Meta-Regimenting Extensionalism 4DSiG, 21 st May 2026 Chris Partridge 1, 2 Andrew Mitchell 1, 2 Sergio de Cesare 2 Oscar Xiberta Soto 1 Mesbah Khan 3 Andreas Cola 4 1 BORO Solutions 2 University of Westminster 3 OntoLedgy 4 Telicent Scope – Extensionalism – a metaphysical choice 2 Partridge, C., Mitchell, A., Cook, A., Sullivan, J., & West, M. (2020). A Survey of Top-Level Ontologies – to inform the ontological choices for a Foundation Data Model. Many of you will be familiar with extensional criteria of identity as a metaphysical choice. We have presented on this topic here to the 4DSiG a few times before. For example, when we presented on the top-level survey (in 2020). Overall goals To raise awareness of what extensionalism is to raise awareness of the connection with formality and computability to make clear extensionalism has a role as an engineering tool for examining critical data infrastructure where it enables us to uncover the implicit underpinnings of critical data infrastructure on the way, to make clear: the concern that so-called ‘theories of meaning’ fail to provide good enough identity criteria and that ‘regimentation’ is a way to relieve this concern a way to construct the underlying extensional semantics to raise awareness of how meta-regimentation drives the evolution of extensionalism – increasing its scope by providing an overview of the meta-regimentation journey 3 Structure Framing: positioning in the broad framework Introducing the ‘extensionalism genealogy’ Regimentation (and ontology) Regimentation pattern example : Extensionalist abstraction Meta-Regimentation: Concrete extensional sets Extensional intension – plurality of worlds Constructional extensionality – theory of things Agentology: (Re-)introducing the agent Extensional indexicality – two-layered architecture – things and agents Extensional uncertainty – agent doxastic accessibility Summary 4 5 Framing: positioning in the broad framework Role: A tool for examining critical data infrastructure Critical data infrastructure (Computer) Data Infrastructure the structures that underlie the (computer) data we use these enable (or inhibit) interoperability they are critical for computers to use and share data Data Infrastructure is often hidden (not just data) so, needs to be ‘surfaced’ – a kind of ethnographical enterprise as we shall see, ontologising is a natural way to surface “ This article is in a way a call to study boring things. Many aspects of infrastructure are singularly unexciting. They appear as lists of numbers and technical specifications, or as hidden mechanisms subtending those processes more familiar to social scientists. It takes some digging to unearth the dramas inherent in system design creating, to restore narrative to what appears to be dead lists . … Struggles with infrastructure are built into the very fabric of technical work.” Star, S. L. (1999). The Ethnography of Infrastructure. is built on archaic foundations from a different era (pre- and early computing) ripe for reengineering as we shall see, regimenting (ontologising) can be a fruitful way to radically evolve the foundations to the new technologies has a clear analogy with more physical, concrete infrastructure 7 style.visibility Extensionalism underpins ‘regimentation’ Extensionalism underpins ‘regimentation’ which starts with the existing conceptual scheme (the existing ‘ordinary’ data structures) tidies it up – and improves it provides the tools for a ‘rigorous forensic investigation’ this surfaces the underlying (often implicit) ontology of the data infrastructure sometimes this reveals a new underlying radical data structure from one perspective this looks like a ‘janitorial’ activity “Here is the task of making explicit what had been tacit, and precise what had been vague; of exposing and resolving paradoxes, smoothing kinks, lopping off vestigial growths, clearing ontological slums . … There is no such cosmic exile. He cannot study and revise the fundamental conceptual scheme of science and common sense without having some conceptual scheme, whether the same or another no less in need of philosophical scrutiny, in which to work. He can scrutinize and improve the system from within, appealing to coherence and simplicity; but this is the theoretician’s method generally.” Quine WVO, Word and Object, 1960 “One comes to philosophy already endowed with a stock of opinions. It is not the business of philosophy either to undermine or to justify these preexisting opinions, to any great extent, but only to try to discover ways of expanding them into an orderly system. … It is not to be demanded that a philosophical theory should agree with anything that the man on the street would insist on offhand, uninformed and therefore uninfluenced by any theoretical gains to be had by changing his mind .” Lewis DK, Counterfactuals , 1973 8 Why take genealogical – lineage – approach Here, we adopt a broadly genealogical approach we track some threads in the lineage of extensionalism “ The goal is to describe the emergence of practices and theories of extensionalism as well as the main transformations for both through the centuries .” an example of using a genealogical approach “ The goal is to describe the emergence of practices and theories of deduction as well as the main transformations for both through the centuries. To this end, I adopt a diachronic, longue durée perspective on these developments. The method adopted is the method of conceptual genealogy, inspired by Nietzschean genealogical analysis … Naturally, the survey to be presented here will be a very condensed, somewhat partial account of these