Universität Osnabrück
Institute of Cognitive Science
Bachelor's Thesis
How tall is John?
A semantic study on the relationship between vagueness
and context-dependence of adjectives
Katharina Berndt
March 29, 2011
1st supervisor: Prof. Dr. Peter Bosch
2nd supervisor: Oleksandr Alyeksyeyenko
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To my grandparents;
without whose support
I wouldn't have been able
to go to university in the first place.
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Contents
1 Introduction
4
2 Vagueness
6
2.1 What is vagueness and where does it occur?
6
2.2 Characteristics of vague expressions
8
2.3 Why there is vagueness and why we need it
11
2.4 Different approaches on vagueness
12
2.5 Gradable adjectives and their role regarding vagueness
14
2.5.1 Gradable adjectives vs. non-gradable adjectives
14
2.5.2 Relative and absolute gradable adjectives
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2.5.3 The positive and comparative
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2.6 Vagueness and other phenomena
3 The sorites paradox
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23
3.1 The sorites paradox resolved by Bosch (1983)
23
3.2 The sorites paradox resolved by Gross (2009)
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4 Context-dependence
27
4.1 Definition of context-dependence in general
27
4.2 Van Rooij (2010) and Bosch (1983) on context-dependence
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5 Conclusion
32
References
33
Acknowledgements
34
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1 Introduction
It seems to be quite an alluring idea that the reason for us being able to
communicate and understand each other arises from the fact that we are in a
position to precisely say what we want. As competent speakers of our mothertongue we should be able to exactly say what we mean, and thus any kind of
inaccuracy should be reduced to a minimum.
But as it appears, this is not the case at all. When looking a bit closer we can see
that we are hardly ever absolute precise in our communications. But why is it,
then, that our language, spoken and written, is full of so-called vague expressions?
Are we not as competent as we think? Are we too ignorant? And do we actually
need to be super precise all the time for people to understand us?
Vague expressions exist in almost all lexical categories and one of the most
common examples linguists use when trying to introduce the phenomenon of
vagueness is the following:
(1) John is tall.
Here, it is obviously the adjective tall that makes this perfectly understandable
sentence in some way intangible and hard for us to judge. How tall do you need to
be to be called tall at all? What about different contexts that require different
comparison classes (that is groups of objects we are comparing the object in
question to) and thus allow for different things to be tall? Why can we say
(example taken from Ludlow (1989)): “This elephant is large and this flea is too”
although a flea is obviously not as big as an elephant? Is it only the context that
matters when dealing with vague expressions?
This thesis is an account on vagueness in general and on vague adjectives
especially. I am going to present different accounts on vagueness and contrast it
with all kinds of phenomena that come along with it, such as ambiguity,
subjectivity, or imprecision. In the last part of the thesis I will portray contextdependence as a feature one needs to talk about when dealing with vagueness, as
vagueness cannot be motivated without linking it (to whatever degree) to contextdependence. My main goal is it then to show in what way vagueness and contextdependence are related and how they both can be accounted for.
Along the way, I will focus on two more questions. On the one hand I want to
examine to what extent vagueness is a phenomenon that (when concerned with
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adjectives) can be seen in the positive form only and why the comparative appears
to be context-independent and can thus not be called vague. On the other hand I
will deal with the question of how the sorites paradox plays a role in the field of
vagueness and furthermore how it can be solved.
I will show you that vagueness is basically everywhere and that it is an inevitable
linguistic feature more often than we think it is. So let's find out, then, how tall
John really is!
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2 Vagueness
In this section I will explain the term vagueness in detail and some of the
phenomena that come along with it. Furthermore I will give a precise overview of
gradable adjectives which play a big role in the examination of vagueness.
2.1 What is vagueness and where does it occur?
On linguistic grounds, vagueness is a complex and multilayered phenomenon that
exists in different forms in almost all lexical categories. Most of the time we are
unaware of the vague use of language and only stumble across it on closer
inspection. Let's take for example sentence (1).
(1) John is tall.
A sentence everyone understands and at least at first has a rough idea of what it
means. But what exactly does it mean for John to be tall? Even if we knew that
John's height was 1.80m we could not render (1) true or false because the adjective
tall is vague and hence we would need more information to decide whether the
sentence is true or false. So the inability of rendering sentences containing a vague
predicate true or false due to a lack of background information may be a first idea
for what it means for a sentence to be vague. Still talking about (1), we would need
to know who or what we are comparing John to, to actually be able to say that John
is tall or not. Surrounded by 12-year-olds we could truthfully assert that John is
tall, whereas in a scenario where John is amidst a team of NBA basketball-players
we would hardly call him tall at all. And comparing him to the average western
man we wouldn't really know whether to call him tall or not. Some may call John
rather tall, others would say he is neither tall nor not tall, and others again would
say he is just not to be called tall anymore.
But not only do we use vague language unknowingly in everyday
conversation, in certain situations we happen to leave things vague quite knowingly
and use vagueness as a linguistic device. In the following I am going to present
some examples of where we make use of vague expressions.
When:
- wanting to be polite and say: “There are a few things that I didn't like about your
presentation” when actually I didn't like it at all,
- wanting to be less precise. It is absolutely appropriate to talk about the 50.000
people that came to the stadium to see the Rolling Stones play when actually there
were exactly 50.134 people,
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- we do not know better. “It is my grandma's birthday next weekend. She's gonna
be really old”,
- wanting to leave room for interpretations or even indirectly leading in the wrong
direction as in the course instructor's “This won't take long” regarding the
homework.
All these examples show that there is vagueness almost everywhere where we are
concerned with language. The percentage of vague language use is obviously larger
in spoken than in written language but still it is a pervasive feature that one needs
to address when dealing with the semantics of language.
So apparently adjectives like tall are vague. Other examples for vague
adjectives are expensive, long, old, or red. What price do you have to pay for a car
for it to be expensive? How many pages must a book consist of to be a long book?
How many months or years ago must this book have been published to be an old
book? And even colours are vague: When does an apple start being a red apple? All
these examples show very clearly that the use of vague language is common and
part of our everyday life communication. But not only adjectives are vague. Also
nouns can be vague. In connection with linguistic theories on vagueness the most
famous noun being vague would be the word heap. How many grains must an
accumulation of rice contain to be called a heap? (I will go into more detail with
this specific example in sections 2.2 and 4.) The same counts for nouns like table
or chair, although their ostensive character is not as strong. What features must an
item have to be called a table? How many legs does it need, does it need legs at all,
would not a simple rock on a meadow count as a perfect picnic-table? The next
lexical category containing vague members is the category of verbs. At what pace
do you start to amble and when does your ambling become walking? What does it
mean for you to say: “I understand.” in any given context? Also adverbs like very
or rather can be vague. How heavy must something be to be very or rather heavy?
The same holds for quantifiers like some, many, or a few, and prepositions like
after or in front of. I will spare the examples for the last two categories as I think
the pattern should be clear by now. In this thesis I will concentrate on adjectives as
to me they are the most interesting and complex cases whilst examining vague
language.
