# The compositional semantics of same

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7 x(x (read (the (((NP\\S)//(NP\\(NP\\S)))//((N/N)\\NP) book)))) NP\\S S S S//(NP\\S) x(x (read (the (((NP\\S)//(NP\\(NP\\S)))//((N/N)\\NP) book)))) NP\\S S//(NP\\S) (read (the (((NP\\S)//(NP\\(NP\\S)))//((N/N)\\NP) book))) S John (and Mary) S//(NP\\S) (John (and Mary)) (read (the (same book))) S LEX The Curry-Howard labeling of this derivation gives the desired meaning as above: (27) (John Mary)(same(f.the(f(book)))(yx.read(y)(x))) This denotation also gives the correct truth conditions for plural cases, with Z possibly taking a plural entity as its value: (28) a. John and Mary read the same books. b. (John Mary)(same(f.the(f(books)))(Yx.read(Y)(x)) c. Z x < John Mary.the(Y.read(Y)(x) books(y)) = Z d. There is a group Z such that for each x of John and Mary, the group of books that x read is Z. 6. Partitives and a Revised Analysis We saw above that same can appear in plural NPs. This includes plural NPs in the complement position of a partitive quantifier: (29) a. Anna and Bill know some of the same people. b. Anna and Bill know most of the same people. c. Anna and Bill know all of the same people. The truth conditions of at least (29a) and (29c) are clear. (29a) will be true just in case there are some people that Anna and Bill both know. (29c) is synonymous with Anna and Bill know the same people, and will be true just in case Anna knows everyone Bill knows and vice-versa. The truth conditions of (b) are less obvious, but there is no doubt as to its grammaticality. I assume that the partitive quantifiers such as some of and most of have category (S//(NP\\S)\NP, and so take a plural entity as their argument, and as in Lasersohn 2008, can predicate a collective property of subgroups of their argument. My denotation for same then gives the following truth conditions for (29a): (30) a. Anna and Bill know some of the same people. b. Z x < Anna Bill.the(Y.some-of(Y)(W.knows(W)(x)) people(y)) = Z c. There is a group Z such that for x of Anna and Bill, the maximal group of people x knows some of is Z. However, this will be true as long as each of Anna and Bill know at least one person, regardless of whether they know anyone in common, since the maximal group of people they know some of will then just be the plural sum of all people. Nor does Barker s analysis give correct truth conditions: (31) a. Anna and Bill know some of the same people. b. f x < Anna Bill.some-of(the(f(people)))(W.knows(W)(x)) c. f.anna and Bill each know some of the f people. d. There is a group of people Anna and Bill each know some of. 7

8 This too will be true just in case Anna and Bill each know at least one person. If we let f be the choice function such that f(people) is the sum of the people Anna knows and the sum of the people Bill knows, then each of Anna and Bill will know some of the f people, even if there is actually no one that they both know. These two analyses do no better with most in (29b). My analysis would give: (32) a. Anna and Bill know most of the same people. b. Z x < Anna Bill.the(Y.most-of(Y)(W.knows(W)(x)) people(y)) = Z c. There is a group Z such that for x of Anna and Bill, the maximal group of people x knows most of is Z. But the maximal group of people that x knows some of will usually not even be defined. Suppose Anna only knows two people. Then she will know most of any group of three people which contains these two. But assuming there at least four people in the universe, there will be multiple groups of three people that Anna knows most of, but she will not know most of the sum of these groups. Barker s account gives a defined refined, but the truth conditions are still incorrect: (33) a. Anna and Bill know most of the same people. b. f x < Anna Bill.most-of(the(f(people)))(W.knows(W)(x)) c. f.anna and Bill each know most of the f people. d. There is a group of people Anna and Bill each know most of. Suppose Anna and Bill know at least one person in common. Let f be the choice function such that f(book) is the plural sum of these people. Then Anna and Bill will both know most of the f people. So Barker s analysis predicts that (29b) will be true just in case there is a person that Anna and Bill both know. But this is clearly not what it asserts. The problem with these analyses is that they talk about the groups of people that x knows some of, when want we need to talk about are just the groups of people that x knows. The partitive comes says something about the overlap of these groups; it does not participate in defining them. So (29a) is equivalent to (34b), not (34a): (34) a. The people Anna knows some of = the people Bill knows some of. b. Some of the people Anna knows = some of the people Bill knows. We can accomplish this by having same take scope over the whole partitive phrase, of category S//(NP\\S), instead of just over the smaller NP. We still want some of the same people to have the category (NP\\S)//(NP\\(NP\\S)), but in order for same to take scope over the partitive phrase and produce this kind of expression, same must have the category ((NP\\S)//(NP\\(NP\\S)))//((N/N)\\(S//(NP\\S))), and therefore semantic type et,et, et,t, e,et,et. The only change in the denotation of same is to accommodate this higher type: (34) Denotation for same: [[same]] = F et,et, et,t R e,et X e. Z x < X.F(gY.R(Y)(x) g(y))(w.w = Z) A type e NP can be lifted to a S//(NP\\S) generalized quantifier with no effect on the meaning, so this denotation still handles the cases in the previous sections. While the previous denotation of same took a non-quantificational NP and turned into a quantificational (NP\\S)/(NP\\(NP\\S)), this same takes an already quantificational S//(NP\\S) and turns it into a different quantificational expression, again of (NP\\S)//(NP\\NP\\S). 8

