Syntax. Andrew Carnie

only two classes of verbs: Stative verbs like sit, sleep, and live and motion verbs like go, dance, run. Use the scientific method construct a hypothesis about kinds of verbs can appear in this construction and which cannot. Test your hypothesis with other verbs.

       CPS6. JUDGMENTS ²⁴

       [Data Analysis and Application of Skills; Challenge]

      Consider the following sentences:

      a)

      1 The students met to discuss the project.

      2 The student met to discuss the project.

      3 The class met to discuss the project.

      b)

      1 Zeke cooked and ate the chili.

      2 Zeke ate and cooked the chili.

      c)

      1 He put the clothes.

      2 He put in the washing machine.

      3 He put the clothes in the washing machine.

      4 He put in the washing machine the clothes.

      d)

      1 I gave my sister a birthday present.

      2 I gave a birthday present to my sister.

      3 That horror movie almost gave my sister a heart attack.

      4 That horror movie almost gave a heart attack to my sister.

      e) Where do you guys live at?

      f)

      1 It is obvious to everybody that Tasha likes Misha.

      2 The fact that Tasha likes Misha is obvious to everybody.

      3 Who is it obvious that Tasha likes?25

      4 Who is the fact that Tasha likes obvious?

Some of these sentences would be judged acceptable by all (or nearly all) speakers of English, while other sentences would be judged unacceptable by at least some speakers. Find at least five native English speakers and elicit an acceptability judgment for each of these sentences (present the sentences to your speakers orally, rather than having them read them off the page). Give the results of your elicitation in the form of a table. Discuss how your consultants’ reactions compare with your own native speaker judgments. If a sentence is judged unacceptable by most or all speakers, what do you think is the source of the unacceptability? Choose from the options listed below, and briefly explain and justify each choice. Are there any sentences for which it is difficult to determine the reason for the unacceptability, and if so, why?

      1 The sentence is unacceptable in the linguistic sense: It would not be produced by a fully competent native speaker of English under any context, and is unlikely to be uttered except as a performance error. It should be marked with a *.

      2 The sentence is marginally acceptable. One could imagine a native speaker saying this sentence, but it seems less than perfect syntactically, and should probably be marked with a ? or ??.

      3 The sentence is fully grammatical in the linguistic sense, but only in some varieties of English. It is likely to be treated as ‘incorrect’ or ‘poor style’ by some speakers because it belongs to a stigmatized variety (an informal or colloquial register, or a non- standard dialect), and is not part of formal written English. We might choose to indicate this with a %.

      4 The sentence is syntactically well-formed, but semantically anomalous: It cannot be assigned a coherent interpretation based on the (normal) meanings of its component words, and should be marked with a #.

       CPS7. COMPETENCE VS. PERFORMANCE

       [Creative and Critical Thinking; Extra Challenge]

      Performance refers to a set of behaviors; competence refers to the knowledge that underlies that behavior. We’ve talked about it for language, but can you think about other cognitive systems or behaviors where we might see examples of this distinction? What are they? Acceptability judgments work for determining the competence underlying language; how might a cognitive scientist explore competence in other domains?

       CPS8. IS LANGUAGE REALLY INFINITE?

       [Creative and Critical Thinking; Extra Challenge]

       [ Note to instructors : this question requires some background in either formal logic or mathematical proofs.]

In the text, it was claimed that because language is recursive, it follows that it is infinite. (This was premise (i) of the discussion in section 4.3.) The idea is straightforward and at least intuitively correct: if you have some well-formed sentence, and you have a rule that can embed it inside another structure, then you can also take this new structure and embed it inside another and so on and so on. Intuitively this leads to an infinitely large number of possible sentences. Pullum and Scholz (2005) have claimed that one formal version of this intuitive idea is either circular or a contradiction.

      Here is the structure of the traditional argument (paraphrased and simplified from the version in Pullum and Scholz). This proof is cast in such a way that the way we count the number of sentences is by comparing the number of words in the sentence. If for any (extremely high) number of words, we can find a longer sentence, then we know the set is infinite. First some terminology:

      Terminology: call the set of well-formed sentences S. If a sentence x is an element of this set we write S(x).

      Terminology: let us refer to the length of a sentence by counting the number of words in it. The number of words in a sentence is expressed by the variable n. There is a special measurement operation (function) which counts the number of words. This is called μ. If the sentence called x has 4 words in it then we say μ(x) = 4.

      Next the formal argument:

      Premise 1: There is at least one well-formed sentence that has more than zero words in it.

      ∃x[S(x) & µ(x) > 0]

      Premise 2: There is an operation in the PSRs such that any sentence may be embedded in another with more words in it. That means for any sentence in the language, there is another longer sentence. (If some expression has the length n, then some other well-formed sentence has a size greater than n).

      ∀n[∃x[S(x) & µ(x) = n]] → [∃y[S(y) & µ(y) > n]]

      Conclusion: Therefore for every positive integer n, there are well-formed sentences with a length longer than n (i.e., the set of well-formed English expressions is at least countably infinite):

      ∵∀n[∃y[S(y) & µ(y) > n]]

      Pullum and Scholz claim that the problem with this argument lies with the nature of the set S. Sets come of two kinds: there are finite sets which have a fixed number of elements (e.g. the set {a, b, c, d} has 4 and exactly 4 members). There are also infinite sets, which have an endless possible number of members (e.g., the set {a, b, c, …} has an infinite number of elements).

      Question 1: Assume that S, the set of well-formed sentences, is finite. This is a contradiction of one of the two premises given above. Which one? Why is it a contradiction?

      Question 2: Assume that S, the set of well-formed sentences, is infinite. This leads to a circularity in the argument. What is the circularity (i.e., why is the proof circular)?

Question 3: If the logical argument is either contradictory or circular what does that make of our claim that the number of sentences possible in a language is infinite? Is it totally wrong? What does