Finitist Set Theory https://en.wikipedia.org/wiki/Finitist_set_theory
"The goal of an engineer who applies FST is to select axioms which yield a model that is one-one correlated with a target domain that is to be modeled by FST, such as a range of chemical compounds or social constructions that are found in nature. ... An applied FST model is always the minimal model which satisfies the applied axioms. This guarantees that those and only those elements exist in the applied model which are explicitly constructed by the selected axioms: only those urs [ https://en.wikipedia.org/wiki/Urelement ] exist which are stated to exist by assigning their number, and only those sets exist which are constructed by the selected axioms; no other elements exist in addition to these." From: Finitist set theory in ontological modeling Avril Styrman & Aapo Halko, University of Helsinki Applied Ontology (2018) Abstract "This article introduces finitist set theory (FST) and shows how it can be applied in modeling finite nested structures. Mereology is a straightforward foundation for transitive chains of part-whole relations between individuals but is incapable of modeling antitransitive chains. Traditional set theories are capable of modeling transitive and antitransitive chains of relations, but due to their function as foundations of mathematics they come with features that make them unnecessarily difficult in modeling finite structures. FST has been designed to function as a practical tool in modeling transitive and antitransitive chains of relations without suffering from difficulties of traditional set theories, and a major portion of the functionality of discrete mereology can be incorporated in FST. This makes FST a viable collection theory in ontological modeling." Relation of finitist sets to processes: The term 'partition level' and the recursive definition of n-member are adapted from: - Seibt, J. (2015) Non-transitive parthood, leveled mereology, and the representation of emergent parts of processes. - Seibt, J. (2009). Forms of emergent interaction in general process theory. https://www.researchgate.net/publication/220607682_Forms_of_emergent_interaction_in_General_Process_Theory "General Process Theory (GPT) is a new (non-Whiteheadian) process ontology. According to GPT the domains of scientific inquiry and everyday practice consist of configurations of ‘goings-on’ or ‘dynamics’ that can be technically defined as concrete, dynamic, non-particular individuals called general processes. The paper offers a brief introduction to GPT in order to provide ontological foundations for research programs such as interactivism that centrally rely on the notions of ‘process,’ ‘interaction,’ and ‘emergence.’ I begin with an analysis of our common sense concept of activities, which plays a crucial heuristic role in the development of the notion of a general process. General processes are not individuated in terms of their location but in terms of ‘what they do,’ i.e., in terms of their dynamic relationships in the basic sense of one process being part of another. The formal framework of GPT is thus an extensional mereology, albeit a non-classical theory with a non-transitive part-relation. After a brief sketch of basic notions and strategies of the GPT-framework I show how the latter may be applied to distinguish between causal, mechanistic, functional, self-maintaining, and recursively self-maintaining interactions, all of which involve ‘emergent phenomena’ in various senses of the term." cf. Locally Finite Theories https://www.jstor.org/stable/2273942 @philipthrift -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/6e50b919-7aff-4811-a230-e1eb771e9cf6%40googlegroups.com.
