Concept Functions & Theories

Functions of a Concept

• Categorization involves grouping concepts and assigning a novel 'thing' to a mental representation
• Example: assigning a 'thing' to the 'set' of DOGs
• Formation of a set requires having the concept of DOG or the conditions upon which it arises
• Cognitive economy avoids having a concept for each individual 'thing'
• Inferences about properties are "running categorization in reverse" as you infer properties if something is a DOG
• Conceptual combination forms novel concepts from old ones
  • Example: DOG + HOUSE → DOGHOUSE
  • The formation of the set requires having DOG & HOUSE or the conditions upon which DOGHOUSE arises
  • Applies to compounds in natural language, which can be transparent (BLUEBERRY, DOGHOUSE) or opaque (STRAWBERRY, JAILBIRD)
  • Applies to phrases/propositions such as "MY GRANDMOTHER LIVES IN A HOUSEBOAT IN AMSTERDAM"
  • The meaning of the whole must derive its meaning from its parts

Concept Theories Overview

• Classical theory: dog = {domesticated canine}; it is decompositional where features are necessary and jointly sufficient
• Prototype theory: dog = {most typical dog} {best dog}; it is decompositional where features have weights evaluated statistically; the category is represented by the prototype
• Theory theory: dog = {a dog theory} {all knowledge of dogs}; it is decompositional where features and hypotheses contribute to the content and is knowledge-based
• Stereotype theory: dog = {dog features} {any dog}; it is decompositional where core properties determine representation
• Embodied theory: dog = {dispositions, 'affordances'}; it is nondecompositional where representations constitute sensory-motor processes
• NeoClassical theory: dog = {domesticated canine; function: pet}; it is decompositional where definitions are necessary and sufficient conditions
• Atomic theory: dog = DOG (the dogness property); it is nondecompositional where lexical concepts are primitive, have no internal structure, and an abstract symbol is triggered by a word/image

Decompositional Theories

• Concepts are composed of more primitive representations (other concepts or 'features')
• Example: DOG = {ANIMATE, CANINE, PET, FURRY...}
• Understanding a word or image requires recovering a set of characteristics from memory
• Conceptual dependency means possessing a concept requires possessing its constitutive concepts ('features')

Nondecompositional Theories

• Atomic lexical concepts are primitive representations with no internal structure
• DOG = [DOG] an abstract symbol in the mind, not the word itself
• A mind-world relation exists where the word 'dog' and the image trigger the abstract symbol DOG, which carries the content DOG
• There is no conceptual dependency, as one does not need other concepts to have the concept DOG

Compositionality

• Compositionality is a test for how good a theory of concepts is
• Thoughts are compositional, meaning is a function of parts (concepts) and structure
• If thoughts are compositional, concepts should obey the compositionality principle where the meaning of the whole is a function of the parts
• A theory must demonstrate that the meaning of a thought/sentence relates to the function of its parts and their combination
• Entails a notion of "classical" composition where the meaning a concept contributes should be stable (e.g., 'LOVE' in "MARY LOVES JOHN" = "JOHN LOVES MARY")
• Concepts are elements of thoughts, represented in different ways
• Thoughts are "propositions"—structured expressions carrying meaning, and propositions are compositional
• Compositionality is a key factor in evaluating concept theories

Concepts and Cognitive Architectures

• Cognitive architecture refers to the "design and organization of the mind" or cognitive systems
• It is a set of principles for constructing cognitive models, not just hypotheses to be tested
• Consists of basic operations, resources, functions, principles whose domain and range are the representational states of the organism
• Cognitive architecture provides a concrete framework for detailed modeling by specifying essential structures, modules, relations, etc.
• Cognitive architecture matters to frames explanations about regularities in the mind/brain
• Cognitive architecture is important for investigating the wired properties of cognitive capacities
• Cognitive architecture is crucial for understanding how units of mental representation (concepts) form thoughts (plans, decisions, language comprehension)
• Cognitive architecture is essential for understanding all representations and processes in the mind/brain
• Cognitive architecture is necessary for understanding human nature and its cognitive 'design' (resources and capacities)

Distinctions in Cognitive Architectures

• Symbolic vs. Connectionist have different views on the nature of representations and processes
  • Symbolic architectures use symbols and rules with Turing-like computations
  • Connectionist architectures use nodes and connections with patterns of activation
• Modular vs. Interactive have different views on the domain-specificity of representations and processes
  • Modular architectures are domain-specific with encapsulation
  • Interactive architectures use a general database with a free flow of information
• Representationalists vs. Eliminativists have different views on mental representations using symbols/nodes vs. neurological states.
• Cognitive theories address units of representation (symbols, nodes, neurons), mental processes (computations, activations, sequences of states), and neurological states

