Edward N. Zalta’s *Principia Metaphysica* argues that the existence of abstract objects, such as propositions and sets, is logically guaranteed by the existence of concrete objects. The book constructs a theory of abstract objects, based on the idea that abstract objects exist in a "domain of abstract objects," distinct from the "domain of concrete objects." This theory explains how abstract objects can be thought about, reasoned about, and manipulated without any implication that they are concrete entities. Zalta's account offers a novel solution to the problem of how we can refer to and quantify over abstract objects, a central issue in contemporary philosophy.
Zalta’s work develops a formal system for reasoning about abstract objects, employing tools from modern logic and set theory. He introduces the concept of "abstract entities" as objects that are not concrete and can possess properties that concrete objects cannot. The book also addresses the ontological implications of abstract objects, arguing for their necessary existence and their role in our understanding of mathematics and logic. Readers gain a precise understanding of Zalta's unique ontological framework for abstract objects.
Key concepts
- Domain of abstract objects — A theoretical realm where abstract entities, such as propositions, exist.
- Domain of concrete objects — A theoretical realm encompassing physical, empirical entities.
- Abstract entities — Objects that are not concrete and can have properties unattainable by concrete things.