   Much has been written about the way in which Leśniewski understood the quantifiers ‘for some’ \((\exists)\) and ‘for all’ \((\forall)\). There are three aspects to the controversy: (1) how the quantifiers are to be read; (2) how they are to be understood; and (3) the logical and philosophical significance of the way they are understood. The controversy arose principally because of a discrepancy between the way in which Leśniewski and Leśniewskians take the quantifiers to mean, and the orthodox way of understanding them, as formulated in particular by Quine. Leśniewski’s student Lejewski recounts how after moving from Poland to Britain he was surprised to find that the local (Quinean) understanding was very different from the one he had grown up with. The problem is exacerbated by the fact that Leśniewski did not produce or even envisage a semantics for his logic, considering, as had Frege and Russell, that his system was already meaningful and had no need of a semantics to be grafted onto it from outside. Historically it is interesting that Quine’s preoccupation with the idea of ontological commitment and its connection to quantification and its domain, go back to discussions he had with Leśniewski when he visited Warsaw in 1933. Quine relates that he and Leśniewski stayed up until late at night disputing whether the use of higher-order variables committed Leśniewski to platonic objects, as Quine thought, or not, as Leśniewski thought. Obviously to a nominalist like Leśniewski the thought that his cherished system should involve him in unwanted ontological commitments would be most repugnant.