9 This new denotation now gives us correct truth conditions for the examples in (29): (35) a. Anna and Bill know some of the same people. b. (Anna Bill)(same(f.some-of(the(f(people))))(yx.know(y)(x)) c. Z x < Anna Bill.some-of(the(Y.know(Y)(x) people(y)))(w.w = Z) d. There is a group Z such that for each x of Anna and Bill, Z constitutes some of the people that x knows. Here Z is the group of people that Anna and Bill both know. (36) a. Anna and Bill know most of the same people. b. (Anna Bill)(same(f.most-of(the(f(people))))(yx.know(y)(x)) c. Z x < Anna Bill.most-of(the(Y.know(Y)(x) people(y)))(w.w = Z) c. There is a group Z such that for each x of Anna and Bill, Z constitutes most of the people that x knows. Here Z is the group of people that Anna and Bill both know, and most of the people that each of them know must be in Z. (37) a. Anna and Bill know all of the same people. b. (Anna Bill)(same(f.all-of(the(f(people))))(yx.know(y)(x)) c. Z x < Anna Bill.all-of(the(Y.know(Y)(x) people(y)))(w.w = Z) d. There is a group Z such that for each x of Anna and Bill, Z constitutes all of the people that x knows. Here Z is the group of people that Anna and Bill both know, and all of guarantees Anna and Bill know no one beside this. The derivation of any of these sentences is essentially the same as the above derivation of John and Mary read the same book: NP (know NP) S NP x(x (know NP)) S x(x (know NP)) NP\\S NP yx(x (know y)) NP\\S yx(x (know y)) NP\\(NP\\S) NP\\S NP\\S (NP\\S)//(NP\\(NP\\S)) yx(x (know y)) NP\\S some-of (the (N/N people)) S//(NP\\S) N/N f(some-of (the (f people))) S//(NP\\S) f(some-of (the (f people))) (N/N)//(S//(NP\\S)) (((NP\\S)//(NP\\(NP\\S)))//((N/N)//(S//(NP\\S))) f(some-of (the (f people)))) yx(x (know y)) NP\\S (some-of (the (((NP\\S)//(NP\\(NP\\S)))//((N/N)//(S//(NP\\S))) people))) yx(x (know y)) NP\\S x(x know (some-of (the (((NP\\S)//(NP\\(NP\\S)))//((N/N)//(S//(NP\\S))) people)))) NP\\S S S S//(NP\\S) x(x know (some-of (the (((NP\\S)//(NP\\(NP\\S)))//((N/N)//(S//(NP\\S))) people)))) S S//(NP\\S) (know (some-of (the (((NP\\S)//(NP\\(NP\\S)))//((N/N)//(S//(NP\\S))) people)))) S Anna (and Bill) S//(NP\\S) (Anna (and Bill)) (know (some-of (the (same people)))) S \\R \\R //R LEX The Curry-Howard labeling again gives us the correct semantics: (38) (Anna Bill)(same(f.some-of(the(f(people))))(yx.know(y)(x)) 9

10 7. Non-NP Triggers Barker observes that an internal reading of same can be triggered by plurals other than NPs: (#) a. John hit and killed the same man. b. Mary read and reviewed the same book. c. Bill ate at the same restaurant every day. Barker is able to account for these cases by generalizing the category of same from (NP\\S)//((N/N)\\(NP\\S)) to the schema (α\\s)//((n/n)\\(α//s)), where α is a variable ranging over categories. The denotation in (12) can be generalized in exactly the same way, generalizing the category from (NP\\S)//(NP\\(NP\\S)))//((N/N)\\(S//(NP\\S))) to ((α\\s)//(np\\(α\\s)))//((n/n)\\(s//(np\\s))). The remaining occurrences of the category NP reflect that same still takes scope over the NP quantifier which contains it, and that this object, which takes scope over the nuclear scope α\\s, is locally an NP. 8. A Remaining Puzzle Barker asks why same always requires the definite determiner the. For instance, why can we not say *John and Mary read a same book instead of John and Mary read one of the same books? Barker s account has an explanation for this. On his analysis, the determiner in the same-np always applies to the output of a choice function f. Since this is guaranteed to be a singleton set, the determiner must be the definite the. So *a same book is ruled out for the same reason as *a longest book. This explanation is not available on the analysis I have presented in this paper. The determiner in the same-np is not restricted to applying to the output of a choice function. The analysis explicitly allows same to take scope directly over quantifier phrases, in order to handle with partitive constructions such as some of the same people. This should rule in other quantifiers which have the same category S//(NP\\S), including *a same book, as well as *every same book and so on. I have more nothing to say on this question except to note a certain trade-off between these two approaches. I have to stipulate that same requires the, but I can then use the properties of the to explain the presuppositions that arise. Barker, on the other hand, has an explanation for why same requires the, but this requires stipulating that same quantifies only over choice functions. And it is precisely the fact that the determiner is guaranteed to apply to the output of a choice function that prevents the from contributing any presuppositions to the sentence, which we have seen it must. 10

11 References Barker, Chris Parasitic scope. Linguistics and Philosophy. 30.4: Carlson, Greg Same and different: some consequences for syntax and semantics. Linguistics and Philosophy. 10.4: Heim, Irene Notes on comparatives and related matters. Ms. (Available at semanticsarchive.net.) Lasersohn, Peter Semantics: An International Handbook of Natural Language Meaning. Moortgat, Michael Categorial type logics. In Johan van Benthem and Alice ter Meulen (eds), Handbook of Logic and Language,

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