Composing Criteria of Individuation Composing Criteria of Individuation Matthew Gotham Department of Linguistics University College London London Semantics Day Queen Mary, University of London 7 May 2014 M Gotham (UCL) Composing Criteria of Individuation 7/5/14 1 / 24
Composing Criteria of Individuation Plan for today Copredication The counting and individuation issue Compositional Theory Comparison with other accounts M Gotham (UCL) Composing Criteria of Individuation 7/5/14 2 / 24
Composing Criteria of Individuation Copredication Copredication The apparent attribution of incompatible properties to a single object. Some examples: (1) Lunch was delicious but took forever. (Asher, 2011, p. 11) (2) The bank was vandalised after calling in Bob’s debt. (3) London is so unhappy, ugly and polluted that it should be destroyed and rebuilt 100 miles away. (Chomsky, 2000, p. 37) M Gotham (UCL) Composing Criteria of Individuation 7/5/14 3 / 24
Composing Criteria of Individuation Copredication Issues ◮ Philosophical ◮ Compositional ◮ Pragmatic and discourse-based ◮ Counting and individuation M Gotham (UCL) Composing Criteria of Individuation 7/5/14 4 / 24
Composing Criteria of Individuation The counting and individuation issue A question of individuation Suppose the library has two copies of Tolstoy’s War and Peace, Peter takes out one, and John the other. Did Peter and John take out the same book, or different books? If we attend to the material factor of the lexical item, they took out different books; if we focus on its abstract component, they took out the same book. We can attend to both material and abstract factors simultaneously. . . (Chomsky, 2000, p. 16) M Gotham (UCL) Composing Criteria of Individuation 7/5/14 5 / 24
Composing Criteria of Individuation The counting and individuation issue Examples (4) Fred picked up three books. (5) Fred mastered three books. (6) Fred picked up and mastered three books. (7) Fred mastered three heavy books. M Gotham (UCL) Composing Criteria of Individuation 7/5/14 6 / 24
Composing Criteria of Individuation The counting and individuation issue Notes from Underground volume 1 The Gambler The Double ◮ Physically: 1 book. Informationally: 3 books. ◮ (5): True, (4),(6),(7): False (4) Fred picked up three books. × (5) Fred mastered three books. � (6) Fred picked up and mastered three books. × (7) Fred mastered three heavy books. × M Gotham (UCL) Composing Criteria of Individuation 7/5/14 7 / 24
Composing Criteria of Individuation The counting and individuation issue volume 1 Notes from Underground volume 2 Notes from Underground volume 3 Notes from Underground ◮ Physically: 3 books. Informationally: 1 books. ◮ (4): True, (5),(6),(7): False (4) Fred picked up three books. � (5) Fred mastered three books. × (6) Fred picked up and mastered three books. × (7) Fred mastered three heavy books. × M Gotham (UCL) Composing Criteria of Individuation 7/5/14 8 / 24
Composing Criteria of Individuation The counting and individuation issue The third criterion Situation 1 Situation 2 v 1 Notes from Underground Notes from Underground v 1 v 2 Notes from Underground The Gambler The Double v 3 Notes from Underground (6) Fred picked up and mastered three books. (7) Fred mastered three heavy books. M Gotham (UCL) Composing Criteria of Individuation 7/5/14 9 / 24
Composing Criteria of Individuation Compositional Theory Preliminaries Key points 1. Nouns supporting copredication denote sets of complex objects—in the case of ‘book’, objects that have a part that is a physical volume and a part that is an informational (abstract) book. 2. Predicates encode criteria of individuation as part of their meaning. 3. Quantifiers access, compose and exploit criteria of individuation. M Gotham (UCL) Composing Criteria of Individuation 7/5/14 10 / 24
Composing Criteria of Individuation Compositional Theory Preliminaries Complex objects Suppose that we combine the books in situations 1 and 2 to make situation 3: v 2 Notes from Underground Notes from Underground v 1 v 3 Notes from Underground The Gambler The Double v 4 Notes from Underground ] s 3 = { v 1 + NfU , v 1 + TG , v 1 + TD , v 2 + NfU , v 3 + NfU , v 4 + NfU } [ [ book ] Problem : In this view, there are 6 books in situation 3. Solution : This set of 6 is never used in plural quantification because of restrictions imposed by determiners. M Gotham (UCL) Composing Criteria of Individuation 7/5/14 11 / 24