developments; an entire library would be needed to cover them all thoroughly. Still, a conceptual genealogy … is an essential piece of the puzzle, and a bird’s-eye view is what is required for my overall argument at this point. …” Catarina Dutilh Novaes, The Dialogical Roots of Deduction (CUP, 2020) Taking the ‘diachronic, longue durée, bird’s-eye view’ helps reveal the underlying fundamental meta-regimentation patterns 9 Introducing the ‘extensionalism genealogy’ Reference versus meaning A formal, computable, principle for avoiding ‘conflation’ Extensionalism is a formal, computable, principle for avoiding ‘conflation’ it provides an in principle means for determining identity an in principle way to avoid ‘confusion’ and ‘conflation’ III Conflation is not Confusion “Let me introduce now the notion of conflation and the distinction between it and confusion. Consider Tom and Dick as different people. Identifying them is a mistake. Identifying them on occasion is confusion. Not noticing the question whether they are identical or different is a conflation. The opposite of conflation is what Plato called Diaeresis. The process of Diaeresis is that of rising the question whether items are identical and deciding that they are not (and perhaps noting and explaining the difference between them).” Bar-am, N. (2008). Extensionalism: The revolution in logic . 11 Extensionalism, formality and computability There is an intimate link between extensionalism, formality and computability Bar-Am makes this link “… once we achieve a fully extensional theory, one in which every expression is replaceable only by coextensive expressions, we have a formal language. In a formal language there is no place for intuitions (and thus no place for intuitive errors). This is why computers communicate only by means of formal languages: they have no intuitions. The search for an extensional theory is, thus, the search for a purely formal logical framework, one that would enable us to perform inferences while not needing to worry about being misled by our fallible human intuitions. ” Bar-Am, N. (2012). Extensionalism in Context. Philosophy of the Social Sciences , 42 (4), 543–560. Extensionalism enables formality and computability 12 Boole – the first advocate of extensionalism With this link in place, one view of the root of extensionalism identifies Boole as the first advocate. “ The first advocate of “traditional extensionalism” within logic seems to have been George Boole (1847). Boole suggested a flat and unequivocal identification of terms with their extensions. He was thus the first logician to strive for a formal extensional language in the modern sense of that term: … He took it as a matter of course that logic is an extensional theory, that is, one in which coextensive terms are always interchangeable salva veritate regardless of context… Boolean logic, then, was the first extensional theory per se, a theory of valid inferences, which could, in principle, be operated by a computing machine, one in which all coextensive terms were taken as synonyms, and so interchangeable with no loss of meaning, and no effect on truth value and validity.” Bar-Am, N. (2012). Extensionalism in Context. Philosophy of the Social Sciences , 42 (4), 543–560. Boole, G. (1854). An Investigation of the Laws of Thought: On which are Founded the Mathematical Theories of Logic and Probabilities . Formalised by Shannon: Shannon, C. (1937). A Symbolic Analysis of Relay and Switching Circuits [PhD Thesis]. MIT. 13 Quine: ‘the’ confirmed extensionalist Quine is a major actor in the genealogy “I am neither an essentialist nor, so far as I know, an existentialist. But I am a confirmed extensionalist . Extensionalism is a policy I have clung to through thick, thin, and nearly seven decades of logicizing and philosophizing. … I was heeding it before knowing the word or having the concept clearly in mind.” Quine, W. V. O. (2008). Confessions of a confirmed extensionalist . Quine characterises extensionality using the slogan: no entity without identity “The urgency of extensionality arises from the demand for individuation: no entity without identity .” Quine, W. V. O. (2000). Three Networks: Similarity, Implication, and Membership 14 Quine: two ‘kinds’ of semantics Central to Quine’s extensionalism is his view on semantics: Bar-Am called Boole’s view ‘traditional’ extensionalism a better name might be ‘naïve’ extensionalism as Frege pointed out, there is more in play than just reference/extension there is both sense (meaning) and reference (in his 1892 paper "On Sense and Reference"; German: "Über Sinn und Bedeutung") from a Quinean perspective this gives semantics a divided architecture: “What philosophers now call semantics better called two: theory of reference and theory of meaning .” Quine Animadversions on the Notion of Meaning (1949) 15 Quine’s bifurcated semantics Quine argues that semantics divides into: theory of reference theory of meaning The theory of reference is extensional: Extensionality means it has entities with (extensional) identity The theory of meaning is ‘intensional’: he forcefully points out that this does not provide a clear notion of identity for ‘meanings’ 16 Quine’s passionate distrust of theories of Meaning Easy to find passages that vigorously ‘condemn’ meaning. 