As all these examples show, vagueness must be closely linked to meaning.
What does it mean for someone or something to be tall, a heap, ambling, very
heavy, some meters away, or in front of a pharmacy? Channel (1994) suggests that
meaning is the result of adding up semantics and pragmatics, that is combining the
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meaning of words with the context in which they are uttered. But still, although
appealing and surely true, this does not explain the phenomenon or even the
existence of vagueness. Bosch (1983) argues that vagueness arises due to
incomplete definition, that is to the fact that we can never know about every single
item we would assign a certain predicate to. He uses the example of a rose and how
we get to know which flowers to call a rose and which not. Simply put, we get told
about some flowers that they are roses and others that they are not. We will never
come to the point where we have seen every single flower there is, and hence must
on our own –only based on our experience with flowers– create a definition for
roses, so that when confronted with a new flower we can decide whether this is a
rose or not. But this obviously does not work all the time. As Bosch (1983) puts it,
there will be cases for which our predicates are not defined. So strictly speaking,
every time we are talking about roses, we are talking about a vague and incomplete
concept of roses. Most of the time in our day-to-day interactions this is of no
interest for us and does not even bother us. I would say we are not even aware of
the very frequent use of actual vague language; and we do not need to as we –at
least most of the time– can communicate and understand each other quite well.
2.2 Characteristics of vague expressions
Ullmann (1962) points out that not only expressions we address vagueness to are
vague but that the term vagueness itself is rather vague. There exists no above all
definition of vagueness and different linguists or philosophers all define vagueness
slightly different so that according to linguist A something may definitely be vague
while linguist B strictly disagrees and philosopher C cannot decide because his
definition lacks for exactly that item. Still there are some important characteristics
which vague expressions must have almost everybody agrees on. The first
characteristic is the already mentioned inability to ad hoc render a vague
expression true or false, or put differently, the fact that the same expression may be
true under circumstance A while false under circumstance B. This goes hand-inhand with Bosch's also already mentioned idea that vagueness arises where there is
a lack of definition. Let's again take a look at the adjective tall. As we have seen at
the beginning of this section, (1) can be true or false, depending on what exact
situation it is referring to. And this again is due to the fact that tall is not fully
defined, that is it lacks information about whether being 1.80m counts as being tall
or not in any given context. Another very common characteristic of vague
expressions is that they allow for borderline cases.
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(2) This book is long.
For a 50-page book, we can certainly say that (2) is false. For a 450-page book we
can doubtlessly state (2) as true. But what about a book that consists of 100 pages?
I assume that some people would agree, others would disagree and I myself would
say the book is neither long nor not long. So in this third scenario, we are dealing
with a borderline case of length (of a book). And now we are not only dealing with
our two truth values true and false but with a third one also, namely maybe/in some
cases yes, in some cases no/neither-nor. That sounds quite appealing in theory but
looking at it more closely we find ourselves confronted with the next problem: Not
only is there no clear boundary between those cases in which our expression turns
out true and those where it does not (and thus we 'invented' the area of borderline
cases), now we have to find a boundary between the true cases, and the false ones
respectively, and the borderline cases. And here we are again, we have to define
some grey area and are entering a vicious circle. This theory of trying to find
boundaries between all the different areas is known as higher order vagueness.
So in theory, the idea of borderline cases is quite helpful to get a first hint
whether an expression is vague or not, but in the end it does not get us any further
in actually finding out where exactly in an expression vagueness is buried. Van
Rooij (2010) sketches a view on which it is exactly the lack of boundaries that
makes a predicate vague; hence there cannot be clear borderline cases. It is
impossible to draw a line between the cases of which a predicate is true and those
of which it is false; even if we know there must be a grey area somewhere it is
impossible for us to clearly draw a line here also. In the end it is impossible for us
to draw any line at all and thus, according to this view, there cannot be any
boundaries. This theory –as opposed to the borderline theory– also works quite
well in practice, still it's ostensive character is not as strong.
Lakoff (1970) developed a test to decide whether a sentence is actually vague
or only ambiguous. He gives the following examples: 'Selma likes visiting
relatives' and 'The chickens are ready to eat' as clear cases for ambiguity, whereas
he states 'Harry kicked Sam' and 'Max left for Rome' to be vague. The ambiguous
cases are quite clear while the vague ones need some more clarification. For
Lakoff, the vagueness lies in the fact that we do not know if Harry kicked Sam with
his left or his right foot, and that we do not know from where, for how long, and on
what purpose Max is leaving for Rome. His test to check if we were right about our
assumptions on these four sentences is now to append an 'and-so-does-X' to each of
the sentences and see under which circumstances the new sentences are true. The
sentence 'Selma likes visiting relatives and so does Mary' is true when either both
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girls like to visit their relatives or when they both like having their relatives over. It
can not mean that Selma likes to visit her relatives while Mary likes it to have her
relatives over. When the new sentence can only be true when both persons are
actually liking the same thing (regardless of which one of them), then the sentence
is ambiguous. The sentence 'Harry kicked Sam and so did Mary' on the other hand
can be true if both, Sam and Mary, kicked Harry with their right foot, if both used
their left foot, but also when Mary uses her left and Sam his right foot. If the new
sentence can be true in case both persons are not doing the exact same thing, then
the original sentence must be vague. So this is a nice test to distinguish ambiguous
from vague sentences, but at the end of the day there is not much more to it than
this.
Van Rooij (2010) discusses yet another characteristic of vague predicates,
namely tolerance and states: “[A] vague predicate is insensitive to very small
changes in the objects to which it can be meaningfully predicated.” Proponents of
this view hence believe that minimal changes of the original object do not
influence the outcome of the sentence; that is, for example, if in (2) we are not
dealing with a 450 page book but actually with one consisting of 449 pages and
still our truth values would not change. This sounds very reasonable as especially
in our daily conversations it seems that this may be the reason for us getting along
so well with our actually quite vague language: It makes no difference to us
whether the book in question has 449 pages, 450 pages, or 452 pages. The range of
change is just too little to bother us. So tolerance allows us to treat very similar
objects under equal
circumstances the same. This idea brings us now to a
phenomenon closely related to tolerance, namely to the paradox of the heap, also
called the sorites paradox.
The paradox results from the fact that predicates like is a heap, is a small
number, or is tall are vague. Let us take a closer look on the predicate is a heap.
Premiss 1:
An accumulation of 1.000.000 grains of rice is a heap.
Premiss 2:
Removing one grain from something that is a heap still
leaves a heap.
Conclusion: One grain of rice is a heap.
Although both premisses seem to be true, the following obligatory conclusion is
definitely false. The question that arises now is where did what go wrong? The
paradox makes use of the same fact that the phenomenon of tolerance does, namely
the indiscernible changes in an object that still makes us agree on the truth values
of our utterances. It simply does not matter whether we are talking about a million
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or only 999.999 grains of rice as it does not make any difference. Why, then, do
vague predicates give rise to this paradox and why are we so tempted to perennially
believe in it although there exist some nice ideas of how to actually dissolve the
paradox? These questions I am going to address and try to answer in chapter 4.
