Today

• In the opening section we look at a useful distinction between rigid and non-rigid designators.
• We then turn again to Frege’s sophisticated referentialism, last mentioned in lecture 2, and explore his motivations and its position in the space of views we are considering. We explore Frege’s view through examining some motivating paradoxes and puzzles.
• We then turn to Descriptivism about proper names, a Fregean view that has been developed and extended by others.
• Kripke, in his famous book Naming and Necessity – first delivered as a series of lectures, more or less extemporaneously – argues against Descriptivism and (more tentatively) in favour of an alternative picture of how names get their referent, the so-called causal theory.
  • The causal theory is not a theory of the semantics of names, but it is certainly compatible with theories which treat names as rigid.
• I turn at the end to an application of Kripke’s tools to a more recent but still famous modal paradox due to Quine.

Rigid Designation

Kripke on Rigid Designation

Let us call something a rigid designator if in every possible world it designates the same object, a nonrigid or accidental designator if that is not the case. (Kripke 1980: 48)

• Descriptions are not rigid designators – which person the prime minister denotes varies from one possible situation to another; if various backroom deals had gone slightly differently, it would denote Tony Abbott.
• But, Kripke will argue, proper names, like Anthony Albanese, are rigid designators.
  • He also argues that natural kind terms, like gold or water, are rigid designators.
  • A thesis Putnam (1975) also accepts, and lies not too far below the surface of his discussion of the Twin Earth scenario.

A test for rigid designation

\(t\) is a rigid designator iff the sentence

The individual that is (was) actually \(t\) could not have existed without being \(t\), and nothing other than the individual that is (was) actually \(t\) could have been \(t\)

expresses a truth. (Soames 2003: 342)

• Apply this test to the name Aristotle: is this sentence true?

  1. The individual that was actually Aristotle could not have existed without being Aristotle, and nothing other than the individual that was actually Aristotle could have been Aristotle.

• Intuitively (1) is true, so Aristotle rigidly designates Aristotle.

• By contrast, Plato’s most famous student is not a rigid designator of Aristotle; had things gone differently, Aristotle might have been a complete unknown. That is, (2) is plausibly false:

  2. The individual that was actually Plato’s most famous student could not have existed without being Plato’s most famous student, and nothing other than the individual that was actually Plato’s most famous student could have been Plato’s most famous student.

A confusion about rigid designation we ought to avoid

If Aristotle is a rigid designator, referring to the same possible individual at each possible world, how is it possible that Aristotle might not have named Aristotle? If Aristotle names Aristotle at each possible world, how is it possible that Aristotle not be the name of Aristotle?

• We evaluate sentences of our language, uttered at actuality, with the actual meanings of the terms. Our word Aristotle names Aristotle; and when we evaluate a sentence of our language involving Aristotle at \(w\), we are evaluating a proposition about Aristotle at \(w\).
• But it need not have been the case that an other-worldly utterance of Aristotle referred to Aristotle. It would have referred – rigidly – to whoever was denoted by a use of Aristotle in w.

Kripke on this potential confusion

When I say that a designator is rigid, and designates the same thing in all possible worlds, I mean that, as used in our language, it stands for that thing, when we talk about counterfactual situations. I don’t mean, of course, that there might’t be counterfactual situations in which in the other possible worlds people actually spoke a different language. One doesn’t say that ‘two plus two equals four’ is contingent because people might have spoken a language in which ‘two plus two equals four’ meant that seven is even. Similarly, when we speak of a counterfactual situation, we speak of it in English, even if it is part of the description of that counterfactual situation that we were all speaking German in that counterfactual situation. … in describing that world, we use English with our meanings and our references. (Kripke 1980: 78)

Frege’s Referentialism Revisited

An old paradox

• What’s going on here?
• Arguably the man in front of Electra is Electra’s brother and Orestes is Electra’s brother must differ in meaning if she knows one but not the other.
• But how could they, given (5) – they differ only by substitution of terms for the same thing?

Rigidity, Intensions, and Extensions

• Since the man in front of Electra is Electra’s brother and Orestes is Electra’s brother share the phrase is Electra’s brother, the difference must derive from the parts they do not share, the various terms for Orestes.

• The noun phrases Orestes and the man in front of Electra share an extension – that is what makes (5) true.

