Problem Set 5 Due: 4/23/15 Theories of Concepts `Would you tell me,' said Alice, a little timidly, `why you are painting those roses?' Five and Seven said nothing, but looked at Two. Two began in a low voice, `Why the fact is, you see, Miss, this here ought to have been a red rose-tree, and we put a white one in by mistake; and if the Queen was to find it out, we should all have our heads cut off, you know. So you see, Miss, we're doing our best, afore she comes, to--'. At this moment Five, who had been anxiously looking across the garden, called out 'The Queen! The Queen!' and the three gardeners instantly threw themselves flat upon their faces. There was a sound of many footsteps, and Alice looked round, eager to see the Queen. Alice in Wonderland by Lewis Carrol (1865). In this passage, Alice learns that queen of heart wanted red roses and the cards are hoping to please her by painting the roses red. Assume that the cards finish the job before the queen arrives. Have they now created “red roses”? 1. Answer this question from the perspective of the: A) classical theory, B) the prototype theory, and C) the theory-theory. Assume that the concept RED ROSE is composed of two concepts (RED and ROSE). For each theory, be sure to explain: how concepts are represented in that theory; what a possible representation of these two constituent concepts would be; and how they could be joined to form the representation of the phrase. [one short paragraph for each] A. For classical theory every concept is a set of necessary and sufficient features [which are grounded in perception]. “Red” would be defined by the percept that is triggered by a particular wavelength of light [fine if you say the concept that is triggered, on this theory concepts are percepts]. Similarly “rose” would be defined in terms of the perceptual features that you consistently experience when encountering a rose (HAVING PETALS, ROUND SHAPED) [fine if you pursue a neo-classical theory with more abstract features such as PLANT]. The meaning of red rose is the union of this feature set [“combination of these features” is fine], so assuming the definitions above that is: ROUND SHAPED, HAVING PETALS and RED. If the new red roses have all those features then the cards have created red roses. [If rose is given a feature that is not present in the painted roses—such as sweet smelling—then the cards have not created red roses because all features are necessary].
Note: some of you tried to make red into a complex concept (having a feature like COLOR in addition to the percept). It was our teaching example of a simple concept. Critically, on the classical theory, categorization is always grounded in features that are triggered by experience via the senses. So RED is triggered whenever you see red and thus it will be present in a red rose. Please note that this is true even in versions of the classical theory that have more abstract features. On these neo-classical theories we have the innate ability to detect instances of abstract notions (like ANIMATE, OBJECT, MALE) on the basis of our sensory experiences. So these abstractions are still perceptually primitive.
B. For prototype theory each concept a set of features (again triggered by sensory experience) and the probability that the feature is present for instances of the relevant kind. These features, along with their weights, provide a graded measure of how prototypical a given instance is for the category. To get the question right the you need to construct a prototype of red and rose. Rose shouldn’t cause difficulty but will be variable (Example: .75 SWEET SMELLING; 1 PLANT; 1 HAVING PETALS; .8 PLIANT; .9 NON-STICKY). Red may be hard, since the only feature that is likely to occur with any consistency is the perceptual experience of that wavelength (so the prototype theory for this concept really reduces to the classical). Combine the prototypes together and evaluate how good an instance of red roses the painted roses are. Ex: given my prototype of rose these are pretty lousy red roses because they are not SWEET SMELLING, PLIANT or NON-STICKY. So the total is less than a twist of red tissue paper sprayed with perfume. If you have different features for rose, you could as well find the painted rose a good red roses.
C. On the theory-theory the meaning of rose depends on the larger theory in which it is embedded. In the case of natural kinds (like roses) this is a theory in which there is some fundamental internal property (an essence) that specifies the kind of plant or animal it is and gives rise to its external properties. Thus the rose is still as much a rose as it ever was, despite the alteration. What is the meaning of red on theorytheory? Presumably it depends on some naive theory of hue (that it is an external property?) . The theory-theory has no claims about composition. One possibility is that it is set intersection: if you meet the theoretically defined criteria for roses (having the internal property) and redness (having the hue), then you are a red rose.
