Posts on: Meaning
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.
In my 2014 paper "Against Magnetism", I
argued that the meta-semantics Lewis defended in "Putnam's Paradox" and pp.45-49
of "New Work" is (a) unattractive, (b) does not fit what Lewis wrote about
meta-semantics elsewhere, and (c) was never Lewis's considered view.
In a
paper forthcoming in the AJP, Frederique Janssen-Lauret and Fraser Macbride
(henceforth, JL&M) disagree with my point (b), and present what they call
"decisive evidence" against (c). Here's my response. In short, I'm not
convinced.
Let's assume that propositional attitudes are not metaphysically
fundamental: if someone has such-and-such beliefs and desires, that is
always due to other, more basic, and ultimately non-intentional
facts. In terms of supervenience: once all non-intentional facts are
settled, all intentional facts are settled as well.
Then how are propositional attitudes grounded in non-intentional
facts? A promising approach is to identify a characteristic
"functional role" of propositional attitudes and then explain facts
about propositional attitudes in terms of facts about the realization
of that role. (We could also identify the attitude with the realizer,
or with the higher-order property of heaving a realizer, but that's
optional.)
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.
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".
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.
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,
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 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.
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.
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.
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.
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.
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."
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.
"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".
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?
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.
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.
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 "Two Concepts of Modality", Alvin Plantinga argues that propositions
aren't sets of worlds, because "you can't believe a set, and a set can't be
either true or false" [208]. I think this argument is better than it might
appear in the rather Ungerian context of Plantinga's paper, where he uses
several arguments of the same kind to support completely crazy views, like
that Lewis is an antirealist about possible worlds.
The traditional job description for propositions says that they are a) the
ultimate bearers of truth-values, b) the content/object of propositional
attitudes, and c) the meanings of declarative sentences. Plantinga is
right that sets aren't the most intuitive candidates for this job: Is the
empty set an 'ultimate bearer' of the truth-value false? Is it the content
of Frege's belief in Axiom 5? Is it what you have to know in order to
understand Axiom 5? Well, intuitively not, but I don't think intuition is
to judge questions like these. More importantly, there are reasons
against the identification of sets with propositions.
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.