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Primary:
Locke, J. An Essay concerning Human Understanding
Frege, G. ‘The Thought’. Secondary: Lycan,
W. G. (2000) Philosophy of Language, London; Routledge.
Martin, R. M. (1987) The Meaning of Language, Cambridge,
MA; MIT Press. Stainton,
R. J. (1996) Philosophical Perspectives on Language, Broadview
Press. Russell,
B. (1919) ‘On Propositions’ in Russell, B (1956) (ed. Charles) Logic and Knowledge, London; Allen and Unwin. Carnap,
R. (1947) Meaning and Necessity,
Chicago: University of Chicago Press. Chierchia,
G. & S. McConnell-Ginet (1990) Meaning
and Grammar, Cambridge, MA; MIT Press.
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The Story So Far
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In
the lectures up to this point we’ve been concentrating upon reference
and considering how language is able to refer. One might have thought that
our real interest in the philosophy of language is in discovering how
meaning works rather than reference, and there is some truth in this.
Nevertheless, we started with reference because it looks like an easier
problem – we at least think we know what is involved in something
‘referring’ to something else, as the name ‘Fido’ refers to the
dog Fido – and because we understand that reference and meaning are
related in such a way that if we know what something means then we know
what it is referring to. At least, that’s a claim that is often made.
Given that some sort of dependency relationship exists between reference
and meaning we’d be justified in thinking that if we could discover how
reference worked we might be in a better position to discover how meaning
works. It turned out not to be as easy as we might have thought it was
going to be, but at least we’ve shown what the problems are. We’ve
seen quite a few different possibilities for a reference theory, and for
each of them we’ve seen advantages and disadvantages. At this point
however we’re going to put reference to one side and look more directly
at the problem of meaning.
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The Entity Theory
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We’re
going to be looking at a general sort of theory of meaning which is about
the simplest and most naively intuitively plausible theory possible.
Simply stated it is that: Meanings
are a sort of object to which we and words stand in some sort of
relationship.
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Motivation for the Entity Theory
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A
theory of meaning should allow us to make sense of the way that we talk
about meaning, or at least, our use of the word in arguments and
explanations. This doesn’t mean that we are bound to accept as a theory
only something which makes all colloquialisms about ‘meaning’ somehow
literally true, but it does mean that we should prefer a theory that
allows us to understand exactly what is being claimed when certain
colloquialisms are being used, and that the understanding should not be
too strained. Think, for example, of the theory that allows us to
understand what we’re talking about when we talk about the sun rising in
the east. We initially prefer the theory that the Sun is an object
characterized by light and heat that moves about the earth and that we see
rising above the horizon in the morning. A perfectly good theory and one
that we should rationally prefer – absent evidence to the contrary –
because it makes the use of the words ‘sun’ and ‘rise’ consistent
with normal usage; as in the statement ‘the balloon rose above the
fairground.’ A better theory, it turns out, has the sun stationary and
being brought into view by the rotation of the earth. This theory allows
us to understand what we’re really saying when we talk about sunrise,
even though it doesn’t exactly reflect the normal use of the word rise,
though the use might be compared to its use in statements like ‘the
mountain rose up before him.’ Well,
what sorts of things do we say about meanings? What are the sorts of
sentences that mention ‘meaning’? i.
We ask questions like, ‘what does this mean?’, or we say that
‘this means that … something’, and in such phrases we can see that
some things are taken to be associated with meanings, or they can be
attributed meanings, or various other paraphrases. Sometimes we say that
some things have meanings. ii.
On other occasions we compare two different sentences and we say
that they are synonymous – meaning that they have the same meaning; as
we might say that ‘all men are mortal’ means the same thing as ‘no
man is not mortal’, or for a word, ‘bachelor’ means the same thing
as ‘unmarried man’. iii.