• But, on Kripke’s diagnosis, one is non-rigid, the other is rigid, and so there are some non-actual possibilities in which they pick out different individuals (tbl. 1).

• Hence they must differ in intension (Elbourne 2011: 4), i.e., a mapping from each possibility to what the phrase denotes in that possibility.

  Table 1: The extensions of Orestes and the man in front of Electra in different possibilities.

  Situation	Ext(Orestes)	Ext(man in front…)
  Actual	Orestes	Orestes
  \(w_{1}\)	Orestes	Pylades
  \(w_{2}\)	Orestes	Agamemnon
  \(\vdots\)	\(\vdots\)	\(\vdots\)

Twain and Clemens

• Consider this case, parallel in some respects to the Electra puzzle (cf. Abbott 2012: 308).

  7. Mary does not know that Samuel Clemens is a writer.

  8. Mary knows that Mark Twain is a writer.

  9. Samuel Clemens is identical to Mark Twain.

  10. Therefore: Mary both knows and does not know that Mark Twain is a writer.

• The Electra puzzle concerned a proper name (Orestes) that was co-referential with a description (the man before Electra).

• The puzzle was resolved by pointing to intuitive differences in their intension. But not clear we can resolve the Twain/Clemens puzzle in the same way – we don’t have any prior grasp on their intensions.

  • Certainly neither we nor Kripke accept that either is non-rigid.

Sense (‘Sinn’) and Reference (‘Bedeutung’)

It is natural, now, to think of there being connected with a sign (name, combination of words, written mark), besides that to which the sign refers, which may be called the reference [Bedeutung] of the sign, also what I should like to call the sense [Sinn] of the sign, wherein the mode of presentation is contained. … The reference of ‘Evening Star’ would be the same as that of ‘Morning Star’, but not the sense. (Frege 1892: 24)

The sense of a proper name is grasped by everybody who is sufficiently familiar with the language or totality of designations to which it belongs. … The same sense has different expressions in different languages or even in the same language. (Frege 1892: 24–25)

• The reference of an expression is the external entity it denotes, familiar from our discussion of externalism.
• Frege’s ‘sense’ is also external: language-independent, grasped by competent speakers, and determines extension and intension.
  • Though different speakers might believe different senses to be associated with the same expression, all senses are public and in principle common (Frege 1892: 26).

Senses

• Frege’s proposal is that all referring expressions – names, descriptions, etc. – have a sense in addition to their reference. Both are aspects of the meaning of an expression.
• The sense presents the reference in a particular guise, a description of some aspect or feature of the reference.
  • The man before Electra presents Orestes in a way that emphasises his position, a position that could be inhabited by other individuals had things been different. Orestes does not present Orestes to us in that way; so the sense is closely tied to the variable intensions we see for these expressions (tbl. 1).
• The reference remains essential, and cannot be replaced by the sense: for, as Frege (1892: 28) notes, in many cases there is a sense but no reference, and it would be difficult to understand our language if we weren’t able to distinguish such empty expressions.

Direct and Indirect Occurrences

• Frege says, ‘If words are used in the ordinary way, what one intends to speak of is their reference’ (1892: 25). If Orestes is the man before Electra is true, that is because the referents of Orestes and the man before Electra are the same.
• But within attitude reports, words are not used in the ‘ordinary way’. Frege says that in reported speech,

words are used indirectly or have their indirect reference. … The indirect reference of a word is accordingly its customary sense. (Frege 1892: 25)

The case of an abstract noun clause, introduced by ‘that’, includes the case of indirect quotation, in which we have seen the words to have their indirect reference coinciding with what is customarily their sense. In this case, then, the subordinate clause has for its reference a thought, not a truth value; as sense not a thought, but the sense of the words ‘the thought, that …,’ which is only a part of the thought in the entire complex sentence. (Frege 1892: 32)

Attitudes to Senses

• Frege’s idea is that attitudes are sensitive to sense, not merely reference; since substitution of co-referring expressions won’t always preserve sense, it makes sense that substitution within attitude reports won’t always preserve truth (Frege 1892: 31).
• That is, when someone knows or believes that \(P\), their knowledge/belief is sensitive to the sense of \(P\), not merely its reference. In fact Frege (1892: 28) seems to think that a thought (a proposition) is the sense of a sentence, so that propositional attitudes like believing and knowing are just relations to senses (Nelson 2024: §2).
  • Frege motivates this in part by his claim that the referent of a sentence is a truth value, True or False (Frege 1892: 29) – for him many sentences will share a reference, and so the sense has to play a significant role in how belief works. But any theory on which \(S\) and \(S'\) differ only by substitution of a co-referring term, so that \(S\) is true iff \(S'\) is, will face scenarios where a speaker believes \(S\) without believing \(S'\).

