into Kripke’s Gödel-Schmidt story in order to test intuitions between the description and the causal-history theories of names. Kripke’s point had been, of course, that proper names refer rigidly, i.e. that ‘Gödel’ refers to Gödel, no matter what (if anything) the speaker or interlocutor associates with it. Put very crudely, whereas the description theory holds that, in the first instance, a name stands for a description and only through it for the object that satisfies it, the causal-history theory holds that a name refers in the first instance to the object so baptised,² and the fact that it may also be known – or supposed – to fit certain descriptions is a secondary aspect. Kripke wanted to prove his point by making reference via the description veer off unexpectedly to another object. If the description theory were right, the idea was, ‘Gödel’ would be short for ‘author of the IT’ and the name should refer to Schmidt rather than Gödel. Kripke thought that our intuitions don’t support this, so his causal-history theory would be corroborated by this thought experiment. In Machery et al.’s version of the story, the set-up reproduces Kripke’s story by claiming that John knows only that one thing about Gödel. If the test persons’ intuitions take John to be talking about (A) the person satisfying the description, the description theory would be right. If, by contrast, they take John to be talking about (B) the person called ‘Gödel’, Kripke’s theory would be right.

The issue with Machery et al.’s probe that concerns us here is the ambiguities it has been shown to contain, so that its results could not serve as philosophical guidance. The first ambiguity highlighted was that between speaker reference and semantic reference (Deutsch 2009; Ludwig 2007). A speaker might erroneously use a name to refer not to its real bearer but to someone the speaker thinks to be the person so called. Against this criticism, the authors argue that ‘Gödel’ in the probe should be read qua type, not token (Machery and Stich 2012, 506; Heck 2018, 254) – the second potential ambiguity – so they think that speaker reference would not be relevant. Heck disputes this, arguing that if their test is about types, it is equally relevant to expressions other than proper names, prominently definite descriptions. However, since Donnellan’s seminal 1966 paper we know that definite descriptions can be used attributively or referentially – the third ambiguity Heck brings into play (2018, 254f). Accordingly, ‘the author of the IT’ can either be used to pick out the person, whoever that is, who satisfies the attribute, i.e. authored the IT; or it could be used referentially to point an interlocutor to the person both the speaker and – the speaker supposes – the interlocutor think of as the author of the IT. Now, Heck points out that Donnellan is concerned with uses, i.e. tokens, of descriptions, not types, but the ambiguity is just what the description theory would reflect (Heck 2018, 255). For illustration, Heck ran a test analogous to Machery et al.’s for such a definite description, where intuitions could diverge in the same way. So, the argument from types is dismissed.

Summing up, the test was designed to find out whether people think that ‘Gödel’ would pick out the person so named (following the causal-history theory of names) or the person of whom the description associated with the name, i.e. author of the IT, is true (following the description theory of names). But it turns out that both theories can be subject to an ambiguity between a ‘literal’ and an ‘intended’ meaning. ‘Gödel’ can (mistakenly) be used to pick out someone the speaker erroneously thinks is Gödel, or the man actually so called – so there is the speaker vs. semantic reference ambiguity that concerns the causal theory of names. Analogously, ‘the author of the IT’ (or any short version of this definite description, for instance ‘Gödel’) can pick out an intended referent of whom the description is not true, or the actual author of the IT – so there is the referential vs. attributive use ambiguity that concerns the description theory of names. Heck’s criticism raised against Machery et al.’s experiment is then that ‘talking about’ is ambiguous in terms of either distinction: it could be understood as speaker’s as well as semantic reference and the relevant term as used attributively as well as referentially.

1.3. The plan for this paper

We will support this criticism by adding a further ambiguity from aboutness theory where we have to distinguish between aboutness and reference, and subject matter and referent. This distinction affects the way we think about the probe, and we will see that here, too, the question is ambiguous. In order to show this, we will start by introducing aboutness in logic and language to the uninitiated. In section 3, we will then explain how aboutness differs from reference, in order to lay the foundation for the main part of the paper. In section 4, we will then be able to show how this makes the experiment’s question ambiguous. In the course of this, it will become clear that we are dealing with multiple embeddings that will be relevant to the evaluation of the situation with respect to our new ambiguity. As will be explained in section 5, the results are meant to give additional theoretical guidance to the design of possible future experiments conducted in this area.

