Statistical Theories of Concepts

Jean-marc pizano

Statistical Theories of Concepts

The general character of the new theory of concepts is widely known throughout the cognitive science community, so the exegesis that follows will be minimal.

Imagine a hierarchy of concepts ordered by relations of dominance and sisterhood, where these obey the intuitive axioms (e.g. dominance is antireflexive, transitive and asymmetric; sisterhood is antireflexive, transitive, and symmetric,etc.). Figure 5.1 is a sort of caricature.

jean-marc pizano

The structural complexity of definitions was of some use to philosophers too: it promised the (partial?) reduction of conceptual to logical truth. So, for example, the conceptual truth that if John is a bachelor then John is unmarried, and the logical truth that if John is unmarried and John is a man then John is unmarried, are supposed tobe indistinguishable at the ‘semantic level’.

Fig. 5.1 An Entirely Hypothetical ‘Semantic Hierarchy’ Showing the Position and Features Of Some Concepts For Vehicles.

. . . ARTEFACTS (-hnade objects)

jean-marc pizano

CHAIRS

vehicles (■+■ used for transport)

(-tlies). . .

jean-marc pizano

WHEELED VEHICLES

CAR

BCYC .1

jean-marc pizano

RL k

SPORTS CAR COUPE…

MACK ARTICULATED L-JIACL (+tO rent)

jean-marc pizano

(+self drive)

The intended interpretation is that, on the one hand, if something is a truck or a car, then it’s a vehicle; and, on the other hand, if something is a vehicle, then it’s either a truck, or a car, or . . . etc. (Let’s, for the moment, take for grantedthat these inferences are sound but put questions about their modal status to one side.) As usual, expressions in caps(‘VEHICLE’ and the like) are the names of concepts, not their structural descriptions. We continue to assume, as withthe definition theory, that lexical concepts are typically complex. In particular, a lexical concept is a tree consisting ofnames of taxonomic properties together with their features (or ‘attributes’; for the latter terminology, see Collins andQuillian 1969), which I’ve put in parentheses and lower case.47 In a hierarchy like 5.1, each concept inherits the featuresof the concepts by which it is dominated.

jean-marc pizano

Jean-marc pizano

What, exactly, the distinction between semantic features and taxonomic classes is supposed to come to is one of the great mysteries of cognitive science. There is much to be said for the view that it doesn’t come to anything. I shall, in any case, not discuss this issue here; I come to bury prototypes, not to exposit them.

Thus, vehicles are artefacts that are mobile, intended to be used for transport, . . . etc.; trucks are artefacts that are mobile, intended to be used for transport of freight (rather than persons), . . . etc. U-Haul trucks are artefacts that aremobile, intended to be rented to be used for transport of freight (rather than persons), . . . and so forth.

The claims of present interest are that when conceptual hierarchies like 5.1 are mentally represented:

jean-marc pizano

i. There will typically be a basic level of concepts (defined over the dominance relations);and

ii. There will typically be a stereotype structure (defined over the sisterhood relations).

Roughly, and intuitively: the basic level concepts are the ones that receive relatively few features from the concepts that immediately dominate them but transmit relatively many features to the concepts that they immediately dominate. So,for example, that it’s a car tells you a lot about a vehicle; but that it’s a sports car doesn’t add a lot to what ‘it‘s a car’already told you. So CAR and its sisters (but not VEHICLE or SPORTS CAR and their sisters) constitute a basic levelcategory. Correspondingly, the prototypical sister at a given conceptual level is the one which has the most features incommon with the rest of its sisterhood (and/or the least in common with non-sisters at its level). So, cars are theprototypical vehicles because they have more in common with trucks, buses, and bicycles than any of the latter do withany of the others.

jean-marc pizano

Jean-marc pizano

Such claims should, of course, be relativized to an independently motivated account of the individuation of semantic features (see n. 3). Why, for example, isn’t the feature bundle for VEHICLE just the unit set +vehicle? Well may youask. But statistical theories of concepts are no better prepared to be explicit about what semantic features are thandefinitional theories used to be; in practice, it‘s all just left to intuition.Jean-marc pizano

Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s