Solving the puzzles

• When Electra knows that Orestes is her brother is true, that is because she has a justified positive judgment of the sense of the sentence Orestes is Electra’s brother.

• But because the name Orestes and the description the man in front of Electra have different senses, it is quite possible for Electra not to positively judge the sense of the man in front of Electra is Electra’s brother , even though the truth of the identity claim (5) ensures that the reference of the two sentences are the same.

• While the premises are all true, the conclusion (6) does not follow: the thing Electra knows is different from the thing she does not know.

• Likewise in the Twain/Clemens case: Frege’s theory allows that two proper names can have different senses, and again substitution of co-referring names needn’t preserve sense or belief.

• In fact Frege appears to think the cases are parallel, in that the sense of a proper name is a description:

  In the case of an actual proper name such as ‘Aristotle’ [the sense] might, for instance, be taken to be the following: the pupil of Plato and teacher of Alexander the Great. (Frege 1892: 24, fn. 4)

Informative Identities

• Frege’s original motivation for the introduction of senses is a puzzle about informative identities.

• Consider a mathematical equation, or the case of Mary discovering that Mark Twain is identical to Samuel Clemens.

• An identity is informative if the terms flanking the ‘\(=\)’ are co-referential but have a different sense; so while ‘\(a=a\)’ cannot be informative, ‘\(a=b\)’ might be:

  If now \(a= b\), then indeed the reference of ‘\(b\)’ is the same as that of ‘\(a\)’, and hence the truth-value of ‘\(a = b\)’ is the same as that of ‘\(a= a\)’. In spite of this, the sense of ‘\(b\)’ may differ from the sense of ‘\(a\)’, and thereby the thought expressed by ‘\(a= b\)’ will differ from that expressed by ‘\(a = a\)’. In that case the two sentences do not have the same cognitive value. (Frege 1892: 42)

Trivial and Non-Trivial Identity

• True identities are always trivial, when it comes to their reference: they all say that an entity is itself, something we surely know a priori about any object. Even ‘\(a=b\)’ is trivial when true.
• But it is informative to be told that a certain term (name, description) denotes the same thing as another – to be told that ‘\(a\)’ and ‘\(b\)’ are co-referential. Frege says this is because the senses associated with the names describe their references in different ways, so it can be surprising to find out they coincide.
  • Note surprise is a propositional attitude, so informative identities get their unanticipated cognitive significance because it is possible for someone to be surprised that \(a=b\) without being surprised that \(a=a\).
  • Frege’s explanation is that the informativeness of identity statements is a product of differing senses; in a way, we are prompted to evaluate them as if they occur in the scope of a tacit attitude operator. (Frege’s official view is that the sense shouldn’t matter outside of a context where the sentence occurs indirectly; quite why attitude contexts are indirect is never really explained on a syntactic basis by Frege.)
• So senses help us with informative identities and with substitution failures in propositional attitude constructions – that is perhaps reason enough to postulate them as part of our semantic ontology.

Frege’s Sophisticated Referentialism Revisited

• Senses are a little like concepts, or ways of thinking about individuals. But Frege thinks we must note

  an essential distinction between the idea and the sign’s sense, which may be the common property of many and therefore is not a part of a mode of the individual mind. For one can hardly deny that mankind has a common store of thoughts which is transmitted from one generation to another.

  The reference of a proper name is the object itself which we designate by its means; the idea, which we have in that case, is wholly subjective; in between lies the sense, which is indeed no longer subjective like the idea, but is yet not the object itself. (Frege 1892: 26)

• So while acknowledging the distinction between sense and reference, Frege thinks both are external things.

