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Lexical Neutrality Composite Meanings

Lexical Neutrality Composite Meanings. Paul M. Pietroski Dept. of Linguistics, Dept. of Philosophy University of Maryland. Examples of Lexical Neutrality. Mass Count Mary had a little lamb, which would have been a sheep among sheep. Singular Plural

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Lexical Neutrality Composite Meanings

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  1. Lexical NeutralityComposite Meanings Paul M. Pietroski Dept. of Linguistics, Dept. of Philosophy University of Maryland

  2. Examples of Lexical Neutrality • Mass Count Mary had a little lamb, which would have been a sheep among sheep. Singular Plural • Collective/Distributive Each of the horses that ate all the hay also ate some grass. • AdicityThe baby kicked, I kicked a stone that was kicked, and Mother Hubbard kicked the dog a bone. • Other Polysemies This book is heavy, but it got a good review in the paper. Torcello is where Venice used to be. Deep greens and blues are the colors I choose. We painted brown dogs with brown paint.

  3. Composite Meanings “things” that • words and phrases “have” • compose in certain ways • humans use, in communication and intrapersonally • Human Languages pair with pronunciations --languages that human children can naturally acquire --procedures that generate boundlessly many meaning-pronunciation pairs in accord with certain substantive constraints

  4. Human Languages: unbounded and constrained • Bingley is ready to please (a) Bingley is ready to please relevant parties (b) Bingley is ready to be pleased by relevant parties • Bingley is eager to please (a) Bingley is eager to please relevant parties #(b) Bingley is eager to be pleased by relevant parties • Bingley is easy to please #(a) Bingley can easily please relevant parties (b) Bingley can easily be pleased by relevant parties

  5. Lexical Neutrality amid Systematic Constraints • The dragon ate a large pizza yesterday • The dragon ate a pizza yesterday • The dragon ate a pizza • The dragon ate some pizza • The dragon ate something • The dragon ate

  6. Lexical Neutrality amid Systematic Constraints • The dragons ate a large lamb yesterday • The dragons ate a lamb yesterday • The dragons ate a lamb • The dragons ate some lamb • The dragons ate something • The dragons ate

  7. Lexical Neutrality amid Systematic Constraints • The sheep ate a large dragon yesterday • The sheep ate a dragon yesterday • The sheep ate a dragon • The sheep ate some dragon • The sheep ate something • The sheep ate We eat fish, and this fish is one of the fish we fish for. on either reading of ‘sheep’

  8. Lexical items can be combined in ways that suggest neutrality with regard to various conceptual distinctions that seem to reflect real distinctions. • Mass Count Singular Plural • Collective/Distributive • Adicity • Other Polysemies Maybe the meanings of ‘lamb’ ‘eat’, ‘kick’, ‘Venice’, ‘pizza’, ‘fish’, ‘green’, ‘idea’, ‘sleep’, ‘furious’, … are so combinable because acquiring a lexicon lets usefface many typological distinctions.

  9. LAMB-BEASTS(xx) LAMB-STUFF(μ) LAMB-BEAST(x) • Mass Count Singular Plural • Collective/Distributive • Adicity • Other Polysemies lamb  LAMB(_) lamb+singularLAMB(_)^ COUNTABLE(_)^ ~PLURAL(_) in acquiring lexical items, kids may label some old concepts and introduce some “neutral” concepts

  10. LAMB-BEASTS(xx) LAMB-STUFF(μ) LAMB-BEAST(x) • Mass Count Singular Plural • Collective/Distributive • Adicity • Other Polysemies lamb  LAMB(_)  eat EAT(_) FUEL-UP(x) CONSUME(x, y) INGEST(x, y) CONSUME(e, x, y) CONSUME(e)^AGENT(e, x)^PATIENT(e, y)

