Mailing List
Back to Top
Issue 6
ISSN 2634-8578
Curated By:
Grey Grierson
Cambridge University
Digital, Hyperobjects, Philosophy
Add to Basket
Share →
Daniel Koehler, 2020
Introduction to Issue 01: Mereologies
Architecture, Architecture Theory, Discrete Architecture, Mereologies, Mereology, Philosophy
Daniel Koehler
University of Texas at Austin
Add to Issue
Read Article: 1570 Words

Part relationships play an important role in architecture. Whether an aspect of a Classical order, a harmonious joining of building components, a representation of space, a partition of spaces, or as a body that separates us and identifies us as individuals. From the very outset, every form of architecture begins with an idea of how parts come together to become a whole and an understanding of how this whole relates to other parts. Architecture first composes a space as a part of a partitioning process well before defining a purpose, and before using any geometry.

The sheer performance of today’s computational power makes it possible to form a world without a whole, without any third party or a third object. Ubiquitous computing fosters peer-to-peer or better part-to-part exchange. It is not surprising then that today’s sharing represents an unfamiliar kind of partiality. From distributive manufacturing to the Internet of Things, new concepts of sharing promise systematic shifts, from mass-customisation to mass-individualisation: the computational enabled participations are foundational. It is no longer the performance or mode of an algorithm that drives change but its participatory capacities. From counting links, to likes, to seats, to rooms: tools for sharing have become omnipresent in our everyday lives. Thus, that which is common is no longer negotiated but computed. New codes – not laws or ideologies – are transforming our cities at a rapid pace, but what kind of parthood is being described? How does one describe something only through its parts today? To what extent do the automated processes of sharing differ from the partitioning of physical space? How can we add, intervene and design such parts through architecture?

The relationship between parts and their whole is called Mereology. In this issue of Prospectives, mereology’s theories and the specifics of part-relations are explored. The differences between parts and the whole, the sharing of machines and their aesthetics, the differences between distributive and collective, their ethical commitments, and the possibilities of building mereologies are discussed in the included articles and interviews.

Just as mereology describes objects from their parts, this issue is partial. It is not a holistic proposal, but a collection of positions. Between philosophy, computation, ecology and architecture, the texts are reminders that mereologies have always been part of architecture. Mereology is broadly a domain that deals with compositional possibilities, relationships between parts. Such an umbrella – analogue to morphology, typology, or topology – is still missing in architecture. Design strategies that depart part-to-part or peer-to-peer are uncommon in architecture, also because there is (almost) no literature that explores these topics for architectural design. This issue hopes to make the extra-disciplinary knowledge of mereology accessible to architects and designers, but also wishes to identify links between distributive approaches in computation, cultural thought and built space.

The contributions gathered here were informed by research and discussions in the Bartlett Prospectives (B-Pro) at The Bartlett School of Architecture, UCL London from 2016 to 2019, culminating in an Open Seminar on mereologies which took place on 24 April 2019 as part of the Prospectives Lecture Series. The contributions are intended as a vehicle to inject foundational topics such as mereology into architectural design discourse.

The Contributions

This compilation starts with Giorgio Lando’s text “Mereology and Structure”. Lando introduces what mereology is for philosophers, and why philosophers discuss mereological theses, as well as disagree one with another about them. His text focuses in particular on the role of structure in mereology outlining that from a formal point of view part relations are freed from structure. He argues that independence from structure might be the identifying link between mereology and architecture. The second article “From Partitioning to Partaking” is a plea for re-thinking the city. Daniel Koehler’s essay points to the differences between virtual and real parts. Koehler observes a new spatial practice of virtual representations that render previous models of urban governance obsolete. He argues that the hyper-dimensional spaces of a big data-driven economy demand a shift from a partitioning practice of governance to more distributed forms of urban design. In “Matter versus Parts: The Immaterialist Basis of Architectural Part-Thinking” Jordi Vivaldi Piera highlights the revival of matter in parallel to the discrete turn in contemporary discourses on experimental architecture. The essay gravitates around the notion of part-thinking in association with the notion of form. Fluctuating between continuous and discrete, the text sets out requirements for radical part-thinking in architecture. As a computational sociologist, David Rozas illustrates the potential of decentralised technologies for democratic processes at the scale of neighborhood communities. After an introduction to models of distributed computation, “Affordances of Decentralised Technologies for Commons-based Governance of Shared Technical Infrastructure” draws analogies to Elinor Ostrom’s principles of commons governance and how those can be computationally translated, turning community governance into fully decentralised autonomous organisations.

Departing from the Corbusian notion of a ‘machine for living’, Sheghaf Abo Saleh defines a machine for thinking. In “When Architecture Thinks! Architectural Compositions as a Mode of Thinking in the Digital Age” Abo Saleh states that the tectonics of a machine that thinks is brutal and rough. As a computational dialogue, she shows how roughness can enable posthumanism which, in her case, turns “tempered” parts into a well-tempered environment. Ziming He’s entry point for “The Ultimate Parts” is the notion of form as the relations between parts and wholes. He’s essay sorts architectural history through a mereological analysis, proposing a new model of part-to-part without wholes. Shivang Bansal’s “Towards a Sympoietic Architecture: Codividual Sympoiesis as an Architectural Model” investigates the potential of sympoiesis. By extending Donna Haraway‘s argument of “tentacular thinking” into architecture, the text shifts focus from object-oriented thinking to parts. Bansal argues for the limits of autopoiesis as a system and conceptualises spatial expressions of sympoiesis as a necessity for an adaptive and networked existence through “continued complex interactions” among parts.

