Lila Gleitman

Henry Gleitman

Carol Miller

Ruth Ostrin

Fearful Symmetry:

‘Similar” and similar concepts

The semantics of symmetryFor all x, y: R x,y R y,x

If X

is equal to

matches

meets Y

then Y

is equal to

matches

meets X

Is ‘similar’ a symmetrical concept?

Tversky, 1977

“Assess the degree to which

(a) North Korea is similar to Red China.

(b) Red China is similar to North Korea.

1 2 3 4 5

Not at all somewhat completely

Result: North Korea is more similar to Red China than Red China is to North Korea.

(just as)

North Korea might be more hostile to Red China than Red China is to north Korea.

QED: ‘Similar’ is an asymmetrical concept.

Some unanswered questions

1.Why are you surprised?

“Drown is an asymmetrical concept.”

Some unanswered questions1.Why are you surprised?

“Drown is an asymmetrical concept.”

2. Is similarity just like hostility?

Symmetricals Asymmetricals

equal similar

match drown

cousin father

Although the violations of symmetry are statistically significant and experimentally reliable, the effects are relatively small. Consequently symmetry…may provide a good first approximation to similarity data…at the same time, one should not treat such a representation, useful as it might be, as an adequate psychological theory of similarity.

An analogy to the measurement of physical distance illustrates the point. The knowledge that the earth is round does not prevent surveyers from using plane geometry to calculate small distances on the surface of the earth. The fact that such measurements often provide excellent approximations to the data, however, should not be taken as evidence for the flat-earth model. (Tversky & Gati, p. 97)

3. Are there any symmetrical concepts?

(a) The least of the citizens

Some unanswered questions

is equal to the president.

(a) The least of the citizens is equal to the president.

(b) The president is equal to the least of the citizens.

(a) The bicycle is near the garage. (b) The garage is near the bicycle.

(a) Sam met the pope. (b) The Pope met Sam.

- Symmetrical predicates are grammatical iff: intransitive and plural; and

Iff: the plural is interpreted reciprocally.

- Similar is a well-behaved symmetrical predicate, one of hundreds (it satisfies these diagnostics).

The real diagnostics of symmetry

- Symmetrical predicates are grammatical (1) if intransitive iff plural; and

(2) that plural is interpreted reciprocally.

- Similar is a well-behaved symmetrical predicate, one of hundreds (it satisfies these diagnostics).

- Later, I’ll return to the apparent asymmetries in their readings.

Iff intransitive, then plural:

1. The man and the The shirt and the woman drown. button match. 2. The woman drowns. ? The button

matches.

3. The man drowns and ?The shirt matches and

the woman drowns. the button matches.

4. The man and the woman The shirt and the button

drown each other. match each other.

5. The woman drowns the man. The button matches the shirt.

asymmetrical symmetrical

1. The man and the woman drown. The shirt and the button match.

2. The woman drowns. 3. The man drowns and the woman drowns. 4. The man and the woman The shirt and the

button drown each other. match each other.

5. The woman drowns the man. The button matches the shirt.

6. The man drowns the woman. The shirt matches the button.

Conjunction entails its conjuncts for asymmetricals but its reciprocal for asymmetricals

1 entails 2 and 3. 1 entails 4, 5, and 6.

Predicate T Score Predicate T Score

Equal S 4.89 love S 2.44

Identical S 4.89 copy A 2.22

Marry A 4.78 safe S 2.00

Match S 4.17 hit A 1.89

Divorce A 4.11 bounce A 1.67

Resemble S 4.11 unpleasant S 1.61

Meet A 4.00 hurry A 1.56

Similar S 3.94 inferior S 1.22

Near P 3.94 inside P 1.28

Argue A 3.11 drown A 1.28

Collide A 3.50 better S 1.22

Kiss A 2.89 less S 1.22

40 predicates rated for symmetry*

2 groups rank order correlations: all preds rho = 9.3; syms. = 9.4, p > .001)

Predicate T Score Predicate T Score

Equal S 4.89 love S 2.44

Identical S 4.89 copy A 2.22

Marry A 4.78 safe S 2.00

Match S 4.17 hit A 1.89

Divorce A 4.11 bounce A 1.67

Resemble S 4.11 unpleasant S 1.61

Meet A 4.00 hurry A 1.56

Similar S 3.94 inferior S 1.22

Near P 3.94 inside P 1.28

Argue A 3.11 drown A 1.28

Collide A 3.50 better S 1.22

Kiss A 2.89 less S 1.22

(2 groups rank order correlations: all preds rho = 9.3; syms. = 9.4, p > .001)

Complexity of this picture (henceforth ignored)

John and Mary look alike/ are akin.

They are far apart/ close together.

Which sounds better?

Sam met. Sam and the Pope met.

The frog eats. The frog and the flea eat.

Joe took off his shoes. Joe took his shoes off.

