1

Conceptual mappings and beyond

!  Basic mathematical concepts (proper) in our Biological endowment?

!  No, … not really !  Some non-mathematical building blocks, though

!  How do we get from, say, subitizing to Mathematics proper?

!  Meta-symbolic reference !  Conceptual mappings and other cognitive

mechanisms for human imagination

Conceptual mappings and beyond: Taking everyday meaning seriously

! Send her my warm helloes ! Waaaay back in the 50s … ! Cognition is the ability to think ahead

! We are coming to the end of the quarter … !  It is 20 minutes ahead of 1 o’clock ! Halloween is almost here, … etc.

Taking everyday meaning seriously

! Send her my warm helloes ! Waaaay back in the 50s … ! Cognition is the ability to think ahead

! We are coming to the end of the quarter … !  It is 20 minutes ahead of 1 o’clock ! Halloween is almost here, … etc.

! Something conceived as something else

… and at meaning in everyday “non-linguistic” expressions

NO words grammar clear segmentation and order explicit propositions logical operators etc.,

Cognitive Linguistics

!  Language as a cognitive phenomenon !  Semantics (and even Grammar) as cognitively

driven (Langacker, Talmy, Lakoff, Fauconnier, etc.)

!  Hypothesis about Thought, Cognition, and Abstraction investigated with linguistic methodologies (data: sentences, illustrations, etc.)

What makes Human imagination possible? Conceptual mappings

!  A. Image-schemas !  B. Conceptual metaphor !  C. Conceptual metonymy !  D. Conceptual blend !  E. Fictive motion !  … and many others

2

A. Image-schemas

! Container-schemas

! Source-Path-Goal schemas

The cognitive friendliness of Venn Diagrams

A is a subset of B

B A

A intersection B

A B

The complement of A union B

!  Inference-preserving mappings !  From Source to Target domain

He is still a cold person Send her my warm helloes

B. Conceptual metaphor

!  Inference-preserving mappings !  From Source to Target domain

He is still a cold person Send her my warm helloes

!  A fundamental distinction: !  Metaphorical expressions (Linguistic raw data) !  Conceptual metaphor (Cognitive, Thought):

inference-preserving cross-domain mapping.

B. Conceptual metaphor

Example: Time As Unidimensional Space !  Two main conceptual metaphors that model the

inferential structure of many metaphorical expressions

a)  “Ego-moving” !  We’re coming to the end of the year

b)  “Time-moving” !  Her birthday is approaching

Núñez, 1999 Núñez & Sweetser, 2006 Núñez, Motz, & Teuscher, 2006

a) Ego-moving Mapping

Source Domain Space (sagittal)

Target Domain Time

front of ego future behind ego past

ego’s location present/now

ego’s motion passing of time

3

b) Time-moving Mapping

Source Domain Space (sagittal)

Target Domain Time

front of ego future behind ego past

ego’s location present/now

motion of objects passing of time

Time As Unidimensional Space a)  “Ego-moving”

We’re coming to the end of the year b)  “Time-moving”

Thanksgiving is approaching

!  Mappings preserve inference: !  spatial transitive relations mapped onto temporal ones !  agency (passive vs active role in action), etc. !  “truth” is relative to mappings

!  Meaning and inferences are brought forth !  Effortlessly and (largely) unconsciously

C. conceptual metonymy

!  “Moscow hasn’t replied yet” !  “The double-cheeseburger wants another

coke” !  “Give $5 to the taxi-driver”

! A part stands for the whole

!  “Moscow hasn’t replied yet” !  “The double-cheeseburger wants another

coke” !  “Give $5 to the taxi-driver”

! A part stands for the whole

Mapping compositionality

! Conceptual Metonymy and Conceptual Metaphor usually combine in complex ways !  “The bombing of Baghdad has separated

Washington and Paris even further”

D. Conceptual Blending

4

Input Space 1: Economic indicators Input Space 2: Martyrdom of San Sebastian

Selective projection: shapes of graphs (I1) piercing of arrows (I2) passivity (I2)

Blended Space

Purely imaginary

domain with new

precise inferences!! But not … numerical magnitude (I1) nudity (I2) location of arrows (I2)

E. Fictive Motion

•  Talmy (1996, 2003) observed that we often talk (unconsciously and effortlessly, but with precision) about static objects (literal or metaphorical) as if they were dynamic

•  This phenomenon manifests itself in language

•  Landmark-trajector (figure-ground) construal

E. Fictive Motion

•  The fence stops right after the tree. •  The boarder between Switzerland and Germany runs

along the Rhine. •  The Equator passes through many countries •  The California coast goes all the way down to San

Diego •  After Corvisart, line 6 reaches Place d’Italie. •  Right after crossing the Seine, line 4 comes to

Châtelet. •  Unlike Tokyo, in Paris there is no metro line that goes

around the city.

Conceptual mappings and psycho-neurological reality

Empirical/experimental evidence? Psycholinguistic experiments Real-time speech-gesture co-production Neuroimaging (fMRI) Electrophysiological measurements …

UNCONGRUOUS CONGRUOUS UNCONGRUOUS minus CONGRUOS

SCA

LP 4

00 m

sSC

ALP

600

ms

Left Frontal ROI Central (CZ) ROI

CONG UNCON

Rigth Oxipital ROI

** * *

Psychological-bodily reality? Why Gestures? !  A detailed study of Gestures can help

answering fundamental questions about language, brain, and thought

!  Gesture-speech co-production is universal !  Astonishingly co-timed speech-gesture co-production !  Common neural bases !  Developmentally, speech and gesture are closely related !  Provide rich information about deixis, manner, and RPs

(often complementary to speech) !  Preservation and construction of semantics (iconics and

metaphorical gestures): built-in

5

PZ neurons

Graziano, Hu, & Gross, 1997

which responded to: - tactile stimuli on the front of the face - visual stimuli near the face

Multisensory area in Superior Parietal Cortex (visual-somatosensory)

Sereno and Huang, 2006

SFS

AnG

VIP

PZ

SI 7b

MT+

V3A/V7

You are approaching Christmas vs.

Christmas is approaching

Block Design Study

Left hemisphere

Auditory cue

Núñez, Huang, and Sereno, 2007

V3A/V7

MT+

7b

VIP PZ

SI

SFS

AnG

Right hemisphere

You are approaching Christmas vs.

Christmas is approaching

Block Design Study

Auditory cue

Núñez, Huang, and Sereno, 2007