Construction in the Formal Sciences

Introduction

The notion of construction figures centrally in mathematics and other formal sciences. An idealized, infinitary constructional approach is successfully applied to set theory, which provides the foundation for contemporary mathematics. C-FORS aims to develop new, similarly groundbreaking applications of the constructional approach. This will be the largest concerted effort to date to develop a foundation for the study of intensional entities, e.g., propositions and properties, where a variety of paradoxes still arise, with no agreed-upon solution nearly a century after set theory received its proper foundation.

Limitations of Current Understanding

However, infinitary constructions are poorly understood, and there is no known way to apply the constructional approach to intensional entities. C-FORS aims to overcome these limitations by developing a critical but liberal conception of construction inspired by my increasingly popular potentialist metaphysics and philosophy of mathematics. This will be achieved by using two theoretical tools developed by me, inspired by constructive mathematics, but only recently generalized so as to overcome various limitations and thus permit novel applications.

Groundbreaking Applications

C-FORS makes a range of groundbreaking applications of these tools, thus achieving a lasting impact on several disciplines:

1. Philosophy: I provide radical alternatives to the currently fashionable use of typed languages and exotic non-classical logics.
2. Foundations of Mathematics: I develop a pioneering constructional approach that retains the strength of set theory while incorporating insights from the constructive tradition.
3. Formal Ontology: I launch a rigorous approach to constructed entities.
4. Formal Semantics: I develop novel theories of propositions and properties, and a new logical foundation for the study of nominalization and group formation.

Interdisciplinary Research

Overall, C-FORS offers pioneering interdisciplinary research where philosophy and logic yield—and are themselves constrained by—novel applications to the formal sciences.