On the other hand we may say that a sentence or a phrase is
ambiguous – meaning that it has more than one meaning; as we might say
that ‘every man loves some woman’ is ambiguous. It may mean that every
man has a woman of his very own whom he loves, or it may mean that there
is a woman who is loved by every man. Or we might say that the word
‘dust’ has two meanings. To dust something may mean to remove dust
from things – like when we’re doing housework; or it may mean to put
dust on things – like when we’re preparing pastries or looking for
fingerprints. (Actually that’s quite an unusual ambiguity because the
two meanings are opposites of each other. Think of more for the tutorial.)
iv.
We also think that there are other sorts of relationships that
exist between meanings than mere identity or difference. The most
interesting of these being entailment. We think that we can know whether
some sentences are true or not just by knowing the truth or other wise of
some other sentences because the meanings of the sentences are related in
some special way. Thus we can know that ‘Bob is 6 feet tall’ means
that ‘Bob is more than 3 feet tall’. Or ‘Bob is a bachelor’
entails that ‘Bob is a bloke.’ Or ‘Cain killed Abel’ implies
‘Abel is dead.’ That’ll
do for a quick survey of the way the word ‘meaning’ gets used. I ask
you only to observe that in many cases the way that ‘meaning’ occurs
in those sentences is strongly reminiscent of the way that words are used
when they are being used to name some really existing object. To speak of
things having meanings, reminds us strongly of the way that people have
limbs, or children have toys, and so on. To speak of two meanings being
the same might remind us of our speaking of two cars being the same, or
two books, or two whatevers. To speak of a word having two meanings is as
if we were speaking of a person having two cars or two books. Of course we
don’t have to speak like this,
there’s almost always a way of paraphrasing our talk of meaning so that
it doesn’t look so much like we’re talking about objects, but that
would require making a conscious effort – and why should we do so unless
we’ve already decided that meanings can’t be anything like objects. This
is all to motivate the initial assumption that meanings are
objects of some sort. We can see why we should initially prefer a theory
of meanings that states that they are some sort of object. But what sort
of object?
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The Idea Theory
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The
first proposal is that we should take ideas to be those objects. The
theory is thus that: Meanings
are ideas
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Motivating the Idea Theory
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It’s
no great mystery why we would we say such a thing. Just think what we
usually have in mind when we ask what a speaker meant by stating such and
such. We usually want to know what it is that the speaker had in mind when
they made the statement. We want to know what thought they intended to
express – or at least to communicate – by making that statement. The
process as we imagine it is: the speaker has an idea in mind that they
wish to communicate, they translate that idea into some set of sentences
in a language, they make a statement using that sentence, and we hear the
sentence and translate out of it to discover the original idea. Thus an
idea has been successfully passed from one person to another. This
relationship has been widely recognised. In the reading that I gave you
you’ll see that Locke says that ‘words in their primary or immediate
Signification, stand for nothing, but the Ideas in the Mind of him that
uses them …’ [bk. 2, ch. 3] and similarly, we can find passages where
Hume says, for example [Enquiry, sec. 2], that When
we entertain, therefore, any suspicion, that a philosophical term is
employed without any meaning or idea (as is but too frequent), we need but
enquire, from what impression is
that supposed idea derived? And if it be impossible to assign any,
this will serve to confirm our suspicion. Finally
we may see that Aristotle taught Alexander that ‘spoken words are the
symbols of mental experience.’ [De
Int. 16a3] He also added the observation that ‘Written
words are the symbols of spoken words [an observation which, if it had
been taken to heart, would have very much speeded the translation of the
Mayan hieroglyphs]. Just as all men have not the same writing, so all men
have not the same speech sounds, but the mental experiences, which these
directly symbolize, are the same for all, as also are those things of
which our experiences are the images. We’ll
see the point of this clever observation in just a moment. Here we can
simply remark that from such observations and claims it is an easy step to
say that meaning just is the
corresponding idea. Indeed some of those authors would have certainly
believed that to be the case.
