  Is there then a third way to understand the quantifiers that is neither referential nor substitutional? Such a way has been suggested by Guido Küng, based on the young Leśniewski’s reading of the quantifiers as “for all [some] meanings of the variable ‘\(x\)’ ”. Take this preamble to be what Küng calls a prologue functor, which mentions the expression ‘\(x\)’, but takes its matrix (the part after the quantifier, within the upper corners) to be a context of use of the variable, and takes the variables to range over meanings, in Leśniewski’s case, extensions (Küng 1977). Again there is something right and something wrong about this. If extensions are (as standardly understood) various kinds of sets, nothing could be more abhorrent to Leśniewski. He laid great store on logic not being committed to the existence of anything, being ontologically neutral: no existence statement is a theorem of any of his systems. So to have found that after all he is committed, by the back door as it were, to the hated sets, would have been a bitter blow. The correct insight of this understanding is that neither objects nor expressions are what quantifier expressions range over. They do not range over extensions either: they do not range over anything. But for each category of expression there are numerous ways in which an expression of that category can mean. A sentence can be true or it can be false. A name can name one thing, or several things, all things, or no things at all. Functor expressions mean according to the way the outputs of their combinations mean when their inputs have certain meanings. Given a domain of individuals, in principle all possible ways of meaning are delimited for all categories of expression. Quantifiers tap into this potentiality. But it goes against the nominalist grain of Leśniewski’s thought to reify all the different potential ways an expression could mean as if these were additional objects. So when Leśniewski told Quine his use of quantified variables in categories other than names did not commit him to platonic objects, he was being truthful. What he was committed to, from the moment he accepted bivalence of truth and falsity onwards, was that expressions of the various categories may be variously meaningful.