17 “The domain of meanings of expressions is hopelessly intensional and in trouble over individuation. Propositions, seen as meanings of sentences, are conspicuous here. Properties themselves might be seen correspondingly as meanings of adjective phrases. Properties, meanings, and necessity were violations of extensionality that I repudiated without regret.” Quine, W. V. O., Føllesdal , D., & Quine, D. B. (2008). Confessions of a confirmed extensionalist and other essays . Harvard University Press. “The residual myth of meaning is this myth that there is a certain critical degree of affinity of terms. Synonymy is that degree of affinity. De sensu occurrences are occurrences where that degree of affinity suffices for inter changeability. When we try to find a criterion for that cut-off point, we sense the quality of myth that invests it.” Quine, W. V. O. Cognitive Meaning (1979). “The lore of meaning is a pale gray lore, black with fact and white with convention.” W. V. O. Quine, “Two Dogmas of Empiricism,” in From a Logical Point of View (1961), p. 10. “Uncritical semantics is the myth of a museum in which the exhibits are meanings and the words are labels. To switch languages is to change the labels. Now the naturalist's primary objection to this view is not an objection to meanings on account of their being mental entities, though that could be objection enough. … Semantics is vitiated by a pernicious mentalism as long as we regard a man's semantics as somehow determinate in his mind beyond what might be implicit in his dispositions to overt behavior .” Quine, W. V. (1969). Ontological relativity, and other essays . “Meaning is what essence becomes when it is divorced from the object of reference and wedded to the word.” W. V. O. Quine, From a Logical Point of View (1961), “Two Dogmas of Empiricism,” p. 22. “If we give up the thought of such a boundary, we give up the thought of sameness of meaning. In so doing we give up the thought of anything that might be called a meaning; for there is no entity without identity.” Quine, W. V. O. Cognitive Meaning (1979). “Properties, meanings, and necessity were violations of extensionality that I repudiated without regret.” Quine, W. V. O. (2008). Confessions of a confirmed extensionalist and other essays . Harvard University Press. “… little is to be hoped for from a theory of meaning which is at present meaningless by its own standards— or would be if it had standards by which to judge.” Quine, W. V. O. (1949). Animadversions on the Notion of Meaning. “For the theory of meaning the most conspicuous question is as to the nature of its objects: what sort of things are meanings?” Quine, From a Logical Point of View , “Two Dogmas of Empiricism,” p. 22. style.visibility ppt_w ppt_h style.visibility ppt_w ppt_h style.visibility ppt_w ppt_h style.visibility ppt_w ppt_h style.visibility ppt_w ppt_h style.visibility ppt_w ppt_h style.visibility ppt_w ppt_h style.visibility ppt_w ppt_h style.visibility ppt_w ppt_h The DC Comics (brutal) version 18 With thanks to "The Clash of Cape and Cowl", writer Edmond Hamilton, artist Curt Swan, in World's Finest Comics #153 (Nov. 1965) Regimentation (and ontology) (rational reconstruction) Regimentation and ontology In Quine’s world, the regimentation transmutes ordinary language into formal structure this builds the ontology Decock (2002) talking about The Roots of Reference (1973) “The initial question "What is there?" has been entirely reformulated. The vagueness and ambiguity of ordinary language is dissolved by means of logic. Ontological questions only make sense in a logically regimented theory. The ontological question thus becomes: "What are the values of the bound variables?" The immediate but hitherto empty answer to this question is that theories determine to what values of the variables we are committed. We have not a beginning of an answer to what there is, but we have a criterion for existence and a place to search for objects, namely our logically regimented theories .” Decock , L. (2002). Trading Ontology for Ideology: The Interplay of Logic, Set Theory and Semantics in Quine’s Philosophy Quine ( Decock , above) frames this in terms of logic (we can think of it in terms of our regimented formal data structures ) 20 The nature of (Quinean) regimentation Regimentation is a tool for transmuting meaning into reference Regimentation can't expose antecedent meaning/synonymy because there's no determinate synonymy that would let "exposing" be a coherent operation Regimentation is a constructive choice rather than an analytic recovery – from this it follows that regimentation produces determinate content rather than capturing it hence Carnap’s use of the term rational reconstruction (for a somewhat similar process) Carnap, R. (1928). Der Logische Aufbau der Welt (Vol. 11). 21 Shifting the focus from language to data For Quine, in the mid-20 th Century the focus is ordinary language this is riddled with obscurity he fixes this by regimenting the ordinary language into an extensional language For the modern 21 st Century world, the more interesting focus is our ‘ordinary’ data this is also riddled with obscurity fix this by regimenting (in a data pipeline) into an extensional data structure bCLEARer is an example of a data regimentation tool focusing on delivering extensionality Partridge, C., Mitchell, A., de Cesare, S., & Beverley, J. (2024, October 23). Broadening Ontologization Design: Embracing Data Pipeline Strategies. STIDS 2024, Twelfth International Conference on Semantic Technology for Intelligence, Defense , and Security. https://www.academia.edu/129382330 Partridge, C., Guinard, A., Mitchell, A., & Xiberta Soto, O. (2025). bCLEARer Pipeline Architecture Framework eManual . BORO Solutions. https://borosolutions.net/bclearer-pipeline-architecture-framework-emanual 22 Regimentation pattern example: Extensionalist abstraction Dynamic, expanding higher-order universe Fregean Abstraction: Example 1: Shapes as Class of Equivalence Classes 24 ‘same shape’ partitions figures into equivalence classes — each class is a shape Figures ⟹ partitioned by ‘same shape’ Triangles Circles Rectangles ⟹ members of Shapes { Triangles, Circles, Rectangles, … } shape(a) = shape(b) ↔ a ∼ b Frege (1884) Die Grundlagen der Arithmetik Fregean Abstraction: Example 2: Directions as Class of Equivalence Classes 25 ‘parallel to’ partitions lines into equivalence classes — each class is a direction Lines ⟹ partitioned by ‘parallel to’ Direction α s Direction β s ⟹ members of Directions { Direction αs, Direction βs, … } dir(a) = dir(b) ↔ a ∥ b Frege (1884) Die Grundlagen der Arithmetik Fregean abstraction Fregean abstraction not (yet) extensional abstraction is dynamic introduces new abstract objects introduces two levels of abstract objects classic examples: directions (in the Euclidean plane) are abstracted from a set of parallel lines the individual directions and the general ‘directions’ object shapes (e.g. circle) as equivalence classes of similar figures the individual shapes and the general ‘shapes’ object For Frege these abstract objects had both sense (meaning) and reference 26 Quinean ‘abstraction’ Quinean ‘abstraction’ collapses (regiments) the abstract object into just an extension – a set can be seen as more construction than introduction Quinean abstraction pattern becomes an extensionalist tool a standard regimentation process in the extensionalist toolkit Quinean abstraction leads to higher-order sets Direction (and Shapes) have sets as their members Extensionalism comes with a natural commitment to higher-order sets Leads to the uses of powersets in the regimentation process see: Partridge, C., Cesare, S. de, Mitchell, A., & Odell, J. (2016). Formalization of the Classification Pattern: Survey of Classification Modeling in Information Systems Engineering. Software & Systems Modeling , 1–37. https://doi.org/10.1007/s10270-016-0521-5 27 Meta-regimentation Introducing meta-regimentation Quine’s regimentation focuses on regimenting our ordinary language in the bCLEARer case: our ‘ordinary’ data this can be seen as regimentation from the inside deploying the extensionalist tool on the ‘ordinary’ language/data When one steps back and takes genealogy’s bird’s eye view one can see that there has been ongoing regimentation of the extensionalist framework itself where the scope of extensionalism is refined and extended this can be regarded as ‘meta-regimentation’ 29 30 Meta-regimentation Concrete extensional sets a small example The posited constituents of Quine’s extensionalism The constituents of Quine’s extensionalism: physical four-dimensional objects classes – of both physical objects and classes For Quine, both of these were ‘posits’ “a device for working a manageable structure into the flux of experience” “As an empiricist I continue to think of the conceptual scheme of science as a tool, ultimately, for predicting future experience in the light of past experience. Physical objects are conceptually imported into the situation as convenient intermediaries -- not by definition in terms of experience, but simply as irreducible posits comparable, epistemologically, to the gods of Homer. Let me interject that for my part I do, qua lay physicist, believe in physical objects and not in Homer's gods; and I consider it a scientific error to believe otherwise. But in point of epistemological footing the physical objects and the gods differ only in degree and not in kind. Both sorts of entities enter our conception only as cultural posits. The myth of physical objects is epistemologically superior to most in that it has proved more efficacious than other myths as a device for working a manageable structure into the flux of experience.” … “Physical objects, small and large, are not the only posits. … Moreover, the abstract entities which are the substance of mathematics-ultimately classes and classes of classes and so on up are another posit in the same spirit. Epistemologically these are myths on the same footing with physical objects and gods, neither better nor worse except for differences in the degree to which they expedite our dealings with sense experiences.” Quine, W. V. O. (1951). Two Dogmas of Empiricism . 32 The issue By the mid 20 th century, from an ontological perspective, sets were typically regarded as abstract objects there is an understandable bias against abstract objects if one is a naturalist they raise trickly questions about how they can be known and how they can cause anything Quine realised sets were indispensable to science then, especially if one wanted to formalise mathematics one had to tolerate them accepted that this was an awkward compromise 33 The meta-regimentation People realised that one could challenge the claim that sets are abstract Maddy, P (1980) Perception and Mathematical Intuition. Or, more sophisticatedly, take a deflationary approach and undermine the distinction Lewis, D (1986) On the plurality of worlds A classic way of illustrating the point is to show sets have a location something an abstract object (one would assume) cannot have 34 Lewis’s argument – an extract Lewis deflates the distinction: and the concerns evaporate “A spectator might well assume that the distinction between ‘concrete’ and ‘abstract’ entities is common ground among contemporary philos­ophers, too well understood and uncontroversial to need any explaining. But if someone does try to explain it, most likely he will resort to one (or more) of four ways” … “Second, the Way of Conflation: the distinction between concrete and abstract entities