We prove that Z in definable in Q by a formula with 2 universal quantifiers followed by 7 existential quantifiers. It follows that there is no algorithm for deciding, given an algebraic family of Q-morphisms, whether there exists one that is surjective on rational points. We also give a formula, again with universal quantifiers followed by existential quantifiers, that in any number field defin...

In this paper, I address the categorial status of quantifiers and similar expressions in German. Traditionally, they are assigned either of two classes: determiners and adjectives. I argue that German quantifiers in principle are ambiguous and can be realized alternatively as determiners or adjectives. The categorial status is mirrored by the declension of attributive adjectives following these...

Both numerals and quantifiers (like some) have more than one possible interpretation (i.e., weak and strong interpretations). Some studies have found similar behavior for numerals and quantifiers, whereas others have shown critical differences. It is, therefore, debated whether they are processed in the same way. A previous fMRI investigation showed that the left inferior frontal gyrus is linke...

Timothy Williamson has argued that in the debate on modal ontology, the familiar distinction between actualism and possibilism should be replaced by a distinction between positions he calls contingentism and necessitism. He has also argued in favor of necessitism, using results on quantified modal logic with plurally interpreted second-order quantifiers showing that necessitists can draw distin...