Informal semanticsconservativity is a proposedlinguistic universal which states that anydeterminer${\displaystyle D}$ must obey the equivalence${\displaystyle D(A,B)\leftrightarrow D(A,A\cap B)}$. For instance, theEnglish determiner "every" can be seen to be conservative by theequivalence of the following two sentences, schematized ingeneralized quantifier notation to the right.^[1][2][3]

1. Every aardvark bites.${\displaystyle ⇝every(A,B)}$
2. Every aardvark is an aardvark that bites.${\displaystyle ⇝every(A,A\cap B)}$

Conceptually, conservativity can be understood as saying that theelements of${\displaystyle B}$ which are not elements of${\displaystyle A}$ are not relevant for evaluating the truth of thedeterminer 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 asdenotations of natural language expressions. For instance, consider the imaginary determiner${\displaystyle shmore}$ defined so that${\displaystyle shmore(A,B)}$ is true iff${\displaystyle |A|>|B|}$. If there are 50 biting aardvarks, 50 non-biting aardvarks, and millions of non-aardvark biters,${\displaystyle shmore(A,B)}$ will be false but${\displaystyle shmore(A,A\cap B)}$ 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 asverb phrases.^[4]

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

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

• Jon Barwise
• Lindström quantifier
• Universal grammar

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