Lecture #11 (March 02)

Features

Discrete attributes of objects

Prototype Theory in Continuous Feature Space

Compute central tendency (eg. mean) for each category, compute distance between new instance + each category mean, and compute similarity of each instance to each category mean + use this to classify based on similarity

Mean/SD measuring spread of distribution

Basically computing groupings with averages that represent the categories with positive and negative

Exemplar Theory in Continuous Feature Space

Compute the distance between each new instance + each stored exemplar; Computed + classified based on similarity

What is the main focus in prototype view?

Mean; The most typical ex

Is there exponential decay for prototype or exemplar and new instance?

Yes

Linearly Separable Category (In Hyperplane Model)

There exists a line that separates two features; There is an optimal linear classification boundary

Classification Boundry

The approx boundary between positive + negative

Linear Bonds

Easy to kind of classify on a plane; A moreso straight line to sep features

Quadratic Bounds

Humans can handle these + linear bounds are a special case; When the line is somewhat curvy to sep features

Theory Theory

People don’t categorize things just by similarity or feature-matching - they use implicit “theories” about how the world works; Categorize and concepts involve background knowledge + context, and depend on a theory of the world

Philosophical Holism

Concepts cant be understood in isolation

Conceptual Coherence

Why is dog a reasonable category but women, fire, and dangerous things is not?; A category is conceptually coherent if its members belong together because of the same underlying explanation

What do psychologists believe post-1960 believe about concepts and their boundaries? (modern understanding of concepts)

Concepts are “fuzzy” BUT the role of concepts is inferential, only definitions have inferential properties, concepts cant be definitional, so therefore concepts cant be inferential

What do psychologists believe post-1960 believe about concepts and their properties? (modern understanding of concepts)

The key role of concepts is inferential (rex barks bc rex is a dog and dogs bark) + only definitions have inferential properties (depends on classical model)

Prob → only defs have inferential properties + concepts cant be definitional, meaning that concepts cant be inferential

Concepts cannot be definitional, so therefore, concepts cant be inferential → doesnt make sense

Does the modern understanding of concepts make sense?

No

Says that only defs have inferential properties + concepts cant be definitional → therefore concepts cant be inferential

Atomism

Concepts are atomic concepts; Implies that all (including modern) concepts are innate

Ex. Helicopter + Plastic Surgery are innate concepts

Complex Concepts

Have meanings that are related to the meanings of the individual concepts

Compositionality

Refers to the way meanings of individual concepts combine to form meanings of complex concepts; Works perfectly in Russel’s theory of definite descriptions

Ex. Brown cow should mean something thats a combo of the word brown and the word cow

Russel’s Theory of Definite Descriptions

Compositionality works perfectly

Ex. BROWNCOW(x) → BROWN(x) & COW(x)

Ex. REDBALL(x) ←→ RED(x) & BALL(x)

Ex. The boy goes to the movies means [some combo of the meanings of the, boy, goes, to, the, and movies]

What do Empiricists Argue about Complex Combinations + Concepts?

Argue that concepts are complex combinations of primitive sensory experience + we use internal mental processes to reason about them

BUT → can you interpret sense data without innate assumptions?

What do Rationalists Argue about Complex Combinations + Concepts?

Argue that concepts are complex combinations of primitive internal ideas; These internal ideas are critical to our interp of sense data

BUT → is it possible to know about the world without empirical observation

Compositionality

We understand complex ideas because we understand their parts and how those parts are put together

What does Compositionality Req?

1. Complex ideas have meanings that are computable from the meanings of their constituents

2. Concepts can combine freely (productivity) (if you can understand John loves Mary you can understand Mary loves John)

3. Concepts have systematic relations (DOG and MAMMAL are related in a way thats dif than DOG and CAT)

Productivity in Compositionality

Concepts can combine freely

Ex. If you can understand John loves Mary, you can understand; You can understand (and generate) new combinations of concepts you’ve never seen before, as long as you know the parts and the structure

What does Compositionality Req?

Systematic Relations in Compositionality

Understanding one concept implies understanding other, related concepts in a structured way

Ex. DOG and MAMMAL are related in a way thats dif than DOG and CAT

Fodor’s Compositionality Argument

While compositionality works perfectly in the classical model, it is difficult or impossible to work with prototypes; Instead compositional concepts take on new meanings (like pet fish)

Ex. Classically, a purple cow is a thing that is both purple and a cow

But with prototypes, a purple cow, should be something that is both prototypical of cows + prototypical of purple things (which is not true here)

Are human concepts compositional?

For some complex concepts, the combined concept does NOT seem to derive properties only from the individual concepts (ex. pet fish → has characteristics that neither pets nor fish usually have)

Other complex concepts combine in unpredictable ways (gold fish is a fish thats colored gold vs gold bar, a bar thats made of gold)

Possible Solutions to if human concepts are compositional

• Human concepts arent really prototypes (not fuzzy)

• Conceptual combination in prototypes works some other way, to be discovered

• All compositional concepts are innate including helicopter, telescope, bingeworthy, etc (literally only Fodor)