Dynamic Abstraction

Any abstractionist approach to thin objects faces the threat of paradox, as illustrated by Frege’s inconsistent Basic Law V. The neo-Fregeans Hale and Wright respond by severely restricting the class of acceptable abstraction principles. Their approach is static in the sense that they hold the domain fixed. This approach to abstraction is criticized, and an alternative approach is developed which permits abstraction on a vast class of equivalence relations. This alternative approach is dynamic in the sense that abstraction on an extensionally specified domain (i.e. a domain specified by means of a plurality of objects) may result in a larger such domain. A form of absolute generality is nevertheless possible, provided that the associated domain is understood in an intensional sense (i.e. it cannot be specified by means of a plurality).