  11. LAMB-BEASTS(xx) LAMB-STUFF(μ) LAMB-BEAST(x) • Mass Count Singular Plural • Collective/Distributive • Adicity • Other Polysemies lamb  LAMB(_)  kick KICK(_) KICKED(x) KICK(x, y) WAS-KICKED(y) KICK(e, x, y) KICK(e)^AGENT(e, x)^PATIENT(e, y)

  12. Language Acquisition Device prelinguistic concepts  various cognitive modules  Human Faculty of Language a few uses of lambLexical Item a Pronunciation paired with a Meaning (and maybe some other information)

  13. Language Acquisition Device prelinguistic concepts  various cognitive modules  Human Faculty of Language a few uses of lamb <PHON:lamb (other info) SEM:lamb> a few uses of eat <PHON:eat (other info) SEM:eat> a few uses of kick <PHON:… book (other info) Venice SEM: …> green …

  14. lexical items are remarkably COMBINABLE in meaningful ways Language Acquisition Device prelinguistic concepts  various cognitive modules  Human Faculty of Language a few uses of lamb a few uses of eat a few uses of kick book Venice green … but these presumably VARY along many dimensions, including… --mass/count --singular/plural --collective/distributive --adicity --type/token --intentional/spatial --etc.

  15. What are Human Linguistic Meanings? • What are the meanings of atomic HL-expressions? • easy, eager, ready • lamb, eat, Venice • dog, brown, paint • What are the meanings of complex HL-expressions? • Easy guests eagerly please those who are ready for them. • Little lambs eat ivy in Venice, whose residents eat lamb • We painted brown dogs with brown paint. • How can atomic meanings be so neutral while complex meanings are so constrained?

  16. What are Human Linguistic Meanings? • Representations of a special sort Meaning[Fido] = the concept Fido Meaning[dog] = the concept dog(_) Meaning[brown dog] = &[brown(_), dog(_)] • Representeds of a special sort Meaning[Fido] = the dog Fido Meaning[dog] = the FregeanBegriffis-a-dog(_) Meaning[brown dog] = &[is-brown(_), is-a-dog(_)] concepts as composable mental symbols: how and why do we get neutral concepts? Begriffs as functions from entities (e.g., dogs) to truth values: how and why do we get attached to neutral functions?

  17. Meanings as Instructions for How to Build Concepts Meaning[dog] = fetch@address:dog dog(_) Meaning[brown] = fetch@address:brown brown(_) Meaning[brown dog] = Join(Meaning[brown], Meaning[dog]) = Join(fetch@address:brown, fetch@address:dog) brown(_)^dog(_) executing a lexical instruction accesses a concept that can be combined with others via certain (limited) operations

  18. Meanings as Instructions for How to BuildConcepts Meaning[dog] = fetch@address:dog dog(_) Meaning[brown] = fetch@address:brown brown(_) Meaning[brown dog] = Join(Meaning[brown], Meaning[dog]) brown(_)^dog(_) executing a phrasal instruction builds a concept that is combinable with others via certain (limited) operations | MORE RESTRICTED THAN TARSKIAN CONJUNCTION

  19. Meanings as Instructions for How to BuildConcepts Meaning[dog] = fetch@address:dog dog(_) Meaning[book] = fetch@address:book spatial-book(_) content-book(_) Meaning[water] = fetch@address:water functional-water(_) science-water(_) a fetchable concept must be combinable with others, but… a “lexical address” need not be the address of exactly oneconcept an instruction may be executable in two or more ways (perhaps including adhoc ways)

  20. Meanings as Instructions for How to BuildConcepts Meaning[dog] = fetch@address:dog dog(_) Meaning[book] = fetch@address:book spatial-book(_) content-book(_) Meaning[mimsy] = fetch@address:mimsy a “lexical address” need not be the address of exactly oneconcept and some instructions may not be executable (there might be nothing to fetch)

  21. Meanings as Instructions for How to BuildConcepts in some cases, executing a Meaning will yield a CONCEPTthat has an extension relative to a “situation” in which the Meaning was executed in othercases, not so much