2.3 Why there is vagueness and why we need it
Not only is vagueness almost everywhere where we are dealing with language, I
would go so far as to say that vagueness is an important if not necessary feature to
successfully communicate in the first place. Channel (1994) states that “[...]
understanding of vague language use in English would appear to be valuable in any
field which teaches, analyses, or uses English language.”. This becomes clearer
when on the one hand we see foreigners speaking english on a rather high level and
still feel that they sound somewhat clumsy and too intent on being correct, all of
which is due to their inability to use vague language; while on the other hand we
have native english speakers who for academic purposes need to learn being more
precise. So adapting to a new language requires the learner to somehow lose some
of his strict and very correct understanding of the new language, while mothertongue speakers often have their difficulties when it is appropriate to be less vague.
(cf. Channel (1994))
Most of the time when we are dealing with a vague term put into a sentence,
this sentence will in the end turn out to be vague itself. On the assumption that old
is a vague term, chances are good that the sentence 'I am reading an old book.' is
also vague (which it actually is). Van Rooij (2010) points out that this does not
always have to be the case. Sometimes vague terms can be helpful to make a
statement more specific, especially when we are dealing with measure phrases.
Combining a measure phrase like 3 feet with the vague term tall gives us the more
precise phrase 3 feet tall. (cf. van Rooij (2010)) We can already see that vagueness
–although the term itself is afflicted rather negatively– has some advantages and
positive traits to it which are helpful in communicating with others.
What is of importance here is that the “[…] speaker's intention and hearer's
interpretation have sufficient overlap. How much overlap is sufficient is at stake
[…].” (van Rooij (2010)) Bosch (1983) thinks likewise and states that “[…] precise
communication […] is an interactive process […]”. That is we do not need to be as
precise as possible to be understood, we only need to know how precise we have to
be. And that differs from context to context. When talking to my linguistic-wise
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unversed friends about some new findings concerning the sorites paradox I
probably should not go into too much detail –hence leave some things rather vague
on purpose– so that I do not bore or lose them along our conversation. On the other
hand, if I were to talk like this to some linguistic students about the exact same
findings they would probably tell me to go and read up on it again. Here it would
be appropriate for me to be more precise and to use my knowledge about the
linguistic skills and competence of my conversational partners. By choosing how to
talk to different people about the same thing, I am trying to match their contextmodels (of the subject in question) and intentions (of our conversation) with my
own to better guess how precise I need to be for them to understand me. As Bosch
(1983) puts it, the speaker needs to adjust to his audience by adding specifications
or leaving them out intentionally. He further states: ”Human communication in
general […] is a matter of reconstructing the other's context-model as a part of
one's own context-model.” This counts for the above mentioned case, where I have
to figure out how great a knowledge about semantic theories my opponent has, but
also for less complex situations. It makes a huge difference when we are talking
about different context-models while thinking we are in sync about them; for
example, when we talk about the god we believe in. While I believe in Buddha, you
believe in Allah, and a third person's 'god' may be Mother Nature. When all of us
assume we are talking about the same god we would probably not get very far in
our conversation, all of this due to wrong presuppositions about the other's contextmodel.
All of this shows that the phenomenon of vagueness is a rather complex,
interesting and important one in the semantic study of language. As it is such a
broad and (I am tempted to say) vague field, there have been many theorists trying
to narrow it down and this is why there are different approaches on vagueness; the
most common ones of which I am going to present in the next section.
2.4 Different approaches on vagueness
There are three main approaches on vagueness which I will shortly introduce and
criticise in the following.
The first one is called fuzzy logic, an opponent view to the prevalent twovalued logic where we only have the two possibilities of something being either
true or false. Fuzzy logic however belongs to the family of many-valued logics as it
is dealing with infinitely many truth values. That is we are dealing with a scale of
truth values from 1 being fully true to 0 being absolutely false.
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(3) The cologne cathedral stands in Cologne.
(4) Osnabrück is the main city of Lower-Saxony.
(5) Osnabrück is a large city.
A sentence like (3) would thus yield 1 as its truth value as the sentence is obviously
correct. (4) on the other hand, would yield 0 as a result because it is Hannover that
is the main city of Lower-Saxony. These examples are still pretty clear and in no
way different to the two-valued logic approach. But while a sentence like (5) could
neither be valued true nor false with the two-valued logic ad hoc, applying fuzzy
logic we could get something like (5) is true to degree 0.45, that is it is definitely
not to be called large nor could you call it not large; hence we need something in
between and that is something fuzzy logic can provide. Still this approach is very
debatable and not very popular as it obviously has a few unsatisfactory properties
to it, the biggest of which is the fact that those degrees that are not exactly 1 or 0
lack specification and accuracy and often need to be guessed. Opponents of fuzzy
logic claim that for sentences like (5) it is not impossible to decide whether they
are true or false, but that it is the inaccurate choice of words or a lack of
background information that is the problem here. When we know that for a German
city to be large it must have at least 100.000 inhabitants and we also know that
Osnabrück is a German city and has a good 160.000 inhabitants, we can suddenly
render (5) as true and do not need more than our two truth values being 1 and 0.
The second approach is called supervaluationism which states that there are
'truth value gaps' for borderline cases, that is if John's tallness can neither be
mapped onto the positive extension of tall nor on the negative one, then we are
dealing with a borderline case and according to supervaluationists this case would
just simply yield us no truth value at all. Still, in this approach, sentences can not
only be true, false, or neither, they can also be supertrue. If by precisely dividing all
our cases of being tall to be either true or false –regardless of how we would
actually do this– our borderline case (let's assume that (1) is a borderline case here)
would be either true or false as shown in (6).
(6) John is tall or John is not tall.
Thus, although John is a borderline case of tallness and would actually be said to
be neither tall nor not tall, according to supervaluationism (6) is supertrue. This
approach is a highly theoretical one and does not provide an actual idea of how to
precisely divide our set of individuals albeit this being the crucial point of the
whole idea of supervaluation. And if that was possible at all, we would not have to
deal with the phenomenon of vagueness in the first place (at least not in that much
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detail), which still we somehow do, and hence to me this idea of supervaluation
does not seem to get us anywhere. Another very similar reason for many people to
be sceptic about this view is that alluding to the paradox of the heap we would get
a sentence like 'There exists a number of grains of rice that is a heap and if we
reduce that number by one single grain we do not have a heap anymore'. That
obviously violates premiss 2 and thus seems untenable.
The last approach I want to indicate here is epistemicism which builds on the
idea that there are actually no borderline cases at all but that it is rather due to our
ignorance that we cannot state certain vague expressions to be either true or false.
We are simply unknowing about some facts; only because we do not know where
on a however defined scale, for example, being tall begins, this does not mean that
there just is no such boundary. Similar to the supervaluation theory, the epistemic
view is very, if not too theoretical and thus in my opinion hardly applicable. And
still, all those approaches are somewhat helpful in grasping and understanding the
phenomenon of vagueness a bit better.
