Posts on: Language
I finally got around to adding the papers from Janssen-Lauret and Macbride
2023 to the search corpus at https://www.david-lewis.org. It's
a wonderful collection with lots of treasures. I want to comment on an
intriguing passage on pp.71f., from an abandoned 1969 textbook project
on confirmation theory.
First, some context. At this point in the manuscript, Lewis has
introduced \(\mathcal{M}\) as a
probability measure on the propositions expressible in a language \(\mathcal{L}\) with classical boolean
connectives; \(\mathcal{C}\) is the
associated conditional probability measure, defined by the ratio
formula. Lewis notes that conditional probabilities are often read as
"the probability of C if A", which suggests that \(\mathcal{C}(C/A)\) might equal \(\mathcal{M}(C\textit{ if }A)\), where
'\(C\textit{ if }A\)' is the material
conditional. But that's obviously false. Lewis continues:
I (somewhat randomly) picked up Kripke 2011 the other day. This
is Kripke's first engagement with the problem of empty names. What
struck me is the biased selection of examples. Most of the paper is
concerned with names of fictional characters like 'Sherlock Holmes', and
Kripke only seems to consider simple utterances in which they figure as
the subject, like (1).
Bare indicative conditionals are bewildering, but they become
surprisingly well-behaved if we add an 'else' clause.
Intuitively, 'if A then B' doesn't make an outright claim about the
world. It says that B is the case if A is the case – but what
if A isn't the case?
An 'else' clause resolves this question. 'If A then B else C' makes
an outright claim. It says that either B or C is the case, depending on
whether A is the case. That is: the world is either an A-world, in which
case it is also a B-world, or it is a ¬A-world, in which case it is a
C-world. For short: (A∧B)∨(¬A∧C).
Some ability statements sound wrong when affirmed but also when denied. Santorio (2024) proposes a new semantics that's built around this observation.
Suppose Ava is a mediocre dart player, and it's her turn. In this context, people often reject (1):
(1)Ava is able to hit the bullseye [on her next throw].
It's obviously possible that Ava gets lucky and hits the bullseye. But ability seems to require more than mere possibility of success. A common idea, which Santorio endorses, is that ability comes with a no-luck condition, something like this:
Suppose there are no objective moral facts. It's tempting to think that this calls for a special semantics for moral language. Perhaps moral statements somehow express moral attitudes rather than describe the world. The trouble is that moral statements seem to behave like ordinary descriptive statements. Not only can we freely conjoin moral and descriptive statements. We can even use the same words – say, 'you ought to leave' – to express a moral attitude but also to report the implications of some contextually salient norms. It would be nice if we could use a standard descriptivist semantics for 'ought' statements even if we don't believe in objective normative facts.
Ability modals have a "specific" and a "general" reading. If a pianist is locked in a piano-free cell, they can play the piano in the general sense, but not in the specific sense. Roughly, an agent has the "general ability" to φ if they have the internal constitution required to φ. They have the "specific ability" to φ if, in addition, the external circumstances make it possible for them to φ.
What is the connection between the two notions? Some, e.g. Mandelkern, Schultheis, and Boylan (2017), hold that 'S can φ' expresses specific ability, and that the general reading results from the application of a tacit genericity operator 'Gen'. This is a natural idea, given that general abilities are often called 'general'. (Mandelkern, Schultheis, and Boylan (2017) even call them 'generic'!) The proposal is also tempting for accounts of ability that only directly capture the specific reading. (The locked-in pianist, for example, clearly wouldn't succeed to play the piano if they tried.)
Remember the miners problem. Ten miners are trapped in a mine and threatened by rising water. You don't know if they are in shaft A or shaft B, and you can only block off one of the shafts. Let's not ask about what you ought to do, but about what you can do. Specifically, can you save the ten miners?
According to the simple conditional analysis, you can save the miners iff you would succeed if you tried. So what would happen if you tried to save the miners?
I assume you don't actually try to save the ten miners. You keep both shafts open, knowingly causing the shortest miner to drown. Let's assume that (unbeknown to you) the miners are in shaft A. If you tried to rescue the ten miners, you would arbitrarily choose one of the shafts to block. Let's say you would choose shaft A, simply because you like the letter 'A'. You don't think this is relevant: you don't think the miners are any more likely to be in shaft A than in shaft B. But you have to make your choice somehow. Might as well make it based on your irrelevant preference for the letter 'A'.
A common assumption in discussions of abilities is that phobias restrict an agent's abilities. Arachnophobics, for example, can't pick up spiders. I wonder if this is true, if we're talking about the pure 'can' of ability.
The problem is that 'can' judgements (and 'ability' judgements) are often sensitive to relevant preferences or norms: I might say that I can't come to a meeting (or that I'm not able to come) because I have to pick up my kids from school. This is what I'd call an impure use of 'can'. I don't actually lack the ability to come to the meeting. It's just that doing so would come at too high a cost. Perhaps arachnophobia similarly associates a high cost with picking up spiders.
According to a popular view about counterfactuals, a counterfactual hypothesis 'if A had happened…' shifts the world of evaluation to worlds that are much like the actual world until shortly before the time of A, at which point they start to deviate from the actual world in a minimal way that allows A to happen. 'If A had happened, C would have happened' is true iff all such worlds are C worlds. The time "shortly before A" when the worlds start to deviate is the fork time.
Now remember the case of Pollock's coat (introduced in Nute (1980)). John Pollock considered 'if my coat had been stolen last night…'. He stipulates that there were two occasions on which the coat could have been stolen. By the standards of Lewis (1979), worlds where it was stolen on the second occasion are more similar to the actual world than worlds where it was stolen on the first occasion. Lewis's similarity semantics therefore predicts that if the coat had been stolen, it would have been stolen on the second occasion. This doesn't seem right.
In this post, I'll develop an RSA model that explains why 'if A or B then C' is usually taken to imply 'if A then C' and 'if B then C', even if the conditional has a Lewis/Stalnaker ("similarity") semantics, where the inference is invalid.
I'll write 'A>C' for the conditional 'if A then C'. For the purposes of this post, we assume that 'A>C' is true at a world w iff all the closest A worlds to w are C worlds, by some contextually fixed measure of closeness.
It has often been observed that the simplification effect resembles the "Free Choice" effect, i.e., the apparent entailment of '◇A' and '◇B' by '◇(A∨B)', where the diamond is a possibility modal (permission, in the standard example). But there are also important differences.
Let's continue. I'm going to present a new (?) model of free choice. Free choice is the phenomenon that a disjunction embedded in a possibility modal conveys the possibility of both disjuncts. 'You may have tea or coffee', for example, conveys that you may have tea and you may have coffee. Champollion, Alsop, and Grosu (2019) present an RSA model of this effect, drawing on the "lexical uncertainty" account from Bergen, Levy, and Goodman (2016). I'll present a model that does not rely on lexical uncertainty.
In this post, I want to compare the Rational Speech Act approach with the Iterated Best Response approach of Franke (2011). I'm also going to discuss Franke's IBR model of Free Choice, turn it into an RSA model, and explain why I find both unconvincing.
Let's back up a little.
Lewis (1969) argued that linguistic conventions solve a game-theoretic coordination problem.
Let's model a few situations in which the hearer does not assume that the speaker has full information about the topic of their utterance.
Goodman and Stuhlmüller (2013) consider a scenario in which a speaker wants to communicate how many of three apples are red. The hearer isn't sure whether the speaker has seen all the apples. Chapter 2 of problang.org gives two models of this scenario. The first makes very implausible predictions. The second is very complicated. Here's a simple model that gives the desired results.
var states = ['RRR','RRG','RGR','GRR','RGG','GRG','GGR','GGG'];
var meanings = {
'all': function(state) { return !state.includes('G') },
'some': function(state) { return state.includes('R') },
'none': function(state) { return !state.includes('R') },
'-': function(state) { return true }
}
var observation = function(state, access) {
return filter(function(s) {
return s.slice(0,access) == state.slice(0,access);
}, states);
}
var hearer0 = Agent({
credence: Indifferent(states),
kinematics: function(utterance) {
return function(state) {
return evaluate(meanings[utterance], state);
}
}
});
var speaker1 = function(obs) {
return Agent({
options: keys(meanings),
credence: update(Indifferent(states), obs),
utility: function(u,s){
return learn(hearer0, u).score(s);
}
});
};
showChoices(speaker1, [observation('RRR', 2), observation('GGG', 2)]);
Bergen, Levy, and Goodman (2016) assert that "the rational speech acts model, and neo-Gricean models more generally, cannot derive distinct pragmatic interpretations for semantically equivalent expressions".
In the previous post, I gave a counterexample. I presented an RSA model that explains why 'pockets' is interpreted as plural and 'a pocket' as singular, even though the two expressions are semantically equivalent.
In this post, we'll model different kinds of scalar implicature. I'll introduce several ideas and techniques that prove useful for other topics as well.
Let's begin with the textbook example, the inference from 'some' to 'not all' (for which Goodman and Stuhlmüller (2013) give an RSA-type explanation).
A speaker wants to communicate the results of an exam. The available utterances are 'all students passed', 'some students passed', and 'no students passed'; for short: 'all', 'some', and 'none'. We can represent their meaning as functions from states to truth values:
var states = ['∀', '∃¬∀', '¬∃'];
var meanings = {
'all': function(state) { return state == '∀' },
'some': function(state) { return state != '¬∃' },
'none': function(state) { return state == '¬∃' }
};
I've been playing around with the Rational Speech Act framework lately, and I want to write a few blog posts clarifying my thoughts. In this post, I'll introduce the framework and go through a simple application.
The guiding idea behind the Rational Speech Act framework is to model speakers and hearers as rational (Bayesian) agents who think strategically about each other's behaviour. A hearer doesn't just update on the literal content of an utterance, but on the fact that the utterance has been made, by a speaker who anticipated that the speaker would update in some such way.
In its purest form, this kind of reasoning leads to an infinite regress. To interpret your utterance, I need to figure out why you made it. To do that, I need to figure out how you thought I would interpret the utterance, which depends on what you believe about what I believe about why you made it, and so on.
Magri (2009) points out that the computation of scalar implicatures appears to be insensitive ("blind") to contextual knowledge. This is indicated by the oddness of sentences like (1) and (2):
(1) Some Italians come from a warm country.
(2) John is sometimes tall.
Plausibly, these sound odd because their implicature-strengthened meaning clashes with our background knowledge that – in the case of (1) – all Italians come from the same country and – for (2) – that people's height is a stable property.
Has it been noted that McGee conditionals seem to clash with the Simplification of Disjunctive Antecedents (SDA)?
Consider the following conditional, inspired by McGee (1985).
(1) If a Republican had won then if it hadn't been Reagan then it would have been Andersen.
For context, imagine a scenario in which there were exactly two Republican candidates for the office in question, called Reagan and Andersen. Neither won. In this kind of context, (1) seems fine. So does (2).
(2) If Reagan or Andersen had won then if Reagan hadn't won then Andersen would have won.
Now, SDA (in its strong form) is the hypothesis that a conditional of the form 'if A or B then C' is equivalent to the conjunction of 'if A then C' and 'if B then C'. Applying this to (2), we would predict that (2) is equivalent to the conjunction of (3) and (4).
It is well-known that disjunctive possibility and necessity statements appear to imply the possibility of the disjuncts:
(FC) \( \Diamond(p \lor q) \Rightarrow \Diamond p \land \Diamond q \).
(RP) \( \Box(p \lor q) \Rightarrow \Diamond p \land \Diamond q \).
The first kind of inference is known as a "free choice" inference, the second is "Ross's Paradox".
For example, (1a) seems to imply (1b) and (1c):
(1a) Alice might [or: must] have gone to the party or to the concert.
(1b) Alice might have gone to the party.
(1c) Alice might have gone to the concert.
In chapter 3 of his dissertation, Booth (2022), Richard Booth points out that (FC) and (RP) underdescribe the true effect.