2. Aboutness in the philosophy of logic and language

Aboutness is the way a text relates to its subject matter, with ‘text’ to be understood in the technical, linguistic sense as a meaningful, coherent language utterance.³ To stick to our present theme, a book could be about Gödel’s Vienna, a paper about the impact of the Incompleteness Theorem, and a statement about Gödel himself, to give a few examples. There are therefore three elements involved: texts, subject matters, and the way the two relate to each other.

Aboutness theory has so far focused mainly on aboutness and subject matter, using indicative sentences or conditionals as their textual elements. Accounts vary regarding how much room they leave to other sorts of text such as books, talks, etc., and also other kinds of sentence such as questions or commands, but this will not concern us here. Views also vary about whether subject matter is objectual, and thereby roughly synonymous with ‘topic’,⁴ or propositional in structure, and thereby closer to a question.⁵ Thus the topic accounts would consider ‘Gödel’ a subject matter, whereas the propositional accounts’ subject matter might be ‘whether Gödel was the author of the Incompleteness Theorem’. And most of the work in aboutness theory has focused on the technicalities of aboutness proper, which can be explicated as a relation between text and subject matter, or as a property a text may have. Tools used range from grammatical and quantitative explications, to logical consequence and modal (truthmaker) accounts. Despite these differences, today all accounts agree on the fact that subject matter plays an important role in meaning; that sentences and their negations are about the same subject matter; and that texts must somehow be relevant to their subject matter(s).

For our question of whom John ‘is talking about’, this means that, depending on which of these views is taken, aboutness theory can concern individual statements John makes, or a longer conversation John has about Gödel; and it can tell us about the subject matter ‘Gödel’, or about a subject matter ‘whether φ(Gödel)’. For present purposes, objectual subject matters are more important than propositional ones.

3. Aboutness vs. reference

Aboutness is frequently confused with reference, and subject matter with referent(s). This is particularly the case when the text in question is an individual sentence, rather than a longer text. What underlies the confusion is probably the fact that grammatical nouns can stand for both; although they are not the only tools of reference nor for indicating a subject matter, they are very frequently used for either or both of these purposes. For the present debate, it is especially important to distinguish clearly between the two, and I will show in the following that they are really quite different from a philosophical point of view.

When we want to describe a state of affairs, we usually verbally single out an object and predicate something of it. Such a description can convey the product of an act of imagination, or the content of an observation. In either case, we will be saying something about the object, but in the case of an observation statement,⁶ we are talking about an object with which we are, or were, in direct epistemic contact. An important aboutness theorist, Ryle (1933a, 1993b), thinks that for an object to be able to serve as a referent, it must be physically there in the world; imaginary, including conceptual, objects can’t. Goodman (1961) also gives separate accounts for worldly and for fictitious subject matters. In fact, the whole problem of ‘empty names’ is due to some version of this demand, a demand we accept, at least for the purposes of this paper. In this same spirit, de Ponte, Korta, and Perry (2020) give a detailed, fine-grained account of what statements involving empty names can refer to, to which we will return.⁷

In making an observation statement, we are therefore doing two things at once: we refer to the perceived object and we say something about it. But the two need not coincide. We can refer to objects without saying anything about them, for instance when we just utter the name to draw somebody’s attention to them, and we can talk about objects without their existence in the world, most obviously in fiction, but on Ryle’s view also when we speak of conceptual or abstract, rather than concrete objects. As a heuristic, it will usually be the case that objects can serve as referents when it is possible to mis-describe them but nevertheless succeed in picking them out.

For anyone not already on board with the ontological demand, it should be stressed that these views are not concerned with grammatical reference, i.e. the various linguistic options of singling out grammatical objects, but rather with the semantics and pragmatics of reference, i.e. the linguistic act of drawing attention to, and often enough saying something about, an object, portion of stuff, or event in the world, for instance. Whereas grammatical reference is of concern to linguists, the philosophical aspects of reference make metaphysical demands for reference to be successful. It is these philosophical aspects that concern us here.