2.5 Gradable adjectives and their role regarding vagueness
In this section I come to talk about the vagueness of gradable adjectives and will
give a detailed overview of the field of gradability in general. I will also explicitly
discuss the positive form of gradable adjectives as they seem to play a special role
regarding the phenomenon of vague adjectives.
2.5.1 Gradable adjectives vs. non-gradable adjectives
The whole lexical category of adjectives can be divided into two groups, namely
gradable and non-gradable adjectives. Take for example sentences (7a), (8a), and
(9a) that contain gradable adjectives, and sentences (10a), (11a), and (12a) as
samples containing non-gradable adjectives.
(7a) This is a big street.
(8a) My shoes were expensive.
(9a) The theatre is full.
(10a) My dog is dead.
(11a) They are married.
(12a) The table is wooden.
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The adjectives in sentences (7a) – (9a) are in some way measurable and allow for
the comparative and superlative. They can also be modified by qualitative adverbs
such as rather, very, or slightly. Hence, sentences (7b) – (9b) are absolutely fine
and grammatically correct.
(7b) This is a very big street.
(8b) My shoes were more expensive than yours.
(9b) Of all this month's shows, today the theatre is the fullest.
While, if we wanted to, we could easily measure how big the street is exactly, how
much more expensive my shoes were than yours, or how many seats in the theatre
are actually taken, it is impossible to measure non-gradable adjectives in any
similar way. Furthermore, they cannot be used in the comparative or superlative
form but only in their positive form. They also cannot be modified by qualitative
but only by intensifying adverbs like absolutely, entirely, or completely. All this is
shown in sentences (10b) – (12b). (The '*' indicating the incorrectness of the
following sentence.)
(10b) *My dog is slightly dead.
(11b) * They are more married than we are.
(12b) This table is entirely wooden.
As we have seen, sentences (10b) and (11b) do not sound right while (12b) on the
other hand is grammatically correct.
The adjectives in sentences (7a) – (9a) are not only gradable, they are also
vague. The bigness, expensiveness, and fullness of something can only be
accounted for if we know what we are comparing it to. A street may be considered
a big street in Osnabrück (regardless of what is exactly meant by big), but
compared to streets in Los Angeles it may suddenly seem pretty small. We also do
not know what it means for a pair of shoes to be expensive or a theatre to be full.
We have to conclude that these adjectives must be vague.
Due to their lack of measurability, non-gradable adjectives on the other hand
are not vague. Sentence (10a) is either true, if I used to have a dog and it had
passed away at some point in the past, or it is false and my dog still alive or I never
even had a dog in the first place. The truth conditions of the sentence do not change
under different circumstances and thus the sentence, here more specifically the
adjective dead, can not be vague. If my dog has actually died, we cannot construe a
(sane) scenario in which my dog would not be dead but still alive. The same
counts for sentences (11a) and (12a): either someone/something is married/wooden
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or in any other case they are simply not. Regardless of the context, these sentences
should always reveal the same truth values.
So we have seen that it is gradable adjectives only that give rise to vagueness
and hence I will concentrate on those in the following.
2.5.2 Relative and absolute gradable adjectives
The group of gradable adjectives can also be divided into two subgroups, namely
relative and absolute ones. Adjectives like tall, long, or big, which we already have
discussed to a certain extent, are examples for being relative. Their truth values
behave relative to the context in which they are uttered, they can be used in
comparative and superlative forms, they allow for borderline cases and activate the
sorites paradox. But now take a look at the following sentences:
(13) The door is open.
(14) The antenna is bent.
(15) The floor is flat.
These adjectives definitely differ in some respect from the above characterised
relative gradable ones as it seems that their truth values are independent of any
circumstances. Also it is in question whether there can be borderline cases of
openness, bentness, or flatness and if these adjectives allow for the sorites paradox.
Still, they can be used in comparative and superlative forms, as well as they can be
modified by qualitative adverbs (we can say something is more open or slightly
bent) and thus must belong to the group of gradable adjectives. As it turns out,
these adjectives “[…] generate entailments that sentences with relative adjectives
lack […].” (van Rooij (2010)) That is we can easily conclude from sentence (16a)
to (16b) but not from sentence (17a) to (17b).
(16a) The door is more open than the gate. ⇒
(16b) The door is open.
(17a) John is taller than Mary. ⇏
(17b) John is tall.
The reason for this is that adjectives like the ones in (13) – (15) need to possess the
property they describe to a minimal or maximal degree, whereas relative adjectives
are not limited in such a way. Hence, these adjectives are called absolute gradable
adjectives.
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Sentences (13) and (14) contain minimal standard adjectives; for a door to be
open it must not be fully closed, that is it needs a minimal openness to it to be not
called closed, but open. Here, It does not matter how big an angle the door is open,
relevant is only that there is a minimal state of openness beneath which the door
cannot be claimed to be open anymore. It is impossible to be less than open and
still be open. The same counts for the adjective bent. There exists a point (if visible
to the naked eye, measurable by hand, or only accounted for with the most highly
developed technical devices) beneath which an antenna is just not bent anymore
and that hence marks the minimal degree of bentness. The adjective in sentence
(15) in contrast is a maximal standard one, as for a floor to be flat it needs to be
completely flat; it does not suffice to be flat only here and there, and be bumpy in
between. This in turn means that any maximal standard adjective denotes in its
positive form the only and most possible degree to which an object can possess the
property that is attributed by that same adjective. If (15) is true and the floor indeed
flat, there cannot be any other object being flatter. It is nonsense to say
(18) The floor is flat, but the table is flatter.
This explains quite articulately why there cannot be any borderline cases for
absolute gradable adjectives. There is just no grey area for which open, bent, or flat
are not sufficiently defined (we are not talking about how open, bent or flat
something might be but only about the fact whether something is in the first place).
This leads to the assumption that absolute gradable adjectives also behave
differently when put into a sorites paradox. And as it appears, this is the case. Take
a look at the following two examples, the first for a maximum standard, the second
one for a minimum standard adjective (taken in their ideas from Kennedy (2006)):
1) Premiss 1:
Premiss 2:
A theatre in which every seat is taken is full.
A theatre in which there is one seat less taken than in a full
theatre is full.
Conclusion: Any theatre with one seat taken is full.
2) Premiss 1:
Premiss 2:
A rod that is bent to a degree of 5 is bent.
A rod that is to one degree less bent than a bent rod is bent.
Conclusion: A rod that has 0 degrees of bend is bent.
We can see immediately that the paradox does not arise with either of these two
examples as in both cases we can render the second premiss false and hence the
whole argument makes no sense anymore. The switch in the first example takes
place in the first change already: When going from 'every seat is taken' to 'every
17
but one seat is taken', we cannot, strictly speaking, still talk about a full theatre. In
the second example it is the last transformation, namely the one from 'has one
degree of bend' to ' has zero degree of bend', we can definitely render false. This, in
fact, is the reason why absolute gradable adjectives do not trigger the sorites
paradox: As opposed to relative adjectives, we can always find the exact step at
which our second premiss turns out false.