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Advantages of the Idea Theory
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The
advantages of the idea theory are fairly clear. To begin with it explains
the relationship that I’ve just suggested motivated the theory in the
first place. But consider also that it seems to be able to explain the
uses of the word meaning – what we might call the observed facts about
meaning – that we noted earlier. i.
Synonymy. To say that two sentences mean the same thing is the same
as saying that they are both associated with the same idea. ‘All men are
mortal’ expresses the same idea as ‘no man is not mortal’. This also
explains how it is that we can say, for example, that ‘Londres est jolie’
means the same thing as ‘London is pretty’; and ‘to ploion estin en
Byzantio’ means the same as ‘the ship is in Istanbul’. Apparently,
in each case, the sentences are just different ways of encoding the same
idea. ii.
Ambiguity. To say that a sentence can mean two different things is
to say no more than that the sentence can be associated with two distinct
ideas. In the example mentioned above, the sentence can be associated with
the idea that every man has a woman of his very own whom he loves, or it
can be associated with the idea that there is a woman who is loved by
every man. How we are to determine which association is to be understood
in any particular use of the sentence is a matter that need not detain us
here. iii.
Recall that we know that meanings are such that in virtue of the
relations between their meanings we can go from ‘Cain killed Abel’ to
‘Abel is dead.’ If we accept that ideas are the sort of things that
can have that sort of relationship then we can see how the idea theory can
explain that. There is an obvious sense in which some ideas contain
other ideas – as the idea of a BACHELOR
contains the idea of a MAN. Given
that it’s able to explain these facts, and it makes our
‘meaning’-talk interpretable almost naively, it looks like a good
first attempt at a theory of meaning.
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Problems with the Idea Theory
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Unfortunately,
it’s not that good an attempt. There are problems that make the theory
unacceptable. a.
What are Ideas? Images? The
first problem, which I’m not going to spend much time on, is just that
we really need a theory of what ideas are if we’re going to make them do
the work that we’ve set for them. In this respect you might think that, at
best, all this theory could achieve is to shift the explanatory burden
from a philosophy of language to the philosophy of mind. That may not be a
bad thing, maybe meaning is a
fundamentally mental act, but it doesn’t ultimately solve our problem of
how things (unspecified) come to
mean. Generally
speaking, people tend to think of ideas as being some sort of mental image
– like a picture being displayed in the theatre of the mind. The idea of
a dog is thus supposed to be a mental image of a dog. But this can’t
really be what’s going on, because my idea of a dog doesn’t include
all the things that a picture would have to include in order to be taken
as a picture of a dog. Moreover, a picture of a dog has to be a picture of
some particular breed of dog, be it poodle or schnauzer or beagle or
whatever. My idea of a dog somehow includes all these breeds. It can’t
be a composite picture because, for example, I don’t know what the
composite picture of a dog with a tail and one without a tail would tell
me. And then, of course, there’s the problem of our having ideas of
things that we just don’t have mental images of: like thousand-sided
objects, or people who are not the present king of France. Again, for
mental images to be the meanings of terms they have to somehow be
associated with those terms, but it’s not at all clear how this
association is to be understood. It can’t be just any sort of
co-occurrence, because I can have mental images of any sort going through
my head while I’m talking to you right now without that changing in the
slightest what I’m meaning when I’m talking to you. Just then I was
thinking of pork chops – but you’d be wrong to think that I was
talking about pork chops – until now, that is. For
this and other reasons the idea theory rather hangs in limbo until someone
comes up with a more reasonable story of just what is to count as an idea.
Until then the recourse to ideas looks like sweeping the problem under the
carpet. (And it’s no good just saying: well, we’re not talking about
mental images, it’s more like a ‘concept’, or a ‘thought’, or
some other similar term. That’s just pushing the problem around under
the carpet.) b.