There are therefore a number of differences between reference and aboutness. First, aboutness is a relation internal to language. In being meaningful, a piece of text is concerned with something, and any such thing it is concerned with is one of its subject matters. One might say that a subject matter relates to the meaning of a text like a part of speech relates to the syntax of a text. Reference, by contrast, is a cross-categorical relation, pointing the interlocutor to an object. Indeed, the whole point of reference is to single out the (worldly) referent, whereas the point of a subject matter is that we learn, say, demand, or inquire something about it.

Therefore, there is an important ontological difference between aboutness and reference. A text’s subject matter is ontologically independent of the world; it depends instead on the text. It need not exist outside one particular text, but it can be shared between several texts, and can, of course, correspond to something in reality (in modal realism understood as ‘our world’). Conversely, a referent is by definition something that exists independently and outside of the referring term (the obvious exception being rare cases of self-reference like ‘this word’). A referent must therefore exist ontologically prior to the referring term (or coincide with it in self-reference cases), while a subject matter can be created by the text that is about it. Thus, ‘my computer’ successfully refers to the device on which I write this, while ‘Once upon a time, there was a fairy’ creates the fairy as a subject matter.

An upshot of the ontological differences is that reference can fail while aboutness cannot. ‘My computer’ would fail to refer if I didn’t have a computer, but the fairy becomes a subject matter as soon as a text is about it. And in the case of successful reference, what is predicated of the referent can be true or false – where which it is, is independent of language (unless, of course, the referent is a linguistic item). Aboutness, by contrast, is established as soon as a text has a subject matter, which it arguably does as soon as it is meaningful, and that, in turn, is surely the essential aspect that makes a string of words a text. Instead of truth or falsity, the criterion is then intelligibility.

The epistemic difference is very nicely explained in Russell’s well-known passage in ‘Descriptions’ (1919), where he stresses that names of fictitious persons don’t refer:

[I]t is of the very essence of fiction that only the thoughts, feelings, etc., in Shakespeare and his readers are real, and that there is not, in addition to them, an objective Hamlet. When you have taken account of all the feelings roused by Napoleon in writers and readers of history, you have not touched the actual man; but in the case of Hamlet you have come to the end of him. (1919, 169)

So what Shakespeare wrote about Hamlet made Hamlet one of the play’s subject matters, just as what the historians write about Napoleon makes Napoleon their subject matter. But as far as Hamlet is concerned, a subject matter is all he’ll ever be, while Napoleon, in addition to being an object of aboutness, could also be referred to – by his contemporaries at least (some presentists might caution).

It is worth noting that subject matter is something that falls out from a text, as it were. The text’s main purpose may well be to express, state or ask something else, and individual subject matters are often only part of what a text deals with.⁸ Nevertheless, texts usually don’t just state a subject matter (there are special cases, such as labels or signs, which may be taken to do only that); instead, having a subject matter just is saying, or asking, something about it. Carnap in his Logical Syntax of Language proposed a criterion according to which a statement is about a subject matter when the truth of the statement matters to our knowledge of the subject matter’s properties (Carnap [1934] 1968, 37:285 (§74)). This criterion is of course much too narrow, but the underlying idea is surely right. Compare this to reference which is achieved by singular terms (names, definite descriptions, demonstratives, pronouns), whose main purpose it is to single out and point to an object. Even if they may highlight specific aspects of that object in referring to it, when anything is said about the referent, reference comes first and what is said about the referent is usually contributed by an additional form of predication.

Let us now see how the reference – aboutness distinction can be applied to Machery et al.’s case.