Another interesting difference between absolute and relative adjectives is the
behaviour of antonym pairs. It is possible to draw conclusions from sentences
containing absolute adjectives about their antonym, while this is impossible for
relative adjectives. (Note, that there is at least one exception to this: The absolute
antonym pair empty-full does not behave in the following way due to the fact that
both are maximal standard adjectives and are not like any other antonym pair
composed out of one maximal and one minimal standard adjective.)
(19) The antenna is bent. ⇒ The antenna is not straight.
(20) The floor is not flat. ⇒ The floor is bumpy.
(21) John is tall. ⇏ John is not small.
(22) This book is not long. ⇏ This book is short.
Kennedy (2006) sketches an experiment where the primary goal was to
compare “[…] adult's and children's ability to contextually shift a standard of
comparison […]” (Kennedy (2006)); on a more coarse level, this experiment can
also be used to find out whether a gradable adjective is relative or absolute.
Participants were shown two objects and then given an instruction which of the two
to hand over. The first setup would contain two objects of different size (for
example pencils) which were individually judged to be both long or small
beforehand. Then the participants would get asked to hand over the long one. No
problems arose during this setup as we are dealing with a gradable adjective,
namely long, and even if both objects had been judged to be small before,
participants would hand over the object being of greater length. The second setup
would present two glasses being filled with a different amount of water, while none
being completely full. Confronted with the request to hand over the full one,
participants would not know what to do and not hand over anything. This can be
explained by the fact that now we are dealing with absolute adjectives in their
positive form and thus an expression like 'the full one' can only be attributed to
something that is actually full and not only fuller than something it is compared to.
18
Still, if we would request to hand over the fuller one, that is use the comparative
instead of the positive form, we would get the same results as in the first setup. As
there seems to be a big difference whether we use the comparative or positive form
of an adjective, I want to portray some of the features that go along with the
different use of adjectival forms in the next section.
2.5.3 The positive and comparative
Recalling sentence (1), we remember that for John to be tall his height needs to
stand out to some degree in a beforehand defined context. Looking now at the
comparative in sentence (23), reveals a somewhat different picture.
(23) John is taller than Mary.
Here, John's tallness is explicitly compared to Mary's tallness and thus we do not
need to define any context whatsoever to be able to render (23) true or false. If
John's height exceeds the height of Mary than John is taller than Mary; still, this
does not give us any hint about John being tall or not and hence, although it may
feel strange, we have to conclude that the comparative does not entail the positive.
All we know so far is that the comparative is apparently context-insensitive, that is
we only need to know the actual height of John and Mary (or see them together)
and no further information to truthfully utter (23).
Kennedy (2006) uses the following example to point out when we can use the
positive and when we should use the comparative form.
(24) The long book is mine.
(25) The longer book is mine.
In a scenario where there are in fact only two books and the one containing more
pages is mine, both sentences seem to work at first. And in case my book has 400
pages while the other one only has 150, either sentence is fine. But imagine my
book being 100 and the other being only 99 pages long. My book is still the longer
one (thus (25) is still true) but is it the long one, also? Probably not. The difference
between the length of the two books seems just to be too little to actually account
for one of them to be long and for the other one not to be long. It seems that the
positive form can only be used if there is a big enough difference between the two
objects in question while the comparative is even applicable when we are dealing
only with marginal differences.
The fact that we are unwilling to state (24) in the second scenario is closely
related to the phenomenon of the sorites paradox. We feel unable to draw a
19
boundary between 99 and 100 pages, making any 99 page book a not long one,
while stating at the same time that a 100 page book is indeed to be called long. If
we didn't feel unable to do so, there would be no problem with the sorites paradox
either as it would be easy for us to render the second premiss false by indicating the
exact boundary where the predicate changes its truth values.
At this point I want to end my discourse on adjectives and go back to
vagueness on a more general level.
2.6 Vagueness and other phenomena
There exist quite a few linguistic phenomena that often appear in coherence with
vagueness. In the following I will give a short overview of the most frequent ones
and will link them to or distinguish them from the phenomenon of vagueness as we
have sketched it so far.
Ambiguity: As ambiguity we understand the phenomenon that a word or a whole
expression can have two or more unrelated meanings and thus different lexical
entries. Very common ambiguous words are, for example, bank (as in 'financial
institution', or 'sand accumulation at a river site'), or bar (as in 'place where you get
drinks', or
'piece of candy'). Ambiguous sentences like 'Selma likes visiting
relatives' we have already discussed in section 2.2, as well as a test proposed by
Lakoff to distinguish between vague and ambiguous expressions.
Subjectivity: Some people may argue that vagueness is partly due to subjectivity
and the fact that everyone perceives the world a little differently. Why is it that,
when looking at a picture of the same Caribbean beach, some people would
describe the sea to be blue, while others would call it turquoise or opal green? How
come we have different concepts about the same colour? I suggest this is due to
Bosch's (1983) already mentioned lack of definition, and I think subjectivity is only
loosely related to vagueness (at least as long as we are not dealing with personal
preferences or taste in general).
Prototypes/Stereotypes: Prototypes in linguistic respect denote a standard or typical
example of objects that possess a certain property. When dealing with vague
concepts such as the noun bird we immediately have a probably very similar image
of a bird in our head; still penguins and bats are as much a bird as robins and
blackbirds. The existence of prototypes is a hint for a predicate to be vague as the
existence of a prototypes normally means that there must also be less prototypical
20
members falling in the same category. And thus, when talking about an expression
for which there exists a prototype, we use a vague term as we do not know which
member of the family we are actually talking about. Still, it is obviously not
necessary for a vague expression to have a prototype as gradable adjectives
generally come along without one, and yet they are without question to be called
vague. Stereotypes on the other hand are a mostly oversimplified and a previously
fixed idea about groups of objects and can easily be falsified when confronted with
new members of that group. Still, stereotypes are very persistent and often
detaining when it comes to the interpretation of predicates. (For more information
on this, see Bosch (1983).)
Imprecision: Imprecision often occurs in measure phrases, for example, if we say
'The tree is 5 meters high', something that could easily mean that the tree is actually
only 4,85 or 5,20 meters high. Kennedy (2006) quotes Pinkal (1995) who accounts
for this using the term 'natural precisification'. According to Kennedy, this sentence
would be imprecise but not vague as in the actual sense of the expression there is
nothing vague to it. It is only the pragmatic use of the sentence (and the fact that
we would accept a tree of 4,85 meters in height to be called 5 meters high) that
makes the sentence seem vague. This is to be compared to the sentence 'The tree is
high' which is actually vague.
Indeterminacy: The phenomenon of indeterminacy relates to the fact that for some
vague expressions it is unclear what kind of measurement they are referring to.