  22. Meanings as Instructions for How to BuildConcepts Meaning[lamb] = fetch@address:lamb lamb(_) Meaning[eat] = fetch@address:eat consume(_) eat(_) more permissive than lamb-beast(x) more “natural” more permissive ROOM FOR TWO (related) KINDS OF NEUTRALITY --two or more fetchable concepts at one lexical address --fetchableconcepts may be introduced as neutral

  23. EAT(_) CONSUME(_) • restrict EAT(_) to get CONSUME(_) • relax CONSUME(_) to get EAT(_) • build both concepts from more basic concepts • take both concepts as basic

  24. [eat+pastlamb] • EAT(_)^PAST(_)^[THEME(_ , _)^LAMB(_)] • |_______| compare: &[CONSUME(…, μ); LAMB-STUFF(μ)] &[INGEST(…, μ); LAMB-STUFF(μ)] EAT(_)^PAST(_)^[THEME(_, _)^[ONE(_)^LAMB(_)]] |_______________| [eat+past a lamb] compare: &[CONSUME(…, x); LAMB-BEAST(x)] &[SHARE(…, x); LAMB-BEAST(x)]

  25. [eat+pastlamb] • CONSUME(_)^PAST(_)^[THEME(_ , _)^LAMB(_)] • |_______| executing eatthis way yields a more restricted concept CONSUME(_)^PAST(_)^[THEME(_, _)^[ONE(_)^LAMB(_)]] |_______________| [eat+past a lamb]

  26. [eat+pastlamb] • EAT(_)^PAST(_)^[THEME(_ , _)^LAMB(_)] • |_______| [eat+past] • CONSUME(_)^PAST(_) EAT(_)^PAST(_)^[THEME(_, _)^[ONE(_)^LAMB(_)]] |_______________| [eat+past a lamb]

  27. [eat+pastlamb] • EAT(_)^PAST(_)^[THEME(_ , _)^LAMB(_)] • |_______| CRUCIAL: the “neutral” concepts need not be primitive even if they are fetched via lexical roots. Don’t analyze beast-concepts in terms of neutral-concepts just because lambis a component of a lamb and LAMB(_) is a component ofONE(_)^LAMB(_) EAT(_)^PAST(_)^[THEME(_, _)^[ONE(_)^LAMB(_)]] |_______________| [eat+past a lamb]

  28. Another Route to the Same Conclusion Meaning[dog] = fetch@address:dog dog-beast(_) Meaning[brown] = fetch@address:brown brown(_) Meaning[paint] = fetch@address:paint paint-stuff(_) dog(_)applies to an entityiff that entity is a dog paint(_) applies to some stuffiff that stuff is paint brown(_) applies to ??? iff that ?? is … ?

  29. Believe, if you like, that • any “stuff” is a portion/quantity of stuff • paint/paint(_) applies to things of a special sort: paint-portions • there are some “minimal” paint-portions that are the basic elements of a lattice whose supremum is the totality of paint P123 P12 P13 P23 P1 P2 P3 Metaphysics is notthe solution

  30. Without Neutral Nouns, Adjectives are Puzzling If the meaning of brown is… • a concept,does it apply to certain dogs and paint (portions)? • Meaning[brown] = brown(_) • Meaning[brown dog] = brown(_) & dog(_) • Meaning[brown paint] = brown(_) & paint(_) • a function,what does it map to (truth) values? • Meaning[brown] = λ? . T  Brown(?) • Meaning[brown dog] = λe . T Brown(e) & Dog(e) • Meaning[brown paint] = λπ . T Brown(π) & Paint(π)

  31. Double Bookkeeping for Adjectives? Meaning[dog] = fetch@address:dog dog(e) Meaning[brown] = fetch@address:brown brown-thing(e) brown-stuff(π) Meaning[paint] = fetch@address:paint paint(π) dog(e)applies to an entityiff that entity is a dog paint(π) applies to some (portion of) stuffiffthat stuff is paint

