Categories and Concepts

Categories versus Concepts

• Objects
• Natural kinds
• People
• Events
• Ideas

• Some kind of identification procedure
• Inferences which can be made either strongly or weakly.

Categories and Computational Complexity

• Without categories we'd have to treat each new instance as if it were one of a kind
• Categories allow for prediction
• Categories allow for communication
• Categories allow for abstract thought

Two Issues We'll Talk About

• How do you determine whether an instance belongs to a category?
• What makes categories good categories?

Classical View of categories

• Basically says that categories membership is determined by matching a definition
• Category membership is defined by a set of features which are
• Wholly necessary (each feature must be present)
• Jointly sufficient (If each feature is present that's all you need)
• Evidence For Classical Categories: The idea of classical categories was developed by early philosophers and some linguists, and their evidence for the idea was based on a linguistic and logical analysis of a circumscribed group of categories for which the classical model seems to work:
• Triangle: A closed figure with three sides.
• Even number: Any whole number which when divided by 2 does not leave a remainder.
• Bachelor: An adult male who has never been married.
• Problems for the classical view:
• For most concepts it is difficult to specify a complete set of necessary and sufficient features (Wittgenstein).
• Categories show graded structure
• When people are provided with examples of a category some examples are judged to be more typical than other examples.
• For instance, a robin is more typical of the category bird than is ostrich.
• People identify typical instances more quickly than atypical instances too.
• Unclear cases: Should a rug be considered furniture, clock radio. Subjects disagree with each other about these examples and even disagree with themselves on different occasions.
• Even classical categories show graded structure and unclear cases. Should a priest be considered a bachelor?

The Prototype Model

• The claims of the Prototype account
 
• There are no necessary and sufficient features for categories
• Instead categories are defined in terms of a set of typical or likely features.
• Category members share a family resemblance.
• Category membership is determined by comparing the instance to a category Prototype.
• The view assumes that prototypes are pre-stored in memory***
• Prototype is a kind of average of all the group members. The prototype does not correspond to any actual group member but is a summary of all the group members.*
• Evidence in favor of the prototype model
• Posner & Keele (1967): Presented people with dot patterns that were variations of a never shown prototype.  In a later classification test subjects could classify the never seen prototype as easily they could patterns that they had previously studied.

Exemplar Models of categories

• Assumptions of the Exemplar Model
• Every instance of a category is stored in memory. These instances are called exemplars of the category
• There is no pre-stored prototype.
• To decide if something is a member of a category, you retrieve (some number--perhaps all) of exemplars of that category from memory.
• Average Distance Approach:  To determine if the item is a member of the category you determine how similar the item is to each of the exemplars and then compute the average similarity
• Nearest Neighbor Approach: Find the exemplar that is most similar to the instance you are trying to categorize.  If it is similar enough, then say its a member of the category.
• How does that solve the problems of the prototype model?
• Context influences which exemplars are retrieved.
• Can use exemplars to determine variability as well as central tendency.

Knowledge based categorization

• The relationship between a example and a category is like that between a theory and data.
• Classification is not simply a matter of matching attributes but instead requires that the example have the right explanatory relationship to the theory organizing the concept.
• Example: What is the definition of "mother"?  Its not enirely intrinsic to the person.  Being a mother is defined by a set of relationships to other people.  Same is true with other categories.  Although there are physical features of CHAIRS, perhaps what's really central to being a chair is that its a device designed by people for other people to sit on.  Its physical features in fact are a function of its purpose.

The Basic Level

• The existence of categories decreases computational complexity, but it raises some computational complexity questions of its own.
Bird Animal Winged thing Flying thing Animal that lays eggs Two legged animal Not a library book Bird or piece of cheese ETC.

• Hierachical Levels:
• Subordinate: A level that's more specific than the basic level (DINING ROOM CHAIR)
• Basic Level: The level at which people prefer to categorize things (CHAIR)
• Superordinate: A level that's more general than the basic level (FURNITURE)
• People prefer to categorize at an intermediate level--The basic level
• First level learned
• Most common level named
• Most general level where shape is maintained
• Most bang for the buck. Feature listing experiments.
• Why the basic level?
• People want categories that are informative.  If you know something is a member of a category you can make inferences.  The SUBORDINATE LEVEL maximizes informativeness
• People want to keep things simple by minimizing the number of categories they need to keep track of.  They want to limit cognitive complexity.  The SUPERORDINATE LEVEL minimizes cognitive complexity.