4. The ambiguity spelled out

Machery et al.’s way of formulating the question is:

When John uses the name ‘Gödel’, is he talking about: … (2004:B6)

By giving the test persons two choices – effectively Schmidt and Gödel, the crook (I shall call this invented character ‘Ködel’⁹ to distinguish him from real Kurt Gödel) – they are getting another two options out of the way. One is: nobody. People not trained to distinguish use from mention, might well have thought that John could be using the name ‘Gödel’ without talking about anyone. This is something both Ryle (1933a) and Goodman (1961) have pointed out: uttering ‘Gödel’ is neither necessary nor sufficient for talking about Gödel. The choice between the two replies does not allow for the mere mention option. But by forcing a choice, Machery et al. are also inhibiting another possible reply: both. Imagine John has become a little obsessed with the Incompleteness Theorem, and he also has a soft spot for unusual personalities. If the possibility is suggested to him, John might say: ‘I would love to meet Gödel!’ and would surely be talking about both the man (Ködel) and the author of the Incompleteness Theorem (unbeknownst to him, not Ködel but Schmidt). These two options are ruled out by the way the question is posed.

The options that remain – viewed from the perspective this paper takes – are to do with whether ‘talking about’ is to be understood referentially or as subject matter. In the test question, ‘talking about’ implies that John says or asks something about ‘Gödel’. Now, as explained above, John can only successfully refer to Kurt Gödel, since Schmidt does not (and did not) exist. The intended reference to Schmidt via the definite description ‘author of the IT’ would therefore fail, the unkind Ködel story is untrue of Kurt Gödel, but if John’s friend Jack were to tell it about him, he would still successfully refer to Gödel, even if some of what he would be saying about Gödel was false. But could there not be something like ‘in-story reference’ by which Jack might still refer successfully to Schmidt? Not on Russell’s and Ryle’s views. Although they don’t explicitly deal with this question, their ontological demands would be obsolete if they allowed for fictitious reference. Also de Ponte et al., who sometimes loosely talk about ‘fictionally referring’, specify that they actually consider fictional statements to be identifying rather than referring to the object of the singular term (2020, 390fn2).

Another question of relevance to reference in the test case is whether we want to allow reference to something of whose existence the referrer is entirely ignorant – for instance, Schmidt in the case of John. This could not work if the speaker were convinced that their statement is fiction. For instance, if I were to say something intentionally invented – say, ‘Bandersnatches are hibernating late this year’, I would be very surprised if you disputed my statement, telling me that it is completely normal for bandersnatches to hibernate at this time of year, thereby implying that my statement was truth-apt and ‘bandersnatches’ had referents. The other possibility, inadvertent reference to something of whose existence the speaker is ignorant, only exists for descriptions which are supposed to be definite taking the speaker to one referent but then turn out not to be satisfied by that referent, or not by that referent alone, but rather (also) by another object. This is, of course, the type of scenario Kripke wanted to create (and show to fail) by suggesting to try and take ‘Gödel’ as synonymous for ‘author of the IT’ and have someone other than Gödel satisfy the definite description. Part of the problem with his example is that ‘Schmidt’ is an empty name, which distorts our intuitions substantially (we will get to this later). We might respond differently, had he used another well-known mathematician for his example.

The case is different for aboutness. Someone denoted by the name ‘Gödel’ is certainly one of John’s subject matters as ‘talking about Gödel’ means that he produces, or contributes to, a text which contains or demands information about someone denoted (in the text) by ‘Gödel’. And likewise, a person by the name of ‘Schmidt’ would be a subject matter of Jack’s.

So, there is an element of domain to both aboutness and reference. Aboutness takes place within a text, and what is and what isn’t part of the text is crucial to what is its subject matter. Reference, by contrast, takes place in a context which determines the domain of possible referents. As the case at hand is quite complex with multiple embedding of stories, we must be careful not to lose sight of what we are evaluating. We will go from smallest to largest.

a.	John’s beliefs

John believes that Gödel is the author of the Incompleteness Theorem (IT). These beliefs stem from what he has been told in college – our first text, T1. Let’s take anything John says or asks about Gödel to contribute to T1. T1 is thereby a text one of whose subject matters is Gödel, the author of the IT. John talking about Gödel here just is him talking about the author of the IT, even if that aspect may not always be relevant to what is said or asked about Gödel.

If John is a student at Princeton in the early 1970s, what he hears and says about Gödel has a nearby referent on even the ontologically most demanding accounts of reference. Reference to Gödel can be successful and statements about him are truth-apt. For many people around John, ‘Gödel’ and ‘author of the IT’ are mutually substitutable salva veritate.

b.	Kripke’s story

In Kripke’s story, text T2, Gödel is a fraud. He plagiarised Schmidt’s work, and Schmidt is the author of the IT. We therefore have, among others (such as ‘fraud’, ‘plagiarising’, ‘mathematical work’, etc.), the two subject matters Gödel (Ködel) and Schmidt, and authorship of the IT is ascribed to Schmidt in the story.