  32. One Response: Double Bookkeeping for Adjectives Meaning[dog] = fetch@address:dog dog(e) Meaning[brown] = fetch@address:brown brown-surfaced-thing(e) brown-stuff(π) Meaning[paint] = fetch@address:paint paint(π) dog(e)applies to an entityiff that entity is a dog paint(π) applies to some (portion of) stuffiffthat stuff is paint

  33. Singular Noun Neutrality: Mass/Count Plural The brown dog is expensive. The brown dogSing is expensive. The brown dog(–Count) is expensive. The brown dogs are expensive. Every one of the brown dogs is expensive. The brown paint is expensive. The brown paintSing is expensive. The brown paint(–Count) is expensive. The brown paints are expensive. Every one of the brown paints is expensive. The rabbitSingis brown. The rabbit(–Count) is brown. Most of the rabbitSing is brown. But it has a white tail. Most of the rabbit(–Count) is brown. It has been overcooked. The bananaSingis brown The banana(–Count) is brown.

  34. Meaning[brown] = fetch@address:brown brown-thing(e) brown-stuff(π) Meaning[brown dog] = Join(Meaning[brown], Meaning[dog]) &[brown-thing(e), dog(e)] &[brown-stuff(π), dog(π)] Meaning[brown paint] = Join(Meaning[brown], Meaning[paint]) &[brown-thing(e), paint(e)] &[brown-stuff(π), paint(π)]

  35. But Less Redundancy Would be Nice dog+sdog+dog [+PL (+CT)] [–PL (+CT)] [–CT] Meaning[brown√dog+s] = Join(Meaning[brown], Meaning[dog], Meaning[+PL]) brown(_)^[dog(_)^plural(_)] Meaning[brown√paint] = Join(Meaning[brown], Meaning[paint]) brown(_)^paint(_)

  36. Meaning[√dog] = fetch@address:√dog Meaning[√dog+count] = Join(fetch@address:√dog, fetch@address:+count) Meaning[[√dog+plural] = Join(Meaning[√dog], fetch@address:+plural) One is free to add… Meaning[dog] = Meaning[√dog+count] = fetch@address:dog Meaning[dogs] = Meaning[dog+plural] = Join(Meaning[dog], Meaning[+plural])

  37. Meaning[√paint] = fetch@address:√paint Meaning[√paint+count] = Join(fetch@address:√paint, fetch@address:+count) Meaning[√paint+plural] = Join(Meaning[√paint], fetch@address:+plural) One is free to add… Meaning[paint] = Meaning[√paint] Lexicon as stock of atomic elements vs. Lexicon as memorized list

  38. Examples of Lexical Neutrality • Mass Count Mary had a little lamb, which would have been a sheep among sheep. Singular Plural • Collective/Distributive Each of the horses that ate all the hay also ate some grass. • AdicityThe baby kicked, I kicked a stone that was kicked, and Mother Hubbard kicked the dog a bone. • Other Polysemies This book is heavy, but it got a good review in the paper. Torcello is where Venice used to be. Deep greens and blues are the colors I choose. We painted brown dogs with brown paint.

  39. Very Little Evidence for Semantic “Supradyadicity” fetch@address:give give(e, a, r, p) She gave the museum a painting give(e, a, p) She gave (to) the museum a painting She gave a painting to the museum fetch@address:kick give(e, a, r, p)She kicked the dog a bone kick(e, a, p)She kicked (to) the dog a bone She kicked a bone to the dog

  40. Very Little Evidence for Semantic “Supradyadicity” fetch@address:sell sell(e, a, r, p)She sold the museum a painting. sell(e, a, r, p, ??)She sold the museum a painting for $1 sell(e, a, p, ben)She sold the painting for Bob sell(e, a, p) She sold the painting sell(e,p) The painting was sold to Bob