Mary ran up a hill. Mary ran up a bill. 1 2 3 4 5 Just the somewhat totallySame different different

Effects of Plurality

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

1

Pre

fere

nce

for P

lura

l

Symmetricals

Asymmetricals

(Grammatical if intransitive if plural)

How similar are these in meaning?

North Korea and Red China are similar.North Korea and Red China are similar to each other.

The principal and the pupil hurried.The principal and the pupil hurried each other.

1 2 3 4 5completely somewhat not at all

Effects of reciprocality

1

2

3

4

5

Symmetricals Asymmetricals

Mea

n c

on

stru

al c

han

ge

Yes, but how about North Korea?

How similar are these in meaning?

North Korea is similar to Red China.Red China is similar to North Korea.

The pupil hurried the principal.The principal hurried the pupil.

North Korea and Red China are similar.Red China and North Korea are similar.

The pupil and the principal hurried.The principal and the pupil hurried.

1 2 3 4 5completely somewhat not at all

Nominal Order

0

1

2

3

4

5

Sentence Type

Mea

n Co

nstru

al

Chan

ge

Symmetricals

Asymmetricals

Nondirectional DirectionalNondirectional Directional

Effects of nominal order

Active and Stative Predicates

0

1

2

3

4

5

Mea

n Sc

ore Directional

Non-directional

Symmetrical Stative Symmetrical Active Asymmetrical Combined

Sym. Stative Sym. Active All Asymmetrical

Accuse/?Suspect/ him of treason.

He is giving/?knowing/ the answer.

X is being mean/?similar to/ Y.

What Joe does is give/?know/ the answer.

States and Events (or acts)

Causal role of the nominal pair I

Figure: a moving or conceptually moveable object whose site, path, or orientation is conceived as a variable the particular value of which is the salient issue. Ground: a reference object, itself having a stationary setting within a reference frame, with respect to which the Figure’s path, etc., is characterized.

Default figure-ground assignments

cabbages and kingsDrunks and lamppostsNorth Korea and Red China2 + 2 and 4Sam and The PopeYour eyes and limpid pools

Which would you rather say?

The asymmetry of syntactic structure…

S

NP VP

Pred NP

the zup sym the rif

…maps onto conceptual asymmetry.

Causal role of the nominal pair

1. Tversky: “Which would you rather say?”

2. Kelly & Bock, 1986: Preference in conjoined nominals (marginally reproduced by us)

3. Scrambling:

The bicycle married the garage.

The copy kisses the painting.

Preference for standard nominal order is the same in 15 of 20 comparisons (p = .02, sign test).

Causal role of the syntax I

near: If there was this humungous bicycle statue in the square and this little garage on wheels going around it.

meet: If my sister was more famous than Merrill Streep.Equal: If you were talking about the heights of those presidents…

Similar: If it was the weather, maybe North korea has the very best weather for a vacation.

valency:

basis of comparison (category):

The zup The Rif Same Irrelevant

Older/ younger

Less famous

Bigger

Less mobileMore important

Causal role of the syntax II: The zup is similar to the rif.

Important 0.45 7.3***

Famous 0.38 5.1***

Old 0.41 6.3***

Big 0.38 5.8***

Immobile 0.15 2.6**

***p < .01, ** p < .02

mean t(df) = 19

Means across subjects (1st N = -1, 2nd N= +1).

Important 0.45 9.0***

Famous 0.36 7.6***

Old 0.40 8.6***

Big 0.37 7.4***

Immobile 0.20 2.1*

***p < .01, ** p < .05

mean t(df) = 25

Means across predicates (1st N = -1, 2nd N= +1).

Two accounts of symmetry

1. Reciprocal conjunction: the expression of symmetry is syntactically derived.

2. Lexicon: Symmetry is an item-specific property.

Ancient linguistics: Coordinate and Reciprocal Conjunction (Gleitman 1962)

[[…x…] and […y…]] […x and y…]

John eats & Bill eats / John and Bill eat.

[[…x..y…] and […y…x…]] […x and y…each other…].

John pushes Bill and Bill pushes John /

John and Bill push each other.

Pruning under symmetry

S S

NP VP NP VP

V Recip V

They meet t They eat

Pruning under symmetry

S S

NP VP NP VP

V V

They meet They eat

-- L. Gleitman, 1962

The reciprocal surfaces in many languages (though often identical to the reflexive)

Modern times: the symmetry is in the lexicon

Where no constructional solution will do:

John and Bill are cousins/fathers.

Where the domain of applicability differs

John and Mary kissed/kissed each other.

The entailment is one way (counterexamples)

John and Mary resembled/encountered.

“Pruning” is in any case lexically stipulative.

The asymmetry is in the syntactic structure…

S

NP VP

Pred NP

the zup sym the rif

Imposing different roles on the nominals

What this means

(pace Tversky and defaults be damned).

The dominance within the categorial relationship is read off of the phrase structure tree

The man is tied to the tree.

The man is tied to the tree.

The tree is tied to the man

The tree is tied to the man

The Syntax Has the Last Word.