• This sort of proposal should be familiar from Lecture 2, e.g.,

  thoughts [=propositions] are neither things in the external world nor ideas. A third realm must be recognized’ (Frege 1918: 302)

Descriptivism

Descriptivism: Names and Descriptions

• Descriptivism is the view that the meaning of a name is an implicit description (or perhaps a cluster of descriptions).

  Descriptivism

  The meaning of a name NN is given by (a cluster of) descriptions associated with NN.

• If the meaning of a name is its sense, then Frege seems to be a descriptivist.

• If concepts are associated with descriptive classificatory rules, then most internalists are descriptivists.

• A popular view. It was orthodoxy up until 1970, and remains a significant position in the discipline:

  PhilPapers survey results for philosophers of language

  Accept or lean toward	Number
  Millian	41.9% (72/172)
  Fregean/Descriptivism	32.6% (56/172)
  Other	25.6% (44/172)

The Cluster of Descriptions Theory of Names

[T]hough proper names do not normally assert or specify any characteristics, their referring uses nonetheless presuppose that the object to which they purport to refer has certain characteristics. But which ones? Suppose we ask the users of the name ‘Aristotle’ to state what they regard as certain essential and established facts about him. Their answers would be a set of uniquely referring descriptive statements. Now what I am arguing is that the descriptive force of ‘This is Aristotle’ is to assert that a sufficient but so far unspecified number of these statements are true of this object. … To use a proper name referringly is to presuppose the truth of certain uniquely referring descriptive statements, but it is not ordinarily to assert these statements or even to indicate which exactly are presupposed. (Searle 1958: 170–71)

Motivating Descriptivism: Establishing Reference

• Frege motivates descriptivism in arguing for the role of sense. But in fact the use of names to refer at all seems parasite on some recipe for attaching them to individuals:

  [A] basic problem … is how we can determine what the referent of a name, as used by a given speaker, is. According to the description view, the answer is clear. If ‘Joe Doakes’ is just short for ‘the man who corrupted Hadleyburg’, then whoever corrupted Hadleyburg uniquely is the referent of the name ‘Joe Doakes’. However, if there is not such a descriptive content to the name, then how do people ever use names to refer to things at all? … ordinary names refer to all sorts of people, like Walter Scott, to whom we can’t possibly point. And our reference here seems to be determined by our knowledge of them. Whatever we know about them determines the referent of the name as the unique thing satisfying those properties. … Frege and Russell, then, appear to give the natural account of how reference is determined here…. (Kripke 1980: 27–28)

• Another motivation comes from existence questions: did Jesus exist? seems to be asking did someone fit the Jesus-description?

What is the meaning of a proper name?

• Frege posits that the meaning (Sinn) of a proper name is given by a public description that determines the referent and is common to all speakers.
• We associate an additional private sense to a name, by attaching our own description, but Frege says these ‘ought not to occur in a perfect language’ (Frege 1892: 24, fn. 4), where the public sense will also determine the private description.
• Searle responds: what matters isn’t logical perfection. If each competent speaker associates some private description, then
  1. The (public) sense will be the collection of all of these descriptions; and
  2. The referent will be whatever satisfies ‘a sufficient but so far unspecified number of’ (Searle 1958: 171) these descriptions.
• The upshot, if anything like this is right: since descriptions are non-rigid, so too are names.
  • This appears to be how Frege wants the non-triviality of identities to be explained: there is a genuine possibility that the identity could have been false, in possibilities where the names denote different things than actually.

Weak Descriptivism (Soames 2010: 81)

• Maybe the descriptive sense just encapsulates what speakers need to know to fix the referent of a name – to establish a referential connection.

• That is, maybe the cluster of descriptions associated with the name Aristotle is what we all need to grasp in order that we all latch onto that guy Aristotle in our thought and talk:

  (D−)

  Every competent speaker using a name NN associates it with a description cluster \(D\) such that NN is the unique satisfier of (most of) \(D\). (cf. Kripke 1980: 71)

• But having latched on to him, we are now thinking about him in a less mediated way.

