Lecture 1Locke and the iconic theory of meaning

Locke, An Essay Concerning Human Understanding (1689), III.ii

Words mark ideas

For Locke, the goal of language is to be understood, which here means being made rationally intelligible. Not in a very deep sense: just “I had a goal, constraints, opportunities, so I acted as I did.” To understand someone is to know their mental states (beliefs, desires, goals, reasoning) and how those states rationalize each other and their behavior. Rationality matters a lot for Locke.

So words “mark ideas.” Ideas are the things we reason with: pictures before the mind that we manipulate in order to reason. Locke is an empiricist: all ideas come from experience.

• Worry: it seems very hard to share ideas themselves. But perhaps you give me an image of your having the image.
• Nice feature: it’s easy to see what it would mean for an idea to be right or wrong; we can point to false beliefs. So there are two ways to assess someone’s mental states: by the relations between them (do they rationalize each other?), and by their truth or falsity.

We can compose meaning-bearing elements to understand new sentences: different parts are different ideas, and some parts are operations on those ideas. To understand “Taylor Swift is watching a game at Harvard Stadium,” take your image of Taylor Swift and your image of the stadium during a game and smush them together.

Three touch-points for a theory of language

A philosophical theory of language should answer to three things, and Locke’s covers all three:

1. Rational explicability. We use language to make ourselves intelligible to each other.
2. Truth. Some of language is properly assessed as true or false.
3. Systematicity. We understand novel sentences from the meanings of their parts and how they’re put together.

Locke’s project is about the rational, the semantic, and the systematic. It sets aside, e.g., the way poetry makes us feel.

Objections: Berkeley’s triangle and the word “not”

• Berkeley. Locke has to say reference is fixed by resemblance. But a mental picture of a triangle is always of some specific triangle, and we can still reason about triangles in general.
• Functional vocabulary (small words that don’t obviously stand for things, like and, or, not). And is easy: for “Mary and Jane ate a cookie,” combine the two images. Not is hard. What image corresponds to “Taylor Swift is not walking”?
  • Not a picture of her walking, since then it would mean the same as “Taylor Swift is walking.”
  • Not a picture of her walking with a bar through it. HandoutThat image doesn’t resemble any situation in the world.
  • Not a picture of her doing something else, because asserting the sentence doesn’t commit you to her doing anything in particular.
• Or looks just as hard. HandoutSo do quantifiers (“fifteen,” “some,” “none”) and tense.

Frege’s alternative: start from systematicity

Locke took nouns and verbs as the paradigm and then had to fit everything else in. Frege starts from the other end: from systematicity (“an infinite use of finite means”) and from functional vocabulary like and and not. He asks what nouns and verbs must mean for that to work. Truth comes first; rationality is dealt with later.

Lecture 2Frege: function and concept

Frege, “Function and Concept” (1891)

Review: the three touch-points

• Rational explanation is key for Locke: rational reaction as opposed to pure causation.
• For language to be assessed as true or false, it has to be about the world. (It’s hard for music to be about something.)
• Language must be systematic: an infinite use of finite means.

Locke started with rational explanation. Frege starts with systematicity.

Motivation: is arithmetic analytic?

For Kant, some a priori knowledge is unpuzzling because it’s just containment: “all bachelors are unmarried” is analytic. But math is weird. The concept “7 + 5” doesn’t seem to contain “12,” yet “7 + 5 = 12” is clearly a priori. So Kant calls arithmetic synthetic a priori.

Frege wants to show that arithmetic is analytic after all: its first principles can be proved from definitions using logical laws alone. But proofs written in natural language might smuggle in unnoticed assumptions. So he builds the Begriffsschrift (“concept-script”), a formal (higher-order) logical language that lets nothing through that wasn’t expressly assumed. That’s why systematicity matters so much to him.

Numbers vs. numerals. A numeral is the symbol we write; a number is the abstract object it refers to. So numerals stand to numbers as names stand to people.

Connectives as truth functions

A function is a rule taking an argument to a value. Negation flips a truth value, so it looks a lot like a function, and so does and:

not(x) = True if x = False; False if x = True
and(x, y) = True iff x = True and y = True

Take “Mary ran and Jane did not run.” If and is a function from two truth values to one, then the sentences it combines must refer to truth values. Sentences refer to the True or the False.

Predicates as functions, names as arguments

If “Mary runs” refers to the True, what are “Mary” and “runs” doing? Something has to output the True. Frege: “runs” is the function (from objects to truth values, giving True exactly for things that run) and “Mary” is the argument. In lecture this was presented as a free choice.

The same pattern shows up everywhere:

• the capital of ( ) countries → cities; Germany ↦ Berlin
• the husband of ( ) people → people

Force vs. content

• Content: how the world is according to the sentence; what can be true or false.
• Force: what the speaker is doing with that content, such as asserting it (committing to its truth), wondering about it (“I wonder… maybe…”), etc.

Frege wants to keep these apart, because force doesn’t pass through every operator. Asserting “Mary ate a cookie and Jane ran” commits you to “Mary ate a cookie”; asserting “Mary ate a cookie or Jane ran,” or “it’s not the case that Mary ate a cookie,” doesn’t. The same content appears without being asserted.

