Open-ended generality

In the debate on absolute generality, many authors have defended a relativistic position, namely that quantifiers are always restricted to a less than all-inclusive domain. Consequently, they hold that an unrestricted quantification over everything is not possible. One problem for such a view is the need to explain the apparent absolute generality of logical laws, like α=α or ~(α∧~α). The standard response appeals to schemas. In this paper, I begin by examining the reasons why schematic generality has such a strong appeal in this debate, which rely on their open-endedness. However, I also raise an objection to show that schemas cannot be a good substitute for quantificational generality, due to the fact that they do not express propositions with a determined truth-value. The second part of the paper is dedicated to develop a different kind of generality, which is both open-ended (as schematic generality) and expresses a proposition with a determined truth-value (as quantificational generality). From a formal point of view, I will make use of a modal approach, in which the modality must be taken as primitive. The paper ends with a comparison of this form of generality and schematism, and argues that the former is to be preferred over the latter.