is just the distinction between individuals and sets, or between particulars and universals, or perhaps between particular individuals and everything else.” … “Third, the Negative Way: abstract entities have no spatiotemporal location; they do not enter into causal interaction; they are never indiscernible one from another.” “The Negative Way and the Way of Conflation seem to disagree rather badly. As for the first part, the denial that abstract entities are located, I object that by this test some sets and universals come out concrete. Sets are supposed to be abstract. But a set of located things does seem to have a location, though perhaps a divided location: it is where its members are. Thus my unit set is right here, exactly where I am; the set of you and me is partly here where I am, partly yonder where you are; and so on. ... You could just declare that an abstract entity is located only in the special way that a set or a universal is located - but then you might as well just say that to be abstract is to be a set or universal. Your talk of unlocatedness adds nothing.” Lewis, D. K. (1986). On the plurality of worlds . 35 Extensionalising Modal Intension: Plurality of Worlds 37 Extensionalising Modal Intension Modal logic was clearly recognised as something that extensional early-20 th Century logic could not handle Introducing possible worlds gave an extensional way to deal with the modal talk of modal properties now had a clear ontology 1.1 Extensionality Lost Extensionality is a well known and generally cherished feature of classical propositional and predicate logic. Modal logic, by contrast, is intensional. ... Modal logic, therefore, is intensional: in general, the truth value of a sentence is determined by something over and above its form and the extensions of its components. Absent a rigorous semantic theory to identify the source of its intensionality and to systematize intuitions about modal truth, validity, and logical consequence, there was little hope for the widespread acceptance of modal logic. … 1.2 Extensionality Regained “The idea of possible worlds raised the prospect of extensional respectability for modal logic, not by rendering modal logic itself extensional, but by endowing it with an extensional semantic theory — one whose own logical foundation is that of classical predicate logic and, hence, one on which possibility and necessity can ultimately be understood along classical Tarskian lines.” Menzel, Christopher, "Possible Worlds", The Stanford Encyclopedia of Philosophy (Fall 2025 Edition), Edward N. Zalta & Uri Nodelman (eds.). 38 Possible worlds Our world is the actual world there are other possible worlds, where things that are possible happen anything that is possible will happen on some possible world “On the face of it, anyway, it seems quite reasonable to believe that … there is a maximally inclusive situation encompassing all others: things, as a whole or, more succinctly, the actual world . … Most of us also believe that things, as a whole, needn't have been just as they are. Rather, things might have been different in countless ways, both trivial and profound. History, from the very beginning, could have unfolded quite other than it did in fact: … In any case, no matter how things had gone they would still have been part of a single, maximally inclusive, all-encompassing situation, a single world. Intuitively, then, the actual world is only one among many possible worlds .” Menzel, Christopher, "Possible Worlds", The Stanford Encyclopedia of Philosophy (Fall 2025 Edition), Edward N. Zalta & Uri Nodelman (eds.). 39 Captures the modal aspects of properties This is a useful (essential?) as it captures the modal aspects of properties Most properties have a modal aspect Quine uses the example of renate – having a kidney cordate – having a heart in the actual world, it could be that every creature with a heart also had a kidney – and vice versa thus, the extensions of renate and cordate are identical this would seem to mean they are identical if one allows possible worlds, then if it is possible for a creature to have a heart and not a kidney then this will be the case on some possible world so, if one allows extensions over possible worlds, the two terms have different extensions 40 Constructional Extensionality: Theory of things Semantic era: relation of words to objects In the semantic (theory of reference) era, extensionalism looked at the relation of words to objects – or better – of words to other objects, some of which are not words … or Introduction by Professor Nelson Goodman to First Carus Lecture by Professor Quine ( Quine, W. V. (1973). The Roots of Reference ) … he is going to discuss an important relation of words to objects—or better—of words to other objects, some of which are not words—or even better, of objects some of which are words to objects some of which are not words. ” and the criteria of identity is often defined in a similarly semantical fashion § 62 We need a criterion for numerical identity “… If for us the symbol a is to denote an object , then we must have a criterion which determines in every case whether [the symbol] b is the same as [the symbol] a, even if it is not always within our power to apply this criterion.” Frege, The Foundations of Arithmetic In the context of logic, often in terms of the relation between words – and only indirectly objects the classic example being the salva veritate test for expressions: “A substitutivity principle says that, if two expressions are coextensional … either can be substituted for the other in any sentence salva veritate , that is, without altering the original sentence's truth value.” Menzel, Christopher, "Possible Worlds", The Stanford Encyclopedia of Philosophy (Fall 2025 Edition), Edward N. Zalta & Uri Nodelman (eds.). 