In Kripke’s story, the definite description ‘author of the IT’ picks out Schmidt; what a fictional statement about Gödel, itself fictionally made by a character in Kripke’s story, picks out will have to be part of the story as well. But note that we also have parafictional statements (in the sense of de Ponte, Korta, and Perry 2020)¹⁰ about ‘Gödel’ made by people in talking about the fictional characters Ködel and Schmidt. Both of them are perfectly acceptable subject matters, but neither of them is an acceptable referent. Things get tricky when a statement crosses borders between fiction and reality, such as ‘Kripke concocted a story about Gödel to the effect that he had stolen the IT from someone called Schmidt’. Here, the first part of the sentence has a referent, Kurt Gödel, but it also identifies a subject matter, Ködel, to which ‘he’ in the second part of the sentence anaphorically points back.

c.	Machery et al.’s story

Text T3, the story told by Machery et al., embeds T1 and T2 by adding John to T2. John’s questions and statements will reflect his T1 beliefs, beliefs that are inconsistent with what T3 tells us to be the case, which is the same as in T2 with respect to the IT. Note, however, that John and his beliefs are as much subject matters of T3 as ‘Gödel’ (Ködel) and Schmidt are. His beliefs are part of what T3 says about those subject matters, including the fact that they run counter to what T3, by incorporating T2, says about Ködel and Schmidt. – So much for aboutness, but how about reference?

Since John is himself a fictional character, he cannot leave the story, as it were, nor point outside of it. So there can be no question of John actually referring to Kurt Gödel. With what T3 says about John, we’ve ‘come to the end of him’. However, fictional reference can certainly be (fictionally) ascribed to him by Machery et al. But whether such fictional acts of reference involving the name ‘Gödel’ are to point to fictional Ködel, or rather to Schmidt, or both, will again be part of the story. The only aspect relevant to our debate that can be discussed is whether that story is plausible. Just as Heck has stressed, it would seem that this, in turn, will depend on what T3 tells us that John says or asks about when using the name ‘Gödel’.¹¹ Here are some ways plausibility judgments could go.

If according to the T3 fiction John by saying ‘Gödel’ intends to refer to the person called Gödel who is the author of the IT, reference will surely seem to fail for instance in

(1) When did Gödel work out the IT?

Question (1) has no straightforward answer in T3 because there is simply no one in T3 who is both named ‘Gödel’ and has worked out the IT, a fortiori no time when he did so. However, even fictional statements can have different subject matters and depending on whether the subject matter is Ködel or the IT, the question will require a different answer. If about Ködel, the answer of someone in the know (in T3) would have to be: ‘He didn’t.’ If by contrast, the subject matter is the IT, the answer: ‘In 1930, but his name wasn’t Gödel, but Schmidt.’ might be plausible (cf. Yablo 2014, chapter 9 for explanation). This means that in the former case, fictional reference would plausibly go towards Ködel, in the latter to Schmidt.

Note that this answer does not yet imply an attributive use in Donnellan’s sense as intended by Kripke, which would supposedly pick out whoever is the author of the IT. But maybe the following could plausibly do so:

(2) Gödel must have worked hard to prove the IT.

Heck, with a similar example, thinks it does (2018, 257). But this would mean ignoring the other things even John must know about Gödel, contrary to Kripke’s intended set-up (more on this in the next section). Compare this to

(3) Nicolas Bourbaki must have worked hard to write the Theory of Sets.

As a pseudonym shared by several mathematicians, ‘Bourbaki’ is much closer to the kind of open singular description we get for instance with ‘the tallest person in the next room’, where who that is remains yet to be determined (and – if two or more are of equal height – may turn out not to be singular, as is in fact the case with the authors of Theory of Sets). That said, whether ‘Bourbaki’ works more like an attributively used descriptive term or rather like a generic, is a question for another day.

