Overview Monotonicity Stratified Reference Grounded SR Conclusion Gather -type predicates: massiness over participants Jeremy Kuhn New York University North East Linguistic Society 45 at MIT November 1, 2014 [slides: https://files.nyu.edu/jdk360/public/papers/Kuhn-gather-slides.pdf] Jeremy Kuhn, New York University Gather -type predicates: massiness over participants 1 / 42
Overview Monotonicity Stratified Reference Grounded SR Conclusion Section 1 Overview Jeremy Kuhn, New York University Gather -type predicates: massiness over participants 2 / 42
Overview Monotonicity Stratified Reference Grounded SR Conclusion Two kinds of collective predicates ◮ Predicates like gather and be numerous have both been described as “collective predicates.” (1) a. The students are numerous. b. * Marco is numerous. (2) a. The students gathered. b. * Marco gathered. Jeremy Kuhn, New York University Gather -type predicates: massiness over participants 3 / 42
Overview Monotonicity Stratified Reference Grounded SR Conclusion Two kinds of collective predicates ◮ However, the two classes of predicates differ with respect to plural quantifiers (e.g. all , most , several ). (Winter 2001, Champollion 2010) (3) Gather -type predicates a. The students gathered. b. All the students gathered. c. * Each student gathered. (4) Numerous -type predicates a. The students are numerous. b. * All the students are numerous. c. * Each student is numerous. Jeremy Kuhn, New York University Gather -type predicates: massiness over participants 4 / 42
Overview Monotonicity Stratified Reference Grounded SR Conclusion Two kinds of collective predicates ◮ However, the two classes of predicates differ with respect to plural quantifiers (e.g. all , most , several ). (Winter 2001, Champollion 2010) (5) Gather -type predicates a. The students gathered. b. All the students gathered. c. * Each student gathered. (6) Numerous -type predicates a. The students are numerous. b. * All the students are numerous. c. * Each student is numerous. Jeremy Kuhn, New York University Gather -type predicates: massiness over participants 4 / 42
Overview Monotonicity Stratified Reference Grounded SR Conclusion Two kinds of collective predicates ◮ All the students/puzzle pieces/jurors/axioms... Gather -type predicates Numerous -type predicates gather be numerous be similar be a group of ten meet form a pyramid disperse suffice to defeat the army be consistent (axioms) be inconsistent (axioms) hold hands return a verdict of ‘not guilty’ fit together be a group of less than ten disagree be denser in the middle Jeremy Kuhn, New York University Gather -type predicates: massiness over participants 5 / 42
Overview Monotonicity Stratified Reference Grounded SR Conclusion The intuition ◮ Numerous -type predicates generally involve an emergent property of the whole group... ◮ be numerous , be a group of ten — the number of individuals; ◮ return a verdict of ‘not guilty’ — the legality of returning a verdict; ◮ be incompatible (of a set of axioms) — the logical properties of the set. ◮ Gather -type predicates allow ‘distributive sub-entailments’... (Dowty 1987) ◮ gather — individuals went to the same place as someone else; ◮ fit together — puzzle pieces connect with some other piece. Jeremy Kuhn, New York University Gather -type predicates: massiness over participants 6 / 42
Overview Monotonicity Stratified Reference Grounded SR Conclusion The take-home message ◮ The take-home message from this talk: The gather / numerous distinction is analogous to the mass/count distinction in the nominal domain and the atelic/telic distinction in the temporal domain. nouns verbs verbs (w.r.t time) (w.r.t. participants) mass water look at an apple gather count chair eat an apple be numerous Jeremy Kuhn, New York University Gather -type predicates: massiness over participants 7 / 42
Overview Monotonicity Stratified Reference Grounded SR Conclusion Solving problems ◮ However, monotonicity (either as divisibility or cumulativity) both overgenerates and undergenerates the class of gather -type predicates, so no account to date has provided a successful entailment-based diagnostic. ◮ Here, I build on these intuitions, repairing the problems with two innovations: I. In the spirit of Champollion 2010, gather -predicates have Stratified Reference, not monotonicity. II. Gather -predicates display a homomorphism between the mereology of individuals and the mereology of situations (as in Kratzer 1989, Fine 2012). Jeremy Kuhn, New York University Gather -type predicates: massiness over participants 8 / 42
