On quantifiers for general propositions

Supplement to “symmetric Propositions and Logical Quantifiers”

This document contains propositions, proofs, and supplementary discussion supporting claims made in the paper “Symmetric propositions and logical quantifiers,” Journal of philosophical logic, forthcoming (henceforth SPLQ). Unless explicitly mentioned otherwise, all references are internal. Section, but not subsection, headings correspond to those of SPLQ. (The latter has no subsections.)

Children's interpretations of general quantifiers, specific quantifiers, and generics.

Recently, several scholars have hypothesized that generics are a default mode of generalization, and thus that young children may at first treat quantifiers as if they were generic in meaning. To address this issue, the present experiment provides the first in-depth, controlled examination of the interpretation of generics compared to both general quantifiers ("all Xs", "some Xs") and specific ...

On residuated lattices with universal quantifiers

We consider properties of residuated lattices with universal quantifier and show that, for a residuated lattice $X$, $(X, forall)$ is a residuated lattice with a quantifier if and only if there is an $m$-relatively complete substructure of $X$. We also show that, for a strong residuated lattice $X$, $bigcap {P_{lambda} ,|,P_{lambda} {rm is an} m{rm -filter} } = {1}$ and hence that any strong re...

Topic Accents on Quantifiers

On Judgements and Propositions

Dear Hans-Jörg! In the seventies and early eighties we have been colleagues in the ‘Automatentheorie und Formale Sprachen’ group at TU Berlin and shared many interests. Later we departed into different fields of research and followed different directions of thought. It is thirty years now that we have completed our PhD at TU Berlin, and this year is your sixtieth birthday. Since the times at AT...