42 Constructional era for extensionalism Constructionalism provides a semantics-free extensionalism one that focuses on the ontology provides a kind of ‘theory of things’ Leaves behind the link with semantics (and reference) no need for semantics just a theory of things No longer a Quinean ‘theory of reference’ now a theory of the construction (building) of things 43 Similar move to the shift from value to object identity In the database community there developed a recognition that identity and data values different “Codd [1970] introduced the notion of user-defined identifier keys to represent the identity of an object. … There are several problems with identifier keys which are due to the fact that the concepts of data value and identity are mixed.” Khoshafian , S. N., & Copeland, G. P. (1986). Object identity. Similarly, here the focus shifts from the terms used to the objects and their identity from a ‘theory of referring terms’ to a ‘theory of objects’ 44 Constructionalism: as a process The constructional process: “ On this conception of ontology, one starts with some constructors and some givens. Then new objects emerge by construction, that is, from the application of constructors to objects. So the resulting ontology can be characterised by three parameters: the givens with which one starts, the constructors one employs, and the objects that emerge from applications of the constructors. Among the latter, we allow both constructed objects—the direct outputs of the construction—and traces of the construction process itself.” Florio, S., & Linnebo , Ø. (2022). Core Constructional Ontology: The Foundation for the Top-Level Ontology of the Information Management Framework 45 Another way: major benefits Major benefits to this approach, here are some: “We now want to highlight four of its main benefits. Categorical differences are constructional differences : in constructional approaches, different kinds of objects can be distinguished from one another by the manner in which they are constructed. So categorical differences are explained by constructional differences. Dependency : some objects are built from others and hence “depend on” them. This provides an explanation of ontological dependence and the associated notion of grounding. Reduction : the ontology is built out of a relatively small set of initial objects and thus achieves fundamental ontological parsimony in the sense of Schaffer 2015 . Consistency : construction can be a basis for consistency, avoiding paradoxes such as those of Russell and Burali-Forti, although we need to take care with the construction process. In our case, this is achieved by requiring that the construction be “bottom-up” in the sense that the properties of the constructed objects are determined by the properties of the inputs to the construction.” Florio, S., & Linnebo , Ø. (2022). Core Constructional Ontology: The Foundation for the Top-Level Ontology of the Information Management Framework 46 Visualising the constructional process 47 Partridge, C., Mitchell, A., & Grenon, P. (2021). A Framework for Composition: A Step Towards a Foundation for Assembly . CDBB. https://www.repository.cam.ac.uk/handle/1810/321335 Mathematical perspective Mathematical structure of constructionalism is of an initial algebra used in theoretic computer programming for data structures See e.g.: Burstall , R. M., & Goguen, J. A. (1982). Algebras, Theories and Freeness: An Introduction for Computer Scientists. https://doi.org/10.1007/978-94-009-7893-5_11 Chen, X., Lucanu , D., & Rosu, G. (2024). A Unifying Logical Foundation for Initial Algebra Semantics and Induction . SSRN. https://doi.org/10.2139/ssrn.4745240 The slogan they use to characterise initial algebras is: ‘ no join, no confusion ’ in our constructional world: ‘ no join ’ means: every object has a constructional history in other words, is constructed ‘ no confusion ’ means: the rules are clear about when constructional history collapse/converge the identity of objects is clearly given together these are clearly ‘extensional’! see: Partridge, C. (2021). A Framework for Composition—A step towards a foundation for assembly: An Introduction . https://www.academia.edu/100869747/ 48 technically, given our earlier ‘definition’ this is ‘no confusion or conflation ’ – “ Not noticing the question whether they are identical or different is a conflation ” style.visibility Our early constructional papers You may be interested in following our journey in our papers: De Cesare and Partridge 2016, “BORO as a Foundation to Enterprise Ontology” Partridge, Cesare, et al. 2017, “Developing an Ontological Sandbox: Investigating Multi-level Modelling’s Possible Metaphysical Structures” Partridge, Mitchell, Loneragan, et al. 2019, “Coordinate Systems: Level Ascending Ontological Options” Partridge, Mitchell, Loneragan, et al., 2019 “The Fantastic Combinations and Permutations of Co-ordinate Systems’ Characterising Options: The Game of Constructional Ontology” 49 Agentology: (re-)introducing the agent 51 Two agentological steps forward The constructional approach provides an extensional ontology without semantics Agentology – gives back one aspect of an extensional semantics that someone (an agent) utters the term that refers provides an agent-centred perspective Two enhancements – both agential indexicality ( de se and nunc ) uncertainty 52 Extensional indexicality: two-layered architecture: things and agents What is indexicality? Lots of examples in the literature “In a memorable children’s story, Winnie-the-Pooh follows the tracks of what he thinks might be a woozle; until he realizes that he has been ‘Foolish and Deluded’ and that the tracks are his own. 2 Similar ideas recur in many stories from classical mythology to science fiction. 