This is where the iconic theory fails badly. It’s fine with and but fails on not, because on the empiricist picture, having an image before the mind is believing it.

What Frege wants is a semantics you can plug and chug through to get truth values. Open question: how does any of this give us rational explanation?

Lecture 3Frege: sense and reference

Frege, “On Sense and Reference” (1892)

Recall that Frege’s semantics is built from functions and the objects they take as arguments, so names are central. (On papers: the question should be central, with a clear criterion for an answer.)

Hesperus and Phosphorus: informative identities

Take an identity statement “a = b.” The “is” here is the is of identity, not the copula of “I am good.”

• Hesperus is Hesperus.
• Hesperus is Phosphorus.

If a name’s contribution is just its referent (the Reference View), both say the same thing about Venus. But the first is trivial and the second was an astronomical discovery. So what makes one analytic and the other empirical?

The Name View answers that “a = b” is about the names. Frege rejects it (two arguments in the reading).

Cognitive significance

Compare “Andy is a bachelor” with “Andy is an unmarried man.” The two have different associations but are analytically equivalent. Frege cares only about what bears on our rational capacities, our reasons for believing and acting, and not about associations.

Sense as mode of presentation

Frege’s solution is sense: the mode of presentation of the referent, the way it is presented to you. Think of one view of a mountain as opposed to the mountain itself. HandoutHiking: “this mountain is this mountain” vs. “this mountain is the mountain I saw this morning.”

You can approximate a mode of presentation as an image, but modes of presentation are not mental images. The pill example:

• Draw twice from a pile of indistinguishable pills, getting the same pill both times. The images are identical, but you have two modes of presentation, since you don’t know it’s the same pill.
• Now follow one pill continuously with your eyes. The image may change, but there’s only one mode of presentation.

Modes of presentation can also be shared: two people can see the same view of a mountain. Images can’t. HandoutFrege’s telescope: the image in the lens is public, the image on each observer’s retina is private. On the (controversial) Frege–Schlick view, we can’t even ask whether the contents of two people’s minds are similar.

How sense determines reference

Generalize the model: a sense is like a descriptive criterion. “Hesperus” has a sense like “the first heavenly body visible in the evening sky”; Handout“Phosphorus,” “the last heavenly body visible in the morning sky.”

How does language attach to the world? A word is conventionally tied to a sense, the sense is a descriptive condition, and the referent is whatever satisfies it.

• “H = H” is trivial: take the same sense on both sides and follow it out into the world. Of course it’s true.
• “H = P” is informative: the criteria are different, so you have to check empirically that they pick out the same thing (they do).

Sense and successful communication

• Co-reference isn’t enough. Paderewski was a famous pianist who later became Polish prime minister. You say “Paderewski is a great musician”; I’ve only met him as a politician and tell him “your music is wonderful!” Same referent, yet communication failed. HandoutSimilarly, Hannah Smith: I form a true belief from your true claim, but about a different Hannah Smith.
• Sharing all beliefs isn’t required. HandoutA conception is everything one person associates with a term; it varies person to person and is irrelevant to communication.

So sense is the middle ground: co-reference is necessary but not sufficient, and sharing all your beliefs is sufficient but not necessary. Frege does admit that senses vary between people (the “Aristotle” footnote) and calls this an imperfection of language. HandoutHe says it can be tolerated as long as the referent is the same, which sits uneasily with the communication principle.

Lecture 4Russell: on denoting

Russell, “On Denoting” (1905)

Empty names and negative existentials

Some names and descriptions are empty: “the planet farthest from the Sun,” “the largest natural number,” or a name a journalist invents to attribute fabricated quotes. “The planet farthest from the Sun is larger than Pluto” seems like a whole thought, but if the description refers to nothing it’s semantically just “     is larger than Pluto.” Frege offers two answers: such sentences really are empty, so neither true nor false (Sense and Reference), or the description gets a dummy referent (Function and Concept).

The sharpest form of the problem is the negative existential:

1. A subject–predicate sentence with a referring subject is true iff the subject refers to something that has the predicated property.
2. “The present King of France does not exist” is such a sentence.
3. It’s true.
4. So “the present King of France” refers to something.

Meinong bites the bullet: the King “subsists” without existing. Russell wants to avoid this.

Referring vs. quantifying noun phrases

Referential noun phrases talk about particular things (“Mary,” “the professor for PHIL 147”). Quantificational ones express generalizations (“someone,” “fifteen people,” “everyone in this course,” “many students”). For Russell, “everything,” “nothing,” and “something” are defined from the primitive “C(x) is always true.” Quantification can’t be reduced to reference: “Every person in the room wears glasses” equals “Andre, Barbara, and Clyde wear glasses” only given the extra fact that they’re all and only the people in the room.

Quantified sentences have the shape Quantifier · Restrictor · Nuclear scope (“Every F G”), and “Some F G” can be defined as “not: all F not-G.”

The Theory of Descriptions

“The TF for PHIL 147 teaches a couple of sections” implies existence and uniqueness: there is exactly one TF, and that TF teaches a couple of sections.