Merging aspects of ‘collective’ and ‘individuality,’ in “Codividual Architecture within Decentralised Autonomous System” Hao Chen Huang proposes a new spatial characteristic that she coins as the “codividual”. Through an architectural analysis of individual and shared building precedents, Huang identifies aspects of buildings that merge shared and private features into physical form. Anthony Alviraz’s paper “Computation Within Codividual Architecture” investigates the history and outlook of computational models into architecture. From discrete to distributed computation, Alviraz speculates on the implications of physical computation where physics interactions overcome the limits of automata thinking. InSynthesizing Hyperumwelten”, Anna Galika transposes the eco-philosophical concept of an HyperObject into a “Hyperumwelt”. While the Hyperobject is a closed whole that cannot be altered, a Hyperumwelt is an open whole that uses objects as its parts. The multiple of a Hyperumwelt offers a shift from one object’s design towards the impact of multiple objects within an environment.

Challenging the notion of discreteness and parts, Peter Eisenman asks in the interview “Big Data and the End of Architecture Being Distant from Power” for a definition of the cultural role of the mereological project. Pointing to close readings of postmodern architecture that were accelerated by the digital project, Eisenman highlights that the demand for a close reading is distanced from the mainstream of power. The discussion asks: ultimately, what can an architecture of mereology critique? The works of Herman Hertzberger are an immense resource on part-thinking. In the interview “Friendly Architecture: In the Footsteps of Structuralism”, Herman Hertzberger explains his principle of accommodation. When building parts turn into accommodating devices, buildings turn into open systems for staging ambiguity.**

The issue concludes with a transcript from the round table discussion at the Mereologies Open Seminar at The Bartlett School of Architecture on 24 April 2019.


The contributions evolved within the framework of Bartlett Prospectives (B-Pro) at The Bartlett School of Architecture, UCL. I want to thank Frédéric Migayrou for his vision, commitment and long years of building up a research program, not only by architecture but through computation. I would like to thank Roberto Bottazzi for the years of co-organising the Prospectives Lecture Series, where plenty of the discussions that form the backbone of this issue took place. Thanks to Mario Carpo for raising the right question at the right time for so many people within the program, thanks to Andrew Porter for enabling so many events, to Gilles Retsin, for without the discrete there are no parts, Mollie Claypool for the editing and development of Prospectives journal, and Vera Buehlmann, Luciana Parisi, Alisa Andrasek, Keller Easterling, Matthew Fuller, John Frazer, Philippe Morel, Ludger Hovestadt, Emmanuelle Chiappone-Piriou, Jose Sanchez, Casey Rehm, Tyson Hosmer, and Jordi Vivaldi Piera for discussions and insights. 

I want to thank Rasa Navasaityte, my partner in Research Cluster 17 at B-Pro, for driving the design research. Thank you for the research contributed by the researchers and tutors: Christoph Zimmel, Ziming He, Anqi Su, Sheghaf Abo Saleh, and to all participants, specifically to highlight: Genmao Li, Zixuan Wang, Chen Chen, Qiming Li, Anna Galika, Silu Meng, Ruohan Xu, Junyi Bai, Qiuru Pu, Anthony Alviraz, Shivang Bansal, Hao-Chen Huang, Dongxin Mei, Peiwen Zhan, Mengshi Fu, Ren Wang, Leyla El Sayed Hussein, Zhaoyue Zhang, Yao Chen, and Guangyan Zhu.

The issue includes articles that evolved from thesis reports conducted in the following clusters: Ziming He from Research Cluster 3 tutored by Tyson Hosmer, David Reeves, Octavian Gheorghiu, and Jordi Vivaldi in architecture theory. Sheghaf Abo Saleh, Anthony Alvidrez, Shivang Bansal, Anna Galika, Hao Chen Huang from Research Cluster 17 tutored by Daniel Koehler and Rasa Navasaityte. If not indicated directly, the featured images, graphics of this issue are by Daniel Koehler, 2020.

Suggest a Tag for this Article
Mereology, WanderYards, Genmao Li, Chen Chen and Xixuan Wang, RC17, MArch Urban Design, The Bartlett School of Architecture, UCL, 2017.
From Partitioning to Partaking, or Why Mereologies Matter
Architecture, Building, Digital, Digital Architecture, Discrete Architecture, Mereologies, Mereology, Participatory Design, Virtual
Daniel Koehler
University of Texas at Austin
Add to Issue
Read Article: 5574 Words

Parts, chunks, stacks and aggregates are the bits of computational architecture today. Why do mereologies – or buildings designed from part-to-whole – matter? All too classical, the roughness of parts seems nostalgic for a project of the digital that aims for dissolving building parts towards a virtual whole. Yet if parts shrink down to computable particles and matter, and there exists a hyper-resolution of a close to an infinite number of building parts, architecture would dissolve its boundaries and the capacity to frame social encounters. Within fluidity, and without the capacity to separate, architecture would not be an instrument of control. Ultimately, freed from matter, the virtual would transcend from the real and form finally would be dead. Therein is the prospect of a fluid, virtual whole.

The Claustrophobia of a City that Transcends its Architecture

In the acceleration from Data to Big Data, cities have become more and more virtual. Massive databases have liquefied urban form. Virtual communication today plays freely across the material boundaries of our cities. In its most rudimentary form virtuality is within the digital transactions of numbers, interests and rents. Until a few years ago,  financial investments in architectural form were equatable according to size and audience, e.g. as owner-occupied flats, as privately rented houses or as lease holding.[1] Today capital flows freely scatter across the city at the scale of the single luxury apartment. Beyond a certain threshold in computational access, data becomes big. By computing aggregated phone signal patterns or geotagged posts, virtual cities can emerge from the traces of individuals. These hyperlocal patterns are more representative of a city than its physical twin. Until recently, architecture staged the urban through shared physical forms: the sidewalk, lane or boulevard. Adjacent to cars, walkable for pedestrians or together as citizens, each form of being urban included an ideology of a commons, and grounded with that particular parts of encountering.