  41. for some lock y, e was a jimmying by x of y & for some knife z, e was (done) with z a thief jimmied a lock with a knife (x) (y) (z) ‘jimmy’ λy . λx . λe . T  e is a jimmying by x of y

  42. Why not… And why is passivizingOK? The lock was jimmied. a thief jimmied a lock a knife (x) (y) (z) ‘jimmy’ λz.λy . λx . λe . T  e is a jimmying by x of ywith z

  43. for some thief x, e was (done) by x& for some lock y, e was a jimmying of y & for some knife z, e was (done) with z v a thief jimmied a lock with a knife (x) (y) (z) ‘jimmy’ λy.λe.JimmyOf(e, y) # λy.λx.λe.JimmyByOf(e, x, y) # λy.λz.λe.JimmyWithOf(e, z, y) # λy.λz.λx.λe.JimmyByWithOf(e, x, y, z)

  44. for some thief x, e was (done) by x& e was a jimmying & for some lock y, Patient(e, y) & for some knife z, e was (done) with z v a thief jimmied a lock with a knife (x) (y) (z)  Jimmy(e) & Past(e) ‘jimmy’ λy.λe.JimmyOf(e, y) JimmyOf(e, y)  Jimmy(e) & Patient(e, y)

  45. LAMB-BEASTS(xx) LAMB-STUFF(μ) LAMB-BEAST(x) • Mass Count Singular Plural • Collective/Distributive • Adicity • Other Polysemies lamb  LAMB(_)  kick KICK(_) KICKED(x) KICK(x, y) WAS-KICKED(y) KICK(e, x, y) KICK(e)^AGENT(e, x)^PATIENT(e, y)

  46. LAMB-BEASTS(xx) LAMB-STUFF(μ) LAMB-BEAST(x) • Mass Count Singular Plural • Collective/Distributive • Adicity • Other Polysemies lamb  LAMB(_)  eat EAT(_) FUEL-UP(x) CONSUME(x, y) INGEST(x, y) CONSUME(e, x, y) CONSUME(e)^AGENT(e, x)^PATIENT(e, y)

  47. The linguists ate the pizzas Xy[XyPizza(y)] xy[(yx) Pizza(y)]Xy[OneOf(y, X) Pizza(y)] there is a set, x, such thatthere are sm things, the Xs, such that each thing, y, is such thateach thing, y, is such that ity is an element of itxity is one of themX iffity is a (relevant) pizzaiffity is a (relevant) pizza does the English sentence imply, in addition to the pizzas, (1) a further set/collection of the pizzas (2) a thing eaten that that has the pizzas as “elements”

  48. The linguists counted the sets Xy[XySet(y)] xy[(yx) Set(y)]Xy[OneOf(y, X) Set(y)] there is a set, x, such thatthere are sm things, the Xs, such that each thing, y, is such thateach thing, y, is such that ity is an element of itxity is one of themX iffity is a (relevant) setiffity is a (relevant) set does the English sentence imply, in addition to the sets, (1) a further set/collection of the sets (2) a thing eaten that that has the sets as “elements”

  49. TWO CONCEPTIONS OF PLURAL VARIABLES Five entities: a, b, c, d, e Link: dba=d⊕b⊕a a mereologicalsum with 3 atoms (d, b, a); it can be the value of a singular variable Boolos: dba=e, no; d, yes; c, no; b, yes; a, yes five answers to a yes/no question: is … a value of an unsingular variable?

  50. TWO CONCEPTIONS OF PLURAL VARIABLES a = 1,b = 10,c = 100,d = 1000,e = 10000 Link: 01011 = 1000⊕10⊕1 a mereologicalsum with 3 atoms (d, b, a); it can be the value of a singular variable Boolos: 01011 = 1000+10+1 five answers to a yes/no question: is … a value of an unsingular variable?

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