This solves the puzzle. “The present King of France does not exist” means it is not the case that there is exactly one present King of France:

¬∃x (Kx ∧ ∀y (Ky → y = x))

There is no subject term left to refer to anything, so there’s no need for Meinong.

Scope: “The King of France is not bald”

The scope of an operator is what it applies to: compare 2(3) + 2 = 8 with 2(3 + 2) = 10, or “I saw the woman with binoculars.” Quantificational expressions enter scope relations; referential ones don’t. Since descriptions are quantifiers, “The present King of France is not bald” has two readings:

• It’s not the case that the present King of France is bald. true: there is no such king
• The present King of France is such that he is not bald. false

Compare “All that glitters is not gold.” On “The present King of France is bald,” Frege says it’s neither true nor false; Russell says it’s false.

Section 2 review

• For Frege, “the King of France does not exist” comes out neither true nor false, but it’s obviously true. For Russell it is true, as the negation of an existence-and-uniqueness claim. (Does Frege have a response here?)
• For Russell, quantifiers don’t have reference: “everyone” doesn’t refer to specific people. (Could quantifiers refer to the whole world, as though the world had the property of existing?)
• Russell likes his view because it’s better ontologically (no subsisting non-existents), and perhaps epistemically.
• Correspondence theory of truth: “S” is true iff S is among the true things. Open questions: what is Russell’s theory of what makes something true, and of how communication and mutual understanding happen, i.e. how words attach to objects (see Lec 5)?

Lecture 5Russell: acquaintance and description

Russell, “Knowledge by Acquaintance and Knowledge by Description” (1910)

Sense-data and acquaintance

Start with colour (or X-) constancy: when the light changes, my perception of my pencil and the underlying sense-data change, but perception at a higher level doesn’t really.

For Russell, what I’m most immediately aware of is sense-data. HandoutThese are mental entities, the counterparts of images, sounds, and tastes, that account for what experience is like. We are acquainted with sense-data, and acquaintance is infallible: seeing a pencil can go wrong, but there’s no appearance/reality gap for sense-data themselves.

That’s a substantive claim, though. The speckled hen: I see a hen with lots of speckles in the distance, and it seems to have an indeterminate number of them. Does the sense-datum have an indeterminate number of speckles?

Three accounts of intentionality

Something has intentionality when it’s about something. Three accounts so far:

• Iconic theory: resemblance. The problem is that an image must resemble its object in some respects, or else everything resembles everything. Specifying which respects requires interpreting the image, and that defeats the purpose, since the theory was meant to explain what an idea is about.
• Frege: descriptive criteria (senses).
• Russell: descriptive and causal. A thought is about a thing because that thing causes the sense-data I’m aware of and I think descriptive thoughts about it. Issue: many things are causally responsible for my current sense-data, so how do we get the right description? (To think more about.)

Russellian propositions

Propositions are the meanings of sentences beyond the words: one proposition can be expressed in many languages, which makes them a good way to pin down what a disagreement is about. HandoutThey’re also the objects of belief. For Russell, a proposition contains the objects it’s about plus the properties and relations predicated of them, as an ordered structure:

⟨Sun, Moon, occludes⟩ ≠ ⟨Moon, Sun, occludes⟩

Order matters, since “the Sun blocks the Moon” ≠ “the Moon blocks the Sun.”

Names as disguised descriptions

What about fake names? A con artist introduces “Joe Smith, who’s excited about this opportunity.” How is the victim’s thought meaningful? Their proposition isn’t about Joe Smith but about “the man introduced to me as a backer.” The name is short for a description, so it doesn’t refer.

• A logically proper name contributes an object itself to the proposition.
• The test: if you can suppose the subject doesn’t exist and the proposition is still meaningful, the subject is a description, not a name.
• Since we can always build Cartesian skeptical scenarios, this applies to everything outside our current sense-data.

What drives Russell: when it seems to me that I’m entertaining a proposition, I really am. I can be wrong about whether it’s true, but not about whether I’m thinking a contentful thought. And propositions contain what they’re about, so their constituents must be things whose existence is guaranteed, which means sense-data.

Lecture 6Quine: quantifiers and propositional attitudes

Quine, “Quantifiers and Propositional Attitudes” (1956)

Recall the three touch-points: rational explanation, systematicity, and aboutness. Quine is interested in two ways of ascribing belief, and in whether that implies a metaphysical difference (two kinds of belief).

Ralph and Ortcutt: substitution in belief reports

Ralph suspects the man in the brown hat is a spy. He thinks the man he saw at the beach (a pillar of the community) is not. Unbeknownst to Ralph, they are the same man, Bernard J. Ortcutt.

1. Ralph believes that the man in the brown hat is a spy.
2. The man in the brown hat is the man on the beach.
3. ✗So Ralph believes that the man on the beach is a spy.

The inference fails, which is weird if functions don’t care about the way their argument is denoted. This is a failure of substitution, due to perspective (like sense). HandoutSuch a context is referentially opaque.