Figure 1 – (left to right) Floor area comparisons between housing projects from the Brutalist era (top) and today (bottom): Previ, Atelier 5 vs Seguro, Kerez La Sainte-Baume, Le Corbusier vs The Mountain, BIG; La Muralla Roja Calpe, Bofill vs Communal Villa, Dogma. Image: Daniel Koehler.

In contrast, a hyper-local urban transcends lanes and sidewalks. Detached from the architecture of the city, with no belonging left, urban speculation has withdrawn into the private sphere. Today, urban value is estimated by counting private belongings only, with claustrophobic consequences. An apartment that is speculatively invested displaces residents. The housing shortage in the big cities today is not so much a problem of lack of housing, but instead of vacant space, accessible not to residents but to interests they hold in the hyper-urban.[2] The profit from rent and use of space itself is marginal compared to the profit an embodied urban speculation adds to the property. The possibility of mapping every single home as data not only adds interest, like a pension to a home but literally turns a home into a pension.[3] However this is not for its residents but for those with access to resources. Currently, computing Big Data expands and optimises stakeholders’ portfolios by identifying undervalued building assets.[4] However, the notion of ‘undervalued’ is not an accurate representation of assets.

Hyper-localities increase real estate’s value in terms of how their inhabitants thrive in a neighbourhood through their encounters with one another and their surrounding architecture. The residents themselves then unknowingly produce extra value. The undervaluing of an asset is the product of its residents, and like housework, is unpaid labour. In terms of the exchange of capital, additional revenue from a property is usually paid out as a return to the shareholders who invested in its value. Putting big data-driven real estate into that equation would then mean that they would have to pay revenues to their residents. If properties create surplus value from the data generated by their residents, then property without its residents has less worth and is indeed over-, but not under-, valued.

Figure 2 – (left to right) City in a Building, City as a Building and City as an Element of Architecture. Image: University of Innsbruck, Daniel Koehler with Martin Danigel and Jordi Vivaldi, 2016-2018.

The city uses vehicles for creating public revenue by governing the width of a street’s section or the height of a building. Architecture’s role was to provide a stage for that revenue to be created. For example the Seagram Building (van der Rohe, Johnson, 1958) created a “public” plaza by setting back its envelope in exchange for a little extra height. By limiting form, architecture could create space for not only one voice, but many voices. Today, however, the city’s new parameters hidden in the fluidity of digital traces cannot be governed by the boundaries of architecture anymore. Outlined already 40 years ago, when the personal computer became available, Gilles Deleuze forecasted that “Man is not anymore man enclosed”.[5] At that time, and written as a “Postscript on the Societies of Control”, the fluid modulation of space prospected a desirable proposition. By liquefying enclosures, the framework of the disciplinary societies of Foucault’s writings would disappear. In modern industrial societies, Deleuze writes, enclosures were moulds for casting distinct environments, and in these vessels, individuals became masses of the mass society.[6] For example, inside a factory, individuals were cast as workers, inside schools as students. Man without a cast and without an enclosure seemed to be freed from class and struggle. The freedom of an individual was interlinked with their transcendence from physical enclosures.

Figure 3 – The Hyper-Nollie Plan, Daniel Koehler, 2019. Image: Daniel Koehler, 2019.

During the last forty years, the relation between a single individual and the interior framed architecture rightly aimed to dissolve the institutional forms of enclosures that represented social exclusion at their exterior. Yet, in this ambition alternative forms for the plural condition of what it means to be part of a city were not developed. Reading Deleuze further, a state without enclosures also does not put an end to history. The enclosures of control dissolve only to be replaced. Capitalism would shift to another mode of production. When industrial exchange bought raw materials and sold finished products, now it would buy the finished products and profit from the assemblies of those parts. The enclosure is then exchanged with codes that mark access to information. Individuals would not be moulded into masses but considered as individuals: accessed as data, divided into proper parts for markets, “counted by a computer that tracks each person’s position enabling universal modulation.”[7] Forty years in, Deleuze’s postscript has become the screenplay for today’s reality.

Hyper-parts: Spatial Practices of representations

A house is no longer just a neutral space, an enclosing interior where value is created, realised and shared. A home is the product of social labour; it is itself the object of production and, consequently, the creation of surplus value. By shifting from enclosure to asset, the big data-driven economy has also replaced the project behind modernism: humanism. Architecture today is post-human. As Rosi Braidotti writes, “what constitutes capital value  today is the informational power of living matter itself”.[8] The human being as a whole is displaced from the centre of architecture. Only parts of it, such as its “immanent capacities to form surplus-value”, are parts of a larger aggregation of architecture. Beyond the human, the Hyper-city transcends the humane. A virtual city is freed from its institutions and constituent forms of governance. Economists such as Thomas Piketty describe in painstaking detail how data-driven financial flows undermine common processes of governance, whether urban, regional, or national, in both speed and scale. Their analysis shows that property transactions shelled in virtual value-creation-bonds are opaque to taxation. Transcending regulatory forms of governance, one can observe the increase of inequalities on a global scale. Comparable to the extreme wealth accumulation at the end of the nineteenth century, Piketty identifies similar neo-proprietarian conditions today, seeing the economy shifting into a new state he coins as “hypercapitalism”.[9] From Timothy Morton’s “hyper-objects” to hypercapitalism,  hyper replaces the Kantian notion of transcendence. It expresses not the absorption of objects into humanism, but its withdrawal. In contrast to transcendence, which subordinates things to man’s will, the hyper accentuates the despair of the partial worlds of parts – in the case of Morton in a given object and in the case of Piketty in a constructed ecology.