Compositionality We’ll
continue to talk about mental images as a place-holder for a satisfactory
theory of ideas, but even if some reasonable story about ideas could be
told, that wouldn’t be the end of the problems for the theory. There’s
also the problem of maintaining the principle of compositionality. If the
meaning of a sentence is to be understood as the compositional product of
the meaning of the terms that occur in the sentence, then do we not have
to assume that all the terms that occur in the sentence are themselves
meaningful? If that’s the case then there’s a problem because many
terms that occur in a sentence just don’t seem to be associated with any
sort of idea. When I say ‘the pen is in my hand’, I’m quite happy to
say that the idea for ‘pen’ could be a mental image of a pen
(fountain, ball point, quill?), and the idea for ‘hand’ could be a
mental image of a hand, but what am I supposed to be associating with
‘the’ or ‘my’ or ‘in’ here? It doesn’t seem that there’s
any idea associated with those terms at all – certainly there’s no
image involved. Isn’t this then the same as the Millian reference
problem? If there are things without meanings/ideas in
the sentence then the meaning/idea of
the sentence can’t be just a compositional result of the meanings of the
parts. Well,
maybe. I don’t know that I find this a particularly convincing
objection. I suppose it is possible that the idea theorist could claim
that there are two kinds of term in a language: there are, first, the
terms that are associated with ideas, like ‘hand’, ‘pen’, and so
on; and, second, there are terms that are not associated with ideas but
which tell us how the other ideas are to be composed into a larger idea.
In that case, if we wanted, we could claim that there are two types of
meanings. There are meanings that are ideas, and there are meanings that
are functions. In either case it would be OK for us to say that the
meaning of a sentence is the compositional result of the meaning of its
parts. c.
Intersubjectivity We
want the meaning of ‘dog’ to be the same for everyone who understands
the word. We want the meaning of the sentence ‘Napoleon was a coarse
man’ to be the same for everyone who understands it. Meaning has got to
be intersubjective. But some people argue that this can’t be the case if
meanings are going to be equated with ideas, because ideas are
paradigmatically subjective;
they exist wholly and only in people’s minds (ignoring for the moment
objections about the reality of wide
content such as Putnam and twin-Putnam would make.) Everyone has their
own mental image of a dog or of Napoleon and there is no reason to think
that they’re going to be identical with each other. In fact, even if the
mental image of Napoleon was exactly the same in each person they still
wouldn’t be identical: there would still be more than one meaning for
each term. I
suppose you could claim in this case that you weren’t really interested
in ideas or mental images themselves, but rather in ideas or mental images
as types; just as our theory of grammar likes to talk about sentences but
doesn’t care about any particular token of a sentence. The sentences
that I’m uttering are tokens of a type that the grammarian is
interested in, but then the theory that we’re proposing is not a
theory of ideas as meanings, but of some strange abstract objects that
constitute the similarities between ideas as meanings. This is a
reasonable idea in itself, but it would require some development and
certainly lacks the obvious clarity of the idea theory. Perhaps we should
look at the plausibility of such a thing.
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The Proposition Theory
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Our
second proposal is that we should take propositions to be the objects that
are identifiable with meanings. The theory is thus that: Meanings
are propositions.
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Motivating the Proposition Theory
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We’ve
already seen one reason why the idea theorist might be persuaded to move
into a claim that he’s not interested in actual ideas but in some
abstract object that ideas have in common. There’s another reason too,
and that is that there are sentences that seem to be meaningful but do not
correspond to any actual ideas in anyone’s mind. Let’s suppose that I
run one of those automatic text generating programs that you can find on
the internet. I pipe all its output straight into a speaker mounted on a
rock in the Gobi desert. There it emits perfectly reasonable sentences
that have never been heard by anyone and have never given rise to any
ideas in anyone’s mind. In what way could an idea theorist claim that
the sentences are meaningful because of their being somehow in a
relationship with an actual idea? He could not. And yet, we can look at
the record of the sentences generated and see that they were meaningful
even before we looked at them, so there has to be something other than the
corresponding existent idea which gives them meaning. One
way to answer this problem is to make the move from actual ideas to things
that are potential ideas – or perhaps we might say, that are potentially
the contents of ideas. These odd, abstractions we call propositions. On
this story the sentences being broadcast over the Gobi are meaningful
because they are in some sort of correspondence with thinkable thoughts.