Kennedy (2006) uses the example of the expression 'Chicago is larger than Rome'
which reveals different results whether we are looking at the population or the
sprawl of the city. But while indeterminacy can be seen in all adjectival forms, that
is in the positive, comparative, and superlative, vagueness appears to be limited to
the positive form only. Still, Kennedy (2006) points out that the “[…] resolution of
(indeterminacy) is a prerequisite for the resolution of (vagueness).”
Open texture: Bosch (1983) discusses open texture which is said to be the
possibility of vagueness; that is to construct very strange, untypical, and nonmundane scenarios in which a well-known concept may become doubtful and thus
vague.
Pragmatic halo: The pragmatic halo is a set of objects or situations that is close
enough to an original object or situation having some kind of property. The
sentence (taken from van Rooij (1010)) 'John is 2 meters tall' would have a
pragmatic halo ranging from about 1.97 to 2.03 meters. A method to avoid
21
pragmatic halos (and hence so some degree vagueness) would be to insert the word
exactly into the vague measure phrase in question. In our case we would get 'John
is exactly 2 meters tall' which would not leave room for a pragmatic halo.
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3 The sorites paradox
As the sorites paradox plays and important role in the semantic studies about
vagueness and context-dependence, I will discuss it in this chapter in some more
detail and will sketch two ways of solving it as proposed by Gross (2009) and
Bosch (1983).
For clarity reasons I will state the paradox again:
Premiss 1:
An accumulation of 1.000.000 grains of rice is a heap.
Premiss 2:
Removing one grain from something that is a heap still
leaves a heap.
Conclusion: One grain of rice is a heap.
The core of the paradox is that the conclusion is definitely false although both
premisses seem to be true. There are some people that actually tried to solve this
paradox and two of these approaches I will shed some light on now, as especially
these seem to have some strong points.
3.1 The sorites paradox resolved by Bosch (1983)
Bosch uses in his argumentation a slightly different predicate, namely the vague
predicate 'is a small number'. His sorites hence looks as follows:
Premiss 1:
1 is a small number.
Premiss 2:
If n is a small number, so is n+1.
Conclusion: Any natural number ≥ 1 is small.
He suggests not to use the predicate-expression as a constant but as a function from
context-models to concepts. This way, we are able to account for the contextdependent interpretation of the predicate which in Bosch's argument plays a big
role. He creates different context-models (which I will not explain in full depth; for
further information see Bosch (1983)) which eventually show that we can not treat
the predicate 'is a small number' in connection with the number 2 the same in all
runs through our sorites. According to Bosch's models, the problem lies in Premiss
2: In the first application we get here 'If 1 is a small number, so is 2' and in the next
application it is 'If 2 is a small number, so is 3'. Regarding the number 2 in both
applications, Bosch states: “[…] we cannot guarantee that the property referred to
be the predicate-expression “is a small number” is the same in both applications of
the second premiss.” (Bosch(1983)) And hence we cannot conclude that the
23
number 2 is always a model of one single context.
It is rather the case that for every new run through our paradox we need to
reconstruct the context-model for the second premiss as it is impossible that one
model can hold for a whole sorites series and still this is what we always
misconceive (which is in fact the reason for the paradox to arise). Bosch sums up
his findings in the following very clear and crisp passage:
Now, if we decide for a number m that it is to count as small, the second
premiss of the sorites forces us to also count m+1 as small. But this does
not bind us with respect to our decision about whether or not m+1 is a
small number, when we are faced with that question independently, i.e.
not in the context arising after the decision on the number m, but in the
same context in which the first decision (on m) was made.
Although in his argumentation Bosch every now and then notes that all he is saying
not only counts for the predicate 'is a small number' but also for predicates like 'is a
heap' or any other, I am not quite assured if this is actually the case. Let's take the
predicate 'is a heap' and let's say that (for argument's sake) we would account for an
accumulation of grains to be a heap at around 20.000 grains. Still, we could not say
where exactly our context-model had to change for the sorites to stop and not lead
to a contradiction. Bosch's solution seems to only work in case we are dealing with
a short sorites series in the first place. His attempt to counteract objections like that
does not fully convince me, as he states that in case we are dealing with a non
completely defined concept it is nonsense to further think about it unless the
concept is fully defined. But is not exactly this the point, that we just do not have
completely defined concepts of everything? And is not this in turn the reason for us
asking questions like 'What is a heap?' in the first place? I still think Bosch makes
some good points in his argumentation and I will come to talk some more about his
work when dealing with the question to what extent vagueness can be accounted
for by context-dependence in section 4.1.
3.2 The sorites paradox resolved by Gross (2009)
A more recent attempt to solve the sorites comes from Gross (2009) who not only
presents a quite appealing solution to it but also provides us with some
explanations why it is that we are so easily to 'believe' the paradox in the first
place.
The main point he is making –that also distinguishes him from most others
24
trying to solve the paradox– is that the use of a vague term does not necessarily
succeed in contributing to content at all (cf. Gross (2009)). He uses the example of
a set of 100 colour chips ranging from being definitely red to being definitely
orange. Put into a sequence from the most red chip to the most orange one, it would
be impossible to distinguish the colours of two neighbouring chips. So we are
dealing here with a somewhat different but still discernible sorites series. Throwing
all these chips into a bag now and asking someone to get a red chip out of it, would
not bring you any problem at all, that is it just does not seem to matter whether
there may be chips we cannot clearly identify as belonging to the one or the other
colour. Only if we ask to partition all chips into red and orange ones we will not get
a satisfactory result for there will be chips in this task for which it is impossible to
state whether they are red or orange. So, when confronted with a sentence like 'The
number of red chips is even' we could not render it true or false, although we
perfectly understand the sentence and are aware of the context it is presented in.
Gross reasons that this is the case because “[…] the lack of partition results in the
failure of the predicate to express a property: an utterance of the sentence would
thus fail to express a proposition.” Applied to the sorites that means that in case a
full partitioning is not possible, we cannot just go on with it as if it was possible.
And if there is a possible partitioning, then we are not bothered with the sorites
anyway as we can at some point easily render the second premiss false. So either
we are not allowed to use the sorites because the predicate fails to express a
proposition at all, or we do not need it in case a full partitioning is possible. From
this it follows that we actually do not need the sorites at all and that there –even
more striking– should not even be such a thing as the paradox in the first place. But
why is it, then, that we are so appealed by the idea of it? Why is this phenomenon
when dealing with vague expressions so stuck in our heads? Gross tries to also give
some explanations to these questions.
Gross observes “[…] that vagueness usually just doesn't matter […]” and that
to we just –at least to a certain degree– do not care about its roots and things that
come along with it. Still, when confronted with the sorites argument, we are all
puzzled at first and wonder why it is that two true premisses lead to a false
conclusion. Even after we are presented with a dissolution of the paradox, we still
feel the force of the argument and are somewhat unwilling to let go of it. We want
to construct that context in which our two premisses would work, something, Gross
claims, that is due to our nature wanting to make sense out of things, and that at the
same time goes “beyond our conscious control”. Summing up, he states:
25
And even if we consciously conclude that our inability to identify an
appropriate context for the sorites is owing to the absence of such a
context, not to our ignorance or inadequacy, this doesn't mean that the
would-be argument loses all force, psychologically speaking: again, the
automatic nature of our interpretative skills places them to a certain extent
beyond our control.
