 Hello, this is the final e-lecture of our ambiguity and vagueness trilogy. The central question we are going to discuss here is how to decide whether a certain case of multiplicity of readings is an instance of ambiguity or one of vagueness. To do this, several tests have been developed to distinguish the clear cases of ambiguity from the clear cases of vagueness and to provide a basis for deciding on the problematic examples. The following tests will be discussed in this e-lecture. We will first look at the identity test. We will then deal with tests that involve sense relations and will last but not least discuss a test that discusses the truth conditions that are involved in the examples at questions. But before we apply any of these tests, let us quickly repeat the central ambiguity and vagueness types in order to distinguish them later. Ambiguity is defined as the phenomenon of one linguistic item having several meanings. Here are the main types. Lexical ambiguity, examples such as bank, for example. Structural ambiguity, well our example here is she is an English teacher. Referential ambiguity, the example illustrated here, well it could be something like John kissed his girlfriend. And four students who shot three professors is one of the famous examples of scope ambiguity. Vagueness by contrast is defined as the phenomenon of one linguistic item allowing several interpretations. Here are the main examples. Referential vagueness, you know the difference between hills versus mountains. We discussed that in the vagueness e-lecture. Indeterminacy of meaning, Linda's car is she the owner? And lack of specification which you can find in verbs of motion such as goal, which is not precisely specified as to what sort of vehicle you used or how you moved. The question we are going to address now is how can we keep these phenomena apart? Well, we need a test involving a context that helps us to isolate the respective readings of a linguistic unit. A general problem however with such ambiguity tests is that they fail to apply in some situations and sometimes give unclear answers. The main reason for this is the selectivity of the context. So it is this we have to define very precisely. Ambiguity tests require inventing a sentence or a phrase and a context where all readings, all possible readings are available, not just one of them. One such context is the so-called do-so context known as the identity test. Let us look at this one first. The identity test relies on what is known as the identity constrained on a back reference of forms like do-so that refer back to their main clause, do-so too, so is, has so, so has and so on and so forth. All these forms are used to avoid repeating a verb phrase. Here is an example. Mary visited the bank. Now visiting the bank can have two readings. Reading one here abbreviated to R1 is that Mary went to the money institute. She visited the money institute. Reading two, she visited the river embankment. If we now add a do-so clause, such as so did Linda, the meaning selected for the verb phrase visited the bank must be repeated in the reduced construction and so did Linda. So in both parts, only one reading is possible. If Mary visited the money institute and so did Linda, Linda must have also visited the money institute and cannot have gone to the river bank. Such conflicting interpretations are not possible. It follows that the whole sentence and hence the word bank has two distinct readings and is therefore ambiguous. Let us now take an example where conflicting interpretations are possible. Here is one. Mary adopted a child. The lexine child can have several interpretations among them, a boy or a girl. So Mary adopted a child could mean that Mary adopted a child who's a boy or Mary adopted a child who's a girl. If we now add our do-so clause, well in this case it'll be a has-so clause, so has Linda, the meaning selected for the verb phrase can also be identical in both parts. Mary adopted a child who's a boy, so has Linda, she also adopted a boy. But this time conflicting interpretations are possible too. So this is our new possibility. The child adopted by Mary does not need to have the same gender as the one adopted by Linda. So boy and girl do not correspond to distinct readings of child. Therefore child is not ambiguous but unspecified or vague in this case for gender. So whereas in cases of ambiguity and identity of reading is required, vagueness allows this reading crossover as a sort of interpretation alternative. So much for identity tests. The sense relation test exploits the network of sense relations connecting the lexical items of a language. Two meanings, that is two lexemes. Here the lexemes one and the lexemes two illustrated by L1 and L2. Two lexemes are claimed to be ambiguous if they have genuinely independent sense relations. That is one sense is in a network of relations with certain other lexemes and another sense is in a different network. And there's no overlap. So this here is impossible. Let us illustrate this. Bank is a homonym. It involves different sense relations. It is for example, that is one interpretation. It is a hyponym of types of buildings. And in a second interpretation, it could be seen as a meronym of the hollownam river. And there is no overlap between these two sense relation networks. So this is clearly impossible, something like that. Thus we have a case of ambiguity, impossibility of overlap. In this case, lexical ambiguity, that is homonymy. This is different with child and its interpretations. So let's look at this next. Here the different interpretations of child, boy, girl, infant, baby and so on are all part of the same hyponymy network. So we have a case of vagueness. In this case, referential vagueness. All interpretations refer to a common hyperonym. Okay, let's finally discuss the truth conditions test. An expression can be labeled ambiguous if its readings have independent truth conditional properties. That is, sentences containing them can be simultaneously true and false relative to the same state of affairs. This observation forms the basis of the truth conditions test. An expression is ambiguous if we can imagine a context in which a yes-no question involving the relevant expression can be answered truthfully with both yes and no. For example, the question, did Mary visit the bank? Could be answered truthfully either in the positive or in the negative way if Mary actually visited the bank? So our assumption is that she did visit the bank. The proposition P is assumed to be true. And then both answers are truthful. Did Mary visit the bank? Yes, she did. She visited the Money Institute? No, she didn't. If she did not. If we contrast this with the question, did Mary adopt the child which involves the vague item child? Now, here we could not choose yes and no at the same time as an appropriate answer. Answer one, where we assume again that adopting a child is the proposition is true. Answer one, yes, she did. Could be a reasonable answer, but then at the same time, no, she didn't. Could not. Hence, if a yes, no question can truthfully be answered with yes and no. We have a case of ambiguity. If not, we are confronted with a phenomenon of vagueness. So that's it. Even though it is often difficult to decide whether a certain case of multiplicity of readings is an instance of ambiguity, where a unit can be associated with several distinct meanings, or of vagueness where a unit is unspecified, that is not clear in context, we have seen that there are several tests that can help us to keep these two phenomena apart. So I hope that this trilogy of e-lectures, ambiguity, vagueness and ambiguity versus vagueness, could shed some light upon these two central phenomena of natural language which superficially look complicated, but at second sight make language so rich. So I have to thank you for your patience.