Mereocausality & Causal Mereotopology: A New Concept

Advances)on)Knowledge)Representation)Journal) Adv. Know. Repr. 2025; volume 5; number: 3. DOI 10.5281/zenodo.17352391. Special Issue on Top-Level and Middle-Level Ontologies. 81 Mereocausality & Causal Mereotopology: A New Concept Robert Rovetto 1 Abstract. How is causality/causation associated with parthood? And do parts and their whole interact in distinct causal manners? I introduce a novel concept I call ‘mereocausality’ and its cognates, merging two foundational topics in theoretical and practical disciplines: causality and parthood (or mereology). Topology is often associated with the latter yielding mereotopology. These two topics have been of great personal intellectual interest, and after a few years of sitting on this idea (and papers), I here express it. I apply inquiry into causality and formal causal relations to mereology, developing a new formal concept: mereocausality, mereocausation, causal mereo(topo)logy, etc. This paper offers a preliminary exploration, offering broad concepts, research questions and terminology for what can be a new branch of inquiry; casual mereology and causal mereotopology. Future work will involve a more structured and rigorous investigation, developing the basic ideas presented here. For this project and study, I hope to produce a conceptual system for exploring the intersection of causality, mereology and topology. A contribution of this work is the creation of a new concept and associated terminology. This work is relevant for a variety of disciplines and activities: philosophy, such as metaphysics; conceptual analysis and development; formal and applied/computational ontology; knowledge representation and reasoning in artificial intelligence; conceptual modeling; semantic data modeling; psychology and linguistics; etc. As an unfunded project to date, formal support and collaborations are desired to pursue this promising line of research. Interested readers should contact the author. 1. Introduction I introduce 2 a novel concept I call mereocausality, and its cognates such as: mereocausation, causal parthood, mereotopological causality, causal mereotopology, and others. These concepts combine those foundational ones of causality, causation, parthood, mereology and topology (or mereotopology). For the purposes of this paper, I present preliminary ideas, sketching what can potentially become a new branch of inquiry, causal mereology. I offer early independent ideas on a long-standing personal interest. In short, I wonder if causality varies among parts and their whole, at different scales, and if it can be usefully and formally characterized in distinct ways. As a preliminary work to be developed, a more structured investigation is left to future work. 1 Robert Rovetto. Email: [email protected]. ORCID: https://orcid.org/0000-0003-3835-7817. 2 This concept was first expressed by the author in a section within a 2014 paper submitted to, but rejected from, the Journal of Philosophy, entitled "Causal Relations for Formal Ontology”. That 30-page paper attempted to develop various types of abstract causal relations. Advances)on)Knowledge)Representation)Journal) Adv. Know. Repr. 2025; volume 5; number: 3. DOI 10.5281/zenodo.17352391. Special Issue on Top-Level and Middle-Level Ontologies. 82 Future work will involve a systematic development of the concepts and terminology introduced here, and exploration of relevant literature. The contribution of this work is the introduction of novel concepts that may have utility in philosophical and other disciplines, i.e., conceptual innovation with an interdisciplinary character. It specifically but not exclusively aims to contribute to (and is relevant for) the philosophy of causality, and mereology. Moreover, it is relevant across disciplines from philosophy to computational disciplines such as knowledge representation and reasoning. I hope this paper offers innovative and interesting concepts for various lines of intellectual pursuit. The paper is structured as follows: a brief summary of causality and mereology, followed by a description of the core idea, relevant research questions, terminology, and limitations, ending with a future work activities. 2. Causality and Mereology The concepts of causality and causation [1] [3] can and have been distinguished across disciplines. Similarly, there are various mereological accounts. For the purposes of this paper, I cannot summarize the various characterizations of causality and mereology. The concept I introduce here was conceived independently of these theories. Suffice it to say that the concepts of causality and causation essentially express the principle(s), law(s), theory(s) or relation(s) of cause and effect. And, at the very least, they reflect a belief or supposition thereof. The philosophy of causality includes investigation into the metaphysical nature of causality, causality as a relation, the causal relata, and so on. Here, ‘causality’ and ‘causation’ are used interchangeably for simplicity, but a distinction will be mentioned. Mereology [2][4][5][6] is generic (typically philosophical) inquiry into the inter-relations of parts and (their) wholes, i.e., parthood. It is about theory(s) of parthood, the relationship of part to whole. Mereologies are specific formal theories about parthood which may employ symbolic logics. Classical or General Extensional Mereology [2] is an example. Topology is, in part, the study of connectedness, boundary, and the properties of geometric structures (e.g., shapes, surfaces, etc.) under changes of various sorts. It is concerned, for example, with the characteristics of objects that are preserved under homeomorphisms. Mereotopology merges mereology with topology. 