Overview Monotonicity Stratified Reference Grounded SR Conclusion Section 2 Monotonicity and beyond Jeremy Kuhn, New York University Gather -type predicates: massiness over participants 9 / 42
Overview Monotonicity Stratified Reference Grounded SR Conclusion Bounded monotonicity ◮ A good starting point: (7) A predicate P has ε -bounded downward monotonicity iff ∀ x [ P ( x ) ∀ y [( µ ( y ) > ε ∧ y ≤ x ) → P ( y )]] → “If P holds of x , then P holds of all sufficiently large parts of x .” ◮ Mass nouns: For any entity x , if x is water, then any sufficiently large subpart of x is water. ◮ Gather predicates: For any plurality x , if x gathered, then any sufficiently large subplurality of x gathered. ◮ (Bounded monotonicity avoids the Minimal Parts Problem: a single atom cannot be water; a single person cannot gather.) Jeremy Kuhn, New York University Gather -type predicates: massiness over participants 10 / 42
Overview Monotonicity Stratified Reference Grounded SR Conclusion Bounded monotonicity Jeremy Kuhn, New York University Gather -type predicates: massiness over participants 11 / 42
Overview Monotonicity Stratified Reference Grounded SR Conclusion Bounded monotonicity Jeremy Kuhn, New York University Gather -type predicates: massiness over participants 11 / 42
Overview Monotonicity Stratified Reference Grounded SR Conclusion Bounded monotonicity Jeremy Kuhn, New York University Gather -type predicates: massiness over participants 11 / 42
Overview Monotonicity Stratified Reference Grounded SR Conclusion Bounded monotonicity Jeremy Kuhn, New York University Gather -type predicates: massiness over participants 11 / 42
Overview Monotonicity Stratified Reference Grounded SR Conclusion Bounded monotonicity ◮ At a first pass, this seems to do quite well! ◮ gather ◮ If the boys gathered ( = went to the same place at the same time), then any subset of at least two boys gathered. ◮ be similar ◮ If the boys are similar, then any subset of at least two boys is similar. ◮ In fact, Winter 2001 very briefly considers 2-bounded downward monotonicity as a possible diagnostic. Jeremy Kuhn, New York University Gather -type predicates: massiness over participants 12 / 42
Overview Monotonicity Stratified Reference Grounded SR Conclusion ◮ But, n -bounded downward monotonicity faces problems. ◮ Undergeneration: incorrectly rejects some predicates from the gather class. ◮ hold hands , fit together , disagree ◮ Overgeneration: incorrectly admits some predicates to the gather class. ◮ be a group of more than three or less than five , be a group of less than ten , be denser in the middle ◮ Today, I will fix these problems while maintaining the congruence between mass nouns and gather -type predicates. Jeremy Kuhn, New York University Gather -type predicates: massiness over participants 13 / 42
Overview Monotonicity Stratified Reference Grounded SR Conclusion Section 3 The “Tricky Parts Problem” and Stratified reference Jeremy Kuhn, New York University Gather -type predicates: massiness over participants 14 / 42
Overview Monotonicity Stratified Reference Grounded SR Conclusion The “Tricky Parts Problem” ◮ Undergeneration: some gather -type predicates are not 2-bounded monotonic. ◮ hold hands : if all the children held hands, it is not necessarily the case that any two given children held hands with each other. ◮ fit together : if all the puzzle pieces fit together, it is not necessarily the case that any two given puzzle pieces fit together. Jeremy Kuhn, New York University Gather -type predicates: massiness over participants 15 / 42
Overview Monotonicity Stratified Reference Grounded SR Conclusion The “Tricky Parts Problem” ◮ Suppose that six students are holding hands as follows: Jeremy Kuhn, New York University Gather -type predicates: massiness over participants 16 / 42
Overview Monotonicity Stratified Reference Grounded SR Conclusion The “Tricky Parts Problem” ◮ The following set of three students are not holding hands! Jeremy Kuhn, New York University Gather -type predicates: massiness over participants 17 / 42
Overview Monotonicity Stratified Reference Grounded SR Conclusion The “Tricky Parts Problem” ◮ In fact, hold hands is not n -bounded monotonic for any n . ◮ Consider a circle of 2 n students holding hands. The set consisting of every other student in the circle is a subset of n students, and yet the predicate hold hands does not hold of it. ◮ Thus, what we have is not a Minimal Parts Problem. Jeremy Kuhn, New York University Gather -type predicates: massiness over participants 18 / 42
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