  • Once reference is fixed, it is stipulated that the name always refers to that referent. So names would be associated with descriptions, but still rigid. (‘Another theory might be that this description is used to determine a rigid reference’ (Kripke 1980: 58))

Kripke Against Descriptivism

Kripke’s Modal Argument Against Descriptivism

Frege and Russell certainly seem to have the full blown [Descriptivist] theory according to which a proper name is not a rigid designator and is synonymous with the description which replaced it. … If ‘Moses’ means ‘the man who did such and such’, then, if no one did such and such, Moses didn’t exist;… [But] it’s clear that that is not what is meant by ‘Moses didn’t exist’, because we can can ask, if we speak of a counterfactual case where no one did indeed do such and such, say, lead the Israelites out of Egypt, does it follow that, in such a situation, Moses wouldn’t have existed? It would seem not. For surely Moses might have just decided to spend his days more pleasantly in the Egyptian courts. He might never have gone in to either politics or religion at all; and in that case maybe no one would have done any of the things that the Bible relates of Moses. That doesn’t in itself mean that in such a possible world Moses wouldn’t have existed. (Kripke 1980: 58)

The Modal Argument Clarified

11. If Descriptivism is correct, there is some cluster of descriptions \(D\) such that If Moses existed, then Moses satisfied sufficiently much of \(D\) is necessary (Soames 2003: 338).

12. Moses is a rigid designator of Moses, no matter what that guy might have done instead of what he actually did.

13. It is possible that Moses could have existed and done none of the things popularly associated with him, meeting none of \(D\). (From 12; cf. (Abbott 2012: 310–11))

14. If Moses existed, then Moses satisfied sufficiently much of \(D\) is not a necessary truth. (13, semantic ascent)

15. Therefore: Descriptivism is not correct. (From 11 and 14, modus tollens)

Rigid Names and Propositions

• On the basis of cases like Aristotle, Kripke argues that a name NN

  will be rigid even when [the description] D is not. … If NN refers to a man \(m\), then, Kripke suggests, NN is F has the same semantic content as that man is F, used in a context in which ‘that man’ demonstratively picks out \(m\). (Soames 2010: 83)

• But then: take the case where F just is the description the D. Then: The D is the D is trivial, a necessary truth.

• But that man is the D is neither necessary nor trivial.

  In such cases, NN is F [i.e., NN is the D] and D is F [i.e., the D is the D] differ in meaning, and express different propositions. (Soames 2010: 83)

• And if the propositions (meanings of sentences) are different, then the sentences must have constituents that differ in meaning. Since is F means the same in both cases, it must be that NN and D differ.

What About Weak Descriptivism?

• Kripke also attacks weak descriptivism.
• If weak descriptivism says that names are rigid, then it will not be subject to the modal argument.
• But it still makes several strong claims about the importances of descriptions for the entities denoted by a name :
  1. Each speaker takes the associated description to fix a unique referent; and
  2. The actual referent of any name NN in fact satisfies the associated description.
• Kripke argues even this reference-fixing role for descriptions is untenable.
  • Note that these two features of weak descriptivism are also features of descriptivism, so any difficulties we identify weak descriptivism are a fortiori difficulties for descriptivism too.

Against Uniqueness

Consider Richard Feynman, to whom many of us are able to refer. He is a leading contemporary theoretical physicist. Everyone here (I’m sure!) can state the contents of one of Feynman’s theories so as to differentiate him from Gell-Mann. However, the man in the street, not possessing those abilities, may still use the name ‘Feynman’. When asked he will say: well he’s a physicist or something. He may not think that this picks out anyone uniquely. I still think he uses the name ‘Feynman’ as a name for Feynman. (Kripke 1980: 81)

• Suppose someone said: I cannot tell Feynman and Gell-Mann apart. They are clearly talking about two specific physicists – but they explicitly deny that they associate a unique description with each. This is acceptable, but incoherent if weak descriptivism were correct.

Against needing to satisfy the description

Let’s suppose someone says that Gödel is the man who proved the incompleteness of arithmetic … In the case of Gödel, that’s practically the only thing many people have heard about him – that he discovered the incompleteness of arithmetic. Does it follow that whoever discovered the incompleteness of arithmetic is the referent of ‘Gödel’?…

Suppose Gödel was not in fact the author of this theorem. A man named ‘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 it was thereafter attributed to Gödel.… So, since the man who discovered the incompleteness of arithmetic is in fact Schmidt, we, when we talk about Gödel, are in fact always referring to Schmidt. But it seems to me that we are not. (Kripke 1980: 84)

What is Going On?

