Cognitive foundations of measuring and counting and their reflection in determiner systems

Transcription

1 Cognitive foundations of measuring and counting and their reflection in determiner systems Mass and Count in Romance and Germanic Languages December 16-17, 2013 Universität Zürich Manfred Krifka Zentrum für Allgemeine Sprachwissenschaft, Berlin Humboldt-Universität zu Berlin Gefördert durch das BMBF Gefördert durch die DFG (SFB 632) 1 / 14

2 A bit of mereology, for a starter See Champollion & Krifka (to appear) for an overview of mereological notions. Assume: Predicates apply to entities, e.g., gold (a), ring (b) For entities, there is an operation of sum formation: If x, y are entities, then x y is an entity as well, the sum (join) of x and y Sum formation defines a part relation and a proper part relation: x y iff x y = y x y iff x y and not y x Two entities are said to overlap iff they have a part in common: x o y iff there is a z such that z x and z y An entity is called an atom iff it does not have a proper part: AT(x) iff there is no y such that y x An entity is called a P-atom iff it falls under the predicate P, and does not have a proper part that also falls under P: AT(P)(x) iff P(x) and there is no y such that P(y) and y x 2 / 14

3 What is measuring? Measuring: We render certain properties of objects by numbers differences between properties are reflected in differences in numbers Examples: temperature: a is warmer than b purity: a is purer gold than p C(a) > C(b) carat(a) > carat(b) mass a is heavier than b volume: a is more voluminous than b kg(a) > kg(b) liter(a) > liter(b) A difference between C/carat and kg/liter: With kg/liter, we have an extensive measure, e.g. If b a, then kg(b) < kg(a) If not a o b (no overlap), then kg(a b) = kg(a) + kg(b) Archimedean property: If kg(a) > 0, and b a, then kg(b) > 0 And this is relevant for natural-language semantics! two hundred kilograms of steel vs. *two hundred degrees Celsius of steel eighteen ounces of gold vs. *eighteen carats of gold Why does language care about the nature of the measure function? 3 / 14

4 Measuring and nominal constructions Let s contrast: (a) eighteen ounces of gold (x) iff x is gold, and x has a weight of 18 ounces. (b) *eighteen carats of gold (x) iff x is gold, and x is gold to degree 18/24. With P = (a), but not with P = (b), we have: If P(a) and b a, then not P(b) Hence (a) but not (b) is quantized. We therefore can assume: a nominal construction [ NP NUM MEASURE (of) NOUN] must lead to a quantized predicate; i.e. it must specify a property that does not hold for parts of the object, hence the measure term must denote an extensive measure function. Notice: an apparently arcane mereological property influences the distribution of measure terms in core syntax. This is not a quirk of English, or of European languages: similar restrictions hold for measure terms in other languages. Hagit Borer s suggestion of a phrase #P Qualitative and quantitative modifications in different shells: [ #P zehn Kilogramm [ NP rostfreier Stahl]] / *rostfreie zehn Kilogramm Stahl 4 / 14

5 What is counting? Counting similar to extensive measurement, but... based on units of the atomic entities of what is measured, hence... no explicit measure term is necessary. Example: Counting apples apple* (x) = 1 iff apple (x), i.e. if x is a single apple (an apple atom) apple* (x y) = apple* (x) + apple* (y), if not x o y, i.e. no overlap It can be shown that this leads to quantized meaning of e.g. eighteen apples: If apple* (a) = 18 and b a, then apple* (b) = 18 For which predicates P can we define an extensive counting function P*? P itself must be quantized; P must not apply to overlapping entities: If P(x), P(y) and x o y, then P*(x) = P*(y) = 1, but P*(x y) is not defined. apple* (x) = 1 liter (x) = 1 5 / 14

6 What do we need to count? This shows that for counting it is not sufficient to start out with any old quantized predicate P, rather, the predicate P must have the property of being discrete: If P(x) and P(y), then not x o y, i..e. x and y do not overlap. This allows for a 1-1-mapping of P-entities to the number sequence. Cf. Rothstein 2010, Landman 2011 for this point. Discreteness is guaranteed by gestalt features: fifty head of cattle: Each cattle has a unique head Classifiers referring to shape of objects, e.g. Chinese zhāng for flat objects, gēn for long rigid objects etc. For count nouns in general: they are atomic, but atomicity is not sufficient, they also have to be discrete, in order to allow for counting. In order to be discrete for human cognition, the atoms have to come with a recognizable shape have to be big enough (e.g. rice vs. beans) their shape has to have a border that separates them from other atoms they have to stay constant over time 6 / 14

7 Neat nouns and mess nouns Landman (2011): P is a neat predicate if the P-atoms do not overlap. P is a mess predicate if the P-atoms overlap. Count nouns: are typically neat (they do not overlap) Exceptions: nouns like fence, twig, sequence count noun use requires additional criteria, e.g. a connected fence, a separated twig, a maximal sequence Counting might be dependent on a context: Here are three fences, and over there there are four fences. Many count nouns do not vary with context. Mass nouns: can be atomic, if atomic, they are often mess nouns; cf. e.g. lemonade, but presumably also gold, water, bronze, mud etc.; what may count as smallest parts may overlap. but some mass nouns are neat, e.g. furniture, silverware, shoewear There is evidence that neat mass nouns are cognitively like count nouns, even though they are linguistically mass nouns. Incidentally, mess is a count noun: That s a mess! 7 / 14