• Frege’s solution: in belief reports, words refer to their customary sense (their “indirect reference”). The two descriptions have different senses, so the substitution never applied. This is intuitive: what motivates action isn’t what we’re referring to but how we think of it. Belief reports are about modes of presentation, not referents.
• Russell’s solution: rewrite descriptions as quantifiers (“there’s exactly one man in a brown hat and he’s a spy”), and that doesn’t entail the beach version. Issue: since names are descriptions built from the believer’s own sense-data, we can’t characterize how Ralph is thinking in shareable terms. HandoutFregean senses, by contrast, are public.

De dicto vs. de re ascriptions

“Ralph believes that someone is a spy” can mean:

• (a) just on general principles: there are spies, but he can’t point to one. Ralph believes ∃x(x is a spy)
• (b) he has someone specific in mind. ∃x(Ralph believes x is a spy)

These motivate, and justify, different behavior. Compare “Ernest is hunting a lion”: no particular lion vs. “there is a lion such that Ernest is hunting it.”

The difference is whether the referent is introduced inside or outside the belief report. Co-referring terms can be substituted in de re ascriptions and cannot in de dicto ones.

Quine’s worry about de re belief

Can we say Ralph believes of Ortcutt that he is a spy? It seems so: if he believes that the man in the brown hat is a spy, he believes of that man that he’s a spy, and since de re allows substitution, he believes of Ortcutt that he’s a spy. By the same route from the beach, he believes of Ortcutt that he’s not a spy. So Ralph both does and doesn’t believe of Ortcutt that he’s a spy.

Sometimes we engage the world under a mode of presentation (notional belief). Quine also posits relational belief, a direct relation to the object with no mode of presentation (as “seeing” seems to allow substitution).

Kaplan: reducing de re to de dicto

Suppose all belief goes through a mode of presentation. Then a de re ascription just quantifies over modes of presentation (Kaplan 1968):

• There is some MoP m such that Ralph believes, under m, that Ortcutt is a spy;
• and there is some MoP m′ such that Ralph believes, under m′, that Ortcutt is not a spy.

We divorce the mode of presentation in the reporter’s words from the one quantified over and leave open which one Ralph is using. No contradiction. So there are still two kinds of ascription, which differ semantically, but only one kind of belief: notional.

Moral: a semantic difference doesn’t necessarily mean a metaphysical one. De dicto and de re are kinds of belief ascription; to claim they’re different kinds of belief takes a separate metaphysical argument.

Lecture 7Perry: the essential indexical

Perry, “The Problem of the Essential Indexical” (1979)

Self-locating belief

The paper is from 1979, close in time to Jackson’s Mary case, and the two are quite similar: in the shopper case you can be completely clear about all the facts and still be missing something. What you learn is a purely perspectival fact. What is that new knowledge, and is it an extra kind of fact? This is the challenge of self-locating belief.

The messy shopper and the Doctrine of Propositions

Perry follows a trail of sugar around a supermarket counter, looking for the shopper with the torn sack, and then realizes: “I was the shopper I was trying to catch.” What did he learn?

• It clearly concerns Perry, but it’s distinct from “the shopper with the leaking bag is making a mess,” which he believed all along (Fregean distinctness).
• So some special mode of presentation by which Perry is presented to himself is doing the work.
• It can’t simply be the sense of “I am making a mess,” because that sentence means something different in someone else’s mouth. It isn’t absolutely true or false.

Perry’s target is the Doctrine of Propositions. Propositions:

1. are the objects of belief;
2. are true or false absolutely;
3. obey Frege’s criterion of difference of sense.

We’d like a proposition that explains the change in behavior and satisfies all three. How could that work for indexicals?

Why no description can replace “I”

Try another sense for “Perry”: “the only bearded philosopher in a Safeway west of the Mississippi is making a mess.” That still doesn’t explain why he changes what he does. You need “…and that’s me!”, which is an indexical again. This is the essential indexical: replacing it with any other term destroys the explanation.

An indexical is an expression whose reference depends on context: pronouns, demonstratives, adjectives like “tall,” etc.

Nickel: linguistic vs. conceptual indexicals

Perry’s argument slips between different notions of “indexical.” Consider:

• Every girl turned in her homework. “her” isn’t one person, but it isn’t indexical either
• Perry learned that he was making a mess.
• Perry learned that he, Perry, was making a mess.

Frege: a private sense of oneself

Frege would say there is a special mode of presentation, a thought that leads immediately to action. You can’t grasp my version of it, since your thought can’t move my leg. Each person is presented to themselves in a special, primitive way that only they can grasp. HandoutFrege’s example is Dr. Lauben, who has to use “I” in a public sense (“he who is speaking to you”) to communicate.

Perry grants he has no knock-down argument against these private, limited-access propositions, but he rejects them anyway: he believes “only in a common actual world.” The metaphysical cost is too high.

Relativized propositions

When two people each think “I am making a mess,” they seem to learn the same thing. For Frege that can’t be right: different referents mean different senses and different thoughts.

The fix is to give up Absoluteness. Believing “Garber is President” seems to cause the same action at different times, so treat it as one proposition whose truth value changes over time, and index propositions to times. The proposal is to do the same for people: take the common structure (a relativized proposition with no particular person built in) and evaluate its truth against a particular context. HandoutA Fregean can already relativize to worlds, so this isn’t a deep departure.