When a fully automated architecture emerged, objects oriented towards themselves, and non-human programs began to refuse the organs of the human body. Just as the proportions of a data center are no longer walkable, the human eye can no longer look out of a plus-energy window, because it tempers the house, but not its user. These moments are hyper-parts: when objects no longer transcend into the virtual but despair in physical space. More and more, with increasing computational performance, following the acronym O2O (from online to offline),[10] virtual value machines articulate physical space. Hyper-parts place spatial requirements. A prominent example is Katerra, the unicorn start-up promising to take over building construction using full automation. In its first year of running factories, Katerra advertises that it will build 125,000 mid-rise units in the United States alone. If this occurred, Katerra would take around 30% of the mid-rise construction market in the company’s local area. Yet its building platform consists of only twelve apartment types. Katerra may see the physical homogeneity as an enormous advantage as it increases the sustainability of its projects. This choice facilitates financial speculation, as the repetition of similar flats reduces the number of factors in the valuing of apartments and allows quicker monetary exchange, freed from many variables. Sustainability refers not to any materiality but to the predictability of its investments. Variability is still desired, but oriented towards finance and not to inhabitants. Beyond the financialisation of a home, digital value machines create their own realities purely through the practice of virtual operations.

Figure 4 – The hyper-dimensional spaces of the digital economy are incompatible with cellular architecture. With every dimension added, the hull will gain weight until it absorbs more space than its content. From pure mathematical calculations, the dividends associated with the living cell and count more than its inhabitants. Image: Daniel Koehler, 2019.

Here one encounters a new type of spatial production: the spatial practice of representations. At the beginning of what was referred to as “late capitalism”, the sociologist and philosopher Henri Lefebvre proposed three spatialities which described modes of exchange through capitalism.[11] The first mode, a spatial practice referred to a premodern condition, which by the use of analogies interlinked objects without any forms of representation—the second, representations of space linked directly to production, the organic schemes of modernism. The third representational spaces express the conscious trade with representations, the politics of postmodernism, and their interest in virtual ideas above the pure value of production. Though not limited to three only, Lefebvre’s intention was to describe capitalism as “an indefinite multitude of spaces, each one piled upon, or perhaps contained within, the next”.[12] Lefebvre differentiated the stages in terms of their spatial abstraction. Incrementally, virtual practices transcended from real-to-real to virtual-to-real to virtual-to-virtual. But today, decoupled from the real, a virtual economy computes physically within spatial practices of representations. Closing the loop, the real-virtual-real, or new hyper-parts, do not subordinate the physical into a virtual representation, instead, the virtual representation itself acts in physical space.

This reverses the intention of modernism orientated towards an organic architecture by representing the organic relationships of nature in geometric thought. The organicism of today’s hypercomputation projects geometric axioms at an organic resolution. What was once a representation and a geometry distant from human activity, now controls the preservation of financial predictability.

The Inequalities Between the Parts of the Virtual and the Parts of the Real

Beyond the human body, this new spatial practice of virtual parts today transcends the digital project that was limited to a sensorial interaction of space. This earlier understanding of the digital project reduced human activity to organic reflexes only, thus depriving architecture of the possibility of higher forms of reflection, thought and criticism. Often argued through links to phenomenology and Gestalt theory, the simplification of architectural form to sensual perception has little to do with phenomenology itself. Edmund Husserl, arguably the first phenomenologist, begins his work with considering the perception of objects, not as an end, but to examine the modes of human thinking. Examining the logical investigations, Husserl shows that thought can build a relation to an object only after having classified it, and therefore, partitioned it. By observing an object before considering its meaning, one classifies an object, which means identifying it as a whole. Closer observations recursively partition objects into more unaffected parts, which again can be classified as different wholes.[13] Husserl places parts before both thought and meaning.

Figure 5 – Mereologies, 2016. Image(s): (top) Genmao Li, RC17, MArch Urban Design, B-Pro, The Bartlett School of Architecture, UCL, 2016; (bottom) Zhiyuan Wan, Chen Chen, Mengshi Fu, RC17, MArch Urban Design, B-Pro, The Bartlett School of Architecture, UCL, 2016.

Derived from aesthetic observations, Husserl’s mereology was the basisof his ethics, and was therefore concluded in societal conceptions. In his later work, Husserl’s analysis is an early critique of the modern sciences.[14] For Husserl, in their efforts to grasp the world objectively, the sciences have lost their role in enquiring into the meaning of life. In a double tragedy, the sciences also alienated human beings from the world. Husserl thus urged the sciences to recall that they ground their origins in the human condition, as for Husserl humanism was ultimately trapped in distancing itself further from reality.

One hundred years later, Husserl’s projections resonate in “speculative realism”. Coined By Levi Bryant as “strange mereology”,[15] objects, their belongings, and inclusions are increasingly strange to us. The term “strange” stages the surprise that one is only left with speculative access. However, ten years in, speculation is not distant anymore. That which transcends does not only lurk in the physical realm. Hyper-parts figurate ordinary scales today, namely housing, and by this transcend the human(e) occupation.

Virtual and physical space are compositionally comparable. They both consist of the same number of parts, yet they do not. If physical elements belong to a whole, then they are also part of that to which their whole belongs. In less abstract terms, if a room is part of an apartment, the room is also part of the building to which the apartment belongs. Materially bound part relationships are always transitive, hierarchically nested within each other. In virtual space and the mathematical models with which computers are structured today, elements can be included within several independent entities. A room can be part of an apartment, but it can also be part of a rental contract for an embassy. A room is then also part of a house in the country in which the house is located. But as part of an embassy, the room is at the same time part of a geographically different country on an entirely different continent than the building that houses the embassy. Thus, for example, Julian Assange, rather than boarding a plane, only needed to enter a door on a street in London to land in Ecuador. Just with a little set theory, in the virtual space of law, one can override the theory of relativity with ease.