Champollion, Ciardelli, and Zhang (2016) argue that truth-conditionally equivalent sentences can make different contributions to the truth-conditions of larger sentences in which they embed. This seems obviously true. 'There are infinitely many primes' and Fermat's Last Theorem are truth-conditionally equivalent, but 'I can prove that there are infinitely many primes' is true, while 'I can prove that there are no integers a, b, c, and n > 2 for which an + bn = cn' is false. Champollion, Ciardelli, and Zhang (henceforth, CCZ) have a more interesting case in mind. They argue that substituting logically equivalent sentences in the antecedent of a subjunctive conditional can make a difference to the conditional's truth-value.
I've been reading Fabrizio Cariani's The Modal Future (Cariani (2021)). It's great. I have a few comments.
This book is about the function of expressions like 'will' or 'gonna' that are typically used to talk about the future, as in (1).
(1) I will write the report.
Intuitively, (1) states that a certain kind of writing event takes place – but not right here and now. 'Will' is a displacement operator, shifting the point of evaluation. Where exactly does the writing event have to take place in order for (1) to be true?
Here's a natural first idea. (1) is true as long as a relevant writing event takes place at some point in the future. This yields the standard analysis of 'will' in tense logic:
A lot of rather technical papers on conditionals have come out in recent years. Let's have a look at one of them: Kocurek (2022).
The paper investigates Al Hajek's argument (e.g. in Hájek (2021)) that "chance undermines would". It begins with a neat observation.
There are many conceptions of linguistic meaning. One approach, that I like, assumes that the semantic values we assign to sounds and scribbles function somewhat like the numbers we assign to certain pieces of paper and plastic when we say that they are a "5 pound note" or a "10 pound note": they are a compact summary of the kinds of activities people can perform with the relevant objects. With a 5 pound note you can buy certain kinds of goods. With the sounds 'it is raining' you can inform people that it is raining.
When people like Lewis (1975) spell out this use-based conception of semantics, they generally focus on assertion and information exchange. Roughly, the semantic value assigned to a declarative sentence is identified with the information that is conventionally conveyed by an utterance of the sentence.
Here's an idea that might explain a number of puzzling linguistic phenomena, including neg-raising, the homogeneity presupposition triggered by plural definites, the difficulty of understanding nested negations, and the data often assumed to support conditional excluded middle.
An utterance of
(1a) We will not have PIZZA tonight
conveys two things. Unsurprisingly, it conveys that we will not have pizza tonight. But it also conveys, due to the focus on 'PIZZA', that we will have something else. By comparison,
Neg-raising occurs when asserting ¬Fp (or denying Fp) tends to communicate F¬p. For example, 'John doesn't believe that he will win' tends to communicate that John believes that he won't win.
There appears to be no consensus on why this happens. Some think ¬Fp really does entail F¬p. Others think the effect is an implicature. Still others think it's caused by a presupposition of opinionatedness or "settledness": when we talk about whether Fp holds, we presuppose that F holds either for p or for an alternative to p, denying Fp therefore commits us to F¬p.
An interesting new paper by David Mackay, Mackay (2022), raises a challenge to popular ideas about the semantics of modals. Mackay presents some data that look incompatible with classical two-dimensional semantics. But the data nicely fit classical two-dimensionalism, if we combine that with a flexible form of counterpart semantics.
Before I discuss the data, here's a reminder of some differences between epistemic modals and non-epistemic ("metaphysical") modals.
In my paper "Ability
and Possibility", I argued that ability statements should be analysed as
simple possibility modals: 'S can phi' is true iff S phis at some world
compatible with relevant circumstances.
This view is widely considered inadequate because it seems to violate two
(related) intuitions about ability.
One is that ability requires a kind of robustness: if you have the
ability to phi, then you reliably phi whenever the need arises, under a variety
of circumstances.
A Sobel sequence is a sequence of conditionals with increasingly strong
antecedent. Lewis used Sobel sequences to motivate his "variably strict"
analysis of counterfactuals.
For example, intuitively (1) and (2) might both be
true, which seems to contradict a simple strict analysis:
(1) If the US had destroyed its nuclear weapons in 1965, there would have
been war.
(2) If every country destroyed its nuclear weapons in 1965, there would
have been peace.
Friends of singular thought typically assume that in order to have a singular attitude towards an object, one must either stand in a special acquaintance relation to the object, or have a special kind of mental representation for it. Both of these views face a challenge from our practice of attitude reports: we can seemingly attribute attitudes with singular content even if neither condition is satisfied.
In a well-known example from Sosa 1970, the army generals decide that the shortest man should go first. The Sergeant tells Shorty: 'they want you to go first'. Here the generals need not be acquainted with Shorty, and it is doubtful that they must have a "mental file" for him.
So far, we have looked at cases in which an agent has a descriptive belief (e.g., "the creature approaching through the woods is a bear"), which gets reported as a singular belief ("Mary beliefs Mark is a bear"). But sometimes we attribute singular beliefs even though the subject appears to have only a general (quantified) attitude about the relevant individual.
A murder has been committed. The detective has figured out that the culprit probably comes from a certain mountain village. She knows little about that village, but believes that all its inhabitants are poor peasants. You are one of the villagers. We might say:
Compare the following three sentences.
(1) I thought my husband was a bear.
(2) Mary thinks her husband is a bear.
(3) I think my husband is a bear.
(1) and (2) are ambiguous between a "de re" reading and a "de dicto" reading. But (3) only seems to have the "de dicto" reading. How come?
According to the semantics I have described in earlier parts of this series, an utterance of (3) is true on its de re reading iff (roughly) there is a suitable role R such that (i) in all the speaker's belief worlds, whatever plays R is a bear, and (ii) in the actual world, the speaker's husband plays R.
In the previous post, I have assumed that conversational context somehow determines a unique "suitable role" for each individual under discussion, relative to every epistemic subject. This is an unrealistic assumption.
For example, I believe that Canberra gets cold in winter. But Canberra is known to me as the occupant of many roles. Among other things, I know it as the capital of Australia, as the city in which I lived for most of 2012, and as the destination of my most recent international trip. When I say that I know (or believe) that Canberra gets cold, none of these roles may be particularly salient.
In this post, I'm going to present a first stab of a formal semantics for de re belief reports.
As I explained in the last post, I'm going to assume that for every epistemic subject at every time there is a set of doxastically accessible worlds, representing how the subject takes the world to be. I will sometimes refer to these worlds as the subject's 'belief worlds'.
On that background, we can make the guiding idea behind the Quine-Kaplan model more precise: 'S believes that x is F' is true iff there is a suitable role R such that (1) in all worlds doxastically accessible for S, whatever plays R is F, and (2) in the actual world, x plays R.
This is part 3 of a series on epistemic counterpart semantics (part 1, part 2).
Recall the guiding idea: A de re report 'S believes that x is F' is true iff there is a suitable role R such that (1) S believes that whatever plays R is F, and (2) in fact, x plays R.
I said that these truth-conditions naturally emerge if we treat 'believes' as a modal, quantifying over a set of accessible worlds. So I am going to assume that for any relevant subject in any relevant situation there is a set of "doxastically accessible" worlds which somehow characterise what the subject believes. I want to say a few words to clarify this assumption.
This is part 2 of a series on epistemic counterpart semantics. Part 1 is here.
I want to defend what I called the "Quine-Kaplan model" of de re belief ascriptions. According to this model, 'S believes that x is F' is true iff there is a suitable role R such that (1) S believes that whatever plays R is F, and (2) in fact, x plays R.
In this post, I mainly want to explain what I mean by a "suitable role". This will also bring to light some arguments in favour of the Quine-Kaplan model.
I have decided to write a series of posts on epistemic applications of counterpart semantics, mostly to organise my own thoughts.
Let's start with a motivating example, from Sæbø 2015.
On September 14 2006, Mary Beth Harshbarger shot her husband, whom she had mistaken for a bear. At the trial, she "steadily maintained that she thought her husband was a black bear", as you can read on Wikipedia.
Many sentences can be evaluated as true or false relative to a (possible) context. For example, 'it is raining' is true (in English) at all and only those possible contexts at which it is raining.
This relation between sentences (of a language) and contexts is arguably central to a theory of communication. At a first pass, what is communicated by an utterance of 'it is raining' is that the utterance context is among those at which the uttered sentence is true. (You can understand what is communicated without knowing where the utterance takes place.)
Another paper: "Discourse, Diversity, and Free Choice" has come out at the AJP.
This paper began as a couple of blog posts in January 2007, here and here. At the time, I was thinking about why counterfactuals with unspecific antecedents appear to imply counterfactuals with more specific antecedents. I noticed that a similar puzzle arises for possibility modals in general. My hunch was that this is a special kind of scalar implicature: if you say of a group of things (say, rooms) that they satisfy an unspecific predicate (like, having a size between 10 and 20 sqm), you implicate that different, more specific predicates, apply to different memebers of the group.
My paper "Ability and Possibility" has been published in Philosophers' Imprint. Here's the abstract:
According to the classical quantificational analysis of modals, an agent has the ability to perform an act iff (roughly) relevant facts about the agent and her environment are compatible with her performing the act. The analysis faces a number of problems, many of which can be traced to the fact that it takes even accidental performance of an act as proof of the relevant ability. I argue that ability statements are systematically ambiguous: on one reading, accidental performance really is enough; on another, more is required. The stronger notion of ability plays a central role in normative contexts. Both readings, I argue, can be captured within the classical quantificational framework, provided we allow conversational context to impose restrictions not just on the "accessible worlds" (the facts that are held fixed), but also on what counts as a performance of the relevant act among these worlds.
On the modal analysis of belief, 'S believes that p' is true iff p is
true at all possible worlds compatible with S's belief state. So
'believes' is a necessity modal. One might expect there to be a dual
possibility modal, a verb V such that 'S Vs that p' is true iff p is
true at some worlds compatible with S's belief state. But there
doesn't seem to be any such verb in English (or German). Why not?
What do we use if we want to say that something is compatible with
someone's beliefs? Suppose at some worlds compatible with Betty's
belief state, it is currently snowing. We could express this by "Betty
does not believe that it is not snowing". But (for some reason) that's
really hard to parse.
Gibbard's 1981 paper "Two recent theories of conditionals" contains
a famous passage about a poker game on a riverboat.
Sly Pete and Mr. Stone are playing poker on a Mississippi
riverboat. It is now up to Pete to call or fold. My henchman Zack sees
Stone's hand, which is quite good, and signals its content to Pete. My
henchman Jack sees both hands, and sees that Pete's hand is rather
low, so that Stone's is the winning hand. At this point, the room is
cleared. A few minutes later, Zack slips me a note which says "If Pete
called, he won," and Jack slips me a note which says "If Pete called,
he lost." I know that these notes both come from my trusted henchmen,
but do not know which of them sent which note. I conclude that Pete
folded.
One puzzle raised by this scenario is that it seems perfectly
appropriate for Zack and Jack to assert the relevant conditionals, and
neither Zack nor Jack has any false information. So it seems that the
conditionals should both be true. But then we'd have to deny that 'if
p then q' and 'if p then not-q' are contrary.
It has often been pointed out that the probability of an indicative
conditional 'if A then B' seems to equal the corresponding conditional
probability P(B/A). Similarly, the probability of a subjunctive
conditional 'if A were the case then B would be the case' seems to
equal the corresponding subjunctive conditional probability
P(B//A). Trying to come up with a semantics of conditionals that
validates these equalities proves tricky. Nonetheless, people keep
trying, buying into all sorts of crazy ideas to make the equalities
come out true.
Sometimes, when we say that someone can (or cannot, or must, or
must not) do P, we really mean that they can (cannot, must, must not)
do Q, where Q is logically stronger than P. By what linguistic
mechanism does this strengthening come about?
