1 Introduction to again

Transcription

1 Additive again Introduction to again Cara Feldscher March 9, 206 Michigan State University Examples from the Oxford English Dictionary go back as far as 523 in (5a). (5) a. It is worthe halfe as moche againe as the grasse was worthe. J. Fitzgerald, Surueyeng b. Lent shall be as long againe as it was. Shakespeare, Henry VI The traditional use of again has some meaning of and this has happened before. () a. I ran the race again. Repetitive b. The door was shut again. Restorative/Restitutive c. I shut the door again. (ambiguous) Example denotation from von Stechow (996) scopes over eventualities. (2) again = λp e, s,t λxλs : e [e < s P (x)(e )].P (x)(s). Half again Here, a different usage gives an additive, on top of the original reading. (3) a. Fluffy is half again as tall as Pansy. b. Belle made half again as much as Gaston made. c. The Beast is half again the size of a normal man. d. The pile of loot is half again what we gathered last week. There are some variations without half. (4) a. I only expected to get $20, but I made that again! ($40) b. Your plant is a third again as big as it was a week ago. The definitions for these usages in the OED are as follows: as much again: an additional amount equal to that mentioned, twice as much half as much again: an additional amount equal to half that mentioned, one-and-a-half times as much..2 Why it needs a different denotation from standard again The standard usage is the presupposition that the state/event happened before, and this usage is a repetition of quantity. (6) a. I ran the race again. b. I ran half again as far as you did. There is no presupposition with half again type usages. (7) a. The door is shut again. #It has never been shut before. b. The plant is half again as big as last week. It has never been this big before. This half again phrase is probably not some sort of lexicalized construction because:

2 Other factor phrases such as a third can be substituted. No factor phrase, such as in as much again or that again, is also acceptable. Different word order in British dialects, plus work by Gobeski (20) indicates that factor phrases like half merges with as tall..3 Why wwe can t use a factor phrase denotation Factor phrases like half take a degree and apply the multiple of it to the adjective (Bochnak 200, Gobeski 20). To borrow from Gobeski (20), here is his tree for the structure of factor phrases: (8) half as tall as Mary FP d, e, t, d, e, t half d, e, t DegP e, t d, e, t Deg e, d, d, e, t as AP e, d tall XP d as Mary The whole of his computation is provided in the appendix, but for now here s a simplified denotation for half as tall as Mary adapted from that. (9) half = λf d, e,t λdλx d X [F (d X )(x) d X /2d] half as tall = λdλx[tall(x) /2d] Can we apply again to half as tall and do the same thing of redefining the degree tall takes? Sure. (0) again = λf d, e,t λd λy d Y [f(d Y )(y)} 3d ] again ( half as tall ) = λd λy d Y [[λdλx[tall(x) /2d]](d Y )(y)} 3d ] half again as tall = λd λy d Y [tall(y) (d Y ) d Y = /2(3d )] λd λy d Y [tall(y) d Y d Y =.5d ] This tact works, but requires the assumption that again carries a 3 sort of meaning to it. Additionally, this tact will no longer work if attempting to compute any variations like a third again, that again, as much again. Better for now to attempt to access the degrees separately and add them together. 2 Considering states In order to access both the adjective and the degree, but separately, consider states. 2. Background Events and states can be considered objects in the ontology (Davidson 967, Kratzer 996). () Jones buttered the toast = e[butter(jones,the-toast,e)] Neo-Davidsonian views like Parsons (990) take a conjunctive approach, separating out thematic roles like this: 2

3 (2) Jones buttered the toast = e Agent(e)(Jones) Theme(e)(the toast) butter(e) A conjunctive approach like this would allow for accessing the degree and states separately to construct an additive denotation for again. 2.2 Measure roles If thematic roles of events can be separated out conjunctively, what about states? Here I posit a Measure function, acting like a thematic role for the state, that returns the degree of the measurement of that state. (5) again = λf d, s,t λdλs. s [f(d)(s ) s < s s s Meas(s) = Meas(s ) + d] Running it through: (6) again ( half as tall )( as Mary = λs. s [[tall(s ) Meas(s ) = 2 d M] s < s s s Meas(s) = Meas(s ) + d M ] To access the adjective, there exists a state that is similar to this one, so they must both be of height. Apply the Measure function to the previous state to extract its (halved) degree to add it to the whole one. Added together, they comprise the degree of this state. To start with, hypothesize something like (3). similarly to before. Factor phrases work 3 Summing up (3) half as tall = λdλs[tall(s) Meas(s) = 2 d] (4) half as tall again as Mary Additive again is more similar to the traditional than it appeared at first blush, dealing with the occurrence of a state of the same type. (2) is repeated here for comparison. d, s, t s, t d (7) again = λp e, s,t λxλs : e [e < s P (x)(e )].P (x)(s) again = λf d, s,t λdλs. s [s < s f(d)(s ) s s Meas(s) = Meas(s ) + d] d, s, t half as tall d, s, t, d, s, t again as Mary So again needs to access the state (dimension), and both the degrees, and set a new Meas for the new state of the same dimension. In order to extract tallness, a similarity function ( ) is posited. However, this additive part of the denotation is wholly absent from the traditional. Less unifiable. Finally, usage also gives evidence for the need to extract the degree separately, which argues for the need for a Measure function of sorts, like thematic roles for states. s s = iff they share a scale. Moltmann (205) discussed states being similar, although not with such notation. 3