Returning to T3, it will hardly be plausible that John (in the fiction) refers to anyone but the man Gödel in

(4) Is that Gödel next to Einstein on the photo?

whether or not he takes him to be the author of the IT.

These plausibility considerations already take us a big step towards the final embedding to be considered, the one where we become part of the consideration.

d.	The test situation

Text T4 is the story about the test, which embeds T3. We can take T4 to comprise all the information we have about Gödel, Kripke’s story and intuitions, and Machery et al.’s criticism and experiment. We have learnt that there were test persons presented with T3, but we also know that T2 is Kripke’s invention and that T3 insinuates as much. So, as far as the test is concerned, we as readers are in the same situation as the test persons. What is interesting is that T4’s truth conditions with respect to the Gödel-Schmidt story are the same as T1’s: Gödel was the (unique) author of the Incompleteness Theorem. There is nobody else involved. A fortiori, there is no mathematician Schmidt involved. In spite of this knowledge, we as well as the test persons can think about T2 and T3 and opine on the plausibility of fictional reference to objects appearing in those texts.

Now, it may be objected that Kripke did not intend the Gödel-Schmidt story to be treated as fiction, but rather as a thought experiment – that he did not want us to regard it as on a par with fairy tales, but rather as similar to a factual account about something happening to other people, for instance. The objection therefore regards our response to fiction as different from our response to accounts of factual events.¹² One point against this objection is that Kripke’s choice of a fictitious character, Schmidt, for his story, makes it hard to draw that distinction. Had he used another mathematician (say, Noether), it would have been easier to stress the supposed near-realism of the story. Another is that even in declared fiction, there is a rule to suppose our knowledge of reality to apply unless we are told otherwise. And this is exactly what the thought experiment demands of us. So, I take the objection to fail.

That said, we can rely on a non-fictional explanation of our response to the question, viz. an analogy with concept splitting. There are many cases where some languages comprise a larger extension under a concept than others. A popular example in philosophy is ‘blue’ which comprises what both ‘azul’ and ‘celeste’ in Spanish cover, but perhaps ‘glass’¹³ is an even better example. In English, the word refers to both the material and receptacles made of it. In Spanish, however, there are two unrelated words: ‘vidrio’ for the material and some things made of it, such as a window pane, and ‘vaso’ for what we drink from. The psychologically interesting phenomenon is that once we’ve learnt what each of them means, we can think back on any number of occasions when people spoke of ‘glass’ and neatly distinguish all the ‘vasos’ from all the ‘vidrio’ we encountered long before we knew those words. Learning a new language often causes the learner to make such conceptual splits.

It seems to me that Kripke and Machery et al. ask us to do something very similar, namely to split a subject matter in two. They are asking us to prise apart what we associate with ‘Gödel’ from what we associate with ‘the author of the Incompleteness Theorem’ and thereby also what has been one subject matter in our text. If his authorship of the IT were really the only thing we knew about Gödel – as the story suggests is the case for John – we would be left with nothing to distinguish Gödel from any other object in the world once that unique characteristic is no longer to be his. Reference would be impossible – after all, we would have no other property at our disposal by which to pick him out – and likewise, the subject matter ‘Gödel’ would remain empty. But as indicated above, we – and John – do know more about him, of course: that his name is/was Gödel; from the ‘ö’ we can gather that he probably hails from a German-speaking country; indeed, that he is/was a male human, and again very likely that he is/was a mathematician, because only a mathematician could present someone else’s proof as his own. Without this additional knowledge, I don’t think we could perform the imagination asked of us. But many of us know much more about Gödel, so rather than performing a concept and subject matter split, we are just imagining Gödel not to have done one important thing in his life. It seems to me that this must considerably distort the situation in favour of taking talk using ‘Gödel’ to be about Kurt Gödel.

Compare this to statements about Schmidt. If a statement like (2) were made about Schmidt, but evaluation is to be made in T1, we would have a catastrophic presupposition failure (in Yablo’s terminology (2014, 150)) making the statement unevaluable rather than false. This is clearly not the case with any statement about Gödel or Ködel, to the extent that Ködel statements hinge on Gödel’s existence.

