COG250 - L_2

Reading §

• Concepts and Categorization
  • Concepts play a fundamental role in mental life, reducing the demands on perceptual processes, storage space, and reasoning processes. The document highlights the importance of categorization in coding experiences and making inductive inferences.
  • Taxonomy of Concepts: Concepts are often structured into a taxonomy—a hierarchy where successive levels refer to increasingly general kinds of objects. The concept of “fruit” would be at a high level, “apple” at an intermediate level, and “Macintosh apple” at a low level. The basic level, like “apple,” is often the preferred code for categorization.
• Inductive Inferences:
  • Categorization plays a crucial role in making inductive inferences. Categorizing an object allows us to infer invisible properties from visible ones. For instance, categorizing a round, reddish object on a tree as an apple allows us to infer that it is edible.
• Visual vs. Verbal Categorization:
  • Visual categorization (categorizing based on pictures or objects). Shape plays a significant role in visual categorization.
  • Verbal categorization (categorizing based on descriptive terms)
• Earlier approach to categorization
  • Geometric Approach: The geometric approach, which represents items in a space based on psychological distance, has been successful in representing perceptual objects. However, it faces challenges when applied to conceptual items. The document discusses the metric axioms like Minimality, Symmetry, and the Triangle inequality, and how they sometimes don’t hold for conceptual items.
  • Prototype Representation: The document introduces the idea of a “prototype”—an abstraction about categories that includes the frequent, salient features but doesn’t specify essential features. The contrast model predicts typicality based on similarity to the prototype.
• Tversky’s (1977) Contrast Model
  • Feature-Based Representation:
    • The contrast model is grounded in a feature-based representation of items. It considers three sets of features: common features (shared by both items), features distinctive to one item, and features distinctive to the other.
  • Accounting for Asymmetry:
    • Traditional geometric models assume symmetry in similarity judgments, meaning if A is similar to B, then B should be similarly close to A. However, in conceptual spaces, this isn’t always the case. For instance, an unfamiliar category (like pomegranate) might be judged more similar to a familiar category (like apple) than vice versa. The contrast model can account for such asymmetry, especially when one concept has fewer distinctive features than the other.
  • Violations of the Triangle Inequality:
    • Geometric models operate under the triangle inequality, which sometimes doesn’t hold true for conceptual items. For example, while lemon might be similar to orange and orange to apricot, lemon and apricot might be quite dissimilar. The contrast model can accommodate such violations, especially when the weight given to common features is significant.
  • Compatibility with Prototypes:
    • The contrast model aligns well with the idea of prototypes. A prototype is an abstraction about categories that includes frequent, salient features without specifying essential features. The contrast model can predict typicality based on similarity to the prototype, making it effective for categorization tasks.
  • Addressing Challenges of Geometric Approach:
    • The geometric approach, which represents items in a space based on psychological distance, faces challenges when applied to conceptual items. Tversky’s contrast model offers a satisfactory account of phenomena that troubled the geometric approach, such as violations of minimality, symmetry, and the triangle inequality.
  • Flexibility:
    • The model is flexible and can be adapted to various scenarios. For instance, it can account for the fact that a concept can serve as the nearest neighbor to multiple instances. The model suggests that more abstract concepts, having fewer distinctive features, can be closer neighbors to various instances.

Lecture §

• Importance practice to keep in mind of Cognitive Science
  • Common sense and perception, even though is importance in day-to-day life, its often problematic in doing science (common sense cannot explain common sense)
  • Confuse the direction of cause-and-effect
  • Confuse correlation and causation
  • Confuse formula with formulation
  • Rely in unprincipled distinctions (distinctions that does not exist)
• What are key thing regarding intelligence
  • Intelligence: making sense of environment to solve problems
  • Proposal: the basic ability of Cognition is categorization
• What are the 3 major characteristic of Categorization?
  • Coding and encoding of experiences/entities (abstract useful information, make generalizations)
    • Names are helpful to distinguish human as individuals vs. Category helps to minimize identification of raw material/information (require devotion, time, effort to encounter new information)
  • Inference: use categorization to generalize/to override perceptual error
    • What are the 3 major pattern of Inference
      • Deduction: if the premise is true, then is impossible for conclusion to be false
      • Induction: if the premise is true, it significantly decrease the probability (improbable) that the conclusion is false
      • Abduction: inference to the best explanation

