Cognitive and cultural phenomena (i.e., beliefs, ideas, attitudes, ways of thinking, etc.) can be represented or modeled in a variety of ways. Some people think of the representations that scientists develop as closely related to the way the brain really works. Others see them more as mathematical models which make accurate predictions and which are readily comprehensible. I am in the latter camp. While I think it is a good research strategy to intend to develop representations that are "really" how biological brains do it, I am aware that every representation is necessarily highly situated in the concepts and language of our day. A representation is good if it permits accurate predictions, but the representation should never be confused with the thing itself. A representation is a mapping of the real world into the socially constructed cognitive that humans work in. There will always be alternative representations that are equally good.
Some of the representations are nearly interchangeable, while others are really quite different and would distort the relationships implied by some of the other models.
Here we locate semantic items in a multidimensional space such that every item is assigned coordinates such as (1.56, -0.28) and the semantic similarity of two objects is given by the Euclidean distance between the locations they occupy. If the concept "Steal" is located at (1.56, -0.28) and "Buy" is located at (1.10, 0.50), then the distance between them is defined as the square root of the sum of the squared differences along each dimension (i.e., the square root of 0.462+0.782). For more information, see Borgatti. Elicitation methods for cultural domain analysis..
This is the representation used by MDS.
A taxonomy is basically an ordered tree structure in which all items except one are included in another item. For example, Mike Burton found, for North Americans, that the set of English role terms breaks down this way:
The names for the groups of terms are not necessarily the names used by natives: they are just labels for groupings.
The ability and desire to classify the world into hierarchical tree structures appears to be universal. It is seen in all cultures, and it is strongly apparent in children. It is a fundamental feature of human thought.
The importance of understanding how people categorize the world is widely recognized in many social science literatures including organization studies.
The basic idea in componential analysis is that all items in a domain can be decomposed into combinations of semantic features which combine to give the item meaning. This is a perspective that was first developed in linguistics. Look at these terms for horses and pigs:
|stallion||horse + male + adult|
|mare||horse + female + adult|
|gelding||horse + neuter + (adult | adolescent)|
|filly||horse + female + adolescent|
|colt||horse + male + child|
|foal||horse + (male | female) + baby|
*Colt used to be gender-neutral.
We can reformat as a paradigm:
The lack of separate words male and female horses when they very young suggests that there is no pressing need to know, on a daily basis, what sex they are until after puberty.
Here are the comparable terms for pigs:
|boar||pig + male + adult|
|sow||pig + female + adult|
|barrow||pig + neuter + (adult | adolescent)|
|gilt||horse + female + adolescent|
|shoat||horse + (male | female) + child|
|piglet||horse + (male | female) + baby|
Notice how similar they are to horses.
Notice that the meaning of each term is distinguished by the presence or absence of basic attributes. It is as if we construct mental constructs by combining mental building blocks.
The attributes in this particular analysis -- sex, age, and basic species type -- turn out to be fundamental distinctions that are used over and over again by humans as they order their worlds.
Notice also that the pig domain is completely analogous to the horse domain. This kind of analogical isomorphism is extremely common in human belief and terminological systems. That is, we apply our understanding of one domain to understand or organize another domain.
An example is the componential analysis of North American English kinship terms by Wallace and Atkins:
See how north american english kinship roles are distinguished from each other by three basic attributes: sex, age (generation), and lineal remove. Two of these attributes (age and sex) are the same ones used in the pig and horse domains. Interestingly, these two attributes are also fundamental attributes in human social division of labor and role behavior. In fact, these two are the only two universal attributes that all human societies use to discriminate among members. In small hunter-gatherer societies there are typically only two culturally-determined bases for social differentiation, and these are sex and age.
See the handout of testing cognitive structures for more information on the kinship componential analysis.
A paradigm is a cognitive system in which the system elements are distinguished from each other by having different values on a set of common attributes. These attributes apply to all the items. For example, in the kinship terms, we can take each role and ask 'what generation is it?', or 'what sex is it?'. The answers vary but the questions are always meaningful.
In contrast, the items in a taxonomy do not share a common set of attributes. Consider the folk classification of all matter as belonging to one of three categories: animal, mineral or vegetable (meaning "plant"). Within animal we then have mammal, reptile, fish, insect, bird, and amphibian. Within vegetable, we tree, shrub, grass etc. The distinctions among the groups of animals are not the same distinctions made among the plants. Among plants we might ask whether it has flowers or not. Or whether it has berries. These questions don't make sense for animals. Similarly questions that apply to some animals don't apply to plants: Are the feet webbed or not?
One way to think about the difference between paradigms and taxonomies is that in paradigms, the attributes are applied paradigmatically or in parallel or simultaneously. In taxonomies, the attributes are applied syntagmatically or in series or sequentially. One is cross-sectional and the other longitudinal.
Another way to think about it is that paradigms exist among items that are at the same level of contrast in a taxonomy.
Organizational theory is often paradigmatic. See for example the two by two tables of early contingency theory, such as Perrow's classification of organizational technologies:
|few exceptions||many exceptions|
Or the life-cycle model of leadership:
|low guidance||high guidance|
The paradigmatic approach, together with the assumption of analogical processes is the basis for Levi-Straussian analysis of stories and culture in general.
See the handout devoted to causal networks.
See the handout devoted to schemas.