3. What is Mereocausality and Causal Mereology? Mereocausality and causal mereology is about causality among parts and their wholes. This inquiry is motivated by the question of whether distinct forms of causality exist, whether causality varies at different scales or granularities, and if so, whether the interaction among parts and the whole exhibits distinct forms. Figure 1 presents a visualization of the overall idea for combining causality and mereology into a new concept of mereocausality. Figure 2 elaborates. Advances)on)Knowledge)Representation)Journal) Adv. Know. Repr. 2025; volume 5; number: 3. DOI 10.5281/zenodo.17352391. Special Issue on Top-Level and Middle-Level Ontologies. 83 If causality is one or more principles of cause and effect, then mereocausality may be a one or more principles of cause and effect among parts and their wholes. Mereocausality can thereby be characterized as a specialized form of causality. If causation is construed as one or more causal relations, then mereocausation may be one or more causal relations specifically obtaining among parts and their wholes. In the sense of a field of study, causal mereology is study concerned with the actual or potential causal efficacy, causality, causal relations, or causation among parts and between parts and their whole. It is concerned with phenomena picked out by or described by associated predicates, including cognates such as ‘causal influence’, ‘causal structure’, etc. These are left undefined. This inquiry includes both metaphysical questions about relationships, as well as practical questions about the utility to assert formal distinctions, including formal causal relations among parts and wholes. The distinction between relationships and relation is not needed here, but one may wish to tentatively approximate it as ontological (metaphysics) aspects of the world, and any asserted, prescribed or declared constructs (e.g., predicates in an symbolic logic), respectively. We can identify pertinent questions for mereocausality by considering the concept of causal parts. Causal parts are those parts (of a whole) that have causal efficacy. Noncausal parts, then, are parts that do not have causal efficacy, i.e., they are causally inert. If we accept causal parts, then the transition to that of mereocausality is apparent. If there are causal parts and non-causal parts, then we can ask: Does the causal efficacy, causal power, causal influence, … vary? If so, then upon what does it differ? Does it vary based on the type of part, or the type of interaction (e.g., interaction among parts, from whole to part as in downward causation, etc.)? Advances)on)Knowledge)Representation)Journal) Adv. Know. Repr. 2025; volume 5; number: 3. DOI 10.5281/zenodo.17352391. Special Issue on Top-Level and Middle-Level Ontologies. 84 Figure 1. From mereology and causality to mereocausality Advances)on)Knowledge)Representation)Journal) Adv. Know. Repr. 2025; volume 5; number: 3. DOI 10.5281/zenodo.17352391. Special Issue on Top-Level and Middle-Level Ontologies. 85 4. Some Questions of Merocausality and Causal Mereology Questions about the intersection of mereology, topology and causality can be asked from distinct perspectives. The philosophical perspective is concerned with the nature of the world. Both philosophical and scientific perspectives are concerned with whether it can explain phenomena. The practical (e.g., computationally) perspective is concerned, in part, with the potential need and utility of formally asserting computable symbol structures (e.g., predicates, classes, axioms) for use in information and computational systems. Below I list some questions of mereocausality, some of which may be rephrasing of others and can thereby be merged to avoid redundancy. Note that both research questions of mereocausality and their answers can depend on philosophical (or other) assumptions, including ones stance on, say, the nature of causality. For example, is causality a metaphysical relationship? And what is the nature of parthood (to the degree it has a nature)? The latter question can be partially restated from an operational perspective as: how do parts interact, and how do parts and their whole interact? Upon discovering that interaction, some relationships should become clear. • What is the relationship, if any, of causality to mereology, topology (and mereotopology)? • To the extent that there is