Composing Criteria of Individuation Compositional Theory Preliminaries Distinctness criteria ◮ Say that a group is ‘physically compressible’ iff there are two members of it that are physically equivalent. ◮ E.g. (8) is physically compressible, but (9) isn’t. (8) v 1 + NfU ⊕ v 1 + TG ⊕ v 2 + NfU (9) v 1 + TD ⊕ v 2 + NfU ⊕ v 3 + NfU ◮ Both (8) and (9) are informationally compressible. M Gotham (UCL) Composing Criteria of Individuation 7/5/14 12 / 24
Composing Criteria of Individuation Compositional Theory Preliminaries Composing distinctness criteria ◮ We can express ‘ x is physically compressible’ as ( phys ) comp ( x ). ◮ Compressibilty statements can be complex, e.g.: ( phys ⊔ info ) comp ( x )— x is (physically or informationally) compressible. ◮ E.g. ( phys ⊔ info ) comp ( a ), but ¬ ( phys ⊔ info ) comp ( b ) (a) = v 1 + TG ⊕ v 2 + NfU ⊕ v 3 + NfU (b) = v 1 + TG ⊕ v 2 + NfU M Gotham (UCL) Composing Criteria of Individuation 7/5/14 13 / 24
Composing Criteria of Individuation Compositional Theory Preliminaries Formally: ◮ phys is shorthand for λ x e .λ y e . phys-equiv ′ ( x , y )—the two-place relation of physical equivalence. ◮ ( R ) comp ( x ) is shorthand for ∃ y ∃ z ( y � = z ∧ y ≤ a x ∧ z ≤ a x ∧ R ( y , z ))—the statement that there are two singletons ( y and z ) that are part of the group x and which bear relation R to each other. ◮ ⊔ is the generalized disjunction operator, familar from e.g. Partee and Rooth (1983). ◮ ∴ ( phys ⊔ info ) comp ( x ) ≡ ∃ y ∃ z ( y � = z ∧ y ≤ a x ∧ z ≤ a x ∧ (phys-equiv ′ ( y , z ) ∨ info-equiv ′ ( y , z ))) M Gotham (UCL) Composing Criteria of Individuation 7/5/14 14 / 24
Composing Criteria of Individuation Compositional Theory Lexical entries Compositional theory Novel lexical entries: book ′ ( x ) , phys ⊓ info ◮ [ � � [ book ] ] = λ x e . *book ′ ( x ) , phys ⊓ info ◮ [ � � [ books ] ] = λ x e . heavy ′ ( y ) , phys ◮ [ � � [ be heavy ] ] = λ y e . informative ′ ( z ) , info ◮ [ � � [ be informative ] ] = λ z e . M Gotham (UCL) Composing Criteria of Individuation 7/5/14 15 / 24
Composing Criteria of Individuation Compositional Theory Lexical entries Quantification [ [ three ] ] = λ P e →� t ×R� .λ Q e →� t ×R� . � � � ∃ x | x | ≥ 3 ∧ π 1 ( Px ) ∧ π 1 ( Qx ) ∧ ¬ ( π 2 ( Px ) ⊔ π 2 ( Qx )) comp ( x ) , � π 2 ( Px ) ⊓ π 2 ( Qx ) ∴ [ [ three books ] ] = λ Q e →� t ×R� . � | x | ≥ 3 ∧ *book ′ ( x ) ∧ π 1 ( Qx ) ∧ ¬ (( phys ⊓ info ) ⊔ π 2 ( Qx )) comp ( x ) � � ∃ x , � ( phys ⊓ info ) ⊓ π 2 ( Qx ) M Gotham (UCL) Composing Criteria of Individuation 7/5/14 16 / 24
Composing Criteria of Individuation Compositional Theory Lexical entries Physical individuation [ [ three books are heavy ] ] = � | x | ≥ 3 ∧ *book ′ ( x ) ∧ *heavy ′ ( x ) ∧ ¬ (( phys ⊓ info ) ⊔ phys ) comp ( x ) � � ∃ x , � ( phys ⊓ info ) ⊓ phys � | x | ≥ 3 ∧ *book ′ ( x ) ∧ *heavy ′ ( x ) ∧ ¬ ( phys ) comp ( x ) � � = ∃ x , (10) � phys ⊓ info M Gotham (UCL) Composing Criteria of Individuation 7/5/14 17 / 24
Composing Criteria of Individuation Compositional Theory Composition More pieces of the puzzle mastered ′ ( f ′ , x ) , info � � [ [ λ 1 [ Fred mastered t 1 ]] ] = λ x e . (heavy ′ ( y ) ∧ π 1 ( Py )) , π 2 ( Py ) ⊔ phys � � [ [ heavy ] ] = λ P e → ( t ×R ) .λ y e . *heavy ′ ( y ) ∧ *book ′ ( y ) , ( phys ⊓ info ) ⊔ phys � � ∴ [ [ heavy books ] ] = λ y e . *heavy ′ ( y ) ∧ *book ′ ( y ) , phys � � = λ y e . M Gotham (UCL) Composing Criteria of Individuation 7/5/14 18 / 24
Composing Criteria of Individuation Compositional Theory Composition Copredication ∴ [ [ three heavy books ] ] = λ Q e →� t ×R� . � | x | ≥ 3 ∧ *heavy ′ ( x ) ∧ *book ′ ( x ) ∧ π 1 ( Qx ) ∧ ¬ ( phys ⊔ π 2 ( Qx )) comp ( x ) ∃ x � � , � phys ⊓ π 2 ( Qx ) ∴ [ [ Fred mastered three heavy books ] ] = � | x | ≥ 3 ∧ *heavy ′ ( x ) ∧ *book ′ ( x ) ∧ mastered ′ ( f ′ , x ) ∧ ¬ ( phys ⊔ info ) comp ( x ) � � ∃ x , � phys ⊓ info M Gotham (UCL) Composing Criteria of Individuation 7/5/14 19 / 24
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