Lila Gleitman Henry Gleitman Carol Miller Ruth Ostrin

1. Fearful Symmetry: ‘Similar” and similar concepts Lila Gleitman Henry Gleitman Carol Miller Ruth Ostrin

3. The semantics of symmetry For 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

4. Is ‘similar’ a symmetrical concept? Tversky, 1977

5. “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

6. 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.

7. Some unanswered questions • Why are you surprised? • “Drown is an asymmetrical concept.”

8. Some unanswered questions • Why are you surprised? • “Drown is an asymmetrical concept.” • 2. Is similarity just like hostility? • Symmetricals Asymmetricals • equal similar • match drown • cousin father

9. 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)

10. Some unanswered questions 3. Are there any symmetrical concepts? (a) The least of the citizens is equal to the president.

11. (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.

12. - 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).

13. 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.

14. Iff intransitive, then plural: asymmetricalsymmetrical • The man and the The shirt and the • woman drown. button match. • 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.

15. Conjunction entails its conjuncts for asymmetricals but its reciprocal for asymmetricals • The man and thewoman drown.The shirt and thebutton match. • 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. 1 entails 2 and 3.1 entails 4, 5, and 6.

16. 40 predicates rated for symmetry* 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 4.11unpleasant S 1.61 Meet A 4.00 hurry A 1.56 Similar S 3.94inferior 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)

17. 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 4.17hit A 1.89 Divorce A 4.11 bounce A 1.67 Resemble S 4.11unpleasant S 1.61 Meet A 4.00 hurry A 1.56 Similar S 3.94inferior S 1.22 Near P 3.94 inside P 1.28 Argue A 3.11 drown A 1.28 Collide A 3.50better S 1.22 Kiss A 2.89less S 1.22 (2 groups rank order correlations: all preds rho = 9.3; syms. = 9.4, p > .001)

18. Complexity of this picture (henceforth ignored) John and Mary look alike/ are akin. They are far apart/ close together.

19. Whichsoundsbetter? 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 totally Same different different

20. (Grammatical if intransitive if plural)

21. 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 5 completely somewhat not at all

22. Effects of reciprocality

23. Yes, but how about North Korea?

24. 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 5 completely somewhat not at all

25. Effects of nominal order Nondirectional Directional Nondirectional Directional

26. Symmetrical Stative Symmetrical Active Asymmetrical Combined Sym. Stative Sym. Active All Asymmetrical

27. States and Events (or acts) 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.

28. 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.

29. Default figure-ground assignments cabbages and kings Drunks and lampposts North Korea and Red China 2 + 2 and 4 Sam and The Pope Your eyes and limpid pools Which would you rather say?

30. The asymmetry of syntactic structure… S NP VP Pred NP the zup sym the rif …maps onto conceptual asymmetry.

31. Causal role of the nominal pair • 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).

32. Causal role of the syntax I valency: 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. basis of comparison (category): 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.

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

34. Means across subjects (1st N = -1, 2nd N= +1). mean t(df) = 19 ***p < .01, ** p < .02

35. Means across predicates (1st N = -1, 2nd N= +1). mean t(df) = 25 ***p < .01, ** p < .05

36. Two accounts of symmetry • Reciprocal conjunction: the expression of symmetry is syntactically derived. • Lexicon: Symmetry is an item-specific property.

37. 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.

38. Pruning under symmetry S S NP VP NP VP V Recip V They meet t They eat

39. Pruning under symmetry S S NP VP NP VP V V They meet They eat -- L. Gleitman, 1962

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

41. 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.

42. The asymmetry is in the syntactic structure… S NP VP Pred NP the zup sym the rif Imposing different roles on the nominals

43. What this means The dominance within the categorial relationship is read off of the phrase structure tree (pace Tversky and defaults be damned). The man is tied to the tree.

44. The man is tied to the tree.

45. The tree is tied to the man

46. The tree is tied to the man

47. The Syntax Has the Last Word.