Example 1. My left arm is paralysed. 'I can't lift my (left)
arm any more', I tell my doctor. In fact, though, I can lift
the arm, in the way I can lift a cup: by grabbing it with the other
arm. When I say that I can't lift my left arm, I mean that I can't
lift the arm actively, using the muscles in the arm. I said
that I can't do P, but what I meant is that I can't do Q, where Q is
logically stronger than P.
A might counterfactual is a statement of the form 'if so-and-so were
the case then such-and-such might be the case'. I used to think that
there are different kinds of might counterfactuals: that sometimes
the 'might' takes scope over the entire conditional, and other times
it does not.
For example, suppose we have an indeterministic coin that we don't
toss. In this context, I'd say (1) is true and (2) is false.
(1) If I had tossed the coin it might have landed heads.
(2) If I had tossed the coin it would have landed heads.
These intuitions are controversial. But if they are correct, then the
might counterfactual (1) can't express that the corresponding would
counterfactual is epistemically possible. For we know that the would
counterfactual is false. That is, the 'might' here doesn't scope over
the conditional. Rather, the might counterfactual (1) seems to express
the dual of the would counterfactual (2), as Lewis suggested in
Counterfactuals: 'if A then might B' seems to be equivalent to
'not: if A then would not-B'.
Is 'can' information-sensitive in an interesting way, like 'ought'?
An example of uninteresting information-sensitivity is (1):
(1) If you can lift this backpack, then you can also lift that bag.
Informally speaking, the if-clause takes wide scope in (1). The
truth-value of the consequent 'you can lift that bag' varies from
world to world, and the if-clause directs us to evaluate the statement
at worlds where the antecedent is true.
Many accounts of deontic modals that have been developed in response
to the miners puzzle have a flaw that I think hasn't been pointed out
yet: they falsely predict that you ought to rescue all the miners.
The miners puzzle goes as follows.
Ten miners are trapped in a shaft and threatened by
rising water. You don't know whether the miners are in shaft A or
in shaft B. You can block the water from entering one shaft, but you
can't block both. If you block the correct shaft, all ten will
survive. If you block the wrong shaft, all of them will die. If you
do nothing, one miner will die.
Let's assume that the right choice in your state of uncertainty is to
do nothing. In that sense, then, (1) is true.
Bob's favourite piano piece is Beethoven's Moonlight Sonata. Alice
would like to play Bob's favourite piece, and she can play the
Moonlight Sonata, but she doesn't know that it is Bob favourite piece,
nor can she find out that it is. Can Alice play Bob's favourite
piano piece?
In one sense yes, in another no. It's a kind of de re/de dicto
ambiguity. Alice can play what is in fact Bob's favourite piece, but
she can't play it "under that description", loosely speaking.
Most programming languages have conditional operators that combine a
(boolean) condition and two singular terms into a singular term. For
example, in Python the expression
'hi' if 2 < 7 else 'hello'
is a singular term whose value is the string 'hi' (because 2 < 7). In
general, the expression
x if p else y
denotes x in case p is true and otherwise y. So, for example,
Noam Chomsky's New Horizons in the Study of Language and Mind
contains a famous passage about London.
Referring to London, we can be talking about a location or
area, people who sometimes live there, the air above it (but not too
high), buildings, institutions, etc., in various combinations (as in
'London is so unhappy, ugly, and polluted that it should be destroyed
and rebuilt 100 miles away', still being the same city). Such terms as
'London' are used to talk about the actual world, but there neither
are nor are believed to be things-in-the-world with the properties of
the intricate modes of reference that a city name
encapsulates. (p.37)
I don't know what Chomsky is trying to say here, but there is
something in the vicinity of his remark that strikes me as true and
important. The point is that the reference of 'London' is a complex
and subtle matter that is completely obscured when we say that
'London' refers to London.
Superficially, modal auxiliaries such as 'must', 'may', 'might', or
'can' seem to be predicate operators. So it is tempting to interpret
them as functions from properties to properties: just as 'Alice jumps'
attributes to Alice the property of jumping, 'Alice can jump'
attributes to her the property of being able to jump, 'Alice may jump'
attributes the property of being allowed to jump, and so on.
Perhaps the biggest obstacle to this approach comes from quantified
constructions. If 'Alice may jump' attributes to Alice the property of
being allowed to jump, then 'one of us may jump' should say that one
of us has the property of being allowed to jump. But while this is one
possible reading of the sentence, 'one of us may jump' also has a
reading on which it states that it is permissible that one of us
jumps. There is a kind of de re/de dicto ambiguity here, which
suggests that 'may' can not only apply to properties but also to
propositions.
Often the factors that determine a phenomenon don't determine it
uniquely. Sometimes this changes the phenomenon itself.
Take language. Plausibly, the meanings of our words are somehow determined by
patterns of use, but these patterns aren't specific enough to fix,
say, a unique extension or intension for our language. There is a
range of precise meaning assignments all of which fit our use equally
well. One might leave it at that and say that it is indeterminate
which of these precise languages we speak. But this misses
something. It misses the fact that we don't speak a precise
language. For example, in a precise language, "Mount Everest has sharp boundaries"
would be true, but in English it is false. The logic of a precise
language would (arguably) be classical, but the logic of English is
not.
Consider a long list S1...Sn of sentences such that (a) each Si
is trivially equivalent to its predecessor and successor
(if any), and (b) S1 is not trivially equivalent to Sn.
For example, S1 might be a complicated mathematical or logical
statement, and S1...Sn a process of slowly transforming S1 into a
simpler expression. For another example, S1...Sn might be statements
in different languages, where each Si qualifies as a direct
translation of its neighbor(s) but S1 is not a direct translation
of Sn.
An amusing passage from a recent
paper by Erik and Martin Demaine on the hypar, a pleated hyperbolic
paraboloid origami structure:
Recently we discovered two surprising facts about the
hypar origami model. First, the first appearance of the model is much
older than we thought, appearing at the Bauhaus in the late
1920s. Second, together with Vi Hart, Greg Price, and Tomohiro Tachi,
we proved that the hypar does not actually exist: it is impossible to
fold a piece of paper using exactly the crease pattern of concentric
squares plus diagonals (without stretching the paper). This discovery
was particularly surprising given our extensive experience actually
folding hypars. We had noticed that the paper tends to wrinkle
slightly, but we assumed that was from imprecise folding, not a
fundamental limitation of mathematical paper. It had also been
unresolved mathematically whether a hypar really approximates a
hyperbolic paraboloid (as its name suggests). Our result shows one
reason why the shape was difficult to analyze for so long: it does not
even exist!
So the hypar joins the ranks of phlogiston,
the planet Vulcan,
the largest
prime, or the quintic
formula: objects of inquiry that turned out not to exist.
Suppose I say (*), with respect to a particular gambling
occasion.
(*) A gambler lost some of her savings. Another lost all of hers.
There is an implicature here that the first gambler, unlike the
second, didn't lose all her savings. How does this implicature
arise?
On the standard account of scalar implicatures, we should consider
certain alternatives to the uttered sentences. In particular, I could
have said 'A gambler lost all of her savings' instead of 'A
gambler lost some of her savings'. If true, this alternative
would have been more informative. Since I chose the weaker sentence,
you can infer that I wasn't in a position to assert the stronger
sentence. Assuming I am well-informed, you can further infer that the
stronger sentence is false.
I like a broadly Kratzerian account of conditionals. On this account, the function of if-clauses is to restrict the space of possibilities on which the rest
of the sentence is evaluated. For example, in a sentence of the form
'the probability that if A then B is x', the if-clause restricts the
space of possibilities to those where A is true; the probability of B
relative to this restricted space is x iff the unrestricted
conditional probability of B given A is x. This account therefore
valides something that sounds exactly like
"Stalnaker's Thesis" for indicative conditionals:
One might suggest that for any English sentence S, 'S is true' has the
same meaning as S. Assuming compositionality, it would follow that the
two are intersubstitutable in every context. But they are not.
First of all, they are not intersubstitutable in attitude reports
and speech reports. I don't think this is very problematic because such
reports are partly quotational, and of course expressions with the
same meaning aren't always intersubstitutable inside quote marks. But
'S is true' and S are also not intersubstitutable in simple
intensional contexts, as witnessed by examples like
To some extent, one can account for semantic phenomena without
assigning meanings to words or sentences or thoughts. For instance, we
might say that beliefs and other attitudes are relations to
sentences, i.e. to strings of symbols. Roughly, to believe a
sentence S is to be disposed to utter (or assent to) S (or some
translation of S) under certain conditions. When people talk to each
other, such dispositions may be transferred: after hearing
me utter the sounds "it is raining", you acquire the disposition to
utter those sounds yourself. Apart from communication, we can also
account for things like synonymy and analyticity. Roughly, two sentences
are synonymous if necessarily, anyone who stands in the belief
relation to one of them also stands in the belief relation to the
other. There is no compositional semantics in this picture, because
there is no semantics at all. But there might be recursive rules for
translating from one language to another.
There has been some discussion recently about whether propositions
are true or false absolutely, or only relative to a possible world, or
relative to a world and a time. What hasn't been considered, to my
knowledge, is whether propositions are true or false only relative to
a branch of the wave function of the universe.
For example, suppose we shoot a photon at a half-silvered
mirror. It then enters into a superposition of passing through
and getting reflected: these are the two "branches" of the
superposition. More precisely, it is not the photon that enters into
the superposition, but the entire setup, and there are actually many
more branches, corresponding to various precise paths the photon can
take. Moreover, these branches are only the position branches
of the superposition -- there are other branches of the same
superposition, corresponding to resolutions of other properties.
Extensional contexts are usually defined as positions in a
sentence at which co-refering terms can be substituted without
affecting the truth-value of the sentence. So 'Cicero' occupies an
extensional position in 'Cicero denounced Catiline', but not in
'Philip said that Cicero denounced Catiline'. One might think that a
term t occupies an extensional position in A(t) if and only if all
instances of the following schema are true:
(LL) x=y -> A(x) <-> A(y).
'x=y' is true iff 'x' and 'y' co-refer, and 'A(x) <-> A(y)' is true
iff 'A(x)' and 'A(y)' have the same truth-value. So to say that all
instances of (LL) are true is to say that
Two rather different things sometimes seem to go under the name
"norms of assertion", and it might be useful to keep them
apart. Often, e.g. by Williamson, norms of assertion are characterised
as constitutive norms of a particular speech act. Roughly, a
constitutive norm for an activity X is a norm you must obey, or try to
obey, in order to partake in activity X. The rules of chess are a
paradigm example: to play chess, you have to move the pieces in a
particular way across the board. The other kind of "norm of assertion"
would be a genuine social norm that is normally in force when
people make an assertion.
One of the grave threats to the development of mankind in general,
and philosophy in particular, is the assumption that the objects of
propositional attitudes can be expressed by that-clauses. The
assumption is often smuggled in via a definition, e.g. when propositions
are defined as things that are 1) objects of attitudes and 2)
expressed by that-clauses. No effort is made to show that anything
satisfies both (1) and (2) -- let alone that the things that satisfy (1)
coincide with the things that satisfy (2).
When reading technical material outside philosophy, I am often
struck by the widespread use of non-rigid names and variables. A
typical example goes like this. You introduce 'X' to stand for, say,
the velocity of some object under investigation. When you want to say
that at time t1, the velocity is 10 units, you put exactly this into
symbols: 'at t1, X = 10'. If the velocity changes, we get a violation
of the necessity of identity:
At t1, X = 10.
At t2, X = 20.
Or suppose you have a population of n objects with various
velocities. Your statistics textbook will tell you that the variance
of the velocity in the population is defined as
Suppose we want to follow Frege and distinguish an expression's
denotation from its sense. Suppose also we take the
denotation of a predicate to be its extension: the set of its instances. The following argument
appears to show that this leads to trouble.
- All humans are featherless bipeds, and all featherless bipeds are
human, but there could have been featherless bipeds that are not
human. In short, (Ax)(Hx <-> FBx) & <> (Ex)(~Hx & FBx)).