Parts are not equal. Physical parts belong to their physical wholes, whereas virtual parts can be included in physical parts but don’t necessarily belong to their wholes.  Far more parts can be included in a virtual whole than parts that can belong to a real whole. When the philosopher Timothy Morton says “the whole is always less than the sum of its parts”,[16] he reflects the cultural awareness that reality breaks due to asymmetries between the virtual and the real. A science that sets out to imitate the world is constructing its own. The distance which Husserl spoke of is not a relative distance between a strange object and its observer, but a mereological distance, when two wholes distance each other because they consist of different parts. In its effort to reconstruct the world in ever higher resolution, modernism, and in its extension the digital project, has overlooked the issue that the relationship between the virtual and the real is not a dialogue. In a play of dialectics between thought and built environment, modernism understood design as a dialogue. In extending modern thought, the digital project has sought to fulfill the promise of performance, that a safe future could be calculated and pre-simulated in a parallel, parametric space. Parametricism, and more generally what is understood as digital architecture, stands not only for algorithms, bits, and rams but for the far more fundamental belief that in a virtual space, one can rebuild reality. However, with each resolution that science seeks to mimic the world, the more parts it adds to it.

Figure 6 – Illustrations of exemplary stairs constructed through cubes, Sebastiano Serlio, 1566. Image: public domain.

The Poiesis of a Virtual Whole

The asymmetry between physical and virtual parts is rooted in Western classicism. In early classical sciences, Aristotle divided thinking into the trinity of practical action, observational theory and designing poiesis. Since the division in Aristotle’s Nicomachean Ethics, design is a part of thought and not part of objects. Design is thus a knowledge, literally something that must first be thought. Extending this contradiction to the real object, design is not even concerned with practice, with the actions of making or using, but with the metalogic of these actions, the in-between between the actions themselves, or the art of dividing an object into a chain of steps with which it can be created. In this definition, design does not mean to anticipate activities through the properties of an object (function), nor to observe its properties (materiality), but through the art of partitioning, structuring and organising an object in such a way that it can be manufactured, reproduced and traded.

To illustrate poiesis, Aristotle made use of architecture.[17] No other discipline exposes the poetic gap so greatly between theory, activity and making. Architecture first deals with the coordination of the construction of buildings. As the architecture historian Mario Carpo outlines in detail, revived interest in classicism and the humanistic discourse on architecture began in the Renaissance with Alberti’s treatise: a manual that defines built space, and ideas about it solely through word. Once thought and coded into words, the alphabet enabled the architect to physically distance from the building site and the built object.[18] Architecture as a discipline then does not start with buildings, but with the first instructions written by architects used to delegate the building.

A building is then anticipated by a virtual whole that enables one to subordinate its parts. This is what we usually refer to as architecture: a set of ideas that preempt the buildings they comprehend. The role of the architect is to imagine a virtual whole drawn as a diagram, sketch, structure, model or any kind of representation that connotates the axes of symmetries and transformations necessary to derive a sufficient number of parts from it. Architectural skill is then valued by the coherence between the virtual and the real, the whole and its parts, the intention and the executed building. Today’s discourse on architecture is the surplus of an idea. You might call it the autopoiesis of architecture – or merely a virtual reality. Discourse on architecture is a commentary on the real.

Adrian Bowyer (left) and Vik Olliver (right) with a parent RepRap machine, and the first child machine, made by the RepRap on the left. Image in public domain.
Figure 7 – Adrian Bowyer (left) and Vik Olliver (right) with a parent RepRap machine, and the first child machine, made by the RepRap on the left. Image: public domain.

Partitioning Architectures

From the very outset, architecture distanced itself from the building, yet also aimed to represent reality. Virtual codes were never autonomous from instruments of production. The alphabet and the technology of the printing press allowed Alberti to describe a whole ensemble distinct from a real building. Coded in writing, printing allowed for the theoretically infinite copies of an original design. Over time, the matrices of letters became the moulds of the modern production lines. However, as Mario Carpo points out, the principle remained the same.[19] Any medium that incorporates and duplicates an original idea is more architecture than the built environment itself. Belonging to a mould, innovation in architecture research could be valued in two ways. Quantitatively, in its capacity to partition a building in increasing resolution. Qualitatively, in its capacity to represent a variety of contents with the same form. By this, architecture faced the dilemma that one would have to design a reproducible standard that could partition as many different forms as possible to build non-standard figurations.[20]

The dilemma of the non-standard standard moulds is found in Sebastiano Serlio’s transcription of Alberti’s codes into drawings. In the first book of his treatise, Serlio introduces a descriptive geometry to reproduce any contour and shape of a given object through a sequence of rectangles.[21] For Serlio, the skill of the architect is to simplify the given world of shapes further until rectangles become squares. The reduction finally enables the representation of physical reality in architectural space using an additive assembly of either empty or full cubes. By building a parallel space of cubes, architecture can be partitioned into a reproducible code. In Serlio’s case, architecture could be coded through a set of proportional ratios. However, from that moment on, stairs do not consist only of steps, and have to be built with invisible squares and cubes too.

Today, Serlio’s architectural cubes are rendered obsolete by 3D printed sand. By shrinking parts to the size of a particle of dust, any imaginable shape can be approximated by adding one kind of part only. 3D printing offers a non-standard standard, and with this, five hundred years of architectural development comes to an end.

Figure 8 – Von Neumann’s illustrations describing automata as a set of linkages between nodes. Image: Arthur W. Burks, 1969, public domain.