They are said to express certain propositions.
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Advantages of the Proposition Theory
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The
advantages of propositions over ideas are pretty clear. Since they are
clearly closely related to ideas themselves we can convince ourselves that
they continue to explain the relationship that motivated the idea theory,
and they also seem able to explain the uses of the word meaning that we
noted earlier. i.
Synonymy. Rather than saying that two sentences mean the same thing
just when they are both associated with the same idea, we can say that
they are synonymous if they are both associated with the same proposition,
with the same potential contents of ideas. ‘All men are mortal’
expresses the same proposition as ‘no man is not mortal’. The same is
of course true for sentences in different languages that are supposed to
be saying the same thing. ii.
Ambiguity. We say that a sentence can mean two different things
when it is possible for it to express two distinct propositions. Once
again we are able to set aside the problem of how to determine which
association is to be understood in any particular use of the sentence. iii.
Finally, we can explain how it is that meanings are such that in
virtue of the relations between their meanings we can go from ‘Cain
killed Abel’ to ‘Abel is dead.’, but again, only if we accept that
propositions are the sort of things that can have that sort of
relationship. This is actually an improvement over the idea theory
because, whereas in that theory we had to be satisfied with a merely
metaphorical claim that some ideas contain
other ideas – as the idea of a BACHELOR
contains the idea of a MAN –
it is much less controversial that a proposition can be in an entailment
relationship with another proposition. More
than this of course the proposition theory looks like it’s able to avoid
the problems that we found for the idea theory. iv.
There is no temptation to think of propositions as images (some
Wittgensteinian claims notwithstanding), and therefore the problems that
arise in equating meanings with images do not arise for propositions. It
is not the case that we think that a proposition about a dog has to be a
proposition about some specific sort of dog. Nor do we think that it
entails that the dog have or not have a tail. On
the other hand we may have to answer questions about how a proposition is
to correspond to the content of thoughts about the nonexistence of things,
or about people who are not in
possession of some property (e.g. being kings of France), or about
chiliagons. Presumably, this could be done if we could tell some sort of
story about the compositionality of propositions. v.
Which brings us, of course to another difficulty that was noted for
the idea theory. We want it to turn out that that the meaning of a
sentence is the compositional product of the meaning of the terms that
occur in the sentence. Thus the proposition that a sentence expresses has
to be the compositional product of the propositions that the terms of the
sentence express. Most people will think that’s OK
because they think that the content of ideas is some sort of compositional
thing; but, generally speaking, we don’t think that that parts of a
sentence like ‘the pen is in my hand’ are the sorts of things that
count as propositions. We really want propositions to be the sorts of
things that can be true or false, and it makes very little sense to
propose that a so-called ‘proposition’ that could be expressed by
‘pen’ is either true or false. In fact, we typically declare that
propositions are compositional products of propositions or
concepts, where concepts are supposed to be the abstract,
content-relevant things that are expressed by terms like ‘pen’,
‘hand’, etc. [synonymy – ‘pen’, ‘plume’, etc.; ambiguity –
‘pen’, ‘hand, etc.; entailment – ‘bachelor’, ‘man’, etc.]
They are the abstract equivalents of the ideas of pens, hands, and so on. Of
course there is still the problem of assuming that there is a concept to
be associated with ‘the’ or ‘my’ or ‘in’? It doesn’t seem
that there’s any concept to be expressed by those terms any more than
there was an idea to be expressed. For the time being, however, I’m
still inclined to think that the proposition theorist could make the same
sort of reply that the idea theorist could make to this objection – that
there are two kinds of terms in a language, one that expresses concepts,
and another that tells how the concepts are to be put together to form
propositions. vi.
Finally, we can see that these propositions are just the sort of
thing that can play the necessarily intersubjective role that we require
of meanings. That was one of the reasons for proposing that some abstract
object of this general kind should be tried in the role in the first
place.