- By existential generalisation over the predicate positions, it
follows that (EX)(EY)((Ax)(Xx <-> Yx) & <> (Ex)(~Xx &
Yx)).
- If things in predicate position denote sets of individuals, this
can be read as: there is a set X and a set Y such that X and Y have
the same members and it is possible for something to be a member of Y
and not of X.
- But if X and Y have the same members, then they are identical; and then
nothing could belong to "one of them" without also belonging to "the
other".
- Hence things in predicate position do not denote sets of
individuals.
The argument is modeled on a brief passage (p.13) in Tim
Williamson's latest
paper on the Barcan Formula. Williamson there argues against the
plural interpretation of second-order quantifiers. On this
interpretation, the sentence in (2) can be read as "there are things
xx and things yy such that all xx's are yy's and all yy's are xx's and
it is possible for something to be one of the yy's but not of the
xx's". Williamson objects that if the xx's just are the yy's,
then it is not possible for something to belong to "the ones" without
also belonging to "the others".
There is a mistake on page 49 of Lewis's "Counterfactual dependence
and time's arrow" (1979). Since the mistake seems to be repeated all the
time, it might be worth pointing it out.
Page 49 is where Lewis lists similarity standards for his analysis
of counterfactuals. The analysis, recall, says that "if A were the
case, then C" is true iff the closest A-worlds are C-worlds (or, more
precisely, iff either there are no A-worlds or some A&C-worlds are
closer to the actual world than any A&~C world). Closeness is a matter
of similarity, and Lewis indicates what the relevant respects of
similarity might be for certain ordinary counterfactuals in section
3.3 of his 1973 book, and again in the 1979 article on counterfactual
dependence. Roughly, the closest A-worlds are those that perfectly
match the actual world across as much of spacetime as possible without
diverse and widespread violations of the actual laws. This won't do
for indeterministic worlds, where generally no laws need to be
violated at all in order to ensure perfect match of futures even after
earlier divergence. So Lewis restricts his standards to deterministic
worlds, returning to the indeterministic case in the 1986 postscript
to the 1979 paper.
I'm off to the Blue Mountains for a week. In lieu of philosophical
content, here is a rant on semantic contents and hyperintensions that
I wrote last year.
When philosophers talk about meanings (or contents, or semantic
values), they rarely explain what these things are meant to do -- what
constraints an adequate theory of meaning would have to meet. Trying
to figure out those constraints from what is implicitly used in
discussions and arguments, one gets a laundry list of miscellaneous
features with hardly any theoretical unity. Meanings are supposed to
determine (together with syntactic structure) the truth-value of
sentences; they are supposed to be known by competent speakers; they
are supposed to be conventionally associated with symbols and sounds;
they are supposed to track what a sentence is (intuitively) about, and
also in which possible worlds it is (intuitively?) true; they are
supposed to be part of a model of how our brain processes and
generates words; they are supposed to be possible objects of beliefs
and desires; they are supposed to play various roles in speech act
theory; they are supposed to the referents of 'that' clauses; they are
supposed be such that one can truly utter 'Fred said that P' if and
sonly if Fred uttered a sentence whose meaning is the same as the
meaning of 'P'. And so on and on.
Speaking of chapter six, Williamson here argues that the sentence
1) if an animal escaped from the zoo, it would be a monkey
is not adequately formalized as
1') ![$m[1]](/texer/images/?format=gif&fontsize=12pt&tex=%5Cforall+x+%28Ax+%5Cland+Ex+%5Cboxright+Mx%29)
on the grounds that according to (1'), even the elephants are such that they would be monkeys if they escaped from the zoo. Williamson suggests that an adequate formalization might rather go like this:
Does the semantic value of expressions in a language sometimes depend on other things than their utterance context? That depends on what is meant by "semantic value", but for the most part, I think not.
It can appear otherwise if one identifies the content of an utterance with the main proposition it conveys to competent hearers.
Alice, Bob and Carol are searching for honey. Alice sees a bee hive on a tree near Bob and wants to inform both Bob and Carol about this. That is, she wants Bob to acquire the self-locating belief that there is a bee hive on the tree near him, and she wants Carol to acquire the belief that there is a bee hive on the tree over there near Bob. She achieves both goals simultaneously by pointing at the relevant tree and saying, "there's a bee hive on the tree over there".
Since Alice conveys two different (centered) propositions to Bob and Carol with her sentence, one might conclude that her sentence expresses two different contents, one relative to Bob's context of assessment and one relative to Carol's. Content, then, is relative to both an utterance context and an assessment context. However, it is quite implausible that Alice's utterance really has these two propositions as its literal semantic value. Instead, what she expressed was just the proposition that there is a bee hive on the tree she is pointing at, and Bob and Carol figured out the centered propositions they were meant to learn from this information.
Some properties are inherited from wholes to their parts: if x is (completely) made of steel, then its parts are also (completely) made of steel; if x is in the top drawer, then its parts are also in the top drawer. Other properties are upwards inherited from parts to wholes: if a part of x contains steel, then x contains steel; if a part of x touches the ground, then x touches the ground. Yet other properties are not inherited either way: if x is a hand, then x usually has non-hands as parts and is part of non-hands.
Let's call the class of counterfactual circumstances at which a sentence S is true the C-proposition expressed by S. This is more or less what Kaplan calls the "content" of S. Here are three reasons why the circumstances constituting a C-proposition should be understood as centered possible worlds rather than old-fashioned uncentered worlds.
First reason: centering is needed for modal embeddings. The standard use of C-propositions is the analysis of modal constructions: "it is possible that hummingbirds can fly backwards" is true iff there is at least one relevant circumstance w at which "hummingbirds can fly backwards" is true. Now take a sentence such as "it is early afternoon", or "it is starting to rain". It doesn't make much sense to say of an entire world that it is early afternoon there, or starting to rain. So on the standard view, on which the circumstances in C-propositions are uncentered worlds, we first have to fix a time and place, presumably by drawing on the utterance context: "necessarily, it is early afternoon" is true iff it is early afternoon at every possible world at the time and place of the utterance. So "necessarily, it is early afternoon" is true whenever it is uttered on an early afternoon. That seems wrong.
Here's something puzzling. Suppose sometime in 1869, Frege uttered
1) more people today die of tuberculosis than of cancer.
As far as I know, this was true in 1871, but it is no longer true now. Today, more people die of cancer than of tuberculosis. On the other hand, suppose Frege also uttered
2) I am not particularly well-known among philosophers.
This, too, is no longer true. Today, Frege is exceptionally well-known among philosophers.
Everyone who has taught Kripke and Putnam to undergraduates knows that philosophers nowadays use "truth at a world" in a special, technical sense that requires a lot of explaining. The most straightforward way to assign a sentence a truth value at another world w is to consider an utterance of the same words in w and ask whether or not that utterance is true. But this is not what we mean. Nor do we ask what truth value the sentence has conditional on the assumption that our world is w. (Lewis uses "truth at a world" in roughly this sense in "How to define theoretical terms"; the current convention appears to be really quite new.) What, then, do we mean? I find most introductions of the concept utterly obscure: I'm told to identify the 'proposition expressed' by a sentence in the actual world, and then to 'evaluate' this entity at another possible world. What on earth does that mean?
Somewhat related to the Most Certain Principle is the following constraint on semantic content:
Same-Saying Constraint: if A utters a sentence S1,
and B utters a sentence S2, then they say the same thing iff
S1 and S2 have the same content.
"Saying the same thing" is here obviously not meant as "saying something with the same content". That would make the constraint empty. Rather, it's supposed to be an intuitive, pre-theoretic notion.
Cresswell calls this the Most Certain Principle:
MCP: if we have two sentences A and B, and A is true and B is false, then A and B do not mean the same.
Last year, I thought that this principle was most certainly false: if I say something true that is false at another world w, and somebody in w says something with the same content, then our utterances mean the same while they differ in truth value. To quote myself,
Sometimes, implicatures appear to survive under embedding. Take
1) the column will fail and the bridge will collapse,
which in a suitable context implicates that (the speaker believes that) the bridge will collapse as a result of the column failing. This implicature is still present if (1) gets embedded in, say, a conditional:
2) if it rains, the column will fail and the bridge will collapse;
3) if the column will fail and the bridge will collapse, you'll be in trouble.
(2) is likely to convey that if it rains, the bridge will collapse as a result of the column failing, and (3) that if the bridge will collapse as a result of the column failing, then you'll be trouble.
I gave a talk about the Canberra Plan on Tuesday (slides) in which I mentioned that I disagree with Lewis and Kim about the semantics of "pain": they say "pain" denotes whatever occupies the pain role in the species under consideration (or whatever is the relevant kind); I think "pain" rather denotes the property of being in a state that realises the pain role. One of the reasons I gave for my preference is that "pain" would be rather exceptional if it worked as Lewis and Kim believe.
Lewis once proposed that a 'might' counterfactual ![$m[1]](/texer/images/?format=gif&fontsize=12pt&tex=A+%5CDiamondright+C)
("if A had been the case, C might have been the case") is true iff ![$m[1]](/texer/images/?format=gif&fontsize=12pt&tex=%5Cneg%28A+%5Cboxright+%5Cneg+C%29)
is true. This is sometimes used in defense of controversial philosophical claims, like in Al Hájek's "Most Counterfactuals are False" and in Boris Kment's "Counterfactuals and Explanation". But at least in some cases, the analysis doesn't seem right.
This appears to be a problem for pure epistemic accounts of indicative conditionals (a la Weatherson and Chalmers), on which "if A then B" is true iff the [epistemically] closest worlds verifying A also verify B.
The match cannot be played if it rains; either it has to be postponed or canceled. Which of these will happen is regulated by the rule book, but nobody has looked up the relevant passages so far. All we know is that exactly one of these two conditionals is in the rule book, and therefore true, and the other false:
I've thought a little more about this thing I called 'diamond implicature', and I've come up with the following explanation. I don't know if it's original, and unfortunately, I don't see how exactly it applies to the antecedent of counterfactuals, which is what I am most interested in.
The explanandum is that in many contexts, ![$m[1]](/texer/images/?format=gif&fontsize=12pt&tex=%5CDiamond+%28A+%5Clor+B%29)
appears to imply ![$m[1]](/texer/images/?format=gif&fontsize=12pt&tex=%5CDiamond+A+%5Cland+%5CDiamond+B)
. For example,
<update 2007-01-18>The poll is closed. The results are pretty much as I expected.</update>
To be an electron is to roughly satisfy our electron theory;
to be a banana is to roughly satisfy our banana theory. To say
that electrons or bananas are such-and-such is equivalent to saying
that things (roughly) satisfying a certain theoretical role are
such-and-such.
Thus our Total Theory of the world is arguably a priori equivalent
to its "electron" ramsification or its "banana" ramsification, in
which all occurrences of "electron" and "banana", respectively, have
been replaced by existentially bound variables. What Total Theory adds
to those Ramsey sentences is only the Carnap sentence for "electron"
and "banana": the material conditional with the Ramsey sentence in the
antecedent and Total Theory in the consequent. And this conditional is
arguably analytic.
Lots of interesting stuff came up at the Summer School and the GAP and the A Priori workshop. Here's just two quick notes on something Jason Stanley mentioned in his talk on "Knowledge and Certainty".
Jason argued that knowledge does not entail certainty. He pointed out that in Unger's arguments to the opposite conclusion, "know" is always emphasized, as in:
Robbie has some interesting posts about rigidity. That made me wonder about "the actual number of planets", which no longer denotes the number 9 now that Pluto doesn't count as a planet any more. So what should we say?
- "TANOP" rigidly denoted the number 9 last year and rigidly denotes the number 8 this year. (-- Even though the astronomical facts haven't changed in any relevant way!)
- "TANOP" always rigidly denoted the number 8. (-- So Quine was wrong, but not because he got the astronomical facts wrong, but because he didn't know what he meant by "planet"; in fact, til last week, nobody ever knew what they meant by "planet"!)