3 Characters take various attitudes towards people, whilst not realizing that they are themselves the very people concerned.” … “We can see that such stories might be engaging; but why are they philosophically interesting? The reason is that they highlight a difference between knowledge about the world, impersonally conceived, and knowledge about our place in the world. As David Lewis graphically puts it, they highlight the difference between the information given by a standard map, and that given by a map that is erected in a public place with a ‘You are here‘ arrow. One tells you about the nature of the world; the other tells you, in addition, how you fit into that world. Following Lewis, call the former de dicto knowledge, and the latter de se .” Holton, R. (2015). Primitive Self-Ascription: Lewis on the De Se. In B. Loewer & J. Schaffer (Eds), The Blackwell Companion to David Lewis (pp. 399–410) 54 de se map indexicality 55 Different agents can be ( de se ) in different places – and the world is exactly the same. THEBES ATHENS Uphill Downhill N ATHENS THEBES Uphill Downhill 0 400 300 200 100 400 300 200 100 Indexicality of directional terms Example from Aristotle’s Physics: “… the road from Thebes to Athens is the same as the road from Athens to Thebes; for things need not be identical in all respects because they are the same in some, but only if they are identical in what they actually are—in a word if they are not two the road from Thebes to Athens contrasts with the road from Athens to Thebes.” The description ‘uphill’ and downhill’ depends upon (is indexed to) the direction you are travelling. 56 Pacioli Ruffon Transaction view from nowhere Pacioli view Ruffon View Parties Pacioli Ruffon Purchase Pacioli Ruffon Sale Owner (Owner) Counterparty Owner (Owner) Counterparty {5940675A-B579-460E-94D1-54222C63F5DA} Cash 240 Ducats … … {5940675A-B579-460E-94D1-54222C63F5DA} Cash 240 Ducats … … Indexicality of accounting’s debit or credit? Example from ‘ Thoroughly Modern Accounting: Shifting to a De Re Conceptual Pattern for Debits and Credits ’. (ER 2018). Based upon: Pacioli, L. (1494). Summa de Arithmetica geometria proportioni data debit credit T-Ledger Format {5940675A-B579-460E-94D1-54222C63F5DA} Account Title DEBIT CREDIT (left side) 57 The purchase and sale (and debit and credit) are similarly dependent upon (indexed to) the party who own the ledger they are a single transaction when considered on their own but different when considered relative to one of the parties to the exchange Resolution: making the de se explicit 58 From: Partridge, C., de Cesare, S., Mitchell, A., León, A., Gailly , F., & Khan, M. (2018). Ontology then Agentology: A Finer Grained Framework for Enterprise Modelling 3.1.3 Minimal de se deitic core Only when the system is given the additional breakthrough self-ascription information – shown in Figure 2 – can it work out what to do. In this case, if the system is given the de se data that it is the individual (system) Mega- Bancology , then it can infer it ‘works’ for MegaBank , where MegaBank is an administrator or owner, and carry out the relevant processes. The meta-regimentation manoeuvre: making the agent (as a ‘minimal de se deitic core’) explicit in the system A selection of papers You may be interested in learning more about indexicality Partridge, C. (2002). LADSEB-CNR - Technical report 23/02—A new foundation for accounting: Steps towards the development of a reference ontology for accounting. The BORO Program, LADSEB CNR, Italy. http://www.academia.edu/973258 Partridge, C. (2003, April 1). Shifting the Ontological Foundations of Accounting’s Conceptual Scheme. ECAIS 2003, Sixth European Conference on Accounting Information Systems. https://www.academia.edu/25701483/ Partridge, C., Khan, M., Cesare, S. de, Gailly , F., Verdonck, M., & Mitchell, A. (2018). Thoroughly Modern Accounting: Shifting to a De Re Conceptual Pattern for Debits and Credits. International Conference on Conceptual Modeling (ER 2018), 11158, 134. https://www.academia.edu/44493563 Partridge, C., de Cesare, S., Mitchell, A., León, A., Gailly , F., & Khan, M. (2018). Ontology then Agentology: A Finer Grained Framework for Enterprise Modelling: Proceedings of the 6th International Conference on Model-Driven Engineering and Software Development, 454–463. https://doi.org/10.5220/0006606304540463 59 Extensional uncertainty: Agent doxastic accessibility Basic Pre-(Meta-)Regimentation Uncertainty Challenges 61 {21E4AEA4-8DFA-4A89-87EB-49C32662AFE0} Challenge Examples De Re Individual Modality a person can be in a city at a time Actuality a person can actually be in a city at a time ‘Inconsistent’ Knowledge a person could actually be in Edinburgh or Brighton, but not both, at a time Owned Jane believes Anne was actually in Edinburgh, John believes Anne was actually in Brighton Current Jane believes Anne was actually in Edinburgh now, yesterday she believed Anne was actually in Brighton Modally Consistent Jane cannot believe that Anne was actually in Edinburgh and actually in Brighton at the same time Credence Relations If Anne had breakfast with Effie in Edinburgh, then Anne was in Edinburgh Testimony John tells (testimony) Jane he believes Anne was actually in Brighton Flexible system identity If two departments split, then their