2. For each of the three theories, how does your answer change if we assume that RED ROSE is a single concept (with its own definition, prototype or theory). [~2 sentences each]
A. Classical theory: you collect the set of features that consistently occur in red roses and treat all features as individually necessary and mutually sufficient. This is likely to be the same feature set (ROUND SHAPED, HAVING PETALS and RED), so my answer doesn’t change. B. Prototype theory: you collect the set of features that probabilistically occur for red roses and treat them as determining graded notion of category membership. Since red roses are even more likely to share many features (than all roses) that these painted roses do not, the odds that I see this as a good exemplar of a red rose seem slim. Again, the answer depends on the features you chose. C. On the theory-theory a red-rose would be a natural kind with a specific essence which gives rise to its external properties (such as being red). The red roses don’t have this essence (they have white rose essence) and so changing their color won’t fix things.
Word Learning Many people assume that children learn words through simple association. The child links a label with the correct concept because the label and the concept occurred at the same time. Explain why this simple learning story will not work (provide at least two arguments). Describe three reasons why the child is able to succeed at word learning despite these obstacles. Provide a piece of experimental evidence that supports one of these claims. Be sure to explain the task, the independent variable, the dependent variable and the finding. [2-3 short paragraphs] This question is straight out of the lecture. Simply an opportunity to review A. Why the simple word learning theory is wrong: 1. The correct concepts and the labels do not always co-occur. A lot of sentences children hear are imperatives. E.g. when their parents say “tie your shoes” there is not action of tying the shoes. 2. There are many abstract concepts that cannot be learnt this way. 3. There are a lot of objects in the environment and children need to figure out which one get the label they hear. They probably won’t be able to figure this out the first time they hear it. They may have to hear the label in many different contexts and rule out other possibilities. Therefore, word learning should be slow. However, children learn words pretty fast. Therefore, the simple learning story cannot be true.
4. The ruling out procedure cannot help us with un-detachable parts such as “ear”. It will always co-occur with other parts of the body.
B. 3 reasons kids succeed: 1) there are constraints on the kinds of hypotheses that they consider; 2) they use social cues to focus in on the correct referent; 3) they use syntactic context to figure out the type of meaning (or the focus in on the referent). C. There are a number of examples in the lecture (Brown’s sebbing study, Baldwin eyegaze, the Markman taxonomic bias). Ex. In Baldwin study, two objects A & B are placed. side by side and the experimenter will ask the question “Can you give me the blicket?” to a child (18m) who is looking at one object (A), in one of the two conditions: the experimenter either: (a) looks at A and says: “Look, a blicket!” (Follow-in condition ); or looks at another object (B) instead (Disjoint condition ). Therefore, the Independent Variable (IV) is the Condition. The Dependent Variable (DV) is % correct choices. The results are children did as well in the Disjoint condition as the Follow-in condition. This means that children make full use of social cues.
Entailment For each of the following pair of sentences, specify whether the first entails the second and/or viceversa. Justify, in a concise form, your reply Example 0)
a. Every tall Italian complained b. Every Italian complained (b) entails (a), for (c) would be an incoherent discourse c. Every Italian complained. But not every tall Italian did. (a) does not entail (b), for the following is a coherent discourse: d. Every tall Italian complained, while not every Italian did
1) 2) 3) 4)
a. Every Italian smokes b. Every Italian smokes cigars a. Every Italian smokes b. Every tall Italian smokes cigars a. John solved this difficult problem b. John is intelligent a. Some first year students frowned b. Every first year student frowned
Answers: (1b) entails (1a) because the following is incoherent: c. Every Italian smokes cigars, but not every Italian smokes (1a) does not entail (1b) because the following is coherent:
d. Every Italian smokes, but not every Italian smokes cigars (2a) does not entail (2b) because the following is coherent: c. Every Italian smokes, but not every tall Italian smokes cigars (2b) does not entail (2a) because the following is coherent: d. Every tall Italian smokes cigars, but not every Italian smokes (3a) does not entail (3a) because the following is coherent: John solved this difficult problem, but he is not intelligent (it was a stroke of luck) (3b) does not entail (3a) because the following is coherent: John is intelligent but he didn’t solve this difficult problem (4a) does not entail (4b) because the following is coherent: Some first year student frowned, but not every first year student did (4b) does entail (4a), because the following is contradictory: Every first year student frowned but it is not the case that some first year student did Or Every first year student frowned but no first year student did