From section: imagine two omniscient gods in different places. They know every proposition about the world, yet neither knows which god it is. Only something that just one of them could know would tell them apart.

Perry’s objection and Nickel’s reply

Perry: both Perry and another shopper watching him can believe that “I am making a mess” is true-for-Perry, but they act very differently. The context of belief need not be the context of evaluation.

Nickel: this assumes that believing p is the same as believing that p is true for me. But believing a proposition is different from believing it’s true relative to some parameter. The other shopper believes that Perry’s proposition is true relative to Perry; he doesn’t believe the proposition himself. So the objection doesn’t land.

Lecture 8Strawson: on referring

Strawson, “On Referring” (1950); Donnellan, “Reference and Definite Descriptions” (1966)

Meaning as a rule of use

Strawson rejects representational theories of meaning, on which you understand an expression or sentence by looking at how it represents the world as being. No single theory explains all three touch-points plus motivating action: sense can’t do it all. He also thinks systematicity has been oversold.

• This is a social theory. All of Frege’s problems and points would make sense for a solitary individual; Strawson’s definition is essentially social.
• Example: the meaning of “I” is the rule that it’s “used by someone to refer to themselves in speaking or writing.” It would make no sense to define it by pointing at someone.
• HandoutSo rules of use are not Fregean senses. A sense determines a referent, but one rule for “I” yields a different referent for every speaker.

Expression, utterance, use

• An expression is a type (the expression itself); an utterance is a token (a particular person saying it on a particular occasion).
• A use is in between: two utterances make the same use of an expression iff they refer to the same object (or express the same truth conditions).

Against Russell: meaningful vs. true-or-false

Words don’t refer; people do. Take “The present King of France is bald.” Strawson says Russell conflates two questions:

1. Is the sentence meaningful?
2. Can it be used to express a true-or-false proposition when there’s no King of France?

“Meaningful” just tests whether there’s a coherent rule of use, i.e. whether the rules for the parts fit together, and this sentence has perfectly clear rules. Even so, a particular utterance of a meaningful sentence can fail to make a true-or-false assertion. (Strawson slides between “meaningful” and “significant.”)

Another problem: Russell’s theory applied to “the table is covered with stuff” says there’s exactly one table in the world, which is weird. HandoutThe speaker means the table that’s salient in context; rules for descriptions are partial and lean on context.

Presupposition vs. entailment

Two kinds of things are implied by (true if) a sentence S:

1. entailments of S;
2. presuppositions: background taken for granted.

Handout“It is Mary who won the race” asserts that Mary won and presupposes that someone won. Frege had seen this: “Whoever discovered the elliptic orbits died in misery” presupposes that someone discovered them.

The idea is that p is implied every time you even put the sentence forward, without committing to its truth. Every member of the “present King of France” family commits you to there being a unique present King of France. That makes presupposition a good point against Russell, but not against Frege.

Donnellan: attributive vs. referential uses

1. Attributive: if nothing is the φ, nothing has been said to be ψ. A detective standing over Smith’s mutilated body says “Smith’s murderer is insane,” meaning whoever did this.
2. Referential: even if nothing is the φ, something has still been said to be ψ. At the trial, looking at Jones, someone says “Smith’s murderer is insane” and means Jones, guilty or not.

In the referential case, reference succeeds through the speaker’s intentions and the context, even if nothing is the φ. That something is the φ is a presumption, not an entailment. Handout“The man drinking a martini seems to be enjoying himself” can be true even if he’s drinking water from a martini glass and nobody at the party has a martini.

Lecture 9Kaplan: demonstratives

Kaplan, “Demonstratives” (1989)

Does natural language have a logic? The case of “any”

Russell and Frege thought sentences have truth values and so stand in logical relations. Strawson says natural language can’t be reduced to a formal language with well-defined truth conditions (“no exact logic”). Chomsky thinks you can have formal logic for syntax but not for semantics. E.g. a description doesn’t always have to be satisfied for you to use it successfully (the courtroom murderer from Lec 8).

Evidence that logic is built into language comes from the word “any”:

• I don’t have any money. ✓
• *I have any money. ✗

We’ve internalized some rule, and it’s tied to downward entailment. Positive contexts are upward-entailing; negative ones are downward-entailing (“I don’t have a pizza” ⇒ “I don’t have a pizza with anchovies”), and “any” is allowed in downward-entailing positions. With “every,” the restrictor is downward-entailing and the nuclear scope is upward-entailing: “Everyone who completes any assignment passes” is fine, but “Everyone who takes this class will get any grade” isn’t. So grammaticality is sensitive to logical properties, and those only make sense if sentences have truth conditions.

Compositionality as a problem for Strawson

Recall that a language is compositional iff the meaning of every complex expression is determined by its structure and the meanings of its constituents. Strawson struggles here, because two expressions can have the same rule of use but contribute differently to larger sentences. Handout“I” and “the speaker” are both used to refer to the speaker, yet “If I were silent and Snowball were speaking, I would be a grad student” and “…, the speaker would be a grad student” differ in truth conditions.