    • All tigers are dangerous

      • Don’t have to actually encounter a tiger and learn the experience

    • Flamingo's heart example

      • Use categorization to override perceptual error

  • Simplicity in the basic level (easy to explain using common sense)
    • Difference between common sense and science (Scott Atran)
      • Common sense: Familiar --> Unfamiliar (use obvious to explain complex idea)
      • Science: Unfamilar --> Familiar (use rigid scientific fact to explain the hidden of obvious)
        • Cognitive science: explain why/how to know and explain the obvious (machine can’t detect obvious directly)
• How to understand/explain Categorization
  • Similarity explanation
    • Similarity: mentally group up objects that are similar
  • Problem of similarity
    • 1972 Nelson Goodman
      • People tend to equivocate when using similarity (equivocate logical and psychological meaning)
      • Logical similarity: sharing a lot of properties but not all properties (can be done with any 2 things)
        • Cannot explain categorization, while true, is useless
      • Psychological similarity: relevance property > similarity, without it, its useless
    • Lawrence Barsalou
      • What is relevant is related to our particular goals or context (similarityl isn’t in the things, its in the context)
      • People categorize things relative to goal or contexts
    • Lance Ripps ^def445
      • Sometimes categorization drives similarity judgements

Resemblance Theory §

• What is the similarity argument for Resemblance Theory by Smith
  • Similarity judgements ---[drives]--> judgements of categorization
  • Critiqued by Ripps
• What are the key component for Tversky’s Contrast Model
  • Pretend analyze & formalize, thus mechanization should be ready)
  • $Sim(I,J)=af(I\cap J)-bf(I-J)-cf(J-I)$
  • $f$: function for salience
    • Often referred as implicit contrast class ()
  • $a$: importance of common features of 2 items (infinite)
  • $b$: importance of properties that is unique to $I$
  • $c$: importance of properties that is unique to $J$
  • Problem
    • Formula ≠ formalize
    • The equation does not solve the relevancy issue (need relevance weight, need relevant importance, need relevance common feature…)
• What is Double dissociation, and its relation to resemblance theory
  • Change X without changing Y, change Y without changing X
  • Lance Ripps’ experiment (coin with pizza)
    • Increasing similarity not change categorization judgement (turn outs to be false)
    • Increasing categorization not change with similarity
• What is Smith’s defence with the Two Kinds of Categorization

  • Birds

    • Simiarlity-Based: flies, lays eggs
    • Reasoning-Based: produces offsprings of the same kind

  1. Similarity-based (typical)
     • Focus on perceptual-visual, concrete features (any true thing about an objects)
  2. Reasoning-based (theory-based)
     • Focus on non-perceptual (invisible-abstract) knowledge
     • Want inductive conclusion, but all facts are inductive

Classical Theory of Concept §

• What are some key landmarks in developing Classical Theory of Concept?
  • Shift from naive realism (independence/objective properties) --> Concept (mental representations)
    • Naive realism: things have true properties independence of human knowledge/perception
    • Concept: is a mental definition, definition may refer to: common sense, criterion
  • ★ Aristotle argument for essence:
    • Set of necessary and jointly sufficient conditions for being something (logical properties, innate)
    • Science is the project of finding categories that have essence
• What are the 6 claims of classical theory of concepts
  1. The meaning of a concept can be captured by a conjunctive (连词) list of features
     • $\{X:x\in \mathbb{R},x\ge 0\}$
  2. There are atomic or primitive features
     • $\mathbb{R},\ge ,0$
  3. Each feature is individually (singular) necessary, and all are jointly (the set is) sufficient
     • $X⟺\{x\in \mathbb{R},x\ge 0\}$
     • Necessary (needed 必要的) vs. sufficient (enough 充足的)
  4. What is and what is not a member of concept’s category is clearly defined
     • $-0.00001\notin X$, $0.00001\in X$
  5. All the members of a concept’s category are equally representative
     • $0,1,25,999\in X$
  6. When organized in a taxonomic hierarchy, most result in transitive inference
     • $\{Z\subset X,z\ge 100\}$, $z\in Z⟹z\in X$
     • Taxonomy infer detective reasoning
     • Concepts are transitive (Transitive Inference): subordinate definitions include the definitions of the superordinate

  • Square example for the 6 claims

    1. A triangle is a plane figure, and it has with three equal straight sides, and it has internal angle of 180 degrees.
    2. (3 sides), (3 angles)
    3. Anything that all of the atomic features of a triangle, is a triangle; anything that lacks one of the features, isn’t
    4. In geometry, something either is a triangle or isn’t
    5. No triangle is more triangle than any other square
    6. The definition of a large square includes the definition of a square

• What are the problem of classical theory
  • Wittgenstein: “Not all concepts are connected with necessary and sufficient conditions”
    • Ex. Game, chairs
    • Proposed family resemblance

Active Studying §

Summarize today’s lecture §

• [::Most important/focused topic] Critique of Resemblance theory, 6 claims of classical theory of concept
• [::Most difficult part, why, how to resolve] Remember the 4 main critique for RT, and 6 claims for CTC

What part I didn’t understand, next step actions? §

Review Dates §

• 2023-09-18: 🟨

• 2023-09-25: 🟨

• 🟩 🟨 🟥