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Problems with the Proposition Theory
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So
much for all the good things: are there any serious problems with the
propositional theory that we should be aware of? Of
course there are! a.
What are Propositions? The
first problem, just like the first problem we had with ideas, is to
discover just what it is that we think we’re talking about when we’re
talking about propositions. At the moment all that we know about these
things is that they are supposed to be the ‘content’ of ideas; or they
are whatever it is that ideas have in common when we want to call them the
same idea – which isn’t a very enlightening sort of clarification. In
order to discover a more useful definition of propositions it might be
useful for us to have a look at some of the other things that we know are
true about propositions. i.
To begin with we know that propositions are found in association
with sentences that are making claims about the states of affairs that
obtain in the world. A proposition can be found associated with a
statement or a sentence like ‘the cat is on the mat,’ or ‘the first
essay is due in just about 2 weeks,’ or ‘if only the sun would shine I
would go to the beach.’ It is not found with sentences like ‘Sit down
and be quiet!,’ or ‘who’s that talking?’, or ‘if only there were
chocolate biscuits on the table.’ As
a consequence of this we know that propositions are the sorts of things
that are true or false. (Let us say for argument’s sake that this is
because they do or do not systematically correspond to the facts about the
world.) We cannot say that sentences themselves are true or false because
we know that a sentence like ‘the door is closed’ can be true at some
times and places and false at other times and places. The proposition
expressed by the sentence, however, is always either true or false,
because it is taken to correspond to an entire state of affairs. ii.
We identify propositions in order to talk about them by putting the
sentence that expresses them (or some reasonable paraphrase thereof) in
the scope of a coordinating word ‘that.’ Thus we can talk about the
proposition that the cat is on the mat, or the proposition that the first
essay is due in just about 2 weeks, or etc. We do not identify any
proposition that sit down and be quiet – though there is
an implied proposition that one
should sit down and be quiet. And so on for the other examples. One
of the things that this naturally leads us onto is the fact that
propositions are said to be the sorts of things that we can take
‘attitudes’ towards such as belief or doubt or hope or such like. Thus
we can believe that the first
essay is due in just about 2 weeks, or we can doubt that if only the sun would shine I would go to the beach, and
so on. We’ve looked at propositional attitudes quite a bit in the past
because of the referential opacity of statements of that form. 1.
Russell’s View Perhaps
taking his cue from the second of these observations, Bertrand Russell
proposed that we should define propositions as ‘what
we believe when we believe truly
or falsely.’[1]
And he too says that we should think of propositions as the contents of
beliefs; but he realises that this needs need to be expanded by a story of
what a belief is. Thus: When
a belief, not expressed in words, is occurring in a person, and is
constituted by the feeling of assent, what is actually happening … is as
follows: (a) we have a proposition, consisting of interrelated images, and
possibly partly of sensations; (b)
we have the feeling of assent; (c)
we have a relation, actually subsisting, between the feeling of assent and
the proposition assented to. So
it rather looks like Russell has in mind as the content of belief
something like the representational power of an image supplemented by
sensation data – and I think we have presented sufficiently many
objections to images or their derivative to be able to discount this idea.
2.
The Intensional View These
days, a more popular idea than Russell’s is the view that propositions
are sets of possible worlds. To see how this works we can consider the
sentence:
The cat is on the mat. This
is said to express a proposition; namely, the proposition that the cat is
on the mat. What is this proposition? Well, the basic idea is that the
proposition being ‘expressed’ is the set of all possible worlds in
which the statement would be true. This seems to be an approach taking its
cue from the first of our two observations just above. How does it handle
the facts about meaning that we’ve been interested in? i.
Synonymy. Two sentences mean the same thing if they are both
associated with the same set of possible worlds. ‘All men are mortal’
expresses the same proposition as ‘no man is not mortal’ because it is
true in all the same possible worlds. The same is of course true for
sentences in different languages that are supposed to be saying the same
thing. You may already have spotted a problem with this: that is that on
this view the sentence ‘2+2=4’ means the same thing as ‘1+1=2’
because those statements are both true in all the same worlds. (I.e. all
the worlds.) There is a solution to this and we’ll get to it in just a
moment. ii.