Both approaches on the sorites paradox that I have sketched in this section
require vagueness to be closely linked to context-dependence, a linguistic
phenomenon I am going to address in the next chapter.
26
4 Context-dependence
As in previous sections already adumbrated, the phenomenon of vagueness can not
be accounted for without talking about context-dependence as well. What exactly
is to be understood by context-dependence and to what extent it can be linked to
vagueness, these are questions I am going to answer in this chapter. I will also
sketch and compare the views of Bosch (1983) and van Rooij (2010) on the
relationship between vagueness and context-dependence.
4.1 Definition of context-dependence in general
Zagan (2009) claims that “The meanings of vague predicates fail to determine
precise extensions.” and Gross (2009) states that “A term is context-sensitive if and
only if its contribution to propositional content can vary across occasions of use
without any change in the terms standing meaning in the language”. 1 That is if the
meaning of an expression stays the same throughout different contexts while the
truth value of the same sentence may change. The actual meaning of sentence (26),
that is each meaning of each word combined in one phrase, cannot be changed.
(26) The music is too loud.
Where ever I utter (26), one can conclude that there is some music playing and that
the volume to which it is tuned up is higher than appropriate. Still, we do not know
how loud too loud actually is and for that to answer we need to know about the
context in which I utter (26). For then only we can conclude if I am right or wrong.
When there is a baby sleeping in the room, having the radio turned on even at a
low level would probably count as too loud already; whereas the same volume in
the same room at a party would most likely count as merely hearable. Not to speak
of a concert where the volume synchronises your heart beat with the bass; in this
case the volume is most probably not called too loud but rather just right. As we
can see, it is the context that decides how we have to judge vague expressions.
This does not only count for vague adjectival phrases but for all lexical categories;
in one context the trunk of tree can describe a prefect bench (when walking
through nature and looking for a place to rest) while in another context we would
never call it a bench at all (when searching for seatings to accompany our new
kitchen table). The same holds for every other category in which there exist vague
1 Gross and some others use the term context-sensitivity where most linguists would talk of contextdependence; I am going to treat them the same but will stick to the latter expression when talking
about it myself.
27
examples, although their ostensive character might not be as strong.
In defining context-dependence, Barker (2005) gives a somewhat more
detailed description. He states that “The context-dependence of vague predicates
consists in at at least three related but distinguishable factors: reliance on a
contextual standard (threshold); reference to a comparison class; and dependence
on conversational and other purposes.” Whatever you may want to compare John's
height with, there must be some kind of threshold above which John would count
as tall and not tall otherwise. Who or what you are John actually comparing to is
the comparison class. The last factor refers to the fact that a vague statement may
serve as a distinct purpose throughout a conversation.
Some linguistic phenomena that are also closely linked to deixis –a term that
quite generally means that understanding words, expressions, or phrases, often
requires some kind of contextual information– are indexicals and anaphora.
Indexicals are on the one hand pronouns such as I, you, they, etc. and on the other
hand words like here and now. The interesting thing about indexicals is that they
not solely depend on the context but more specifically on who uses them where
and when. 'I am here now', uttered by me, refers to me sitting on my desk at 10.20
a.m. on March 21st 2011. Uttered by you, 'I' would refer to you, 'here' to where ever
you may be and 'now' to the exact moment of uttering the statement. Hence, and
that is the important bit here, the referential denotation of indexical words changes,
whereas the reference of vague expressions does not change (provided that there is
no ambiguity). We can conclude that all indexicals are vague but that definitely not
all vague expressions are indexicals.
An example for an anaphoric utterance would be (27):
(27) John is reading a book. He likes it.
He refers to John and it refers to the book, both mentioned in the precedent
sentence. The second sentence on its own would not be very informative as we
would not know who and what are meant be the anaphoric expressions he and it.
Obviously, anaphora is closely linked to the matter of context, also; what is of
importance here is the, more or less direct, previous linguistic context. Anaphora
has nothing to do with vagueness specifically, but understanding the former can
make it a lot easier to understand the latter. That is we understand the second
sentence of (27) because we can refer he to John and it to the book he is reading,
but we still do not really know what it means for John to like the book.
Zagan (2009) distinguishes two types of context-dependence of vague
expressions by also taking indexicals into account. He proposes that there is a
dependence of contents on context (content-contextualism) and a dependence of
28
extension on context (truth-contextualism). The former refers to indexicals as it is
the content of the actual sentence that needs to be closely looked at, while in the
latter case we have to see if the object we are addressing a property to falls into the
extension of exactly this property, that is, Zagan (2009) states, “most likely, the
variation in the extension of vague predicates points to a change in context. It is
not the content (the property expressed by a vague predicate) that varies with the
context of use, […] it is the extension of a vague predicate that varies with the
context of use.” This distinction once more illustrates the difference between
indexicals and other vague expressions.
In the next section I am going to present the different views of van Rooij
(2010) and Bosch (1983) on the topic of context-dependence and its relation to
vagueness.
4.2 Van Rooij (2010) and Bosch (1983) on context-dependence
Van Rooij gives in his paper 'Vagueness and linguistics' (2010) an overview of the
concept of vagueness and certain phenomena that come along with it. One of his
goals is it to contrast vagueness with context-dependence. Already at the beginning
of the paper it becomes clear that van Rooij thinks of the two as being connected
but different phenomena; he states that “Vagueness and context-dependence are in
principle independent properties, although they often co-occur.” To emphasize this
statement he gives the example of the context-dependent adjectives left and right
which are hardly vague at all and then declares nouns like vegetable and bush to be
very vague but not context-dependent. The point van Rooij is making here seems
to be clear, although his examples may be a bit weak. If I got told to have a look at
the house to my left and found there to be four houses, it would be necessary to
further specify the house I am supposed to look at as in this case the term left is too
unspecific, and thus vague.
Later on in his paper, van Rooij specifies his first thought of vagueness and
context-dependence being different properties by saying (referring to the adjective
tall): “Vagueness is not the same as context-dependence, and the argument is
consistent with tall having a precise meaning in each context.” According to him,
for a predicate to have a precise meaning in each context, it needs on the one hand
to be consistent, that is if X is in some context regarded to be tall while Y at the
same time is not, then there cannot be any context in which Y counts as tall while
X does not. On the other hand must it be learnable and computable what the
extension of the predicate is in each context. Recall Bosch's (1983) already
29
addressed definition of vagueness being incomplete definition; that is a predicate is
vague in case it is not defined for each context in advance. We can see that these
two views differ in their core assumption and I will get into a bit more detail about
the differences when later talking about Bosch's paper.