8 Linguistic effects of the neat/mess distinction Magnitude comparison (Barner & Snedeker 2005): What is more water? And, what is more puddles? What is more silverware? And, what is more silver? Distribution of property expressions: The knives and forks are expensive / heavy. Collective and distributive reading. The silverware is expensive / heavy. Appears to have a collective and a distributive reading The silver is expensive. Only collective reading. 8 / 14

9 Mass/count and semantic representation Chierchia 1998: A mass noun like gold, furniture applies to a set of atoms and their sums. A singular count noun applies to a set of atoms. A plural count noun applies to the set of sums of the atoms of the singular count noun. Rothstein 2010: Mass nouns apply to a set of atoms and their sums; all root nouns N root are mass nouns Singular count nouns N count apply to a set of pairs x, k of individuals x and a context k; k imposes non-overlapping individuals x; different contexts k can lead to different atoms for nouns like fence. Plural count nouns apply to this set closed under Krifka, starting 1989: Mass nouns apply to set of atoms and their sums; Count nouns are measure functions based on such sets: e.g. apple* (n)(x) iff x consists of n (non-overlapping) entities x 1, x n such that apple (x 1 ),. apple (x n ) ( natural units of apples). 9 / 14

10 Mass-Count and semantic representation Differences between the approaches: Chierchia: No type-theoretic distinction between mass / count Rothstein: Type-theoretic distinction on the entity level mass nouns: type e, t count nouns: type e k, t, where k: a context. Krifka: Type-theoretic distinction on the predicate level mass nouns: type e, t count nouns: type n, e, t, where n: a number argument. Argument by Rothstein for her approach, based on example by Gillon 1992: The curtains and the carpets resemble each other. a. The curtains resemble each other, and the carpets resemble each other. b. The curtains and the carpets are similar to each other. The curtaining and the carpeting resemble each other. a. Only reading (b). Argument: We need a distinction on the entity level to express this. But: Krifka (1990) argues for a representation in which the curtains and the carpets introduce discourse referents, that the predicate resemble each other can distribute over; no distinction on the entity level necessary. For the treatment of count nouns with variable units (fence, twig), I would have to assume context-dependent measure functions. 10 / 14

11 Linguistic reflexes of Count One linguistic reflex of count-hood is pluralization: Count nouns (but not mass nouns) pluralize: apples, *golds Pluralization is based on counting functor *: apple (x), iff x is apple, no quantitative criterion of application apple* k (1)(x), iff x is an apple-atom in context k (context-dependency becomes relevant for nouns like fence). apple* k (n)(x), defined as usual as a count function PL(apple*) k (x), iff there is an n such that apple* k (n)(x), n ranges by the construction of count functions as a natural number 1 Plural in English should include atoms, cf. A: Do you have children? B: Yes, one. / B: #No, just one. Another linguistic reflex: numeral constructions: Count nouns allow for constructions like one apple, three apples three apple* (x) iff apple* (3)(x) one apple* (x) iff apple* (1)(x) = 1 Choice of singular/plural by agreement, cf. singular noun in Turkish: çocuk child, çocuklar children, but beş çocuk five children Another linguistic reflexes: Singulative forms derived from collective forms in languages like Breton Classifier as expression of count operator in languages like Chinese. 11 / 14

12 Linguistic reflexes of count: Determiners Definite determiners apply to mass and count the apple, the apples, the three apples, the gold Interpretation of definite article (Sharvey 1980, Link 1983) as supremum: the N = the unique x such that N (x), and for all y such that N (y) it holds that y x Examples: the gold = the greatest x such that gold (x) the three apples = the unique x such that three apple* (x), if not unique or non-existent: not defined. the apple = the one apple Indefinite determiners often derived from number word for one: ein Apfel (x) = apple* (x) = 1 Predicts that indefinite determiners are typically used with count nouns existential quantification comes from another source (e.g., Diesing 1992), as we find it also with bare nouns: John ate an/one apple. John ate (some) apples. Difference between indefinite article a and number word one: same meaning, specification of number as 1 different alternatives: one comes with alternatives two, three, a comes with alternative the 12 / 14

13 Indefinite determiners with mass nouns But indefinite determiners can occur with mass nouns: Bavarian, general use of indefinite article (cf. Kolmer 1999): Example: Dees is a Goid. This is gold. Not a general treatment of mass as count: *Zwoa Goid(s) two gold(s) Not related to introduction of discourse referents (existential quantifier), as it occurs with predicative nouns as well (see example above). Explanation: Mass noun is a root noun (cf. Rothstein 2010) Root nouns can be used in compounds, e.g. Bavarian da Goidsuacha the gold seeker Root nouns can be used non-referentially, e.g. Bavarian mia san radl gfarn we did some bicycling Root nouns cannot immediately be used as NPs in syntax. Indefinite article in Bavarian indicates change from root noun to NP English (and Standard German) allow for a zero derivation. 13 / 14

14 Indefinite determiners in exclamatives A case of indefinite determiners with mass nouns in Standard German Examples: Mensch, das ist ein Dreck! boy, that s (a) dirt! Was für ein Gold! what (for) a gold Exclamatives express surprise of the speaker that the topical entity ranges high on a property scale (Rett 2008). Wow, this is so beautiful! The indefinite determiner helps to create a scale: indefinite determiner presupposes a counting function exclamative presupposes a classification of entities on a scale of expectability; the topic is assumed to have a surprisingly high value on this scale this suggests assuming different subkinds of the kind named by the noun that range along the scale these subkinds are distinct and non-overlapping, and hence allow for counting. this licenses the use of the indefinite determiner based on the number word one. 14 / 14