Replicating: A Spatial Practice of Representations

3D printing dissolved existing partitioning parts to particles and dust. A 3D-printer can not only print any shape but can also print at any place, at any time. The development of 3D printing was mainly driven by DIY hobbyists in the Open Source area. One of the pioneering projects here is the RepRap project, initiated by Adrian Bowyer.[22] RepRap is short for replicating rapid prototyping machine. The idea behind it is that if you can print any kind of objects, you can also print the parts of the machine itself. This breaks with the production methods of the Modern Age. Since the Renaissance, designers have crafted originals and used these to build a mould from those so that they can print as many copies as possible. This also explains the economic valuation of the original and why authorship is so vehemently protected in legal terms. Since Alberti’s renunciation of drawings for a more accurate production of his original idea through textual encoding, the value of an architectural work consisted primarily in the coherence of a representation with a building: a play of virtual and real. Consequently, an original representation that cast a building was more valued than its physical presentation. Architecture design was oriented to reduce the amount of information needed to cast. This top-down compositional thinking of original and copy becomes obsolete with the idea of replication.

Since the invention of the printing press, the framework of how things are produced has not changed significantly. However, with a book press, you can press a book, but with a book, you can’t press a book. Yet with a 3D printer, you can print a printer. A 3D printer does not print copies of an original, not even in endless variations, but replicates objects. The produced objects are not duplicates because they are not imprints that would be of lower quality. Printed objects are replicas, objects with the same, similar, or even additional characteristics as their replicator.

Figure 9 – Lionel R. Penrose, drawing for a physical implementation of a self-replicating chain of 3 units in length. Image: Photograph f40v, Galton Laboratory Archive, University College London, 1955.

A 3D printer is a groundbreaking digital object because it manifests the foundational principle of the digital – replication – on the scale of architecture. The autonomy of the digital is based not only on the difference between 0 and 1 but on the differences in their sequencing. In mathematics in the 1930s, the modernist project of a formal mimicry of reality collapsed through Godel’s proof of the necessary incompleteness of all formal systems. Mathematicians then understood that perhaps far more precious knowledge could be gained if we could only learn to distance ourselves from its production. The circle of scientists around John von Neumann, who developed the basis of today’s computation, departed from one of the smallest capabilities in biology: to reproduce. Bits, as a concatenation of simple building blocks and the integrated possibility of replication, made it possible, just by sequencing links, to build first logical operations, and connecting those programs to today’s artificial networks.[23] Artificial intelligence is artificial but it is also alive intelligence.

To this day, computerialisation, not computation is at work in architecture. By pursuing the modern project of reconstructing the world as completely as possible, the digital project computerised a projective cast[24] in high resolution. Yet this was done without transferring the fundamental principles of interlinking and replication to the dimensions of the built space.

Figure 10 – (left to right) Mereologies: WanderYards, 2016, Genmao Li, Chen Chen, and Xixuan Wang, 2016; Enframes, Kexin Cao, Yue Jin, Qiming Li, 2017; iiOOOI, Sheghaf Abo Saleh, Hua Li, Chuwei Ye, Yaonaijia Zhou, 2018 (right). Image(s): RC17, MArch Urban Design, The Bartlett School of Architecture, UCL, 2016-2018.

From Partitioning to Partaking

The printing press depends on a mould to duplicate objects. The original mould was far more expensive to manufacture than its copies, so the casting of objects had to bundle available resources. This required high investments in order to start production, leading to an increasing centralisation of resources in order to scale the mass-fabrication of standard objects for production on an assembly line. Contrarily, digital objects do not need a mould. Self-replication provided by 3D printing means that resources do not have to be centralised. In this, digital production shifts to distributed manufacturing.[25]

Independent from any mould, digital objects as programs reproduce themselves seamlessly at zero marginal costs.[26] As computation progresses, a copy will then have less and less value. Books, music and films fill fewer and fewer shelves because it no longer has value to own a copy when they are ubiquitously available online. And the internet does not copy; it links. Although not fully yet integrated into its current TCP-IP protocol,[27] the basic premise of hyperlinking is that linked data adds value.[28] Links refer to new content, further readings, etc. With a close to infinite possibility to self-reproduce, the number of objects that can be delegated and repeated becomes meaningless. What then counts is hyper-, is the difference in kind between data, programs and, eventually, building parts. In his identification of the formal foundations of computation, the mathematician Nelson Goodman pointed out that beyond a specific performance of computation, difference, and thus value, can only be generated when a new part is added to the fusion of parts.[29] What is essential for machine intelligence is the dimensionality of its models, e.g., the number of its parts. Big data refers less to the amount of data, but more to the number of dimensions of data.[30]

Figure 11 – Enframes, 2017. Image: Kexin Cao, Yue Jin, Qiming Lim, RC17, MArch Urban Design, The Bartlett School of Architecture, UCL, 2017.

With increasing computation, architecture shifted from an aesthetic of smoothness that celebrated the mastership of an infinite number of building parts to roughness. Roughness demands to be thought (brute). The architecture historian Mario Carpo is right to frame this as nostalgic, as “digital brutalism”.[31] Similar to brutalism that wanted to stimulate thought, digital roughness aims to extend spatial computability, the capability to extend thinking, and the architecture of a computational hyper-dimensionality. Automated intelligent machines can accomplish singular goals but are alien to common reasoning. Limited around a ratio of a reality, a dimension, a filter, or a perspective, machines obtain partial realities only. Taking them whole excludes those who are not yet included and that which can’t be divided: it is the absolute of being human(e).

A whole economy evolved from the partial particularity of automated assets ahead of the architectural discipline. It would be a mistake to understand the ‘sharing’ of the sharing economy as having something “in common”. On the contrary, computational “sharing” does not partition a common use, but enables access to multiple, complementary value systems in parallel.

Figure 12 – Physical model, WanderYards, 2017. Image: Genmao Li, Chen Chen and Xixuan Wang, RC8, MArch Architecture Design, The Bartlett School of Architecture, UCL, 2017.

Cities now behave more and more like computers. Buildings are increasingly automated. They use fewer materials and can be built in a shorter time, at lower costs. More buildings are being built than ever before, but fewer people can afford to live in them. The current housing crisis has unveiled that buildings no longer necessarily need to house humans or objects. Smart homes can optimise material, airflow, temperature or profit, but they are blind to the trivial.