Add to this the fact that we know the story to be false – the IT really is Gödel’s work. We try to evaluate the fictional reference in a T2 or T3 scenario, but we live in T4, as it were, and have no problem actually referring to Gödel. Moreover, John’s purported referential intentions are perfectly compatible with our knowledge of the actual facts. It is a question for psychologists to discover how far this will influence our judgment, and a question for reference theorists to decide in how far psychology is important for reference. What it certainly does is to help blur the distinction between aboutness and reference. It is therefore likely to have an impact on our intuitions. As reference requires there to be a referent, we go into the experiment knowing that reference to Schmidt is impossible. We see in the examples in T3 how reference and aboutness can come apart. So mistaking aboutness intuitions for intuitions about reference can seriously distort results. Not knowing what John supposedly said using ‘Gödel’ does not help.

5. The upshot for Machery et al. (2004)

What does this mean for Machery et al.’s 2004 results? The aim of their study was to point out cultural differences between speaker communities in their intuitions about how names work. The distinction between reference and aboutness is not intended (nor apt) to undermine this. Even as the ‘Diversity Challenge’, as Mortensen and Nagel (2016) call it, has been complemented by a flood of work in the intersection between ethics and epistemology, ethics and metaphysics, and also ethics and the philosophy of language,¹⁴ in the 20 years since the publication of Machery et al.’s (2004), the challenge still stands. With intersectionality being recognised as a crucial factor, there is a question whether the differences in response between groups of speakers from different continents might be due to different focuses in education – technology or the sciences vs. the humanities – (itself, of course, a cultural difference), and therefore in linguistic intuitions.¹⁵ But this is not what either Heck (2018) or this paper want to discuss.

The focus here is rather on the many ways in which the probe is ambiguous or lacks specificity. The quality of experiments has improved substantially over the last two decades, in part surely thanks to the criticism waged against early studies designed (rather inexpertly) by philosophers. Today, a study of the kind Machery et al. conducted would be designed with much greater expertise, gained from, or in collaboration with, social scientists, linguists, psychologists and statisticians.

The intention in bringing up the reference/aboutness issue is therefore to point to yet another aspect that future empirical work should take into account when designing studies and phrasing probes. Just as in the ambiguities listed by previous authors, this one, too, will have to be avoided by giving the test persons the right sort of specific statements to judge, rather than just asking the far too broad theoretical question of who John is ‘talking about’ when using the name ‘Gödel’.

6. Conclusion

The experiment Machery et al. ran has been criticised for being ambiguous in various respects. This paper has added one more to the list, like Heck’s related to the test question containing the formulation ‘talking about’, namely the ambiguity between reference and aboutness, and thus between referent and subject matter. Whereas reference is a cross-categorical act involving a referent that exists independently of the referring act, aboutness is an intra-linguistic relation between a text and its subject matter, making no ontological demands on the latter.

In Machery et al.’s probe, the phrase ‘talking about’ could imply both reference and aboutness. Which of the two is intended would only become clear if we were given a specific context of evaluation, for instance by offering sample utterances. As the probe stands, some of the ambiguity depends on what utterance the test persons imagine John to be making.

Moreover, the multiply embedded structure of the experiment is likely to lead to additional confusion between reference and aboutness. To prise it apart, we have analysed four texts: T1, John’s (and our) belief that Gödel is the author of the IT; T2, Kripke’s story according to which Gödel is a fraud and some invented person Schmidt the author of the IT; T3, the study’s probe; and T4, everything we know about Gödel, Kripke’s story, and Machery et al.’s study. T2 embeds T1, T3 embeds T1 and T2, and T4 embeds all three.

Since reference requires the referent to exist, reference is only possible to Gödel and only in T4, and in T1 if John is not fictitious. Aboutness, by contrast, is possible in all four texts and the possible subject matters include both Gödel (real and fraud – we called the latter ‘Ködel’ to avoid confusion) and Schmidt. These multiple possibilities can consequently be expected to be another factor distorting results. So, the aboutness-reference ambiguity adds fuel to Heck’s fire, and is a further aspect future empirical work in this field should cater for.

