Quantification and Ontological Commitment

In his review of a paper by Ajdukiewicz [1], Quine makes the following comments on Leśniewski’s version of the membership connective ‘∈’: One way of viewing Leśniewski’s logic of ‘∈’ (which he called “ontology”) would seem to be this: the variables stand in places appropriate to general terms, the notion of general term being construed broadly enough to include terms which are true of fewer than two objects as well as terms which are true of two or more. Then, where ‘a’ and ‘b’are thought of as general terms, ‘a ∈ b’ is construed as true if, and only if, ‘a’ is true of one and only one object and ‘b’ is true of that object. Leśniewski, and others who have found this part of his logic useful (Kotarbinski, Ajdukiewicz), have entertained an amiable distaste for abstract entities and hence have liked to appeal to general terms, more or less as above, rather than to classes. Too little significance, however, has been attached to the fact that the variables which have been said to stand in places appropriate to general terms are subjected in Leśniewski’s theory to quantification. Such quantification surely commits Leśniewski to a realm of values of his variables of quantification; and all his would-be general terms must be viewed as naming these values singly. If quantification as Leśniewski used it did not commit him squarely to a theory of classes as abstract entities, then the present reviewer is at a loss to imagine wherein such commitment even on the part of a professing Platonist can consist [2].