The Logical Analysis of Plurals and Mass Terms Godehard Link (1983) - PowerPoint PPT Presentation

The Logical Analysis of Plurals and Mass Terms Godehard Link (1983) Ling 720 Presen tation Jon Ander Mendia De em b er 10, 2013 0 Overview 2. Mass T erms Plurals and mass nouns b eha v e similarly in some resp e ts. Main on tribution of the pap er: Extend the logi al language presen ted in PTQ If a and b of a and b to o v er plural and mass terms. (2) a. is w ater is w ater, then the sum is w ater. If a and b of a and b b. are horses are horses, then the sum are horses. Link dubb ed this prop ert y the umulative r efer en e pr op erty of plurals and mass terms. The Plan: expressions a and b 1. The on tology of plurals and mass terms. Ho w ev er: if t w o refer to en tities o-o urring in spa e and time then a � = b . 2. The ingredien ts of LPM but ha v e di�eren t sets of predi ates that an b e true of them, 3. Some appli ations to Mon tague Grammar Example: tak e a ring re en tly made up from some old Egyptian gold. Then the gold 4. A brief �nal remark the ring is made of is old, whereas the ring itself is new. Example: tak e a ommittee onstituted b y all the fa ult y mem b ers under 30. Then, 1 The ontology of plurals and mass terms if the ommittee w as onstituted man y y ears ago it is true that the ommittee is old, whereas the fa ult y mem b ers are y oung. The Basi Question: what do plural and mass nouns denote? Mon tague pro vided if a and b Note: the um ulativ e referen e prop ert y b eha v es the same: are rings, the no a oun t of plural and mass terms in his system, the domain of en tities onsisted in a and b rings a and b gold is still old, whereas the are new. only of a set of singular individuals. 1. Plural T erms The distin tiv eness of these linguisti expressions p oin ts out that ev en if the ring and the gold in the ring share the p ortion of matter they are made of, they are not the (1) a. *The kid met together same en tit y . together � b. The kids met ea h one of the kids met together ys ⇒ . The kids are b o ea h one of the kids is a b o y Link's prop osal: enri h the -underlying- set theoreti metalanguage to a oun t for prop erties lik e um ulativ e referen e, but without app ealing to sets. Ho w do w e a oun t for these di�eren t fa ts? 1

The Logical Analysis of Plurals and Mass Terms (Link 1983) Jon Ander Mendia join: � E, ⊕� Idea 1: within the domain of en tities E w e an distinguish t w o di�eren t (sub)- E an b e de�ned as a ( omplete b o olean) algebra losed under . A , domains: the domain A of atomi individuals and the domain D of �stu� � or p ortions the set of atoms, and D , the set of individual p ortions of matter, are omplete join- predi ates P of matter. subsemilatti es of E generated b y 1-pla e . predi ate P where P = { a, b, c } : (3) E as generated b y the , (4) On tology: a. S attered Singular En tities: x, y ∈ D ( water, gold, air, et .) b. Con rete Singular En tities: x, y ∈ A \ D ( the ring, the ommitte e, the gold in this ring, et .) . Plural En tities: x, y ∈ E \ A ( the rings, the ommitte es, et .) Note: 1. Both mass terms and group nouns are atoms , they are di�eren t en tities from the p ortions of matter or individuals that they are omp osed of (re all the example 1 of the ring and the ommitte e ab ove ). 2. Plural en tities are just sums of individuals (and not sets), as � on rete� as the individuals that serv e to de�ne them and of the same logi al t yp e. 3. Substan es are abstra t en tities and annot b e de�ned in terms of their on rete water ∈ D glass ∈ A manifestations (that's wh y whereas the water in this ). (in E \ D 4. Joining together an y t w o on rete individuals ) returns a plural en tit y (in E \ A (in D ), whereas joining together t w o p ortions of matter ) returns another in D 2 p ortion of matter, an atom . 5. The n ull elemen t 0 is assigned the role of dumm y ob je t to whi h no predi ate ( ≈ applies and whi h an tak e are of denotation gaps in the theory our on ept of garbage). 1 In the ase of group nouns, Link distinguishes to t yp es of predi ates: those that are p ermeable to the inner stru ture of group nouns and those that are not ( variant vs. invariant pr e di ates ): i. V arian t Predi ate: The p ersonnel ommittee is old � the professors is old ii. In v arian t Predi ate: The p ersonnel ommittee met ⇒ the professors met ` ⊕ ' 2 Graphi ally this is represen ted b y app ealing to t w o di�eren t instan tiations of the join op erator for on rete individuals and `+' for p ortions of matter. 2