- "TANOP" changed its meaning in 2006. (-- So when we say that the number of planets is 8 we don't disagree with Quine when he said that the number of planets was 9!)
I think the third option is the only credible one. Would people with sympathies for reference magnetism go for the second? (If you would, do you think it's possible that the members of the IAU, who voted about the new definition last week, might have got the definition wrong?)
*) Oskar Minkowski discovered that dogs whose pancreas is removed develop the symptoms of diabetes.
Suppose this is the first time you've heard the name "Oskar Minkowski". Cases like this are good candidates for causal descriptivism. According to causal descriptivism, my utterance of (*) is true iff there is a person standing at the origin of a certain chain of communication leading to my present use of "Oskar Minkowski", and this person discovered that dogs whose pancreas is removed develop the symptoms of diabetes. This comes close to many people's intuitions about possible cases.
In section 24.D of his "Replies and systematic expositions" in the Schilpp volume, Carnap argues that every theory can be split into a component "representing the factual content of the theory", and another component serving as "analytic meaning postulates [...] for the theoretical terms". In fact, he doesn't speak about every theory, but it seems that what he says is true in general.
Take everything you believe about water, and call that your water theory. Your theory presumably contains things like "water fills our lakes and rivers", "water boils at around 100 °C under normal conditions", "water consists of H2O", and so on. All that is plainly empirical. Now the factual component of your theory, according to Carnap, is its Ramsey sentence: the theory with all occurrences of "water" replaced by a variable and prefixed by an existential quantifier binding that variable. The analytic meaning postulate then is the material conditional of the Ramsey sentence as antecedent and the theory itself as consequent. Let's call that the Carnap conditional of the theory.
Long ago, I worried about how the Ramsey-Carnap-Lewis account of theoretical terms could be applied to predicates. I noticed two reasons why Lewis's proposal to just turn the predicates into singular terms ("Instead of [...] 'F ---', for instance, we can use '--- has F-hood'", HTDTT p.80) is no good: first, it entails that completely false theories, say about witches or gods, leave their theoretical predicates undefined, whereas in fact those predicates are clearly empty (and thus defined); second, the proposal can turn consistent theories into inconsistent theories. This second problem can be generalized: For many predicates, there is no corresponding property that could be denoted by a singular term. Exactly which predicates these are depends on one's theory of properties, but "having parts", "being self-identical", "being a set" and "being a property" are generally good candidates, besides of course "not instantiating oneself".
The semester has now ended and I've returned to working on some long overdue stuff. (More on that soon.)
One thing that has kept me busy during the semester was the philosophy of language course (German) that I've taught. Obviously, this got way out of control. (I wrote 100 pages of handouts because I was so dissatisfied with the available textbooks. I missed two things in particular: applications of results from semantics and philosophy of language to other areas of philosophy (e.g., how the discovery of rigid designation and a posteriori necessity provided the basis for things like type-B materialism and Cornell realism), and an intelligible sketch of how all the different parts of the subject fit together: Grice's analysis of meaning, Kripke's observations about names, Lewis's theory of convention, Montague's model-theoretic semantics, etc. I'm not sure if in the end I did that better, but I've definitely learned a lot in that seminar.)
Peter Menzies and Huw Price, in their forthcoming "Is Semantics in the Plan?" have spotted a mistake in Lewis's "Psychophysical and theoretical identifications". But they don't spot that it's a mistake, and rather think it shows that the Ramsey-Carnap-Lewis-account of theoretical terms is severly limited.
The mistake is that Lewis identifies "theoretical role" with "causal role":
Sentences aren't just about the things they name. You can write an
entire book about the Second World War without ever mentioning the
whole war by name.
Very roughly, a sentence is about something X iff the way X is
matters for the truth value of the sentence. "It's raining" is about
the weather because differences with respect to the weather affect the
truth value of the sentence. By contrast, "it's raining" (or at least
"it's raining in Berlin on July 11, 2006") is not about the Second
World War because any way the Second World War might have been is
compossible with (just about) any state of the current
weather. (Arguably, the current weather counterfactually depends on
details about the Second World War. But what counts is compossibility,
not counterfactual dependence.)
I wonder about the best treatment of the following kind of
context-dependence, and its relation to analyticity and
apriority.
| 1) |
Mozart's piano sonatas are difficult;
France is hexagonal;
there is no more beer;
it is impossible to travel from Berlin to London in less than 3 hours;
Tourists from China are always friendly.
|
Whether such a sentence is true in a given context depends on the
contextually determined domains of quantification, standards of
difficulty, of precision, etc.
I've just noticed that I don't understand those who do not base semantics on use, so I'm asking you for hints or pointers.
Here, very roughly, is the position I don't understand:
Speakers of a language have tacit knowledge of its syntax and semantics. Take Karl. As a competent speaker of German, he tacitly knows that, say, "Berlin" denotes Berlin, "pleite" denotes (or expresses) the property of being broke, and "x ist y" is true iff the thing denoted by x has the property denoted by y. Thus he knows that "Berlin ist pleite" is true iff (or expresses the proposition that) Berlin is broke. That explains why he comes to believe that Berlin is broke upon hearing trustworthy people utter "Berlin ist pleite", and that's why he himself utters "Berlin ist pleite" to tell people that Berlin is broke. The object of semantics is this tacit knowledge of speakers. It has nothing intrinsically to do with use, conventions and the like.
I hope this sounds familiar. I think it's a pretty common position, so I'm a little worried that I don't understand it.
Kaplan, "Demonstratives", p.500:
[I]f I say, today,
I was insulted yesterday
and you utter the same words tomorrow, what is said is different. If
what we say differs in truth-value, that is enough to show that we say
different things.
This criterion is frequently echoed. Here, for instance, is Lycan, Philosophy of Language, p.93:
...words on Twin Earth and the rest diverge in meaning from their counterparts on Earth. Of an Earth utterance and its Twin, one may be true and the other false; what more could be required for difference of meaning?
But the criterion strikes me as very implausible. Consider a possible world
that differs from ours only by containing an extra isolated electron in some remote part of the universe, far outside our galaxy. When I say
"the number of electrons is even", my utterance differs in truth value
from the corresponding utterance of my twin at this world. Does it follow that we mean different things by "number" or "electron"
or "even" (or "is")? No. The obvious explanation is rather that what both
of us mean happens to be true in one world and false in the other.
I think one should not define "context of utterance" so that a context of utterance for an expression must always contain an utterance of the expression (or "truth in a context of utterance" so that a sentence can only be true in a context where it is uttered).
This obviously depends on how or where the term is meant to be used. The use I have mostly in mind is in the semantics/pragmatics of context-dependence, or indexicality.
Competent speakers of English know how to determine the semantic value(s) of a sentence uttered in a given context. Take truth value: we know that
Once upon a time, two quite different roles were assigned to truth-conditions: 1) they are what you know when you understand a sentence and what people communicate with utterances of the sentence; 2) they determine the truth value of the sentence when prefixed with modal operators. Unfortunately, there are sentences where these two roles come apart, namely context-dependent sentences, like "it's raining" and "I am late", and sentences containing rigid designators, like "London is overcrowded" and "Hesperus = Phosphorus". Since virtually all sentences ever uttered belong to one of these two classes (or both), the idea that we can assign to sentences truth-conditions that serve both (1) and (2) must be given up. The common strategy to deal with this at least among philosophers is to regard truth-conditions in the sense of (2) as the proper topic of compositional semantics and to assume that some other ("pragmatic") story will deliver truth-conditions in the sense of (1) out of the truth-conditions in the sense of (2) and various contextual features. I find that cumbersome and unmotivated. In my view, truth-conditions in the sense of (1) should be the primary topic of semantics, and I don't see any reason for the roundabout two-step procedure via truth-conditions in the sense of (2). I wouldn't complain if that procedure turned out to work sufficiently well, but for all I can tell, it doesn't work well at all. So I think it would be better to do compositional semantics directly for truth-conditions in the sense of (1). Since Frank Jackson calls such truth conditions "A-propositions" or "A-intensions", I use "A-intensional semantics" for that project.
I would like to say that
If X necessarily entails all truths, and if X's
A-intension coincides with its C-intension, then X a priori entails
all truths.
For suppose X -> P is not a priori for some truth
P. Then X -> P is an a posteriori necessity. So we need
information about the actual world to know what C-intension X -> P expresses, and whether it is true. But by assumption, this
information is already contained in X, and since X's C-intension
coincides with its A-intension, it cannot be hidden away in X so that
we'd need further information to find out that X contains that
information. Hence X a priori entails X -> P; and so
X -> P is itself a priori.
I had another look at Lewis's trust condition on linguistic conventions. It says that the members of a linguistic community generally take utterances of a sentence as evidence that the sentence is true. My opinion up to now has been that insofar as this condition is correct, it is redundant, and insofar as it is not redundant, it is incorrect.
The condition seems mostly redundant because the convention of truthfulness already requires of everyone to impute truthfulness to others. To be truthful means to try to utter sentences only when they are true. So by partaking in the convention of truthfulness in English, I already expect you to utter "it's raining" only when you believe that it's raining. So unless I believe your opinions about the weather are unreliable, I will take your utterance as evidence for rain. No need for an additional convention of trust.
In August, I posted an argument purportedly showing that if it is
common knowledge within a linguistic community that everyone refers to
the same thing by some name N, then the descriptions individuals
associate with that name can only differ for very remote
possibilities. The argument went like this:
If we know something, it holds in all possible situations that
might, for all we know, be actual. So if we know that our terms
corefer, they do corefer in all situations that might, for all we
know, be actual. And if I know that you know that our terms corefer, they
do also corefer in all situations that might, for all I know, be
situations that might, for all you know, be actual. And if I
know that you know that I know that our terms corefer, they do also
corefer in situations I believe you might believe I might believe
to be actual. And so on. In conclusion, our terms corefer in all
situations that have some chance of being believed (or believed to be
believed, etc.) to be actual in our community. So if we consider the
corresponding functions from possible situations to extensions, our
idiosyncratic functions will only differ for quite remote
possibilities.
There must be something wrong with this argument, for its conclusion is
false. Suppose the description you associate with "quicksand" is
"a bed of loose sand mixed with water forming a soft shifting mass that yields easily to pressure and tends to engulf any object resting on its surface", whereas what I associate with the term is "what you call 'quicksand'". Suppose also it is common knowledge between us that that's the description I associate. So it is common knowledge between us that our descriptions pick out the same stuff. But clearly, I do
not know what kind of phenomenon "quicksand" refers to. That's
why I don't know how to behave when you tell me that there's quicksand
nearby. For all I know, you could be telling me that there's watery
stuff nearby (and mean watery stuff by "quicksand") or that there are houses
nearby (and mean houses by "quicksand"), and so on.
I thought after finishing my PhD thesis I would spend less time thinking and writing about Lewis for a change. But just then, Brian started his Lewis blog raising all kinds of interesting issues, like how to handle theoretical terms in multiply realised theories. I think Lewis's early suggestion to treat the terms as empty in those cases is much worse than he realised (than he realised even later, when he dropped the suggestion). I hope to say more about that later.
What would you say if it turns out that the watery stuff in our rivers and lakes doesn't actually consist of H2O, but of XYZ: would you say that water consists of H2O or XYZ?
What would you say if it turns out that you are Leverrier's wife living in 1845 and the heavenly body your husband calls "Neptune" is not a planet, but a spaceship: would you say that Neptune is a spaceship or a planet?
There's something odd about the second question.
I am disposed to assent to certain sentences under certain conditions, to "it's raining" if it's raining, etc. For each sentence, this determines a function from conditions -- sets of centered worlds -- to truth values. (If I am disposed to assent to S under condition C, that doesn't mean I assent to S in all C-worlds. I need only do so in the closest C-worlds. I am not disposed to assent to "it's raining" under the condition that it's raining and I am halluzinating that it doesn't rain.)
