To Be or Not To Be: Vector ontologies as a truly formal ontological framework

TL;DR

Argues that existing formal ontologies fail Husserl's criteria of a priori validity and contentlessness, advocating a truly Husserlian foundational ontology built on vector-space formalisms. It introduces a vector-space ontology over a space $V$, showing that the axioms of vector spaces can capture core concepts of foundational ontologies while remaining content-free. The author posits that many information systems, including AI, and even human cognition, already rely on vector-like representations, implying broad applicability and interoperability of such a framework. The work targets human-machine interoperability, proposing vector ontologies as a rigorous, scalable means to model and align machine and human worldviews. Future work should explore expressivity, content independence, and potential integration with dialectical or stratified ontologies.

Abstract

Since Edmund Husserl coined the term "Formal Ontologies" in the early 20th century, a field that identifies itself with this particular branch of sciences has gained increasing attention. Many authors, and even Husserl himself have developed what they claim to be formal ontologies. I argue that under close inspection, none of these so claimed formal ontologies are truly formal in the Husserlian sense. More concretely, I demonstrate that they violate the two most important notions of formal ontology as developed in Husserl's Logical Investigations, namely a priori validity independent of perception and formalism as the total absence of content. I hence propose repositioning the work previously understood as formal ontology as the foundational ontology it really is. This is to recognize the potential of a truly formal ontology in the Husserlian sense. Specifically, I argue that formal ontology following his conditions, allows us to formulate ontological structures, which could capture what is more objectively without presupposing a particular framework arising from perception. I further argue that the ability to design the formal structure deliberately allows us to create highly scalable and interoperable information artifacts. As concrete evidence, I showcase that a class of formal ontology, which uses the axioms of vector spaces, is able to express most of the conceptualizations found in foundational ontologies. Most importantly, I argue that many information systems, specifically artificial intelligence, are likely already using some type of vector ontologies to represent reality in their internal worldviews and elaborate on the evidence that humans do as well. I hence propose a thorough investigation of the ability of vector ontologies to act as a human-machine interoperable ontological framework that allows us to understand highly sophisticated machines and machines to understand us.