4 Acknowledgements This work accomplished with a great deal of assistance and input from Marcin Morzycki and Adam Gobeski, as well as from everyone else in the MSU Semantics Lab: Curt Anderson, Ai Taniguchi, Alicia Parrish, Josh Herrin, Abhi Parekh, Chris Bartoluzzi, Tess Huelskamp, and Adam Smolinski. Thanks also to the rest of MSU Linguistics, and the audience today! References Bochnak, M. R. (200, August). Quantity and gradability across categories. In Semantics and Linguistic Theory (Vol. 20, pp ). Davidson, D. (967). The logical form of action sentences. Gobeski, A. (20). Twice versus two times in phrases of comparison. Michigan State University MA thesis. Kratzer, A. (996). Severing the external argument from its verb. In Phrase structure and the lexicon (pp ). Springer Netherlands. Maienborn, C. (2003). Against a Davidsonian analysis of copula sentences. In PROCEEDINGS-NELS (Vol. 33, pp ). Moltmann, F. (205). States versus tropes. Comments on Curt Anderson and Marcin Morzycki: Degrees as kinds. Natural Language & Linguistic Theory, 33(3), Parsons, T. (990). Events in the Semantics of English (Vol. 5). Cambridge, Ma: MIT Press. Schwarzschild, R. (202). Directed scale segments. In Semantics and Linguistic Theory (Vol. 22, pp ). Schwarzschild, R. (203). Degrees and segments. In Semantics and Linguistic Theory (Vol. 23, pp ). Von Stechow, A. (996). The different readings of wieder again : A structural account. Journal of semantics, 3(2), Appendix Gobeski (20) Here is the whole of Gobeski (20) s computation for half as tall as Mary. (8) as = λg e,d λdλx[g(x) d] as tall = λdλx[tall(x) d] half = λf d, e,t λdλx[max{d X : F (d X )(x)} 2 d] half as tall = λdλx[max{d X : tall(x) d X } 2 d] half as tall as Mary = λdλx[max{d X : tall(x) d ( x)} 2 d M] In the version here, half mimics the structure of two times, not twice. (9) two times = λf d, e,t λdλx. d X [F (d X )(x) d X = 2d] Working out half as tall Some incomplete attempt at working out what I posited in (3), repeated here. (20) as tall = λdλs[tall(s) Meas(s) d] half λf d, s,t λdλs[meas(x) = 2 d] half as tall = λdλs[tall(s) Meas(s) = 2 d] 4

5 Schwarzchild (202, 203) TP Schwarzschild (202, 203) separates out the adjective and decomposes the measurement by start and end points, based on evidence from Hindi and Navajo. (Examples repeated in (2) from Schwarzschild (202) and (22) from Schwarzschild (203) respectively.) T is σ. degp (2) anu raaj se lambii hai Anu Raj from tall.fem pres.sng Anu is taller than Raj. (22) Shideezhi shi-lááh át ée=go my.litte.sister sg.obj-beyond 3subj.be=sub nizhóní 3subj.pretty.AA My little sister is prettier than me. A sample computation and tree from Schwarzschild (203) are reproduced here: (23) Tom is taller than Susan DP Tom deg End deg er AP tall DegP Start.PP P than DP Susan (24) er = λσ. (σ) tall = λσ.µ σ = ht than = λx.λσ.(start(σ) = µ σ (x)) DegP = λσ. (σ) (µ σ = ht) start(σ) = µ σ (S) End = λσ.λxλσ.(end(σ) = µ σ (x) Σ(σ)) deg = λxλσ.(end(σ) = µ σ (x)) (σ) (µ σ = ht) (start(σ) = µ σ (S)) deg = λσ.(end(σ) = µ σ (T )) (σ) (µ σ = ht) (start(σ) = µ σ (S)) 5