Figure 13 – Physical model, Slabrose, 2019. Image: Dongxin Mei, Zhiyuan Wan, Peiwen Zhan, and Chi Zhou, RC17, MArch Urban Design, The Bartlett School of Architecture, UCL, 2019.

It is a mistake to compute buildings as though they are repositories or enclosures, no matter how fine-grain their resolution is. The value of a building is no longer derived only from the amount of rent for a slot of space, but from its capacities to partake with. By this, the core function of a building changes from inhabitation to participation. Buildings do not anymore frame and contain: they bind, blend, bond, brace, catch, chain, chunk, clamp, clasp, cleave, clench, clinch, clutch, cohere, combine, compose, connect, embrace, fasten, federate, fix, flap, fuse, glue, grip, gum, handle, hold, hook, hug, integrate, interlace, interlock, intermingle, interweave, involve, jam, join, keep, kink, lap, lock, mat, merge, mesh, mingle, overlay, palm, perplex, shingle, stick, stitch, tangle, tie, unit, weld, wield, and wring.

In daily practice, BIM models do not highlight resolution but linkages, integration and collaboration. With further computation, distributed manufacturing, automated design, smart contracts and distributed ledgers, building parts will literally compute the Internet of Things and eventually our built environment, peer-to-peer, or better, part-to-part – via the distributive relationships between their parts. For the Internet of Things, what else should be its hubs besides buildings? Part-to-part habitats can shape values through an ecology of linkages, through a forest of participatory capacities. So, what if we can participate in the capacities of a house? What if we no longer have to place every brick, if we no longer have to delegate structures, but rather let parts follow their paths and take their own decisions, and let them participate amongst us together in architecture?

Figure 14 – Interior view of physical model, NPoche, 2018. Image: Silu Meng, Ruohan Xu, and Qianying Zhou. RC17, MArch Urban Design, The Bartlett School of Architecture, UCL, 2018.
Figure 15 – Seggregational section, WanderYards, 2017. Image: Genmao Li, Chen Chen and Xixuan Wang, RC17, MArch Urban Design, The Bartlett School of Architecture, UCL, 2017.


[1] S. Kostof, The City Assembled: The Elements of Urban Form Through History (Boston: Little, Brown and Company, 1992).

[2] J. Aspen, "Oslo – the triumph of zombie urbanism." Edward Robbins, ed., Shaping the city, (New York: Routledge, 2004).

[3] The World Bank actively promotes housing as an investment opportunity for pension funds, see: The World Bank Group, Housing finance: Investment opportunities for pension funds (Washington: The World Bank Group, 2018).

[4] G. M. Asaftei, S. Doshi, J. Means, S. Aditya, “Getting ahead of the market: How big data is transforming real estate”, McKinsey and Company (2018).

[5] G. Deleuze, “Postscript on the societies of control,” October, 59: 3–7 (1992), 6.

[6] Ibid, 4.

[7] Ibid, 6.

[8] R. Braidotti, Posthuman Knowledge (Medford, Mass: Polity, 2019).

[9] T. Piketty, Capital and Ideology (Cambridge, Mass: Harvard University Press, 2020).

[10] A. McAfee, E. Brynjolfsson, Machine, platform, crowd: Harnessing our digital future (New York: W.W. Norton & Company, 2017).

[11] H. Lefebvre, The Production of Space (Oxford: Basil Blackwell, 1991), 33.

[12] Ibid, 8.

[13] E. Husserl, Logische Untersuchungen: Zweiter Teil Untersuchungen zur Phänomenologie und Theorie der Erkenntnis.trans. "Logical investigations: Part Two Investigations into the phenomenology and theory of knowledge" (Halle an der Saale: Max Niemeyer, 1901).

[14] E. Husserl, Cartesianische Meditationen und Pariser Vortraege. trans. "Cartesian meditations and Parisian lectures" (Haag: Martinus Nijhoff, Husserliana edition, 1950).

[15] L. Bryant, The Democracy of Objects (Ann Arbor: University of Michigan Library, 2011).

[16] T. Morton, Being Ecological (London: Penguin Books Limited, 2018), 93.

[17] Aristotle, Nicomachean Ethics 14, 1139 a 5-10.

[18] M. Carpo, Architecture in the Age of Printing (Cambridge, Mass: MIT Press, 2001).

[19] M. Carpo, The Alphabet and the Algorithm (Cambridge, Mass: MIT Press, 2011).

[20] F. Migayrou, Architectures non standard (Editions du Centre Pompidou, Paris, 2003).

[21] S. Serlio, V. Hart, P. Hicks, Sebastiano Serlio on architecture (New Haven and London: Yale University Press, 1996).

[22] R. Jones, P. Haufe, E. Sells, I. Pejman, O. Vik, C. Palmer, A. Bowyer, “RepRap – the Replicating Rapid Prototyper,” Robotica 29, 1 (2011), 177–91.

[23] A. W. Burks, Von Neumann's self-reproducing automata: Technical Report (Ann Arbor: The University of Michigan, 1969).

[24] R. Evans, The Projective Cast: Architecture and Its Three Geometries (Cambridge, Massachusetts: MIT Press, 1995).

[25] N. Gershenfeld, “How to make almost anything: The digital fabrication revolution,” Foreign Affairs, 91 (2012), 43–57.

[26] J. Rifkin. The Zero Marginal Cost Society: The Internet of Things, the Collaborative Commons, and the Eclipse of Capitalism (New York: Palgrave Macmillan, 2014).

[27] B. Bratton, The Stack: On Software and Sovereignty (Cambridge, Massachusetts: MIT Press, 2016).

[28] J. Lanier, Who Owns the Future? (New York: Simon and Schuster, 2013).