Acknowledgements

This paper builds on a talk presented at a PLM workshop in Vienna in 2019. I thank the audience, and particularly my commentator Maria de Ponte, for helpful comments. An earlier version of the paper benefitted from discussion by my colleagues at the department of Analytic Philosophy at the Slovak Academy of Sciences. Special thanks are due to Michael Ayers for many helpful comments.

This work was partly supported by the University of Oxford project “New Horizons for Science and Religion in Central and Eastern Europe” funded by the John Templeton Foundation. The opinions expressed in the publication are those of the authors and do not necessarily reflect the view of the John Templeton Foundation.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Correction Statement

This article has been corrected with minor changes. These changes do not impact the academic content of the article.

Notes

1 Kripke (1977, 1980) (among others) There are places where Kripke leaves room for descriptivist aspects (see Heck 2018 for that).

2 Broadly understood as name-giving, i.e. not necessarily in a religious ceremony.

3 There is no universally accepted definition of ‘text’; what counts for our purposes is that a text can be written, spoken or signed, live or recorded, and there is no limitation on its length (although – as we are concerned with utterances and hence tokens – it can be assumed that texts will generally be of finite length). Two helpful definitions are Klaus Brinker’s (my translation): ‘The term “text” denotes a limited sequence of verbal signs that is internally coherent and that, as a whole, signals a recognisable communicative function.’ (Brinker 2010, 17); and De Beaugrande and Dressler’s ‘A TEXT will be defined as a COMMUNICATIVE OCCURRENCE which meets seven standards of TEXTUALITY’ (1981, 3). These are: cohesion, coherence, intentionality, acceptability, informativity, situationality and intertextuality.

4 This is the view of Ryle (1933a, 1933b), Putman (1958), Goodman (1961) and arguably Lewis (1988a, 1988b, 1988c), as well as Plebani and Spolaore (2021)

5 This view is defended most prominently by Yablo (2014 and all his aboutness papers since then) and Fine (2017a, 2017b, 2017c, 2020), but also Perry (1989) or Schipper (2020); cf. Osorio-Kupferblum (2016) and Berto and Hawke (2022)

6 … or observation-related question or longer report, etc. – I will stick to ‘statement’ for brevity.

7 The present distinction follows the spirit of all this work, but not its terminology. For a discussion of Ryle and Goodman on aboutness and reference, see Osorio-Kupferblum (forthcoming).

8 A prominent exception is Yablo’s aboutness theory which aims to give the ‘exact’, i.e. one and only, subject matter of a text, which in his case is restricted to individual sentences, however.

9 Apologies to anyone called Ködel. The Ködel in this paper is in no way related, nor is the name an allusion to them. It is a contraction of ‘Kripke’ and ‘Gödel’ analogous to ‘Kripkenstein’.

10 de Ponte, Korta, and Perry (2020, 392) distinguish the following kinds of statements:

‘(i) ordinary “literal” statements containing proper

names that are purported to refer to actual objects,

and whose truth concerns actual facts;

(ii) fictional statements by authors, narrators and characters

in works of fiction;

(iii) parafictional statements that concern the fictional

facts; and

(iv) metafictional statements. These are ordinary statements

about actual facts about the fiction.’

11 Machery et al.’s probe does not specify that – a point discussed by Heck in detail.

12 I thank Daniela Vacek for pressing this point.

13 I have been asked whether ‘glass’ isn’t simply polysemous. As polysemous words have two (or more) related meanings, this is undoubtedly the case, but from a Spanish speaker’s point of view, so is ‘blue’. Note, however, that neither is a homonym, whereas ‘bank’ famously is. If linguists ran a foreign learners’ test, I expect few English speakers who learn Spanish would confuse ‘banco’ with ‘orilla’, but the confusion between ‘vaso’ and ‘vidrio’ is frequent among beginners, which suggests that the conceptual distinction has to be learnt. But for anyone unhappy with the ‘glass’ example, just replace it by the popular ‘blue’ vs. ‘azul’ and ‘celeste’.

14 Cf. work on epistemic and linguistic injustice, as well as on race, gender and on slurs

15 In her 2023 John Locke lectures, Jennifer Nagel remarks on a suggestion to this effect.