Sometimes, a counterfactual is true even though the consequent is false in the closest world where the antecedent is true:
1) If Hurricane Katrina hadn't hit the town with 200 km/h, completely destroying our house, we would be at home now, watching TV.
Presumably, at the closest worlds where Hurricane Katrina doesn't hit the town with 200 km/h and completely destroys the house, it hits the town a little faster or slower, still completely destroying the house. Even at the closest worlds where the hurricane doesn't completely destroy the house, it destroys it almost completely, still preventing the TV event.
Some forms of descriptivism say that when I utter a sentence with a proper name in it, communication only succeeds if there is a description, a set of properties, you and I both associate with that name. But often such descriptions are hard to find, so some conclude that instead it suffices if you and I refer to the same object with that name, no matter what properties mediate our reference or if it is mediated by associated properties at all.
In fact, shared reference doesn't quite suffice for successful communication. We should also require that the shared reference is common knowledge. If I tell you that Ljubljana is pretty but you have no idea whether by "Ljubljana" I refer to the town you call "Ljubljana" or whether instead I refer to my neighbour or the moon, you don't understand what I'm trying to tell you.
Suppose we want a theory that tells us for all sentences in our language in what possible contexts their utterance is true. Call those functions from contexts to truth values "A-intensions". A
systematic theory should tell us how the A-intension of complex
sentences depend on their constituents. Here are some theories which
are not very satisfactory in this respect.
Theory 1. Each sentence consists of a sentence radical and a fullstop. (The sentence-radical is the entire sentence without the
fullstop.) All sentence radicals have the same semantic value:
God. The semantic value of the fullstop maps this semantic value to a
truth-value. But whether it maps God to true or false
depends on the context of utterance. For instance, in a context in
which it doesn't rain and the utterance of "." is preceeded
by an utterance of "it rains", the value of "." maps God to
false; in a context where "." is preceeded by "2+2=4", it maps
God to true; and so on.
Robbie Williams pointed out that in my recent musings on worms and stages, I ignore the following straightforward characterizations:
Worm Theory: the semantic value of predicates like "rabbit" is a set of 4D worms.
Stage Theory: the semantic value of predicates like "rabbit" is a set of 3D stages.
He's right. I believe that these theories both cannot work, so I don't want to define stage and worm theory that way.
I'm trying to catch up with Dave Chalmers's reading of Scott Soames's Reference and Description. I'm still at chapter 4, and my reaction to it is not quite the same as Dave's. (I began this entry as a comment over there, but it somehow grew way too long.)
Let's stipulate that "Lee" (rigidly) denotes the youngest spy (if there is one). Soames argues that if
Thought experiments about reference often focus on cases where a term intuitively refers to something other than what a certain theory would predict. This way, we can find sufficient conditions for reference. I think it is just as interesting to consider cases where the term does not refer at all, which gives us necessary conditions.
For example, suppose "hydrogen" and "Aristotle" refer causally, that is, denote whatever stands in a certain causal relation to our use of these expressions. Then what would it take to find out that hydrogen does not exist? We would have to acquire etymological information about the causal-historical origin of the term "hydrogen": only if something went wrong in that causal path could we conclude that there is no hydrogen.
David Chalmers has an interesting post on the differences between his and Frank Jackson's versions of two-dimensionalism. It turns out that my reading of a certain passage in "Why we need A-intensions" was right: Jackson believes that truth at a world considered as actual is somehow reducible via de-rigidification to truth at a world considered as counterfactual.
I keep wavering between two different uses of "analytical". This entry is meant to remind me of the difference and of why I should prefer the one over the other.
On the first use, a sentence is analytical if it has a universal A-intension. On the second, a sentence is analytical if one can't understand it unless one believes it (this is what I, unoriginally, proposed last year). The first is the better explication.
Suppose
1) the facts about use etc. underdetermine the semantic value of term
x (to a certain degree).
But
2) the semantic value of x is not underdetermined (to that degree).
Let V1,V2,... be the semantic values between which x is
underdetermined, and suppose V2 is in fact the value (or range of values) of x. What is it
about V2 that makes it the semantic value? Not 'use etc'. But
suppose all obvious candidates like causal facts are part of 'use etc.'. Then the
relationship between x and V2 -- let's call it "reference" -- is
inscrutable insofar as knowing all ordinary facts about use and
causation and so on is not enough to find out that
x refers to V2. There must be something over and above all this that
privileges V2. Let's say (with Lewis) that V2 is a reference
magnet (with respect to x).
Philosophers like to paraphrase away ontological or ideological commitment: how can there be a lack of wine if there are no such
entities as lacks? Because "there is a lack of wine" is only a loose way of saying "there is not enough wine".
So do we suggest that "there is not enough wine" somehow gives the
underlying logical form or linguistic structure of "there is a lack of
wine"? One might think so: if there are no lacks, we can't honestly
use lacks as semantic values in our linguistic theory. So if 1) our
linguistic theory says that sentences of the form "there is an F" are
true iff the relevant semantic value of "F" is non-empty, and if 2)
"there is a lack of wine" has the form "there is an F", and if 3) the
members of a predicate's semantic value are things that (in some
intuitive sense) satisfy the predicate, then, given the truth of "there is a lack of wine", it follows that there are things satisfying "is a lack of wine". Which presumably we wanted to deny. Rejecting (2) seems to be a good way to block the argument: "there is a lack of wine" is
not really a sentence of the form "there is an F"; really, it
is a sentence of the form "there is not enough G".
Apropos conceptual differences, Lewis didn't seem to care much about whether his
analyses exactly matched other people's semantic intuitions:
In "Veridical Halluzination and Prosthetic Vision", he claims that
prosthetic vision is properly called "seeing". He continues:
If you insist that "strictly speaking", prosthetic vision isn't really
seeing, then I'm prepared to concede you this much. Often we do leave
semantic questions unsettled when we have no practical need to settle
them. Perhaps this is such a case, and you are resolving a genuine
indeterminacy in the way you prefer. But if you are within your
rights, so, I insist, am I. I do not really think my favoured usage is
at all idiosyncratic. But it scarcely matters: I would like to
understand it whether it is idiosyncratic or not. (p.280 in Papers
II)
Another example: In Convention, he suggests that a regularity to dress in a particular way doesn't count as conventional if many people conforming to the regularity want others not to conform (so that they can poke fun at them). Realizing that this classification isn't obvious he notes:
If the reader disagrees, I can only remind him that I did not
undertake to analyze anyone's concept of convention but mine. (p.47)
He speaks of reminding the reader because he had already mentioned in the introduction that there might be no clear common concept of
convention. But, he adds, "what I call convention is an important
phenomenon under any name" (p.3).
On rereading Brian's counterexamples paper, I'm not so sure anymore I understand him correctly: Are the semantic values of predicates that are supposed to be fairly natural (unions of ranges of) C-intensions or (unions of ranges of) A-intensions? Philosophical analyses usually spell out A-intensions: they tell us that pain is what occupies the pain role, or that water is the watery stuff, not that pain is C-fiber firing and water H2O. So if the naturalness of semantic values speaks in favour of simple analyses, it should be naturalness of A-intensions. On the other hand, the fish example makes more sense if it is understood as talking about C-intensions (which would also match a suggestion sometimes made by Jackson, e.g. on p.95 of "From H2O to water", that we might analyse "water" as something like "the most natural kind roughly meeting such and such conditions"). The A-intension of "fish" presumably isn't all too natural, among other things it contains whales at worlds where the fishy animals of our acquaintance are mostly whales.
A few more comments on why I think the setup of Weinberg, Nichols and Stich's experiments on intuitions is unfortunate. The problem seems particularly obvious in the experiments on semantic intuitions reported by Machery, Mallon, Nichols and Stich, but I think it carries over to many (though perhaps not all) of the experiments of Weinberg, Nichals and Stich. Here is one of the questions Machery, Mallon, Nichols and Stich asked:
I don't understand what's so bad about admitting that people may use and understand the same words in slightly different ways.
Suppose there is a community of Martians who have a word for true
justified belief, but no word for knowledge. When these Martians learn
English, they might at first take "knowledge" to be synonymous with
their word: the difference hardly shows up in ordinary contexts. So when they use "knowledge", they mean true justified belief.
If people disagree about whether a sentence S is true in a thought experiment, what could explain the disagreement?
1) They disagree about the meaning of S. Perhaps one party uses 'zombie' for revived corpses whereas the other uses it for people without phenomenal consciousness. The disagreement is 'merely verbal'.
That's not to say it isn't a serious disagreement, in particular if both parties think their usage corresponds to the folk conception, that is, if what they disagree about is whether S is true in the thought experiment according to the common, conventional usage of S in their community. In this case the disagreement can't be resolved by mere stipulation.
If you've followed this blog for a while, you'll have noticed that I'm occasionally worried about the status of shared truth-conditions in a linguistic community. Here's my current opinion.
First the problem. We can use language to communicate how things are. By saying "I have a headache" I can let you know that I have a headache roughly because it is common knowledge between us that people typically utter the words "I have a headache" only when they have a headache. In general, a sentence S can be used to convey the information that certain conditions obtain only if both speaker and hearer know that the hearer will take an utterance of S as evidence that the conditions obtain. Let's call those conditions the 'truth conditions of S'. (The name is a bit misleading because it is often used for the counterfactual conditions under which S would be true. In this sense, the truth conditions of "water isn't H2O" are nowhere satisfied. But clearly that sentence could and can be used to convey information, so these counterfactual conditions aren't the truth-conditions I'm talking of. The truth-conditions I'm talking of are the sentence's A-intensions.)
So Lewis says that a language L is used by a population P iff there prevails in P a convention of truthfulness and trust in L.
This requirement for language use seems far too strong, given Lewis's account of conventions.
The most obvious problem is the condition that for a
regularity to be a convention, it must be common knowledge in the
population that it is a convention. Lewis offers some weak readings of this condition, but even his weakest versions rule out that
sufficiently many members of the population may doubt or deny that the
regularity is a convention. So if there were sufficiently many French
speakers who believe that their language is completely innate, they would not partake in the convention of truthfulness and trust in French, and thus not use French, on Lewis's account. It even suffices if sufficiently many French speakers merely believe that there are enough who believe that, or believe that there are enough who believe that there are enough who believe it.
The main difference between Lewis's account of language use in
Convention and his account in "Languages and Language" (and later works) is that in the latter the convention required for a language L to be used is a convention of truthfulness and trust in L, whereas in the former it was only a convention of truthfulness. I wonder if there are any good reasons for this change.
Suppose in a certain community there exists a convention of truthfulness in L. On Lewis's analysis of conventions this means that within the community,
On one of our many conceptions of meaning, the meaning of an expression is what you know when you know the meaning of the expression. I don't think this is a particularly useful conception. Besides, it violates some commonplace truths about meaning, like that expressions of different languages can have the same meaning. For suppose the meaning of the German "schwarz" is identical to the meaning of the English "black". Then by the above rule anyone who knows the meaning of "black" should know the meaning of "schwarz", which isn't so.
It is widely assumed that Lewis takes the objective naturalness of
semantic values to be an important constraint on semantics, needed to
prevent radical indeterminacy of meaning. On rereading some of his
remarks today, I found them a little confusing, and now I think the
situation is far more complicated.
Lewis discusses Putnam's model theoretic argument for radical
indeterminacy extensively in "New work for a theory of universals"
(NW) and "Putnam's paradox" (PP). In both papers, he says there is
something wrong with posing the problem as a problem about language,
because in fact the interpretation of language is settled by the
assignment of content to propositional attitudes (NW 49, PP
58f.). But, he says, focussing on attitudes only relocates the problem
without solving it, so that he might as well talk about language in
the rest of PP, which he does. He points at NW for a discussion of the
properly relocated problem.
I've thought a bit more about the comments Michael Fara left last week, and I don't find my points very convincing any more. The following is partly a correction, but mostly just thinking out loud about a more general semantic question.
