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CHALLENGE PROBLEM SETS

Challenge Problem Sets are special exercises that either challenge the presentation of the main text or offer significant enrichment. Students are encouraged to complete the other problem sets before trying the Challenge Sets. Challenge Sets can vary in level from interesting puzzles to downright impossible conundrums. Try your best!

CPS1. PRESCRIPTIVISM

[Creative and Critical Thinking; Challenge]

The linguist Geoff Pullum reports²¹ that he heard Alex Chadwick say the sentence below on the National Public Radio Show “Day to Day”. This sentence has an interesting example of a split infinitive in it:

But still, the policy of the Army at that time was not to send – was specifically to not send – women into combat roles.

Here, Mr. Chadwick corrects himself from not splitting an infinitive (was not to send) to a form where the word not appears between to and send, thus creating a classic violation of this prescriptive rule. One might wonder why he would correct the sentence in the wrong direction. Pullum observes that the two versions mean quite different things. The policy was not to send women into combat means that it was not the policy to send women into combat (i.e. negating the existence of such a policy). The sentence with the split infinitive by contrast, means that there was a policy and it was that they didn’t send women into combat. It’s a subtle but important distinction in the discussion. Note that putting the not after send would have rendered the sentence utterly unintelligible. With this background in mind, provide an argument that linguists should probably ignore prescriptive rules if they’re trying to model real human language.

CPS2. ANAPHORA

[Creative and Critical Thinking, Data Analysis; Challenge]

In this chapter, as an example of the scientific method, we looked at the distribution of anaphora (nouns like himself, herself, etc.). We came to the following conclusion about their distribution:

An anaphor must agree in person, gender, and number with its antecedent.

However, there is much more to say about the distribution of these nouns (in fact, chapter 5 of this book is entirely devoted to the question).

Part 1: Consider the data below. Can you make an addition to the above statement that explains the distribution of anaphors and antecedents in the very limited data below?

1 Geordi sang to himself.
2 *Himself sang to Geordi.
3 Betsy loves herself in blue leather.
4 *Blue leather shows herself that Betsy is pretty.

Part 2: Now consider the following sentences:²²

e) Everyone should be able to defend himself/herself/themselves.

f) I hope nobody will hurt themselves/himself/herself.

Do these sentences obey your revised generalization? Why or why not? Is there something special about the antecedents that forces an exception here, or can you modify your generalization to fit these cases?

CPS3. YOURSELF

[Creative and Critical Thinking; Challenge]

In the main body of the text we claimed that all anaphors need an antecedent. Consider the following acceptable sentence. This kind of sentence is called an “imperative” and is used to give orders.

1 Don’t hit yourself!

Part 1: Are all anaphors allowed in sentences like (a)? Which ones are allowed there, and which ones aren’t?

Part 2: Where is the antecedent for yourself? Is this a counterexample to our rule? Why is this rule an exception? It is easy to add a stipulation to our rule; but we’d rather have an explanatory rule. What is special about the sentence in (a)?

CPS4. CONSTRUCT AN EXPERIMENT

[Creative and Critical Thinking; Challenge]

Linguists have observed that when the subject of a sentence is close to the verb, the verb will invariably agree with that subject.

1 She is dancing.
2 They are dancing.
3 The man is dancing.
4 The men are dancing.

But under certain circumstances this tight verb–subject agreement relation is weakened (sentence taken from Bock and Miller 1991).

e) The readiness of our conventional forces are at an all-time low

The subject of the sentence readiness is singular but the verb seems to agree with the plural

forces. The predicted form is:

f) The readiness of our conventional forces is at an all-time low.

One hypothesis about this is that the intervening noun (forces) blocks the agreement with the actual subject noun readiness.

Construct an experiment that would test this hypothesis. What kind of data would you need to confirm or deny this hypothesis? How would you gather these data?

CPS5. OFF WE GO ²³

[Critical thinking; application of skills; Challenge]

Consider the expressions off we go and in you go. There seems to be some limits on which prepositions and verbs can be used in this construction.

Considering 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:

1 The students met to discuss the project.
2 The student met to discuss the project.
3 The class met to discuss the project.

1 Zeke cooked and ate the chili.
2 Zeke ate and cooked the chili.

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.

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?

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 the proof given immediately above really prove?