Character and content

Everyone agrees meaning splits in two. For Kaplan:

• Agreement and disagreement need the same content. A: “I’m a skeptic.” B: “No, I’m not a skeptic.” They failed to disagree: same character, different content.
• Content is what gets composed, so it’s what makes compositionality work.

Context, circumstance, and possible worlds

Use possible-worlds semantics: a proposition is true in some worlds and false in others, and asserting a sentence narrows down the worlds.

• The context fixes the interpretation of the sentence: who “I” is, what “here” is, and so on.
• The circumstance is the situation (world) where we evaluate the resulting content as true or false.

The grad-student examples: “I am a graduate student” and “The speaker is a graduate student” agree at the actual world but come apart at other worlds. Donkeys: “If we called a tail a leg, how many legs would a donkey have?” Four, because we evaluate what we say at that circumstance, holding our meanings fixed. But “…what would the correct answer be, if someone asked there?” is five. HandoutLikewise, “If we all spoke French, how many legs would a donkey have?” Four, not “quatre.” So the proposition itself is purely objective: what we say is separate from the words we use to say it.

“I am here now”: logically true but contingent

Traditionally, a sentence is valid iff it can be derived from the empty set of premises, i.e. it’s true without investigation and necessarily true (“P or not P”). But “I am here now” is true whenever you say it, because the context of utterance is also the circumstance of evaluation. Yet it isn’t necessary: I could have stayed home today. So it’s logically true but not necessary. The proposition expressed could easily have been false.

What is a context? Semantics vs. metasemantics

Strawson says context is messy; Kaplan says it’s just “the input to character.”

Kaplan’s Principle 1: the referent of a pure indexical depends on the context, and the referent of a demonstrative depends on the associated demonstration. But this isn’t automatic. You can say “that” without pointing, and for “here” the size of the area (“I live here”) depends heavily on context. So Principle 1 is at best incomplete.

Kaplan’s four components

Lecture 10Lewis: counterfactuals

Lewis, Counterfactuals (1973), ch. 1

Modality and possible worlds

Originally “modality” just meant a way (mode) of being or doing; the lingo comes from Kant. “Mary must keep her promise” is put forward apodeictically, “Mary keeps her promise” categorically, and “Mary may keep her promise” problematically.

Kaplan already treated propositions as implicitly modal. Putting one forward divides the possible worlds by whether it’s true there and says we’re on the true side, so it’s a claim about all worlds. That’s why “BN” and “I” have to be treated as referring expressions, not descriptions: descriptions behave very differently under modal operators (see Lec 12).

Why counterfactuals?

Counterfactuals (“if it had been that p, it would have been that q,” written p □→ q) matter for:

1. the analysis of causation, since a causal relation might just be counterfactual dependence;
2. decision theory, which compares actions by what would happen under each.

Lewis’s theoretical ambitions differ from everyone we’ve read so far:

• The logical project: how can natural language make for valid arguments? Which inference rules are correct for counterfactuals? Some counterfactual inferences are clearly well supported; others just seem faulty.
• The metaphysical project: what are counterfactuals really about? If they’re claims about other worlds, what kind of evidence could we have for them?

The two projects are closely intertwined.

From the material conditional to spheres of similarity

• Material conditional: p ⊃ q is true iff p is false or q is true. It validates modus ponens, but it makes every counterfactual with a false antecedent true. Kangaroos do have tails, so “if kangaroos didn’t have tails, they’d have wings” comes out true.
• Strict conditional: □(p ⊃ q), the material conditional holding in every accessible world. This rules out accidental connections, but it fails on Sobel sequences: “If kangaroos had no tails, they’d topple over; but if they had no tails and used crutches, they wouldn’t.” No single set of accessible worlds makes both halves true non-vacuously. Equivalently, strict conditionals validate strengthening the antecedent, and counterfactuals don’t.

Lewis’s fix uses two pieces of machinery: possible worlds and a similarity ranking. A system of spheres $ nests worlds around the actual world @, with more similar worlds in smaller spheres. Every counterfactual is evaluated against the same ranking, but each one looks at a different region of it.

Features of the ranking show up as logical properties:

• Ties are allowed. Take “If Bizet and Verdi had been compatriots, they’d have been French” and “…they’d have been Italian.” The closest compatriot worlds are tied, some French and some Italian, so both come out false, as we intuitively judge.
• @ is at the top. That’s what licenses modus ponens with counterfactuals. From p □→ q, every closest p-world is a q-world. From p, @ is a p-world, and since it’s at the top it’s one of the closest. So @ is a q-world, i.e. q.
• No transitivity. Indicative conditionals chain; counterfactuals don’t:
  • If Harvard is in Cambridge, it’s in MA; if it’s in MA, it’s in the US; so if it’s in Cambridge, it’s in the US. valid
  • If Hoover had been born Russian, he’d have been a communist; if he’d been a communist, he’d have been a traitor; so if he’d been born Russian, he’d have been a traitor. invalid
  (The Hoover inference seems valid to me, though? Maybe it turns on “traitor to whom.”)