The general question is how to interpret sentences of the form
1) At i, A is F
2) At i, A is not F
where 'i' denotes something like a time or a place or a world. There are a dozen proposals for interpretations of (1) in the temporal case, invoking temporal parts or relations to times or whatever. Most of these proposals can be applied to other indices as well. But let's put that aside. Suppose we understand how to interpret instances of (1) in easy cases. The hard cases I have in mind are cases where A doesn't exist exactly once at i. The precise definition
of these cases depends on the question I've put aside, but I hope it
is reasonably clear what I mean anyway. Not existing exactly once at i
means either not existing at i at all, or multiply existing at
i. Plausible examples of the first kind: I do not exist in 1758; I do
not exist on Alpha Centauri; I do not exist at any world containing
only empty space-time. Controversial examples of the second kind: if I
get split into two persons tonight, I will doubly exist tomorrow; if
river R has two branches where is crosses the border to country C,
R doubly exists at the border to C; if at some world, two people
resemble me to exactly the same degree in all extrinsic and intrinsic
respects, I doubly exist at that world.
Something interesting seems to happen on pp.261f. of Frank Jackson's "Why We Need A-Intensions" (Phil. Studies, March 2004):
How is truth at a world under the supposition that that world is the actual world related to truth at a world simpliciter? It would be good to have an assurance that there are no problems special to the former, as Ned Block convinced me [...]. For some sentences, their A-intension is one and the same as their C-intension. [...] For them, truth at a world and truth at a world under the supposition [that] it is the actual world are one and the same. There is a difference between a sentence's A- and C-intensions if and only if the evaluation of the sentence at a world requires reference back to the way the actual world is as a result of some explicit or implicit appearance of "actually", or an equivalent rigidification device, in the sentence. But when this happens, the role of worlds in settling truth values is the standard one, the one that applies when it is C-intensions that are in question. The only difference is that the value at every world but one depends in part or in whole on how things are at another world. There is no difference in the role of how things are at worlds in settling truth values; the difference is in which worlds are in play. To put the point in terms of a simple example: (a) "The actual F is G" is true at w under the supposition that w is the actual world iff "The F is G" is true at w; and (b) what follows "iff" in (a) contains "is true at w" and not "is true at w under the supposition that w is the actual world".
Many people have complained that they don't understand what it means to evaluate a sentence in a world considered as actual, or that however that is to be done, it won't deliver the results Jackson promises.
On page 305 of "Assertion Revisited" (in the latest issue of Phil.Studies), Robert Stalnaker suggests that the information conveyed by an utterance is the diagonal proposition associated with the utterance iff it is unclear in the relevant context which horizontal proposition the utterance expresses:
[T]he relevant maxim is that speakers presume that their addressees understand what they are saying. In terms of the two-dimensional apparatus, this presumption will be satisfied if and only if the propositional concept for the utterance [a function that assigns to every relevant possible context the horizontal proposition expressed by the utterance in that context] is constant, relative to the possible worlds that are compatible with the context. Our problematic example [of saying "Hesperus is Phosphorus" to O'Leary who doesn't yet know that Hesperus is Phosphorus], and all cases of necessary truths that would be informative (in the sense that the addressee does not already know that they are true) will be prima facie counterexamples to this maxim, and so will require reinterpretation [so that what is said is the diagonal, not the horizontal proposition].
Three comments:
(This is a follow-up to the previous post.) I think I've found a better way to provide for things like population-dependence in a Lewisian semantic framework. The trick is to regard it as a kind of index-dependence without explicitly introducing population-coordinates into the indices.
Recall, we want "pain*" to denote whatever state occupies the pain-role in the relevant population. Unfortunately, the relevant population isn't just the most salient population in the context of utterance, for we want to say things like
This is going to get a bit weird and technical. I wonder how a Lewisian semantics (along the lines of "Index, Context and Content" and "General Semantics") for terms like "pain" can make true everything Lewis says about such terms.
Assume that
1) Necessarily, for all x, x is in pain* iff x is in a state that plays the pain-role in normal members of the kind to which x belongs.
By "the pain-role" I mean the causal role attributed to pain by folk psychology. By "pain*" I mean whatever satisfies the condition expressed by (1). So (1) is more like a definition than an assumption. Lewis believes that our ordinary concept of pain roughly satisfies (1), but for what follows this doesn't matter. I think it's clear that we could have concepts for which something like (1) holds. Lewis's example of having a certain number stored in memory, as denoting a state of pocket calculators, sounds plausible to me (with the pain-role replaced by the role attributed to the state of having a certain number stored in memory by folk pocket calculator theory).
Via Brian, I came across the recent debate in JPhil on whether knowing-how entails knowing-that. Jason Stanley and Tim Williamson make a good case that it does, but Ian Rumfitt makes an even better case that this holds only for one of the two meanings of "knowing how", namely for the one that translates as "savoire comment [faire]" in French, but not for the one that translates as "savoire [faire]". The former provides by far the most natural interpretation (and translation into French) of "Alex knows how to get to the nearest place selling beer". So the fact that
Suppose we want to know whether some thing A has the property of representing B. The first thing to do is to ask what exactly is meant by "representing" in this context. That is, we must inquire into the general conditions under which it would be true that some x represents some y. Then, in a second step, we have to find out whether these conditions are satisfied by A and B.
When I say that semantic properties aren't primitive I mean that there must be an informative answer to the first question for semantic terms. That is, it must be possible to spell out general conditions under which something represents or means or denotes y. And the answer must be specifiable in non-semantic vocabulary. We can do better than saying that x represents y iff it represents y. The answer needn't be simple, nor immediately obvious. As usual, the best approach might be to use thought experiments: if such-and-such were the case, would x represent y? If yes, "such-and-such" can be added as a disjunct to the conditions under which x represents y.
Non-reductive (a posteriori, type-B) materialists say that even though phenomenal terms denote physical states or properties, the phenomenal way things are is not a priori entailed by the physical way things are. This means that no amount of physical information can tell us what our phenomenal terms denote. That is, non-reductive materialism implies that the projects of naturalising linguistic and intentional content are doomed. I would say that contraposititvely, since there are good reasons to believe in the project of naturalising linguistic and intentional content, non-reductive materialism is doomed.
In §7 of "Naming the Colours", David Lewis considers the view that colour terms can be analysed in terms of colour experiences which in turn are identified by "a simple, ineffable, unique essence that is instantly revealed to anyone who has that experience".
Then if it were also common knowledge that everyone in the community becomes acquainted with magenta early in life (and if the community were properly dismissive of sceptical doubts about inverted spectra, etc.), it would be common knowledge throughout the community that magenta is the colour that typically causes experiences with essence E.
Lewis goes on to reject this porposal because it contradicts (type-A) materialism. But he doesn't reject the general idea itself: "[The doctrine of revelation] is false for colour experiences. [Footnote:] Maybe revelation is true in some other cases -- as it might be for the part-whole relation."
Brandt Van der Gaast points out that Michael McDermott proposes something like the semantics I sketched on behalf of type-B materialism in his "The Narrow Semantics of Proper Names" (Mind 1988). That's true. But I think McDermott is almost silent on the matter crucial to type-B materialism, and there is no acceptable way to fill the silence without spoiling type-B materialism.
First, on behalf of type-B materialism a reply to yesterday's
post. (Thanks to Sven Rosenkranz for pointing out something like this to me.)
What makes it the case that the red-quale is the referent of "the distinctive quality of my current red-experience"? Not causal or counterfactual relations. Not demonstrative baptising. Not other kinds of verbal and non-verbal behaviour. Right. But these attempts to naturalize semantic properties are doomed anyway. They presuppose that semantic properties are generally independent of how things appear to us, which they are not. In fact, how things appear to us is an essential component in many "modes of presentation" determining the reference of terms. E.g., the referent of "red" is what appears to us under normal conditions in the way red things appear to us. In a same manner, the referent of "the distinctive quality of my current red-experience" is what appears to me in this distinctive way. Which is the red-quale, which in turn is a property of brain states. But no amount of physical information will tell you how this property of brain states appears to me. Phenomenalism as a semantic doctrine may have been too extreme, but it was not entirely wrong.
I take back what said at the end of my last post about the need to distinguish two kinds of A-intension, one transparent and one intransparent. There's not really any need to do so, and it only leads to a lot of trouble. (For instance, is it a priori that elms satisfy the transparent intension, or the intransparent intension, or both, or neither?) I thought I needed a transparent conception to explicate some sort of speaker meaning and to account for rationality. Certainly, what we need for this is a conception of meanings that it in some sense 'transparent' or 'narrow', but that does not preclude it from making reference to unknown facts about other people or causal chains. For example, the belief that the actual F is not the actual G should not count as irrational (for suitable F and G) even if the actual F is (necessesary) the actual G. But 'F's and 'G's whose A-intension is full of causal and deferential components can nevertheless provide for that, as long as it isn't a priori that the F is the G.
I want to write something about rigidity in the philosophy of mind. But first I have to say more about rigidity. (Apologies in advance: this is all going to be rather basic. But I'll need it, and I found that many people disagree with it.)
Recently I argued that the assumption that ordinary proper names are rigid designators leads to an implausibly excessive form of essentialism. But I don't want to deny the useful distinction between rigid and non-rigid designators. That is, in a sense I do believe in rigid designators. But they are not quite what rigid designators are usually supposed to be.
Suppose we are relativists about moral judgements. That is, we believe that, for example,
"One should not engage in premarital sex"
may be truely asserted by somebody iff according to his moral code (or the moral code of his community, or something like that) one should not engage in premarital sex. The important part here is of course "truely". Noone denies that if you believe that one should not engage in premarital sex then if asked about it, you should say so. That's not relativism. Relativism as I understand it holds that what you said then would be true.
This is a rewrite of last week's posting, which I now find rather
obscure. Basically, I'm trying to introduce A-intensions in a way
different from the possibilities discussed in David Chalmers' "Foundations". The "contextual" approaches he discusses look
like non-starters to me, and I don't like his own "epistemic" account,
partly because of worries about his use of ideal language and partly
because I would very much like to explain a priori knowledge with knowledge
of A-intensions rather than the converse. Most importantly, I think there
is something wrong with the very question he asks. Or at least there's
something wrong with where the question is asked.
"Content" and its cognates are rather theoretical notions. We need them
to do semantics and psychology, but we don't have immediate acquaintance
with them. That's why I find it slightly puzzling when people say that the
content of a sentence or a mental state can be represented by, say,
a set of possible worlds or some kind of labeled tree, whereas in fact it
is no such thing. What do these people think the content is in fact?
Anyway, let's assume that (at least for a certain fragment of English)
sets of centered possible worlds can do duty for (or represent) the content
of sentences. On this account, the content of "it is raining" is
identified with a certain set of centered worlds, namely the set of worlds
where it is raining at the center. By the semantics of negation, the
content of "it is not raining" is the complement of this set. Analogously,
the content of "language exists" is a certain set of centered worlds,
namely the set of worlds where language exists, and the content of
"language does not exist" is the complement of that set.
Linguistic expressions have all kinds of properties. In other words, they
can be alike in all kinds of ways. For example, two sentences (of a
particular language) can be alike in that
- they have the same truth value
- they attribute the same property to the same object
- they are necessarily equivalent
- they are a priori equivalent
- they are such that noone who understands them could regard one as false and the other as true
- they are cognitively processed in the same way in all speakers of the language
- they invoke the same mental images in all speakers
- they invoke the same mental images in some particular speaker
- they have the same use in the community
- they are verified by the same observations
- they are constructed in the same way out of constituents that are
alike in one way or another
and so on. All these properties are, I believe, worth investigating into, and all
of them might be called "semantic".
Here comes the promised reply to Sam's
reply to my previous
posting. In that posting, I first suggested that some sentence S (in a
given language) is analytic iff you can't understand it unless you believe
it. Then I said that, "put slightly differently", S is analytic iff it is
impossible to believe that not-S.
