 Hello. Many natural language expressions are vague. That is, they are unspecified with regard to their meaning. This allows us to be unspecific and create space for the interpretation of words, sentences and texts. The notion of vagueness, about which I'm talking in this e-lecture, however, needs to be distinguished from ambiguity. I talked about it in another e-lecture, which is a property of linguistic units with several distinct meanings. In contrast to ambiguity, where the context usually selects one of the meanings, in cases of vagueness, the context can add information that clarifies the meaning of the vague expression. Let us look at the main examples of vagueness first. The following types of vagueness can be found in language. For example, there's something that we call referential vagueness. For example, let's put it over here, these chairs. Now, it is arguable whether all three pieces of furniture satisfy the meaning of chair, but we will come back to this issue. This is referred to as referential vagueness. Or take this example here where we could say these are John's flags, and this of course is called the indeterminacy of meaning. Does John own these flags? Has he created these flags? Well, indeterminacy of meaning. Verbs of motion, such as go, are often unspecified with regard to the meaning, so they lack a precise specification. Go can involve drive, it can involve walk, it can involve run, and so on and so forth. And last but not least, we have a phenomenon which is often referred to as the disjunction. Let's put it over here. The disjunction of interpretations and the typical case involves sentences which involve the inclusive, connective or vagueness. Commonly involves borderline cases where it is unclear whether or not a given term applies. Words like tall or fat are vague. For example, tall cannot clearly be associated with body height. Is this tall? Do we have to move the line down here and say everything above this height is tall or this? Or even this? Well, we cannot clearly say. Or what is fat? Is it this criterion where we have this sort of size? Or is this fat too? Well, again, as I said, it is difficult to tell. So it is difficult to distinguish tall from not tall. For example, some people may be borderline tall or not clearly tall or not clearly not tall. There is no borderline separating the tall people from the rest or the fat people from the rest. Generally, vague expressions can be said to lack well-defined extensions. They have fuzzy boundaries. Furthermore, a number of terms are habitually used in a loose way. The core meaning of some terms is easily defined, but people habitually apply them in a loose way. For example, the notion of a circle has a clear definition which everyone can grasp. We can describe it mathematically. However, speakers tend to use the word circle very loosely in everyday language. Take this example here. The students stood in a circle around the teacher. Here we do not expect the students to form an accurate circle, yet there is no special or extended meaning of circle involved. A further problem concerns the distinction between vagueness and aspects of generality. It should be clear that vagueness has to be distinguished from speaking in general or over generalized terms. Take two examples in a sentential context. Now, this is our sentential context. I saw something today. For example, we could say I saw a bird today versus we saw an eagle today. Although bird gives less information than eagle, it is not more vague. It is just that bird denotes a more inclusive class. Similarly, someone saying I will get by somehow does not speak vaguely, but in over general terms. The item somehow is not unspecified, rather it has the meaning in some unspecific way or manner. So, after this introduction, let us now look at the four types of vagueness I outlined earlier on in detail. Let us start with referential vagueness. Now, referential vagueness is a property of lexical items whose meaning is in principle clear enough, but for which it may be hard to decide whether or not they can be applied to certain objects. Here are two examples. What is the borderline between a city and a town? How do we distinguish hills from mountains? Well, you all know that especially in the case of hill versus mountain, your personal background plays an important role. Do you live near the sea where you do not even have hills or not? Well, I leave that decision up to you. Here is the second case, indeterminacy of meaning. This type of vagueness involves lexical items and constructions where the meaning itself does not seem to be clearly expressed. That is, it is indeterminate. A good example is the possessive construction in English. The examples I chose on the board here can describe, for example, the paper, John's paper, the paper that John wrote, Linda's car, the car that Linda owns, Mary's glasses, the glasses Mary needs, or Linda's car can also mean the car Linda uses every Monday. Mary's glasses could also mean the glasses Mary has designed and John's paper could be interpreted as the paper that John has to read and so on and so forth. So all these cases are indeterminate as far as their interpretation is concerned. The next case, lack of specification, refers to cases where the meaning, although clear in principle, is only generally specified. For example, the lexine friend is unspecified for gender, race, age, and so on and so forth. Or take verbs. The meaning of an item such as go can clearly be specified. I did it over here in terms of a conceptual dependency theory where go is specified as an action of physical transfer. However, beyond this clear cut semantic specification, it can be used to denote a variety of actions. So the sentence John went home leaves open how John got there. Did he walk? Did he use his skateboard? Did he use his new car? Did he run and so on and so forth? So items such as go are not specified well enough as far as their interpretation is concerned. And finally there are cases where vagueness results from the disjunction of different interpretations in the meaning specification of an item. That is the meaning involves several possible interpretations that exclude each other. And the meaning is unspecified with respect to which of these interpretations holds. The central example of this type of vagueness is the connective or. We discuss that in the e-lecture on propositions and I have to be precise, inclusive or. You know the difference between inclusive and exclusive or then re-consult the e-lecture propositions again. The sentence Mars is a satellite of the Sun or a planet of the solar system. Now this sentence implies that one of the two disjuncts or both disjuncts are true. Thus as we pointed out in the e-lecture propositions the inclusive or and here you see the truth table. The inclusive or can therefore be true under different conditions. And the sentence or more precisely the disjunction itself is vague. Well so much for the four types of vagueness and some general introductory remarks. And of course as far as ambiguity is concerned presupposing that you have already attended the e-lecture on ambiguity. It is often difficult to decide whether a certain case of multiplicity of interpretations is an instance of ambiguity or vagueness. For this reason several tests have been proposed upon which that decision can be based. These tests will be explained and applied in a follow-up e-lecture. So see you there.