Ambiguity. We say that a sentence can mean two different things
when it is possible for it to express two distinct propositions – and
this is to say that it can be taken to determine two distinct sets of
possible worlds. iii.
Best of all, we can now explain
how it is that meanings are such that in virtue of the relations between
their meanings we can go from ‘Cain killed Abel’ to ‘Abel is
dead.’ Curiously enough, it involves us returning to the notion of one
meaning containing another. Now when we say that the meaning of
‘bachelor’ entails ‘man’ we can say that this is because the set
of possible worlds in which some specified thing is stipulated to be a
bachelor is completely contained within the set of worlds in which that
thing is stipulated to be a man. And
the supplementary facts that we’ve been looking at are also explicable
on this theory. iv.
Clearly there is nothing like imagery going on here and therefore
we can see why the problems that arise in equating meanings with images do
not arise for propositions considered as possible worlds. The set of
possible worlds in which something is stipulated to be a dog is not
necessarily identical to any set of possible worlds in which that thing is
stipulated to be some specific sort of dog; in fact it includes
any such set. Nor does the set of possible worlds so specified make any
distinction between dogs with or without tails. We
also have a ready explanation for how a proposition correspond to the
content of thoughts about the nonexistence of things, or about people who
are not in possession of some property (e.g. being kings of France), or
about chiliagons. For example, the proposition that there is no present
king of France is simply the set of possible worlds in which it is true
that no king of France exists. Note that this is the complement of the set
of all those possible worlds in which it is true that a king of France
exists. This seems to suggest that the negation of a proposition is
equivalent to the set theoretical complement of the proposition thought of
as a set of possible worlds. v.
Which takes us naturally to the desideratum of compositionality for
propositions. It turns out that there is a very natural way in which most
of the sorts of compositionality that we’ve been considering so far can
be explained by the possible worlds view. We
can start by continuing the story that we started for propositions that
are truth-functional compositions of other propositions, i.e. that are of
the form not A, A or B, A and B, if A then B, and so on. We’ve already
seen that that the set of possible worlds that constitute the proposition
or the meaning of not A (call it M(not A)) is just the complement of the
set of possible worlds that constitute the proposition or the meaning of A
(call it M(A)). Similarly: M(A or B) = M(A) union with M(B) M(A and B) = M(A) intersection with M(B) M(if A then B) = M(A)c union with M(B)
And
so on. Of course these aren’t the most interesting sorts of composition.
The way that we interpret the proposition ‘The cat is on the mat’ depends
upon us translating the sentence into its logical form – which is
basically the Fregean subject-predicate form that we saw when we were
looking at Russell’s description theory. Such a sentence becomes
something like: On (the cat, the mat) In
this ‘translation’ we have a couple of singular terms and a predicate.
(Don’t worry about the details here.) We treat the terms as picking out
certain objects in every possible world in which they have an application,
and we treat the predicate ‘On’ as picking out pairs of objects in
every possible world such that the first element is ‘on’ the second
element. The sense/meaning/proposition of the sentence given is just the
set of possible worlds in which ‘the cat’ and ‘the mat’ pick out a
pair of elements which occur in the extension of the predicate ‘On’.
And, as you can see, that is just the set of possible worlds where the
statement that the cat is on the mat is true. There’s
plenty of room for improvement in this story, but at this point I’m only
really interested in giving a rough indication of the story that the
proposition theorist can tell. If you want to know more about this I can
recommend a couple of good books, but they’ll all involve a fair bit of
logical notation and some familiarity with phrase structure grammars,
which makes them look harder
than they really are. vi.
Finally, we can see that the possible world view of propositions
gives us the intersubjective role that we were hoping to find for
meanings. It’s quite clear how the propositions can be claimed to be
intersubjective: it’s because the sets of possible worlds with which
they are to be identified are completely independent of and individual.