Symbolic Architectures

• Based on the Turing Machine model
  • Machine's computations or processes encompass reading symbols, writing symbols (B, 0, 1) on a tape, and moving left or right (L, R)
  • Machine's representations use Symbols
  • Operation is based on states specified in a table or program
• Symbols are codes or representations whose physical realization is the pattern of neuronal connections and spike rate
• Posits that symbols are physical patterns
• Symbols are used in computations driven by formal, syntactic rules
• According to Newell (1990), symbols are pointers to data codes, stand for knowledge, and token symbols carry information they stand for
• Symbols point to meaning or data structures

Connectionist Architectures

• Metaphor is the brain and its interconnected neurons or neuronal networks
• Parallel Distributed Processing (PDP), Local is a type of Connectionist Architecture
• Representations are nodes
  • Multiple nodes correspond to features or semantic features
  • Each node can correspond to a major category such as word/DOG
  • Nodes can stand for "features," "microfeatures," or major "concepts" or categories
• Processes are patterns of activation of nodes

Cognitive Architecture Commitments Frame Explanations on the Nature of Concepts

• Symbolic Models for Concepts take a feature-based approach where basic elements carrying meaning are features
  • Concepts are computed by sets of features using rules
  • For example: A = {x, y, z...}, B = {w, x, y...} → C = {w, x, y, z...}
  • Compositionality is important, and concepts need to be bound
• Connectionist Models for Concepts take a feature-based approach where concepts are obtained by the state of the organism during a pattern of activation
  • Has no explicit rules, but (quasi-) unconstrained activation
  • Has no inherent compositionality
  • C = {w, x, y, z...} is a pattern of activation

How Concepts Compose

• Activation in connectionist models may not be sufficient for compositionality
  • Need to know which features constitute meanings
  • Structure matters, [LOVE [MARY, JOHN]] ≠ [LOVE [JOHN, MARY]]

Assumptions on Cognitive Architectures

• Cognitive architectures should account for productivity, systematicity, and compositionality
• Productivity of Mental Representations (MRs) includes indefinitely many complex MRs with a finite number of simplex ones
  • Achieved within a finite system through the combinatorial structure of MRs (elementary MRs combine to form complex ones)
  • Examples include the generation/understanding of many sentences from finite concepts, infinite mathematical operations, and infinite capacity for thoughts by finite means
• Systematicity of Mental Representations includes the capacity to entertain certain MRs which is linked to the ability to entertain others with similar form, due to syntactic structure
  • For example, if you can think "JOHN LOVES MARY," you can also think "MARY LOVES JOHN" with the shared syntactic structure
• Compositionality of Mental Representations includes the meaning of a complex MR which relates to the function of the meaning of its constituent elementary representations AND HOW THEY ARE STRUCTURED
  • Elementary representations contribute (virtually) the same meaning across complex MRs (e.g., 'dog' means DOG across contexts)
  • MARY, LOVE, and JOHN contribute the same way to "JOHN LOVES MARY" and "MARY LOVES JOHN"

Symbolic Versus Connectionist on Productivity, Systematicity, Compositionality, and Mental Processes

• Productivity:
  • Symbolic architectures form finite symbols into infinite expressions due to constituent structure and rule-based recursion, as inference from [A&B] to [A] follows a rule
  • Connectionist architectures use each node as a representation, so adding units changes connectivity and structure; recursion is mimicked, with output and behavioral effects
• Systematicity:
  • Symbolic architectures allow constituent structure thinking like P&Q and Q&P
  • Connectionist architectures lack constituent structure, so states for thinking "John loves Mary" and "Mary loves John" are fundamentally different, requiring different node activations
• Compositionality:
  • Symbolic architectures contain symbols P and Q within thoughts like P&Q, so Q&P contains the same
  • Connectionist architectures function by activating nodes P and Q, which activate P&Q; the node P&Q does not actually contain P and Q
• Mental Processes:
  • Symbolic architectures function by the structure of complex representations; inferences ([P&Q → P], [PorQ, ~Q, ∴P]) get realized by form
  • Connectionist architectures function by activation of nodes, determined by association strengths; inferences ([P&Q → P]) require a connection between nodes P&Q and P

Preliminaries: What is a concept?

• Concepts relate to perceiving the world, natural language, and forming propositions
• Concepts and propositions interact with visual-linguistic architecture involving lexical and sentential semantics, and lexical morphology
• Key attributes of concepts includes the nature of conceptual representation and how concepts compose to form propositions or compositionality
• Definitions of a concept:
  • "Concepts are the building blocks of thought"
  • "Concepts are units of thought, constituents of beliefs and theories, roughly the grain of single lexical items; word meanings are paradigm examples"
• Concepts are the "mental particular" as “having a concept X is having the ability to think about Xs"
• Shared agreement deems that concepts are elements of thoughts, meaning thoughts are concepts put together
• Understanding a concept requires considering its role in a larger worldview including language, meaning, and mind
• Skeptical views suggest that no discrete entity constitutes a concept; conceptual functions might emerge from complex configurations of mechanisms in the world and brain
• There is a commitment to similar ideas like conceptual semantics (representations of word meanings + 3D models) and embodied cognition (mental simulators)
• Concepts are the units of mental content, elements of "meaning," encompassing word meanings, objects, scenes, faces, and how we make sense of the world, and their relationships constitute our knowledge.
• Course will cover:
  • What is a concept (and category)
  • How concepts build knowledge
  • Cognitive architecture/brain design underlying conceptual capacities
  • Productivity and compositionality
  • Main theories of concept representation (sets of features, definitions, prototypes)
  • Diagnostics of compostionality
  • Topics like semantic indeterminacy,conceptual deficits due to brain damage, perceiving objects and faces, and conceptualizing events