• In the Gödel/Schmidt case, we are invited to think it possible that Gödel never was the man who proved the incompleteness theorems.
  • If anyone knows anything about Gödel, it will be that he is the author of the Gödel incompleteness theorem.
• So the only candidate reference fixing description is the author of the incompleteness theorems, and weak descriptivism says that the name Gödel has its reference pegged to whoever did actually discover those theorems.
• So while it is not necessary that Gödel proved the incompleteness theorems (if it is a rigid designator, we can certainly identify another possible world where he did not do so), it cannot be epistemically possible that someone other than Gödel discovered them.
• But that is manifestly something that could, for all we know, turn out to be the case. So it is epistemically possible. So weak descriptivism is false for most names.

The Causal Theory of Reference

Attaching names to things: the Causal Picture

• Kripke sketches an non-descriptivist alternative theory about how a name gets attached to an object (not a full semantics):

  Someone, let’s say, a baby, is born. His parents call him by a certain name. They talk about him to their friends. Other people meet him. Through various sorts of talk the name is spread from link to link as if by a chain. A speaker who is on the far end of this chain, who has heard about, say Richard Feynman, in the market place or elsewhere, may be referring to Richard Feynman even though he can’t remember from whom he first heard of Feynman…. A certain passage of communication reaching ultimately to the man himself does reach the speaker. He then is referring to Feynman even though he can’t identify him uniquely… a chain of communication going back to Feynman has been established, by virtue of his membership in a community which passed the name on from link to link…. (Kripke 1980: 91)

Causal Pictures of Reference and Theories of Meaning

• On this view, a name is like a portrait photograph; the meaning of the name is whoever the photograph is of. No matter what the person looks like in the photograph, or if they are an identical twin so we can’t tell who the photograph is of, nevertheless, there is a subject, and the subject is identified by their causal role.
• How do speakers manage to refer to the same thing by their respective uses of NN?
  • Descriptivists answer: by believing that there is some unique thing which is \(D\) and that NN is the \(D\). Speakers may be causally isolated from that they refer to.
  • Causal answer: by being part of a linguistic community whose use of NN is causally linked (in the right way) to the initial baptism. Speakers need know nothing about what they are referring to, as long as someone does or did: the division of linguistic labour.

Weak Descriptivism and the Causal Theory

16. For any name NN and speaker \(S\), the description \(S\) associates with NN is ‘the referent of those previous uses of NN, whichever they may be, from which my present use acquires its referent’ (Soames 2010: 87).

• This gives us a reference-fixing description which piggybacks off Kripke’s causal story – so if Kripke’s theory gets the referents right, so too will (16).
  • If the name has been correctly introduced by my community from causal contact with some original object, this description uniquely refers to that original referent.
• Does this save weak descriptivism? Arguably not: the description mentions pre-existing reference, and so cannot be the description associated with NN by some competent speakers — those who introduced the name in the first place.

More on the causal link

Obviously the name is passed on from link to link. But of course not every sort of causal chain reaching from me to a certain man will do for me to make a reference. There may be a causal chain from our use of the term ‘Santa Claus’ to a certain historical saint, but still the children, when they use this, by this time probably do not refer to that saint.

An initial ‘baptism’ takes place. Here the object may be named by ostension, or the reference of a name may be fixed by a description [e.g., Neptune or Jack the Ripper]. When the 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. (Kripke 1980: 93–96)

Problem: Reference Change

Change of denotation is … decisive against the Causal Theory of Names. Not only are changes of denotation imaginable, but it appears that they actually occur. We learn from Isaac Taylor’s book Names and their History, 1898:

In the case of ‘Madagascar’ a hearsay report of Malay or Arab sailors misunderstood by Marco Polo … has had the effect of transferring a corrupt form of the name of a portion of the African mainland to the great African Island.

