Lec 1

• My Critics

• What are concepts? Are FROG OR LAMP, OBJECTS THAT WEIGH MORE THAN A GRAM, and JUSTICE concepts? Not trivial to reject so let’s grant them for now. Let’s say concepts are just Fregean senses—a combination of the referenced category and the mode of presentation used.

• If I write a piece about concepts, I will start with listing empirical facts to be explained. Listing theories and occationally mention phenomena risks applying varying standard to different theories. How psychologically relevant the concept OBJECTS THAT WEIGH FORTY POUNDS is related to its inductive protential, which should be demonstrated empirically rather than arguing from an armchair that it is “a perfectly fine concept.”

• Why exactly is Dual Theory no good? How is prototype being non-constituative bad?

  • The lack of definition problem.

• So what happened in the past 27 years?

Laurence, S., & Margolis, E. (1999). Concepts and Cognitive Science, In Concepts: Core Readings, E. Margolis & S. Laurence (eds.), pp. 3-81.

Preliminaries

The Classical Theory of Concepts

• The Definition View; Most concepts encode necessary and sufficient conditions.
• The Containment Model suits better here than the Inferential Model because it makes it clear which are defining features and which are incidental.
• Problems
  • Difficult to obtain definition
  • No evidence that definitional complexity is psychologically real
  • The problem of analyticity.
    • Background: Logical positivists want to say logical and mathematical statements are analytic, tautologies we know a priori. Quine criticizes, pointing out that confirmation is inherently holistic. Individual statements are never confirmed in isolation. No statement can be known a priori that are insulated from empirical test.
    • TODO
  • The problem of ignorance and error
    • Kripke and Putnum’s arguments against descriptivist views. Classical Theory is, in effect, descriptivism applied to concepts.
    • E.g., People used to understand the disease SMALLPOX wrongly and ignorantly. → Then, did they understand the concept, or simply talking about a different concept?
    • “when two people differ on the symptoms they associate with measles, they would appear to be in disagreement; that is, they appear to be arguing about the best evidence for deciding whether measles is present. But if the identity of MEASLES is given by the procedures under which one decides whether it is instantiated, then we'd have to say that the two couldn't disagree about the symptoms associated with measles. At best, they would be talking at cross purposes, one about one ailment, the other about another”
  • The Problem of Conceptual Fuzziness
    • “How can a Classical Theory account of FURNITURE allow it to be indeterminate whether carpets fall under FURNITURE, or explain how we are unable to decide whether carpets fall under FURNITURE?”
    • A possible move is reducing this to the lack of definitions. Given one, such as BLACK CAT as black cat, then fuzziness can come from the fuzziness of BLACK.
  • Cannot explain typicality effects (and its relationship to shared features, speed, & error rates)

Prototype theory

• Interconnected set of features. E.g., Small birds sing and large birds don’t.
• Measures for similarity
  • Amos Tversky’s Contrast Principle.
    • $sim(I,J) = af(I \cap J) - bf(I\setminus J) - cf(J \setminus I)$
    • This does not predict assymmetry of similarity judgment though.
  • One way to account for conceptual fuzziness is that membership based on similarity is not clear cut.
• Problems
  • prototypical primes
    • Prediction by Sharon Armstrong: if typicality effects reveal that a concept has statistical structure, then well defined concepts (people know, and can readily produce, their definitions; such as EVEN NUMBER or GRANDMOTHER) shouldn't exhibit typicality effects.
    • Finding: the number 8 was ranked as a better example of an even number than the number 34 is. Typicality correlates with speed and accuracy of categorization.
    • Reconciliation:
      • Typicality may reflects underlying prototype but not degrees of membership. There are evidential features and constitutive features.
      • Dual Theories of concepts
        • Identification procedure. Quick categorization judgments.
        • Core procedure. When cognitive resources are not limited.
  • The problem of ignorance and error
    • Prototype representations don’t determine the correct extension.
    • We could make the move that substantial deviation from prototype means no a category member. To leave room for misrepresentation, think of dual theories of concepts. Then, we are back to the same situation as Classical Theory.
  • The Missing Prototypes Problem.
    • Fodor: “There may be prototypical cities (London, Athens, Rome, New York); there may even be prototypical American cities (New York, Chicago, Los Angeles), but there are surely no prototypical American cities situated on the East Coast just a little south of Tennessee. Similarly, there may be prototypical grandmothers (Mary Worth) and there may be prototypical properties of grandmothers (good, old Mary Worth). But there are surely no prototypical properties of, say, Chaucer's grandmothers, and there are no prototypical properties of grandmothers most of whose grandchildren are married to dentists.”
    • Concepts like BELIEF, DESIRE, and JUSTICE
    • People can have different ideas of the prototype for the same (or actually different?) concept. People who do not represent any properties as being statistically prominent for the concept DON DELILLO BOOK can still use the concept to support inductive inferences, organize memory, or engage in categorization.
  • Compositionality
    • Fodor: Prototypes of compositional concepts aren't always a function of the prototypes of their constituents. Consider PET FISH.
    • James Hampton: Also consider WOODEN SPOON. It is subject to real-world knowledge that they are larger than other spoons and are used for cooking, not eating.
    • Fodor & Lepore: “one can't allow experience to fix the prototype of a complex concept without admitting that such prototypes are essentially idioms.” and “Prototypes aren't compositional; they work like idioms. Concepts, however, must be compositional; nothing else could explain why they are productive. So concepts aren't prototypes.”
• “prototypes seem more and more like cognitive structures that are merely associated with concepts rather than structures that are part of the nature of concepts. The more it's granted that prototypes are optional, and that the prototypes for complex concepts act like idioms, the less essential prototypes seem to be.”
• “Many lexical concepts have prototypes that are associated with them but that the prototypes aren't in any way constitutive of the concepts.”