Abstract

The present paper wants to develop a formal semantics about a special class of formulas: quantifying statements, which are a kind of predicative statements where both subject- and predicate terms are quantifier expressions like ‘everything’, ‘something’, and ‘nothing’. After showing how talking about nothingness makes sense despite philosophical objections, I contend that there are two sorts of meaning in phrases including ‘thing’, viz. as an individual (e.g. ‘some thing’) or as a property (e.g. ‘something’). Then I display two kinds of logical forms for quantifying statements, depending on how these ‘thing’s are ordered into a whole predication. Finally, an algebraic semantics is proposed for the finite set of quantifying statements to order these into a (fragmentary) dodecagon of logical relations. The corresponding Sub-Model Semantics (hereafter: $$\mathbb {SMS}$$ ) aims to update the usual theory of opposition whilst leading to a research program for other kinds of statement like categorical and even modal propositions.