Furthermore, van Rooij gives a clear explanation why vague adjectives like
tall should not be treated like indexicals. He uses the following sentence as an sen
example (first put up by Ludlow (1989)): 'This elephant is large and that flea is,
too.' If vague adjectives were treated the same as indexicals, the following
sentence would have to be true: 'This elephant is large for an elephant and that flea
is large for an elephant.' Which is obviously nonsense and thus van Rooij correctly
reasons that indexicals are not the same as vague expressions and thus the two can
not be treated the same.
While van Rooij is quite clear about what vagueness is not and how to
differentiate it from other linguistic phenomena, he stays rather vague himself
when it comes to defining vagueness. He states that “Vagueness in linguistics is a
problem about the meaning of linguistic expressions” and “Whether one is tall
depends on a unique gradient contingent fact, one's length. Vagueness of being tall
is then due to the fact that it is unclear whether one's length counts as being tall or
not.” Unfortunately, he does not come up with a well-motivated idea of what
vagueness actually is. Unlike Bosch (1983) who is giving a nice account on the
putative origin of vagueness.
Bosch's paper '“Vagueness” is Context-Dependence. A Solution to the Sorites
Paradox' (1983) reveals the author's point of view on the relationship between
vagueness and context-dependence by only reading its title. The article consists of
two parts, of which the first deals with the classification of vagueness; in the
second part, Bosch gives his solution to the sorites paradox which we have already
discussed in section 3.1. Now, I will concentrate on the first part.
He states that “[…] the vagueness of natural predicates arises from the fact
that they are learned and used always in limited contexts and hence are
incompletely defined.” (For more information on this see section 2.1.) That is we
do not know for each and every context what it means, for example, to be tall and
thus tall is a vague adjective. To decide whether or not a predicate actually assigns
the property it denotes to a given object, we need to further specify the situation in
which the predicate is used. The lack of preciseness of the predicate (thus the
vagueness) is due for it to require more information.
At the beginning of his paper, Bosch argues that concepts –which are
functions from things into truth values– are imprecise and hence vague. Later on,
30
he reasons that it is actually not the concepts that are vague but that it is predicateexpression which are. He concludes “Predicate-expressions would then be
incompletely defined in the sense that a predicate does not yield a concept as its
value for each and every concept.” And this indeed makes sense: Not our concepts
are vague, as the ones we have should be well-defined. What is of importance here
is the fact that we do not have precise concepts (or concepts at all) for all contexts
and thus it should be the actual predicate-expression itself that is vague or –put
differently– not precisely defined. Take again sentence (1) ('John is tall'). As we
have seen many a time (1) is vague because it lacks background information and
according to Bosch, is not precisely defined. So, if our predicate-expression was
more precise, vagueness should not arise. Take sentence (1'), a modification of (1).
(1') John's height is 1.80m and right now he is amongst basketball-players.
John is tall.
(1') is not vague, although it contains the vague adjective tall; but because of the
whole expression being precise, we can render (1') immediately false.
To make his point even clearer, Bosch states “[…] that the vagueness of
predicate-expression is no more than an accompanying feature of the contextdependence of their interpretation […]”. That is vagueness is a phenomenon that
can arise when dealing with the context-dependence of predicate-expressions. This
view appears to be quite different from van Rooij's many others' view. They say
that context-dependence may play a role when dealing with vagueness; and not
that it is context-dependence we are dealing with in the first place that can lead us
to vagueness. Van Rooij (2010) may be right that context-dependence and
vagueness are not the same but only because context-dependence does not have to
be vagueness; while vagueness is always context-dependence. Not every contextdependent expression is vague, but every vague expression is context-dependent.
Van Rooij's (2010) view that for all predicates to be precise they need to be
consistent and their extension must be learnable for every context seems quite
plausible in theory but I think that it is unfortunately not adoptable in practice at
all. Whereas Bosch's account on the relationship between vagueness and contextdependence seems to be more appealing as it also works in practice.
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5 Conclusion
We have seen that, when accounting for vagueness, the most important feature is
context-dependence. Bosch (1983) goes so far as to even say that vagueness is
nothing more than pure context-dependence; a position that differs a lot from many
other semanticists. But as I have shown, he makes some really good points and it
seems that his approach is actually applicable and does not only work in theory.
In this thesis it was my goal to give a comprehensive and detailed overview of the
field of linguistic vagueness. I have shown that vagueness seems to be everywhere
where we are concerned with language in the first place and what characteristics
vague expressions possess. But as it turned out, it seems that there are still aspects
of vagueness which need to be analysed some more for the picture to become
complete.
I could give an explicit account of gradable adjectives and reason that it is the
positive form only that gives rise to vagueness as the comparative (and superlative)
turn out to be context-independent. I portrayed two different approaches on the
sorites paradox, one of which seemed plausible but not applicable to all sorites
series; while the other one works in all cases. I could also give some interesting
hints about why we are so appealed by the sorites paradox in the first place.
I have found the work on this topic very interesting as the field of vagueness
reveals itself as being very complex but still understandable and applicable to
everyday situations. There exist quite some research on this topic and still I think
that we are not done with it yet; or that vagueness is not done with us yet.
There is only one question remaining, namely: How tall is John, then? Well, we do
not know. He may be called tall, yes. But only sometimes.
32
References
Barker, C. (2005). Vagueness. Article number 1083. In: Elsevier's Encyclopedia of
Language and Linguistics, 2nd edition.
Bosch, P. (1983). “Vagueness” is Context-Dependence. A Solution to the Sorites
Paradox. In: Thomas T. Ballmer & Manfred Pinkal (eds.): Approaching
Vagueness. North Holland, Amsterdam. 1983. pp. 189-210
Channel, J. (1994). Vague language. Oxford University Press, Oxford.
Gross, S. (2009). Vagueness in Context. In: Philosophical review 118 (April 2009).
Kennedy, C. (2007). Vagueness and grammar: the semantics of relative and
absolute gradable adjectives. In: Linguistics and Philosophy 30, pp. 1-45
Lakoff, G. (1970). A note on vagueness and ambiguity. In: Linguistic Inquiry 1, pp.
357-359
Ludlow, P. (1989). Implicit comparison classes. In: Linguistics and Philosophy, 12,
pp. 519-533
Ullmann, S. (1962). Semantics. Blackwell, Oxford.
van Rooij, R. (2010). Vagueness and linguistics. In: G. Ronzitti (ed): The
Vagueness Handbook, to appear
Zagan, L. (2009). Vagueness, Context-Dependence, and Perspective. Talk at the
Philosophy of
Language
University of Lodz,
and
Linguistics
Poland, 14-16 May 2009
33
conference
(PhiLang
2009),
Acknowledgements
I would like to thank Peter Bosch for his constant and reliable support throughout
the process of this work. Thank you for all your ideas and input, and for being
there for me longer than I had actually planned for. I also want to thank Paul for
doing the tedious work of proofreading my thesis and not getting too annoyed by
me sometimes being a nuisance. Last but not least I want to thank Viktor for his
invariable support and unconditional motivation; I am sorry for what you had to
put up with the last couple of weeks.
34