The metaphysical project: modal realism

Lewis is a modal realist: other possible worlds are just as real as ours, and “actual” just means this one. Objections:

• The incredulous stare. This is the most common reaction. But everyone has to take some things for granted, and this objection is just people being content to presuppose the explanandum.
• Epistemology. If other worlds are causally isolated from us, how can we know anything about them? Evaluating counterfactuals seems to require contingent truths about other worlds, but we learn contingent truths only through perception, which is causal.
• Ethics. If every possible world is real, then whatever we do, the bad things still happen somewhere. Are we just moving harm and benefit around?

Ersatzism (Ersatz = substitute) is an alternative. The semantics doesn’t need real worlds, only some points of evaluation, a $, and a similarity notion. So you can keep Lewis’s logic and give worlds a different foundation, e.g. as stand-ins (Stalnaker 1976).

Is similarity the right notion?

Similarity is super weird: every world is similar to ours in some ways and dissimilar in others. Ordinarily we have to specify a respect of comparison, but Lewis fixes his spheres by overall similarity, without one.

• Caesar: “If Caesar had fought in Vietnam, he’d have used catapults” vs. “…he’d have dropped an atomic bomb.” Each preserves a different invariant. So maybe different counterfactuals need different similarity notions, set by context?
• Nixon and the button: Nixon is told the USSR has launched a nuclear attack and must decide whether to push “the button”; then it turns out to be a false alarm. “If Nixon had pushed the button, there’d have been a nuclear holocaust” seems true. But isn’t the most similar world one where the button just malfunctions, since the rest of history then stays the same?

Lecture 11Quine: three grades of modal involvement

Quine, “Three Grades of Modal Involvement” (1953)

Quine’s suspicion of modality

Some features of a thing are contingent: Alan Garber is President of Harvard, but he might not have been. Others are supposedly essential: features it couldn’t lose and still exist. Many philosophers treat possibility and necessity as basic concepts and explain other things in terms of them.

Quine prefers a “desert landscape” to the “jungle”: the absolute minimum. That preference comes from a sense of futility. Every few hundred years people reject metaphysics as making no progress.

• Is rationality essential to humans? You construct an edge case, revise, find more cases, and so on. After all that, are we getting anything interesting? Coming up with ever more complicated theories seems degenerating, unlike in physics.
• Hume went all the way: a book with neither abstract reasoning about quantity or number nor experimental reasoning about matters of fact should be committed to the flames as sophistry and illusion.

But Hume is too extreme. We do need modal talk: natural science needs it to tell a law from a mere correlation. (I don’t like this: can’t you do all of natural science without a grounding theory of modality??)

So Quine wants a reconstruction of necessity: an analysis that keeps the parts of our modal talk that commit us to the right things and jettisons the rest. Compare “nations”: we ascribe some really weird properties to them, and we can reconstruct the notion by analyzing it from the ground up. Quine’s verdict on the three grades:

1. necessity as a predicate of sentences: good;
2. necessity as an operator on statements: reducible to the first, but tempting;
3. quantifying into modal contexts: bad, because it leads back into the jungle of Aristotelian essentialism.

Kripke’s Naming and Necessity is aimed squarely at this (see Lec 12).

First grade: necessity as a semantical predicate

Start with quotation. “Cicero was a Roman orator” is about the man. “‘Cicero’ has six letters” is about the name, and it’s true regardless of anything about the man. So substitution fails inside quotes.

Substitution fails for necessity in exactly the same way:

(The necessity conclusion is arguably ambiguous, though. “Necessarily, however many planets there are, there are more than 5” is false. “The number that is in fact the number of planets (9) is necessarily > 5” is true.)

So Quine’s idea is that necessity is a property of sentences: provability in a logical system, i.e. axioms plus rules for proving further theorems. Read “it is necessary that…” as “this sentence is provable: …”. That makes necessity a semantical predicate, true of sentences just as “contains two numerals” is.

• A standard system that can prove arithmetic proves “9 > 5” but can’t even process “planets.” That gives the right truth values.
• Is Alan Garber essentially rational? “Garber is rational” isn’t provable, but “The rational President of Harvard is rational” is. So the question only makes sense relative to a way of speaking about him.

Problems for the first grade

Nickel: there are no essences here at all. On Quine’s view, if you refer to Garber with a term that includes rationality, he’s “necessarily” rational; otherwise he isn’t. So the terms have these features, and the features don’t carry over to the person. It’s like an Anglicized name: having an English name doesn’t make someone English. So it’s better to say that on the first grade there’s no such thing as essential properties.

Which system? Provability is relative to a system, and even laws of nature get relativized: Newton’s laws are provable in some systems and not in others. We can even build systems where it’s not necessary that 9 > 5. Why not build a system with the axiom “x is human ⊃ □(x is rational)”? (Can’t we construct whatever system we need for every claim? Then necessity basically doesn’t exist.) So how do we judge one system better than another? Quine rejects the distinction between what we stipulate to be true and what we have good reason to believe. Is this a metaphysical question? Quine doesn’t want those.