intelligence systems should split Ordinary language/data contains many uncertainties: Simple ‘use case’ (apparently) Simple ‘use case’ to illustrate the challenges: “it is possible that Anne was actually in Edinburgh last Saturday, 30th March 2024”. Prima facie, if we have this intelligence digitally stored, we should be able to report on it when asked. for example, when questioned: “Could Anne (the person of interest) have been in Edinburgh last Saturday?” we should be able to answer: “Yes, possibly.” The use case appears simple, and we might expect that building an information system to hold this information – and provide the right answers would be easy. in our paper: we show that this simplicity is deceptive by illustrating how the use case raises a series of difficult technical formal challenges that need to be overcome by any information system before it can give a satisfactory answer. Partridge, C., Andrew Mitchell, & Cola, A. (2024, October). Digitalizing Uncertain Information . Semantic Technology for Intelligence, Defense , and Security (STIDS 2024). https://www.academia.edu/125111898 62 A way to face the challenges: an agent’s doxastically accessible worlds A form for saying it is contingent (possible but not necessary) that Anne was in Edinburgh on 30th March 2024 that allows it to be possible that she was in Edinburgh, and also that she was not. Given the possible worlds approach, intuitively there exists both a possible Anne who was in Edinburgh and a possible Anne who was not – in different possible worlds. in our foundation, these are different, unconnected objects and the project aims to build the machinery to connect them. Lewis’s answer is to connect the objects with a counterpart relation. this counterpart relation picks out a set of related individuals which we call the individual possibility . With this apparatus we can say: there is an individual possibility ‘Annes’ it is a property whose members are all the possible Annes on all the possible worlds. some of these Annes were in Edinburgh on 30th March 2024, others were not. we can reify the individual possibility – Anne in Edinburgh on 30th March 2024 these are the states of Anne where she is in Edinburgh on 30th March 2024 All this relative to an agent’s beliefs the agent’s doxastically accessible worlds 63 My doxastic actualities We introduce what Lewis calls the believer's doxastic possibilities “We should characterise the content not by a class of possible worlds, but by a class of possible individuals – call them the believer's doxastic alternatives – who might, for all he believes, be himself. Individual X is one of them iff nothing that the believer believes, either explicitly or implicitly, rules out the hypothesis that he himself is X. These individuals are the believer's doxastic possibilities.” [12, pp. 28–9] We call these my doxastic actualities. … This set contains as members all the individuals that could possibly be my actuality - me now. We want to filter these to ‘my doxastic actualities’: those of my actuality individual possibility members who hold the same beliefs as me and whose beliefs are compatible with themselves. Partridge, C., Andrew Mitchell, & Cola, A. (2024, October). Digitalizing Uncertain Information . Semantic Technology for Intelligence, Defense , and Security (STIDS 2024). https://www.academia.edu/125111898 We consider the worlds these doxastic actualities inhabit. 64 Visualizing an agent’s doxastic accessibility 65 world 0 time … Annes Anne in Edinburgh on 30th March 2024s 30th March 2024s Edinburghs world 2 world n … world 1 Individual Possibilities Anne was not in Edinburgh Anne was in Edinburgh Visualise the agent’s individual doxastically actual possibilities Legend 66 world location extension in time person extension in time time slice person-location-time slice intersection my world me (extension in time) world doxastically actual t now current time instance my world doxastically actual The legend gives some hints of the infrastructure needed for this extension: How the agent’s doxastic accessibility, the worlds that conform to the agent’s beliefs, are built up. If you want to find out more: Partridge, C., Mitchell, A., & Cola, A. (2024, October). Digitalizing Uncertain Information . Semantic Technology for Intelligence, Defense , and Security (STIDS 2024). https://www.academia.edu/125111898 Summary Summary – reference, identity and regimentation Characterised extensionalism as motivated by a desire for clear computable (digital) identity criteria to avoid the possibility of conflating identity Described how Quine divides semantics into two broad types: theories of reference (extensional) solid basis for identity and so ontology theories of meaning (intensional) fails the identity test – so not suitable for formal ontology Quinean regimentation making meaning extensional thus: fixing the confusion and conflation in ‘meaning’ migrating ordinary data/language into a formal (ontological) structure set abstraction as an example bCLEARer as an example of an implemented tool 68 Summary – meta-regimentation journey Regimentation – two levels Quinean regimentation as a tool for: fixing the confusion and conflation in ‘meaning’ meta-regimentation as a tool for: extending the reach of extensionalism widening the scope of what can be fixed Examples of meta-regimentation in the evolution of extensionalism constructionalism pure ontological extensionalism (divorcing ontology from semantics) moving from a ‘theory of reference’ to a ‘theory of things’ extensionalising agentology bringing the agent into scope two aspects indexicality uncertainty 69 Questions 70