a fundamental nature of the world, o Does it include distinct forms of causality at distinct scales or granularities? o Is there causality at different scales/granularities? (A metaphysical/ontological question) • If there are distinct forms of causality, what is their nature? (A metaphysical/ontological question) • Is causality different for parts of a whole as compared to one another? • Does the interaction of the parts of a whole exhibit a distinct form of causality as compared with the interaction of the whole with its parts? Or: Is causality different for the part-whole interaction as opposed to whole-part interaction? (Inquiry into downward causation should be helpful.) • Do mereological and topological structures exhibit distinct forms of causality? • What effect does causality have on parts vis-à-vis their wholes? • Do parts causally interact in different ways according to their type or kind? • If parts and their whole exhibit distinct forms of causality, upon what does that depend, or in virtue of what is that the case? • Can we identify, discover, or assert generic or universal physical principles of merocausality? Advances)on)Knowledge)Representation)Journal) Adv. Know. Repr. 2025; volume 5; number: 3. DOI 10.5281/zenodo.17352391. Special Issue on Top-Level and Middle-Level Ontologies. 86 o Can we do so for a subset of types of parts? Or for certain contexts and disciplines (e.g., in biology, chemistry, physics, etc.)? Two aspects of causality and parthood are relevant for formulating questions for causal mereology. One is the possibility to assert distinct kinds of parthood (e.g., functional, material, etc.). The second is the question about causal relata (assuming a causation relation). If there are various mereocausal types of relations… • Do they differ depending on the kinds of part and whole? • Do they differ depending on the casual relata? • Do mereocausal relations vary when considering an external object or part (i.e., external to a given whole) interacting with the given whole (or the parts of the whole)? It is also import to ask methodological, meta-level, meta-philosophcal and explantionfocused questions, such as: • Does it make sense to ask these questions? (A meta-metaphysics question) • Are they answerable? If so, in what way? • Is there a need for making these distinctions? (whether in metaphysics or in data-focused disciplines) o Is there a practical need to make these distinctions in disciplines such as knowledge representation and reasoning (a branch of Artificial Intelligence), computational or applied ontology, conceptual (data) modeling, computational linguistics, natural language processing, geographic information science, etc.? § What is the computational (or other) utility of asserting computable symbol structures for forms mereocausal relations? § What are concrete applications and examples where the concept of mereocausality is needed? • What phenomena can the concept of mereocausality explain? o Can it explain natural language (or linguistic) phenomena? o Can it explain mind-external and –independent phenomena? Lastly, in terms of specific accounts of causality and mereology, we ask the following. Examples of specific accounts are process account of causality and General Extensional Mereology, respectively. • Can two (or more) given accounts be combined in meaningful and useful ways? The various philosophical and non-philosophical accounts of causality [3] will likely yield distinct answers to these questions, and distinct formulations to mereocausal and merotopologico-causal structures and relations. Advances)on)Knowledge)Representation)Journal) Adv. Know. Repr. 2025; volume 5; number: 3. DOI 10.5281/zenodo.17352391. Special Issue on Top-Level and Middle-Level Ontologies. 87 The philosopher will be interested in the preceding questions toward forming metaphysical accounts and individual claims about the world. The practitioner of computational disciplines, and interdisciplinary activities such as knowledge representation and reasoning can ask some of these questions and prescribe answers without making metaphysical claims. The latter would presumably attempt to formulate a consistent and coherent formal (computable) model without necessarily arguing for the metaphysical actuality of the given mereocausal account. Fig 2. Toward a Synthesis of Causal and Mero(topo)logical concepts 5. Terminology This section proposes candidate terms and definitions for causal mereology, i.e., the study of the causal interaction of parts and (their) wholes. The idea that (a) causality may be different among parts and wholes (or during their interactions), i.e., that there are different forms of causality (the metaphysical question), or (b) that we may postulate and formally specify distinct types of causality at various scales or granularities for theoretical and practical purposes, may be express by these terms, forming a preliminary Advances)on)Knowledge)Representation)Journal) Adv. Know. Repr. 2025; volume 5; number: 3. DOI 10.5281/zenodo.17352391. Special Issue on Top-Level and Middle-Level Ontologies. 