Third grade: quantifying into modal contexts

“Somebody stole my cookies” is true iff some object satisfies “x stole my cookies,” regardless of how we refer to it. If Cookie Monster is the blue muppet, “Cookie Monster stole my cookies” and “The blue muppet stole my cookies” must agree in truth value. Quine calls this quantification objectual.

Now quantify into necessity: “Someone is such that it is necessary that they are rational.” That’s true iff some object is necessarily rational, however we refer to it. So it assumes objects have essential properties in themselves: Aristotelian essentialism. (But why must these properties be necessary?)

The same route takes you from a = b to □(a = b):

1. ∀x □(x = x).
2. Hesperus = Phosphorus, so by substitution, □(H = P).
3. But then there’s no world where H ≠ P. That seems wrong, since we learned H = P, which seemed to narrow down the range of worlds.

Lecture 12Kripke: naming and necessity I

Kripke, Naming and Necessity (1972), Lecture I

Why Kripke was revolutionary

Naming and Necessity has three themes:

1. the return of metaphysics, against Quine’s “Three Grades”;
2. the rejection of descriptivist theories of reference (Frege, Russell) in favor of direct reference;
3. the causal theory of reference: what we say depends on how we’re embedded in the social and natural world.

It attacks descriptivism with three arguments: modal, epistemic, and semantic. Lecture I is the modal one. But the result runs into questions. With no role for anything like Fregean sense, what about informative identities, belief ascriptions, and communication?

The Description Theory

When I talk about Aristotle, what makes my intention about the philosopher and not the shipping magnate? The natural answer: I have descriptive information in mind that identifies him, and if you asked for clarification I could give it. Indeed, if I can’t answer, it seems I’m not really talking about anyone. Suppose “wrote the Odyssey and Iliad” is the only description I have of Homer. Then if I say “maybe Homer didn’t write the Odyssey and Iliad,” I don’t seem to be speaking about anyone.

• (v) is the epistemic side. If I know “Aristotle” carries the description “philosopher,” then I know a priori that Aristotle is a philosopher.
• (vi) is the modal side, and both Kaplan-style and Quinean theorists end up committed to it:
  • Comfortable with possible worlds: “Necessarily, if there’s a last great philosopher of antiquity, the LGPoA is a philosopher” is true. If “Aristotle” abbreviates that description (Russell), then “Necessarily, if Aristotle exists, Aristotle is a philosopher” is true as well.
  • Quine: “If Aristotle exists, Aristotle is a philosopher” just is the description sentence, which is provable, and provability is all necessity is.

The modal argument

• (7) It is necessary that the last great philosopher of antiquity was a philosopher. true
• (8) It is necessary that Aristotle was a philosopher. false

So they can’t mean the same thing. Done! “Necessary” works like universal quantification over worlds: every world must conform, and in some world Aristotle never went into philosophy. “The LGPoA” picks out different people in different worlds; “Aristotle” doesn’t.

The argument:

1. Ordinary proper names are rigid.
2. The descriptions a descriptivist could plausibly associate with them are non-rigid.
3. So “necessarily, X is the φ” is false, and (vi) is false.

Why “plausibly”? Descriptions that pick out an object by its essential properties are rigid, like “the natural number between 2 and 4.” But we rarely know enough about essences to pick anything out that way.

Responses: limiting the damage

1. Wide scope. (7) might be false too, read as “the LGPoA, you got that guy? It’s necessary that he was a philosopher.” It has two readings, just like “the number of planets” in Lec 11:
   • It’s necessary that the LGPoA, whoever that may be, was a philosopher. true
   • The LGPoA is such that it’s necessary that they were a philosopher. false
   The descriptivist says a name’s description obligatorily takes wide scope over modal operators, so (8) gets only the false reading. Kripke’s reply (Preface): the argument doesn’t need □ at all. The embedded sentences “The LGPoA was a philosopher” and “Aristotle was a philosopher” differ in truth value at some worlds, so they can’t mean the same thing.
2. Actualized descriptions. Adding “actually” (“the person who was actually the LGPoA”) makes the description rigid.

Both responses concede that (vi) is false; they just limit the damage.

Where does this leave Quine?

Quine would say that talk of essences is just talk, and reflects a mistaken view of the world. Kripke’s point is that people can make sense of “that guy might have lost” (pointing at Nixon) without specifying which description they’re using. Someone who replies “only if you describe him as ‘Nixon,’ not as ‘the winner’” is the one with a philosophical theory. So there’s intuitive content to objects having modal properties, and the burden of proof shifts: Quine can’t treat his view as the default.

Nickel thinks this undersells Quine and oversells Kripke.

• Psychological essentialism (Gelman 2003): there’s a developmental stage where children think lots of things have essential properties (“why are mountains high? so they’re for climbing!”). We have a strong tendency to ascribe essences to things that clearly don’t have them; some adults ascribe essences to race. That doesn’t mean they’re right. Our intuitions can systematically misfire.
• There’s no tabula rasa: like Goodman, we need to take some (but not all) things for granted. But an intuition is a presumption, not at all conclusive. We keep intuitions until they’re rejected.