As Sam notes, the first definition implies that even very complicated
analytic truths have to be believed in order to be understood, which might
be somewhat unintuitive. I'm not sure how bad this is for lack of a clear
example. Sam uses "the sum of the digits of the first prime number greater
than 1 million is even", but this is not analytic, so here I can perfectly
well admit that you may understand it without either believing or
disbelieving it. He also mentions infinitely long sentences, but I don't
believe there are any of those in ordinary languages.
Some expression can't be properly understood unless one believes certain
things: In some sense you don't understand "irrational number" unless you
believe that no natural number is irrational; You don't understand "grandmother"
unless you believe that grandmothers are female; Maybe you don't understand
"cat" unless you believe that cats are animals.
This is all quite vague because "understanding" and "believing" are vague.
I now want to suggest that a sentence is analytic iff you can't understand
it unless you believe it. Analyticity is also vague, so the vagueness of
the explicans is fine for this purpose.
Suppose some theory T(F) implicitly defines the predicate F. If we want to
apply the Ramsey-Carnap-Lewis account of theoretical expressions, we first
of all have to replace F by an individual constant f, and accordingly
change every occurrance of "Fx" in T by "x has f" etc. The empirical
content of the resulting theory T'(f) can then be captured by something
like its Ramsey sentence 
f T'(f), and the definition of f
by the stipulation that 'f' denote the only x such that T'(x), or nothing
if there is no such (unique) x.
In the previous three entries, I've tried to argue that there are no
genuinely implicit definitions: Whenever a new expression is introduced via
an alleged implicit definition, either there is no question of definition
at all, as in the case of new expressions used as bound variables in
mathematics, or there is an explicit definition nearby.
This latter fact, that sometimes explicit definitions are only
nearby, provides a partial vindication of implicit definitions. For
example, let's assume that folk psychology implicitly defines "pain". But
folk psychology itself is not equivalent to the nearby explicit definition.
To get an explicit definition, we have to turn folk psychology into
something like its Carnap sentence. So the theory itself could be called a
genuinely implicit definition.
I've said that an explicit definition introduces a new expression by
stipulating that it be semantically equivalent to an old expression. If
there are no non-explicit definitions, this means that you can only define
expressions that are in principle redundant. Aren't there counterexamples
to this claim?
Consider the definition of the propositional connectives. We can
explicitly define some of them with the help of others, but what if we want
to define all of them from scratch? The common strategy here is to
recursively provide necessary and sufficient conditions for the truth of a
sentence governed by the connective: A 
B is true iff
A is true and B is true.
Scientific theories are often said to implicitly define their theoretical
terms: phlogiston theory implicitly defines "phlogiston", quantum mechanics
implicitly defines "spin". This is easily extended to non-scientific
theories: ectoplasm theory implicitly defines "ectoplasm", folk psychology implicitly defines "pain".
The first problem from the mathematical case applies here too: Since all
these theories make substantial claims about reality, their truth is not a
matter of stipulation. For example, no stipulation can make phlogiston
theory true. That's why, according to the standard Ramsey-Carnap-Lewis
account, what defines a term (or several terms) t occurring in a theory
T(t) is not really the stipulation of T(t) itself, but rather the
stipulation of something like its 'Carnap sentence' x T(x) 
T(t). All substantial claims in T(t) are here cancelled out by the
antecedent.
I often wonder to what extent different theories and approaches in
philosophy of language are conflicting theories about the same matter, or
rather different theories about different matters. For example, some
theories try to describe the cognitive processes involved in human speaking
and understanding; Others try to find systematic rules for how semantic
properties (like truth value or truth conditions) of complex expressions
are determined by semantic properties (like reference or intension) of
their components; Others try to spell out what mental and behavioural
conditions somebody must meet in order to understand an expression (or a
language); Others try to find physical relations that hold between
expression tokens and other things iff these other things are in some
intuitive sense the semantic values of the expression tokens; Others try to
discover social rules that govern linguistic behaviour; and so on. How are
all these projects related to each other?
I'm doing a visual memory test. On the table in front of me are twelve
green and fourteen red apples, and an empty basket. The lights go out, and
the instructor says to me:
"Put all the green apples into the basket". (1)
I try to do what he says. When the lights go on, you, the instructor's
assistant, are given a form on which you are to tick whether I've
correctly or incorrectly fulfilled the task. You see twelve green and two red apples in the basket. What do you tick?
If nothing goes terribly wrong, I will finish the Frege paper tomorrow. Though I'm not sure if it's really the same Frege paper I mentioned previously.
Initially I just wanted to put together all the comments on
Fregean thoughts and Rieger's paradox that I had already posted to this
weblog. That looked like a cheap way to get a termpaper. For some reason
however the paper has now evolved into a discussion about the prospects and
dangers of developing a semantics that can be applied to its own
metalanguage.
On Friday, I wrote:
Conclusion 2: If we want to avoid Bradley's regress, there is
no reasonable way to defend the principle that every meaningful expression
of our language has a semantic value. (Russell's paradox is an independent
argument for the same conclusion.)
Today, I was trying to prove the statement in brackets. This is more
difficult than I had thought.
Semantic paradoxes usually (always?) arise out of an unrestricted
application of schemas like
Frege believes that predicate expressions have semantic values (Sinne and
Bedeutungen) which can't be denoted by singular terms. Hence "the
Bedeutung of 'is a horse'" does not denote the Bedeutung of 'is a horse'.
Before the discovery of Russell's paradox, the only reason he ever gave for
this view -- apart from claiming that it is a fundamental logical fact that
just has to be accepted -- is that otherwise the semantic values of a
sentence's constituents wouldn't "stick together". The more I think about
this reason, the less convincing I find it.
Christian has to write an introductory paper on Quine's "Two Dogmas". I
wouldn't like to do this. I think "Two Dogmas" is excessively overrated,
and should only be read in courses on the history of American philosophy.
Unfortunately, Christian seems to agree with most of my misgivings.
Maybe I find some opposition here.
"Two Dogmas" consists of three parts: §§1-4, §5 and §6. In §§1-4 Quine
argues that there is no distinction to be drawn between analytic and
synthetic statements. His argument appears to be as follows:
Apple was very quick shipping the (free) replacement adapter.
I've decided to bring order into my thoughts about Fregean thoughts by
writing a little paper. If all goes well, I'll hand it in as the termpaper
required for my MA. Since my last entry on this topic, I've found out that
there is a lively discussion among Frege scholars about the structure of
thoughts. Some, in particular Dummett, argue that Frege is, or should be,
committed to this view:
In part II of Meaning and Necessity Carnap defines 'L-determinate designators' for rather specific languages (coordinate languages). I think that a more general definition is possible that pretty much meets Carnaps ideas. This more general definition simply identifies L-determinacy with what we nowadays call rigidity.
Dave Chalmers agrees that any concept can be explicitly analyzed by an
infinite conjunction of application-conditionals. But he wants to
restrict 'explicit analysis' to finite analyses. That certainly makes
sense, but I doubt that there are any concepts for which the
application-conditionals cannot be determined by finite means. For
example, I think it will usually suffice to partition the epistemic
possibilities into, say, 50 zillion cases and specify the extension in
each of these cases. Admittedly, I can't prove that, but the fact that concepts can be learned and our cognitive capacities are limited seem suggestive.
Dave Chalmers told me to
read some of his
papers. I have, and I'll probably say more on the
deducibility problem soon. Here is just a little thought on conceptual
analysis.
Chalmers suggests that we don't need explicit necessary and sufficient
conditions to analyse a concept. Rather, we can analyze it just by
considering its extension in hypothetical scenarios. What is it to
consider a hypothetical scenario? The result seems to depends on how the
scenario is presented. For example, 'the actual scenario' denotes the same
scenario as 'the closest scenario to the actual one in which water is H2O'.
But the difference in description could make a difference for judgements
about extensions. Chalmers avoids such problems by explaining
(§3.2, §3.5) that to consider a scenario is to pretend that a
certain canonical description is true. Hence to analyze a concept, we
evaluate material conditionals of the form 'if D then the extension of C is
E', where D is a canonical description. (Are there only denumerably many
epistemic possibilities or can D be infinite?) Now fix on a particular
concept C and let K be the (possibly infinite) conjunction of all those
'application
conditionals' (§3) that get evaluated as true. Replace every
occurrence of 'C' in K by a variable x. Then 'something x is C iff K' is
an explicit analysis giving necessary and sufficient conditions for being
C.
There may not always be a simple, obvious, or finite
explicit analysis, but at least there always is some explicit
analysis. If moreover satisficing is allowed, it is very likely that we
can settle with something much less than infinite.
Here are, very quickly, some more thoughts on the matters I talked about here
and there, inspired by another discussion with Christian.
You don't have to know much about plutonium to be a competent member of our
linguistic community. One thing you have to know is that plutonium is the
stuff called 'plutonium' in our community. Maybe that alone suffices.
Of course, if noone knew more about plutonium than this, the meaning of
'plutonium' would be quite undetermined. To fix the meaning, it would
suffice if a few persons, the 'plutonium experts', knew in addition
that this element (where each of the experts points at some
heap of plutonium) is plutonium.
This is a continuation of my last post and also partly a reply to concerns raised by my tutor Brian Weatherson.
Imagine a small community consisting of three elm experts A, B, and C.
First case: Each of A, B, and C knows enough to determine the reference of 'elm',
but their reference-fixing knowledge differs. However, they belief that
their different notions of 'elm' necessarily corefer. This is the case Lewis
discusses in 'Naming the Colours'.
Some days ago, Christian and I had an interesting discussion about two-dimensionalism.
While I don't agree with many of his criticisms (forthcoming in Synthese),
I do agree that two-dimensionalism works best if both dimensions belong to
an expression's public meaning. I think that Christian thinks that this
holds only for context-dependent expressions. I think it holds almost
universally. But this may be a matter of terminology: For me it is
part of the meaning of 'the liquid that actually flows in rivers' that this
would not denote H2O if it would turn out that XYZ flows in rivers, whereas
for Christian this is a metasemantic fact. Anyway, problems for
two-dimensionalism come when the first dimension doesn't belong to public
meaning.
Don't miss Brian
Weatherson's very insightful answer
to my posting on
rigidity (from which I've just stripped some irrelevant formalities). I
happily agree with everything he says, so I'll just add a footnote here.
Many advantages of the counterpart theory derive from its denial of the
equivalence between 'a=b', 'possibly a=b', and 'necessarily a=b'. For
example, this allows for a statue to be identical to a lump of gold even
though it might not have been. Since, as Weatherson argues, the rejected equivalence is
built into the customary ('strong') concept of rigidity, that concept must be weakened
to be useful for counterpart-theorists.
I wonder how rigidity can be characterized without begging the question
against a lot of good semantic theories.
Usually, a rigid expression is defined as an expression which has the same extension in all possible worlds (that is, as an expression with a constant intension, or C-intension).This characterization presupposes literal
trans-world-identity between extensions, which is bad, since it carries a
commitment to precise essences of individuals on the one hand and
(presumably abundant) universals as extensions of predicates on the other,
thereby ruling out counterpart theories and accounts on which tropes
or classes are the extensions of predicates.
A sentence is context-dependent if different utterances of it in different contexts have different truth values. A common kind of context-dependence is contingency. For instance, 'there are unicorns' is true when uttered in a world that contains unicorns, and false otherwise. Now look at Convention T:
'p' is true iff p.
When 'p' is context-dependent, it doesn't really make sense just to call it true. However, Convention T certainly isn't meant to apply only to non-contingent (and otherwise non-context-dependent) sentences. So what shall we make of it? Two possibilites come to mind:
1) 'p', uttered in the present context, is true iff p.
![$m[1]](/texer/images/?format=gif&fontsize=12pt&tex=%5CDiamond+A)
" and "![$m[1]](/texer/images/?format=gif&fontsize=12pt&tex=%5CDiamond+B)
". A quick internet search didn't come up with any useful literature on this, so I'd be grateful for pointers.