Question 4: Given that S can be neither a finite nor an infinite set, is there any way we might recast the premises, terminology, or conclusion in order not to have a circular argument and at the same time capture the intuitive insight of the claim? Explain how we might do this or why it’s impossible. Try to be creative. There is no “right” answer to this question. Hint: one might try a proof that proves that a subset of the sentences of English is infinite (and by definition the entire set of sentences in English is infinite) or one might try a proof by contradiction.

Important notes:

1 Your answers can be given in English prose; you do not need to give a formal mathematical answer.
2 Do not try to look up the answer in the papers cited above. That’s just cheating! Try to work out the answers for yourself.

CPS9. ARE INFINITE SYSTEMS REALLY UNLEARNABLE?

[Creative and Critical Thinking; Challenge]

In section 4.3, you saw the claim that if language is an infinite system then it must be unlearnable. In this problem set, you should aim a critical eye at the premise that infinite systems can’t be learned on the basis of the data you hear.

While the extreme view in section 4.3 is logically true, consider the following alternative possibilities:

1 We as humans have some kind of “cut-off mechanism” that stops considering new data after we’ve heard some threshold number of examples. If we don’t hear the crucial example after some period of time we simply assume it doesn’t exist. Rules simply can’t exist that require access to sentence types so rare that you don’t hear them before the cut-off point.
2 We are purely statistical engines. Rare sentence types are simply ignored as “statistical noise”. We consider only those sentences that are frequent in the input when constructing our rules.
3 Child-directed speech (motherese) is specially designed to give you precisely the kinds of data you need to construct your rule system. The child listens for very specific “triggers” or “cues” in the parental input in order to determine the rules.

Question 1: To what extent are (a), (b), or (c) compatible with the hypothesis of Universal Grammar? If (a), (b) or (c) turned out to be true, would this mean that there was no innate grammar? Explain your answer.

Question 2: How might you experimentally or observationally distinguish between (a), (b), (c) and the infinite input hypothesis of 4.3? What kinds of evidence would you need to tell them apart?

Question 3: When people speak, they make errors. (They switch words around, they mispronounce things, they use the wrong word, they stop mid-sentence without completing what they are saying, etc.) Nevertheless children seem to be able to ignore these errors and still come up with the right set of rules. Is this fact compatible with any of the alternative hypotheses: (a), (b), or (c)?

CPS10. INNATENESS AND PRESCRIPTIVISM?

[Creative and Critical Thinking; Challenge]

Start with the assumption that i-language is an instinct. How is this an argument against using prescriptive rules?

CPS11. LEARNING PARAMETERS: PRO-DROP

[Critical Thinking, Data Analysis; Challenge]

Background: Among the Indo-European languages there are two large groups of languages that pattern differently with respect to whether they require a pronoun (like he, she, it) in the subject position, or whether such pronouns can be “dropped”. For example, in both English and French, pronouns are required. Sentences without them are usually ungrammatical:

a) He left.	b) *Left
c) Il est parti. (French) he is gone “He left.”	d) *est parti	(French)

In languages such as Spanish and Italian, however, such pronouns are routinely omitted (1S = first person, singular):

e) Io telefono.	f) Telefono.	(Italian)
I call.1S	call.1S
“I call (phone).”	“I call.”

Question 1: Now imagine that you are a small child learning a language. What kind of data would you need to know in order to tell if your language was “pro-drop” or not? (Hint: Does the English child hear sentences both with and without subjects? Does the Italian child? Are they listening for sentences with subjects or without them?)

Question 2: Assume that one of the two possible settings for this parameter (either your language is pro-drop or it is not) is the “default” setting. This default setting is the version of the parameter one gets if one doesn’t hear the right kind of input. Which of the two possibilities is the default?

Question 3: English has imperative constructions such as:

g) Leave now!

Why doesn’t the English child assume on the basis of such sentences that English is pro- drop?

CPS12. EXPLANATORY ADEQUACY

[Creative and Critical Thinking; Challenge]

In the text above, we said that in order for a hypothesis to be explanatory it had to account for how the system came to be, e.g. it had to account for how children acquire the system. Discuss the following question: Does a syntactician actually have to conduct experiments with children for the hypothesis to be explanatory? Or does it suffice that their hypothesis simply make predictions about how children learn a language, for that hypothesis to be explanatory?

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