They exist as some sort of strange abstract object. Now
the fact that propositions as sets of possible worlds exist as some sort
of strange abstract object gives rise to another problem, but we’ll come
back to that. Let’s deal now with the problem that we saw earlier that
the possible worlds theory doesn’t seem able to distinguish between
propositions that are true in all the same possible worlds but intuitively
‘mean’ different things. The solution that is generally offered for
this problem (originally by Carnap[2])
is to appeal to the structure of the intension as well as to its final set determination. Briefly speaking this
means that you can think of the meaning of a sentence as the intensional
structure that determines the set of possible worlds. If we were to take
this view of things then we’d be able to distinguish the meaning of
‘2+2=4’ from that of ‘1+1=2’ because the intensional structure is
different. The difference is reflected in the routes by which we arrive at
the two extensionally equivalent sets of possible worlds in which the
statements are true. b.
What use are Propositions? So
much for the difficulty of determining what a proposition is supposed to
be. But now we’ve got ourselves to a position where, in order to explain
the meaning of sentences we have to suppose that there are these peculiar
things possible worlds. And not only that, but we have to assume that
it’s not even the possible worlds that are the important things in the
theory but sets of possible worlds. And that’s not the worst of it
because in order to account for all the meaning facts we are going to have
to assume that it’s abstract structure imposed upon these sets.
There’s a couple of objections that can be raised to this. 1.
Occam’s Razor Are
these really the sorts of things that we want to let into the world?
There’s a famous methodological rule of thumb known as Occam’s razor
(also Ockham, etc.) that states ‘entities are not to be multiplied
beyond necessity.’[3]
It means that we should prefer theories that require us to admit as few
new things into the world as possible. (It’s general intent is that the
simplest theory is the best theory.) The objection could be raised, has
been raised, that we are letting into the world a lot
of new objects. Well,
maybe. We’re not actually letting into the world a lot of new kinds of objects. There’s just a lot more of one kind of thing.
And, in fact, we aren’t admitting a new kind of thing at all since all
the possible worlds are just the same kind of thing as the actual world
– they differ only in that they are not actualized, and that’s not an
essential difference. This is one of the responses that David Lewis used
to give to people who queried his claim that possible worlds are real. He
reported that he didn’t get many arguments against this, just an
‘incredulous stare.’ You can certainly be forgiven if you don’t find
it convincing. It’s strongly reminiscent of the Meinongian claim about
the reality of subsisting nonexistents. On
the other hand, we should bear in mind that the Occams’ razor says that
we can’t multiply entities beyond necessity,
and in this context necessity has to be understood as referring to what is
required in order to have an explanation for the things that the theory is
trying to explain. I’ve mentioned several times that Gravity was
objected to on these sorts of grounds, but because it turned out that the
gravity-theory was the best and simplest theory to explain all sorts of
things gravity was eventually accepted as a member in good standing of the
club of necessary entities. If we had a theory that could explain the
meaning facts as well as the possible worlds theory does then we’d be in
a better position to reject the entities that the theory requires.
Unfortunately, the intensionalists say, there isn’t one; so we’ll just
have to bite that bullet. 2.
Causal Power Finally,
we have to ask whether the sorts of abstract objects that we’re
proposing for propositions can play the causal role that we think is
essential for meaning. We think that the fact that the sentences that we
use have meanings is essential to the actions that we and those to whom we
speak take actions. But this means that meanings have to have some sort of
causal power. How can this be if they’re just this sort of weird
abstract object? Similarly,
how can we understand sentences by coming to have some sort of causal
relationship with propositions? If the mind is the causal effect of the
operation of the brain, then understanding a sentence must have some
causal correlate that relates the brain and the abstract object that is
the meaning. But how can this be the case? There
are lots of similar sorts of problems but I think I’ll leave these for
those of you who are interested to explore in an essay question.
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