A simple imaginary case would be this: Two babies are born, and their mothers bestow names upon them. A nurse inadvertently switches them and the error is never discovered. It will henceforth undeniably be the case that the man universally known as ‘Jack’ is so called because a woman dubbed some other baby with the name. (Evans 1973: 195–96)

What’s the problem

• Kripke already acknowledges that reference can change, in the Napoleon case. But in the case of Madagascar, everyone does intend to continue referring to the same thing – and yet reference changes.
• Evans suggests that causation is important – but he thinks, NN refers to \(A\) iff the linguistic community associates a body of information with NN and \(A\) is the dominant causal source of this information.
  • So, since the island is what our information associated with Madagascar originates from, that is the referent.
• Not obvious we need this alternative causal picture:
  • Maybe Marco Polo’s misunderstanding amounts to a new introduction of the name – because MP’s other intentions trump the existing use.
  • E.g., he intends to use the name to refer to whatever the existing users do, and also intends to use the name for the island, because (i) he is acquainted with the island, and (ii) he has the false belief that existing uses refer to the island (Burgess 2014).

Rigid Accounts of Names

What’s the Alternative?

Descriptivism really is a nice theory. The only defect I think it has is probably common to all philosophical theories. It’s wrong. You may suspect me of proposing another theory in its place: but I hope not, because I’m sure it’s wrong too if it is a theory. (Kripke 1980: 64)

• Here’s an alternative theory: Millianism or direct reference – you last saw this theory in Lecture 2! The intension of a name is an object (or, maybe, a constant function from worlds to that object).
  • This is clearly a theory on which names are rigid.
  • It handles the puzzle cases – Gödel/Schmidt, Feynman, Moses, Aristotle have the meanings we expect if direct reference is right, unlike the meanings predicted by Descriptivism.
  • It fits well with a causal theory of how reference gets established.

Direct Reference is not the only kind of Rigid Designation

• Kripke’s argument is that names are rigid designators, and need not be associated by speakers with any particular descriptive content.
• If the intension of a name is constant, then obviously that name denotes the constant object in every possibility we discuss using that name – in other words, if direct reference is correct, then names are rigid.
• The converse claim is not true – there are rigid designators which are not Millian.
  1. Some varieties of weak descriptivism, as already seen.
  2. Also rigidified descriptivism. Consider the actual prime minister. A use of this expression in 2024 denotes Anthony Albanese. But it continues to denote him even when I consider purely hypothetical possibilities: A different person (than the actual prime minster) could have been the prime minister (Compare: I could have been taller than I actually am).
     • The actual F denotes whatever is the F in the actual world, and denotes that thing relative to every possibility we might consider.

Rigidified Descriptions

• If the name Aristotle is associated with the rigidified description the actual teacher of Alexander, descriptivists can resist the modal argument from above.
  • Not the argument against weak descriptivism though.
• For the premise (13) is false: it is not possible that Aristotle could have existed and not been the actual teacher of Alexander.
  • At every possible situation, the word actual refers back to the actual world – that’s why we can say, truly, the actual teacher of Alexander could possibly not have taught Alexander.
• Objection: Aristotle was the teacher of Alexander turns out synonymous with The actual teacher of Alexander was the teacher of Alexander. But the former is a posteriori, the latter a priori – so they can’t be synonymous (Soames 2003: 344).
  • An interesting twist on Frege, who argued from informative identities to the existence of descriptive senses – here we argue against descriptive senses on the basis of informative predications.

Direct Reference and Identity

• But those Frege-style puzzles about informative identities and substitution failures remain. How does the Millian handle the Mark Twain/Samuel Clemens puzzle, if names have no descriptive sense?
  • Kripke’s anti-descriptivist arguments seem to block names having an intension that differs from their extension, so appears to entail that Mark Twain and Samuel Clemens are synonymous, as are the sentences embedding them, Mark Twain is a writer and Samuel Clemens is a writer.
• One approach is to bite the bullet (Abbott 2012: 315): because Mary does know that Mark Twain is a writer, she also knows that Samuel Clemens is. (A view to which we return in lecture 5.)
  • She may not express her knowledge using Samuel Clemens, but she does know it.
  • Note that if we say Mary knows SC is a writer, that suggests she would express her knowledge using the expression SC – this suggestion is wrong, and may be the reason we think Mary knows SC is a writer is false.
• Another approach might be to say that even though Mark Twain is a writer and Samuel Clemens is a writer are synonyms, they do not embed into propositional attitudes in the same way – perhaps those are sensitive to how the proposition is expressed, not just what proposition is expressed (e.g., Abbott 2012: 311–12).
  • Again – a twist on Frege’s idea that in attitude contexts the sentence doesn’t have its usual meaning; here the attitude is sensitive to the form as well as the content of an embedded sentence.