88 terminology for mereocausality or causal mereology. Causality at various granularities may be signified by the term ‘granular causality’, with cognate ‘causal granularity’. Note that the content in Table 1 may be perceived as tautologies, but that is not the intent, and as exploratory work in need of maturation it is subject to revision. Primitives (undefined terms), however, have been noted, and unless otherwise stated, undefined terms are likewise left primitive. Other terms that may be included, and described in future work, include ‘causal relation’. ‘causal structure’ and ‘causal system’. Causal mereology, as a discipline, may be partially expressed by the terms in Table 1. Their meanings is preliminary, pending future research. Table 1: Candidate terminology of mereocausality and causal mereology Term Meaning causal part A part that is causally efficacious3 to/on its whole or some other part of the whole. mereocausality Causality among parts vis-à-vis their whole. Causality among parts and whole. mereocausation (if not synonymous with mereocausality), One or more causal relations that obtains between parts and/or parts and their respective wholes. causal mereology A type of mereology concerned with the causal relationships among part and whole. To the extent that there are causal parts, or to the extent that asserting such an ontological category is useful, it is the mereology of causal parts. It is the study of the part-whole relationships among causal parts, and/or the study of the causal relationships between parts and wholes. causal mereotopology A type of mereotopology that studies the causal relationships among connected parts, or the mereotopology of causal parts. It describes the causal connected of parts and whole. mereotopological causality Causality among parts and wholes which stand in topological relations to one another. mereotopological causation One or more causal relations that obtains when parts and whole stand in topological relations to one another. If we distinguish between causality and causation, we can also describe these concepts as follows. Where causality is the/a principle of cause and effect, then mereocausality is the principle of the cause and effect among parts and their wholes. If causation is the relation of cause and effect, e.g., causality exemplified as a metaphysical relationship, then mereocausation is the causal relations among parts and wholes. To mention in 3 Primitive in this paper. But it may be more precisely characterized as parts which stand in causal relations, exert causal powers, have a causal function, etc. Advances)on)Knowledge)Representation)Journal) Adv. Know. Repr. 2025; volume 5; number: 3. DOI 10.5281/zenodo.17352391. Special Issue on Top-Level and Middle-Level Ontologies. 89 passing, if distinguishing between relation(ship), the instance-universal, type-token, and generic-specific distinction can also be applied: the metaphysical relationship (generic) with relations (specific instances). Mereotopological causality is a type of causality exhibited by parts, their wholes and their topological relations or properties. Concepts of causal connectedness, and corresponding predicates are relevant. Causal mereology (as a discipline) is a type of mereology concerned with the causal relationships among part and whole. To the extent that there are causal parts (or that asserting such a category is useful), it is the mereology of causal parts; the partonomic relationships among parts that are causally efficacious, that causally influence one another. The latter, in turn, may be described as creating some change. Similarly, causal merotopology is a type of mereotopology investigating the causal relationships among connected parts, or the mereotopology of causal parts. It would aim to describe the connectedness of causal parts, i.e., causalconnectedness of parts and whole. There is another way to construe mereocausality, but it does not seem as coherent: as the parts or parthood of causality. But we must ask ‘What are the parts of causality?’ and ‘What are the parts of a causal relation?’ and if these question makes sense. If causal parts are parts that are causally efficacious upon other parts and/or the whole of which they are part, we should also ask about causal wholes. That is, we should consider the topic of downward causation. How does the whole, the unity, causally influence its parts? Is that causation subject to differentiation, i.e., does it admit of distinguishing mereocausal relations? If there is mereocausality and mereocausation (metaphysical question), or if it is useful to assert mereocausal symbol structures and conceptual modeling constructs (the practical question), then mereocausal relations may have the generic categories of Part and Whole as relata. Perhaps a more interesting characterization is via more specific categories, such Biological Part or Functional Part. Figure 3 partially summarizes by illustrating the intersection of the combined concepts and fields of study to form that of mereocausality/causation & mereotopocausality.