Conservativity

In formal semantics conservativity is a proposed linguistic universal which states that any determiner D {\displaystyle D} must obey the equivalence D ( A , B ) ↔ D ( A , A ∩ B ) {\displaystyle D(A,B)\leftrightarrow D(A,A\cap B)} . For instance, the English determiner "every" can be seen to be conservative by the equivalence of the following two sentences, schematized in generalized quantifier notation to the right. Every aardvark bites. ⇝ e v e r y ( A , B ) {\displaystyle \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \rightsquigarrow every(A,B)} Every aardvark is an aardvark that bites. ⇝ e v e r y ( A , A ∩ B ) {\displaystyle \ \ \rightsquigarrow every(A,A\cap B)} Conceptually, conservativity can be understood as saying that the elements of B {\displaystyle B} which are not elements of A {\displaystyle A} are not relevant for evaluating the truth of the determiner phrase as a whole. For instance, truth of the first sentence above does not depend on which biting non-aardvarks exist. Conservativity is significant to semantic theory because there are many logically possible determiners which are not attested as denotations of natural language expressions. For instance, consider the imaginary determiner s h m o r e {\displaystyle shmore} defined so that s h m o r e ( A , B ) {\displaystyle shmore(A,B)} is true iff | A | > | B | {\displaystyle |A|>|B|} . If there are 50 biting aardvarks, 50 non-biting aardvarks, and millions of non-aardvark biters, s h m o r e ( A , B ) {\displaystyle shmore(A,B)} will be false but s h m o r e ( A , A ∩ B ) {\displaystyle shmore(A,A\cap B)} will be true. Some potential counterexamples to conservativity have been observed, notably, the English expression "only". This expression has been argued to not be a determiner since it can stack with bona fide determiners and can combine with non-nominal constituents such as verb phrases. Only some aardvarks bite. This aardvark will only [VP bite playfully.] Different analyses have treated conservativity as a constraint on the lexicon, a structural constraint arising from the architecture of the syntax-semantics interface, as well as constraint on learnability.

Proposed linguistic universal

In formal semantics conservativity is a proposed linguistic universal which states that any determiner D {\displaystyle D} must obey the equivalence D ( A , B ) ↔ D ( A , A ∩ B ) {\displaystyle D(A,B)\leftrightarrow D(A,A\cap B)} . For instance, the English determiner "every" can be seen to be conservative by the equivalence of the following two sentences, schematized in generalized quantifier notation to the right.^[1][2][3]

1. Every aardvark bites.                                                               ⇝ e v e r y ( A , B ) {\displaystyle \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \rightsquigarrow every(A,B)}
2. Every aardvark is an aardvark that bites.     ⇝ e v e r y ( A , A ∩ B ) {\displaystyle \ \ \rightsquigarrow every(A,A\cap B)}

Conceptually, conservativity can be understood as saying that the elements of B {\displaystyle B} which are not elements of A {\displaystyle A} are not relevant for evaluating the truth of the determiner phrase as a whole. For instance, truth of the first sentence above does not depend on which biting non-aardvarks exist.^[1][2][3]

Conservativity is significant to semantic theory because there are many logically possible determiners which are not attested as denotations of natural language expressions. For instance, consider the imaginary determiner s h m o r e {\displaystyle shmore} defined so that s h m o r e ( A , B ) {\displaystyle shmore(A,B)} is true iff | A | > | B | {\displaystyle |A|>|B|} . If there are 50 biting aardvarks, 50 non-biting aardvarks, and millions of non-aardvark biters, s h m o r e ( A , B ) {\displaystyle shmore(A,B)} will be false but s h m o r e ( A , A ∩ B ) {\displaystyle shmore(A,A\cap B)} will be true.^[1][2][3]

Some potential counterexamples to conservativity have been observed, notably, the English expression "only". This expression has been argued to not be a determiner since it can stack with bona fide determiners and can combine with non-nominal constituents such as verb phrases.^[4]

1. Only some aardvarks bite.
2. This aardvark will only [VP bite playfully.]

Different analyses have treated conservativity as a constraint on the lexicon, a structural constraint arising from the architecture of the syntax-semantics interface, as well as constraint on learnability.^[5][6][7]

See also

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• Jon Barwise
• Lindström quantifier
• Universal grammar

Notes

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1. ^ ^{a b c} Dag, Westerståhl (2016). "Generalized Quantifiers". In Aloni, Maria; Dekker, Paul (eds.). Cambridge Handbook of Formal Semantics. Cambridge University Press. ISBN 978-1-107-02839-5.
2. ^ ^{a b c} Gamut, L.T.F. (1991). Logic, Language and Meaning: Intensional Logic and Logical Grammar. University of Chicago Press. pp. 245–249. ISBN 0-226-28088-8.
3. ^ ^{a b c} Barwise, Jon; Cooper, Robin (1981). "Generalized Quantifiers and Natural Language". Linguistics and Philosophy. 4 (2): 159–219. doi:10.1007/BF00350139.
4. ^ von Fintel, Kai (1994). Restrictions on quantifier domains (PhD). University of Massachusetts Amherst.
5. ^ Hunter, Tim; Lidz, Jeffrey (2013). "Conservativity and learnability of determiners". Journal of Semantics. 30 (3): 315–334. doi:10.1093/jos/ffs014.
6. ^ Romoli, Jacopo (2015). "A structural account of conservativity". Semantics-Syntax Interface. 2 (1).
7. ^ Steinert-Threlkeld, Shane; Szymanik, Jakub (2019). "Learnability and semantic universals". Semantics and Pragmatics. 12 (4): 1. doi:10.3765/sp.12.4. hdl:11572/364230. S2CID 54087074.

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