Application: Quine’s Problem with Modality

A Quinean Puzzle (Quine 1980)

17. Possibly, Nixon might not have been the president in 1972. (premise)

18. So: Nixon has the property of being possibly not the president in 1972. (17, property abstraction)

19. But Nixon is the president in 1972. (premise)

20. So: the president in 1972 has the property of being possibly not the president in 1972. (18, 19, substitution of co-referring expressions)

21. So: Possibly, the president in 1972 isn’t the president in 1972. (20, property reduction)

• But (21) is absurd: there is no possible situation in which the F isn’t the F.
• Quine concludes: modal operators are illegitimate, and their presence in a language isn’t well-behaved and leads to contradictions.

Abstraction and Reduction

• The key rules in this puzzle are abstraction and reduction, rules that enable certain rearrangements of the occurrence of names within and without the scope of operators.

  Abstraction

  From \(Op(x \text{ is } F)\), deduce \(x \text{ is such that $x$ is } Op(F)\).

  E.g.,: from Actually, I am tall deduce I am such that I am actually tall.

  Reduction

  From \(x \text{ is such that $x$ is } Op(F)\), deduce \(Op(x \text{ is } F)\).

  E.g.,: from Sally is such that she is not kind deduce It’s not true that Sally is kind.

• These rules are informal versions of rules of \(\lambda\)-abstraction and \(\beta\)-reduction from the Lambda calculus (Alama and Korbmacher 2023), a formal framework for working with function expressions. (The lambda calculus will appear again in lecture 7.)

Solving the Quinean Puzzle

• Things go wrong between (20) and (21).
• The non-rigid designator the president in 1972 denotes different things at different possibilities.
  • My current use of it denotes Nixon; and it really is true that the person I’m talking about has the property attributed to him in (20).
  • But it doesn’t follow that there is any possible situation in which Nixon realises that potentiality he has to have been doing something else in 1972 while still being referred to by the president in 1972 – which is what is required for (21) to follow from (20).
• When we combine a non-rigid designator with a modal operator, property abstraction and reduction can go awry – in this case, moving a non-rigid designator inside the scope of the modal operator induces a shift in referent, so we are not even talking about the same thing between lines (20) and (21).
  • Note things would have been fine had we used a rigidified description, replacing (19) by But Nixon is the actual president in 1972.
• A parallel case involving another invalid argumentative step occurs in the literature on vague identity (Lewis 1988).

Where Quine Goes Wrong

Suppose that someone said, pointing to Nixon, ‘That’s the guy who might have lost’. Someone else says ‘Oh no, if you describe him as “Nixon”, then he might have lost; but, of course, describing him as the winner, then it is not true that he might have lost’. … The first man would say, with great conviction, ‘Well, of course, the winner of the election might have been someone else. The actual winner, had the course of the campaign been different, might have been the loser… So, such terms as “the winner” and “the loser” don’t designate the same objects in all possible worlds. On the other hand, the term “Nixon” is just a name of this man’. When you ask whether it is necessary or contingent that Nixon won the election, you are asking the intuitive question whether in some counterfactual situation, this man would in fact have lost the election. (Kripke 1980: 41)

Thinking About Possibilities

• What could have tempted Quine – and many others – into thinking that (21) follows from (20)? This doctrine:

  TWI

  To understand what is possible for Nixon, we must have a criterion of identity that enables us to pick out counterfactual Nixon in another possible world; and a criterion of identity for being Nixon is a description of Nixon’s qualities. (Kripke 1980: 42–43; cf. Williamson 2013: 144–53)

• That is: what’s to blame is descriptivism.

One thinks, in this picture, of a possible world as if it were like a foreign country. One looks upon it as an observer. Maybe Nixon has moved to the other country and maybe he hasn’t, but one is given only qualities. … So we had better have a way of telling in terms of properties when we run into the same thing as we saw before; we had better have a way of telling, when we come across one of these other possible worlds, who was Nixon. (Kripke 1980: 43)

References