criticizes this belief for reducing the matter to empirical discovery when it seems we should have a formal distinction between referring and non-referring terms or elements of our domain. Lejewski writes further: This state of affairs does not seem to be very satisfactory. The idea that some of our rules of inference should depend on empirical information, which may not be forthcoming, is so foreign to the character of logical inquiry that a thorough re-examination of the two inferences [existential generalization and universal instantiation] may prove worth our while. Lejewski then goes on to offer a description of free logic, which he claims accommodates an answer to the problem. Lejewski also points out that free logic additionally can handle the problem of the empty set for statements like . Quine had considered the problem of the empty set unrealistic, which left Lejewski unsatisfied. Ontological commitment The notion of ontological commitment plays a central role in Quine's contributions to ontology. A theory is ontologically committed to an entity if that entity must exist in order for the theory to be true. Quine proposed that the best way to determine this is by translating the theory in question into first-order predicate logic. Of special interest in this translation are the logical constants known as existential quantifiers (''), whose meaning corresponds to expressions like "there exists..." or "for some...". They are used to bind the variables in the expression following the quantifier. The ontological commitments of the theory then correspond to the variables bound by existential quantifiers. For example, the sentence "There are electrons" could be translated as "", in which the bound variable x ranges over electrons, resulting in an ontological commitment to electrons. This approach is summed up by Quine's famous dictum that "[t]o be is to be the value of a variable". Quine applied this method to various traditional disputes in ontology. For example, he reasoned from the sentence "There are prime numbers between 1000 and 1010" to an ontological commitment to the existence of numbers, i.e. realism about numbers. This method by itself is not sufficient for ontology since it depends on a theory in order to result in ontological commitments. Quine proposed that we should base our ontology on our best scientific theory. Various followers of Quine's method chose to apply it to different fields, for example to "everyday conceptions expressed in natural language". Indispensability argument for mathematical