Meanings of “Meaning”

• Meaning as a sign, for example, clouds mean rain
• Meaning as importance, for example, a phone call meant a lot
• Meaning as purpose or intention, for example, meaning of life
• Meaning as representation or “semantic meaning”, for example, the brain interprets 'dog' as a domesticated canine

Meaning as Representation

• Assumes meaning = representation where a "code" in the brain exists for things in the world; this code represents the referent
• Linguistic meaning comes from thoughts
• Thought meanings are original: word 'dog' is as concept DOG
• Focus lies on the nature of concepts, as in how DOG is represented and what knowledge in the brain stands for dogs

The Problem of Representation in the Brain

• The first problem concerns the ability of the physical brain to represent the world as understood by neuroscience and cognitive science:
  • Neuroscience studies how information is encoded and transmitted in neuronal networks, which helps to understand physical storage and processing of knowledge
  • Cognitive science focuses on features, properties, symbols, and nodes that account for knowledge at the functional level, emphasizing representations and processes
• The second problem concerns the format of the representation, which can manifest in different forms:
  • Imagistic (analogical), abstract (symbolic), features, properties, and multiple forms
  • Relates to rules/algorithms and databases of symbols

Sense and reference

• Sense is the idea or representation that stands for something
• Reference is the something out there which the sense stands for
• One finds two expressions with the same referent having different senses
• Words express ideas and concepts, but words are not concepts
• Words can have multiple meanings and uses
• Concepts can only be expressed in sentences
• Lexical concepts are expressed by monomorphemic words such as kill, dog, love, and eye
• Phrasal concepts are expressed by complex linguistic tokens such as "My grandma lives...", Dogs, Impossibility, and I love Cinnabon...
• Focus is on the nature of lexical concepts (and categorization) and how they are represented and processed in the brain

The Classical Theory

• Concepts serve as definitions that are based on necessary and sufficient conditions for category membership
  • Uses all features to determine a concept, such as semantic markers and universality of some concept types
  • (Neo)Classical views use semantic templates to represent definitions in syntax

Historical Context

• John Locke (1632-1704): in Essay Concerning Human Understanding (1690) presented that:
  • Simple ideas (features/perceptual concepts) and complex ideas are made of simple ones
  • Ideas come from sensation or reflection
  • Complex ideas are voluntary combinations allowing different individuals to have different ideas of the same thing based on included/excluded simple ideas
  • Matching object to idea based on accumulated/reflected properties
  • Empiricist view claims possessing a concept relies on "reflection" of accumulated features
• Locke and Hume claim that ideas/attributes are concepts as features and thus requires a theory of features/attributes

Ideas and Attributes from Various Thinkers

• Boring (1942): Parameters refer to general properties that vary continuously or discretely
• Bruner et al. (1959): Any discriminable feature of an event is susceptible to variation with functional aspects
• Bruner et al. (1959) on Values of Attributes: Range of hues (e.g., orange for an orange)
• Bruner et al. (1959) on Defining vs. Criterial Attributes:
  • Defining attributes are immutable and given by convention
  • Criterial attributes are flexible, and based on judgment

A Study of Thinking

• Bruner et al. (1959) posited that:
  • One learns defining/criterial attributes
  • Joint attributes serve for categorization
  • Concept attainment is involved in successive decisions
  • "Strategies" represent regularities in decision-making
  • Process of concept attainment is outside of conscious awareness
  • Subjects learn necessary and sufficient conditions through examples

Definitions as Sets of Markers and Rules

• Katz (1972) claimed that:
  • The meaning of a new sentence is a compositional function of parts and syntax
  • Understanding sentences depends on knowing morpheme meanings
  • Semantic language contains a dictionary formally specifying senses and rules
  • A semantic component within language exists with a dictionary with projection rules
  • Semantic representation of concepts exist as Senses of expressions
  • Mental dictionaries include semantic markers

Evidence from Neuropsychology

• Patients with left temporal lesions show double dissociations suggesting concepts have constituent features
• Semantic representation consists of sets of "defining" features and conceptual deficits involve loss of defining features

Problems with Conventional Views

• Can concepts/categories be represented by necessary and sufficient conditions with sets of features/markers?
• Is compositionality compatible with concept theories?

Classical theory and the Probabilistic turn

• Wittgenstein (1889-1951) claimed that language words are not precise and are based on common family attributes
• Putnam (1975) challenged traditional views and analyticity by claiming that:
  • Natural kind terms do not have precise definitions
  • Words can be attached to wrong extensions
• There are problems of defining the conditions of primitive concepts