Inquiry – Special issue on Operators vs Quantifiers

Inquiry invites submissions for a special issue on Operators vs Quantifiers. We are looking for contributions of at most 8000 words (including footnotes but not including references). The issue will be guest-edited by Max Kölbel and David Rey. To submit a paper, please follow the standard procedure for submitting papers to Inquiry but make sure to select the option “special issue Operators vs Quantifiers” when submitting. For direct queries, please contact the guest editors at or Deadline for submissions: September 1st, 2017.

General theme:

A number of age-old and recent debates in several branches of philosophy depend in some way on the competition between two apparently different approaches to modelling linguistic phenomena: on the one hand the approach that employs binding expressions (e.g. quantifiers) and variables, and on the other hand the approach that employs intensional operators.

For example, the most standard approach to modality treats expressions like “possibly” as intensional operators. A competing approach treats them as binding quantifiers (“There is a possibility x, such that …x …”). In the treatment of tense, the situation is reverse: the traditional intensional treatment of phenomena of tense, as introduced by Prior, is now a minority view, while a quantificational/referential treatment has become standard. Analogous alternatives present themselves in the treatment of countless other embedding expressions that shift some feature: “somewhere”, “in some way”, “on every standard”, “given what he knows” etc.

In fact, even “some” and “all” can be modeled not only as variable-binding expressions but also as operators, as in an Aristotelian syllogistic or term logic. Famously, the inventor of logic himself started logic off without variables, which prompted Geach to complain that Aristotle had started it off on the wrong foot. An unjustified complaint, as has been shown by many, including Schönfinkel, Quine and Sommers. The present-day controversy in semantics between the standard approach and a variable-free semantics à la Jacobson seems to be the contemporary version of this dispute.

It may be an historical accident that the most mainstream semantic approaches combine an operator treatment of some phenomena with a quantifier treatment of other phenomena. Only some extremists argue for a variable-free pure operator approach (e.g. Jacobson), or for a operator-free pure variable binding approach (e.g. Schaffer).

It therefore seems worth exploring what exactly is at stake in a choice between the alternatives: Do we need to employ both operators and quantifiers in a mixed semantics? If so, are there any principled reasons for deciding which approach to use in which case? Are there reasons of theoretical convenience or elegance? If we do not need to employ both, which of the two purist approaches should we choose?