[29] N. Goodman, H. S. Leonard, “The calculus of individuals and its uses,” The Journal of Symbolic Logic, 5, 2 (1940), 45–55.

[30] P. Domingos, The Master Algorithm: How the Quest for the Ultimate Learning Machine Will Remake Our World (London: Penguin Books, 2015).

[31] M. Carpo, “Rise of the Machines,” Artforum, 3 (2020).

Suggest a Tag for this Article
Mereology and Structure
Components, Composition, Mereologies, Mereology, Philosophy
Giorgio Lando
University of L'Aquila
Add to Issue
Read Article: 4106 Words

In this short paper I illustrate what is mereology for philosophers, and which reasons lead philosophers to discuss mereological theses and disagree one with another about them. I will focus in particular on the role of structure in mereology and propose a rather simple account of what structure is from the viewpoint of mereology. As we are going to see, many philosophical controversies in mereology concern the issue of whether mereology should account for structure or not, and which role (if any) structure plays in mereology. I will also present some examples of philosophical controversies about mereological principles, and of the reasons which might be brought for choosing one side or the other in these controversies.

An additional purpose of the paper is to suggest that structure is a broad topic of common concern between architecture and philosophical mereology. In their discussions about structure, mereologists do often resort to examples involving buildings and villages. These examples – I am going to use some of them in what follows – are extremely simple, to the point of naïveté. The frequent usage of these examples might depend on the rough intuition that there are indeed some connections between mereology and architecture, and the concept of structure might be the link between them.

What Is Mereology About?

Let us begin by asking what is mereology. Mereology is the theory of two (mutually related) relations: parthood and composition. Parthood is a one-one relation between a part and a whole. These are some instances of parthood: 

my left hand is part of my body; 

Portugal is part of Europe; 

an atom of oxygen is part of a molecule of water; 

a handle is part of a door; 

the word ‘salad’ is part of the sentence ‘I eat a salad’.

The other relation which, together with parthood, is the subject matter of mereology is composition, a many-one relation. Composition indeed connects many entities (the components) to a single entity (the composed entity). Consider a rather simplistic house with a base, four outer walls, a roof and nothing else. The base, the four walls and the roof compose the house. Another example is the following: the Netherlands, Belgium and Luxembourg compose Benelux.

Composition is definable in terms of parthood. The composed entity is expected to include all the components as parts and not to include anything extraneous to the components. Also the latter feature of the composed entity can be expressed in terms of parthood, namely by requiring that every part of the composed entity has at least a part in common with at least one of the components. 
In order to express the resulting definition of composition in terms of parthood we can first define the relation of overlap, which holds between two entities if and only if they have at least a part in common (P is the relation of parthood; ⚬ is the defined relation of overlap):

Overlap: x ० y ≡def ∃z (z P x ⋀ z P y)  

Now, composition can be defined in terms of parthood and overlap (which has in turn been defined in terms of parthood above) as follows (C is the relation of composition; xx is a plural variable for the components; ≺ is the relation of being one of):

Composition: xx C y ≡def ∀z (z ≺ xx → z P y) ⋀ ∀z (z P y → ∃w (w ≺ xx ⋀  z ० w))

According to this definition, some entities xx compose one entity y if and only if every entity z that is one of xx is also part of y and every entity z that is part of y is such that there is an entity w that is one of xx and overlaps z.

What do mereologists say about parthood and composition? They attribute some features to these relations. The attributed features are generally expected to be formal or topic-neutral, in the sense that the features are not expected to depend on which kinds of entities are part of one another or compose one another. For example, the features of parthood and composition are expected by mereologists to be independent of whether we are considering the parts of a human body, the parts of a chemical molecule, or the parts of a town. Mereology is also formal in a more general sense, inasmuch as mereology never attempts to identify the parts of something or to establish what composes what: it is not the expected duty of mereology to establish what are the parts of a car, or of a building, or what composes a sentence. 

Mereological principles consist in attributions of some formal features to parthood and composition. Let us consider some examples of mereological principles and of formal features which these principles attribute to parthood and composition. In considering these examples, it is important to keep in mind that every mereological principle (any attribution of formal features to parthood and composition) is controversial, including the following examples. It can also be controversial whether the principles at stake are really formal: given a candidate principle, it might be objected that it holds when parthood is instantiated by, say, buildings, while it fails when parthood is instantiated by animal organisms. 

A mereological principle about parthood defended by many philosophers is for example that parthood is a transitive relation (transitivity is the formal feature which this principle attributes to parthood): if a is part of b and b is part of c, then a is part of c. Here are three more or less controversial instances of transitivity (involving various kinds of entities, in coherence with the expected topic-neutrality of mereological principles): 

if a handle is part of a door and the door is part of a building, then the handle is part of the building;

if my left hand is part of my left arm and my left arm is part of my body, then my left hand is part of my body;

if an MP is part of the Italian Parliament and the Italian Parliament is part of the Inter-Parliamentary Association, then the MP is part of the Inter-Parliamentary Association. 

Principles about parthood also concern the problem of whether the chains of parthood terminate or not. Do the chains of parthood terminate downwards? Does everything have a part that is different from itself no matter how deep you go down? Or is there a bottom layer of mereological simples (i.e. entities without further parts)? In the other direction, do the chains of parthood terminate upwards? Is everything part of something different from itself? Or is there a top layer, the mereological universe (i.e. an entity such that everything is part of it, and it is part of nothing different from itself)? Mereological principles can dictate an answer to these questions. 

These principles can be applied to matters of potential architectural or urbanistic concern. As regards downward termination, a problem of potential architectural concern is whether there is a bottom layer of parts of a building (say: the layer of bricks, or the layer of the smallest pieces which are visible to the human eye). As regards upward termination, a problem of potential urbanistic concern is whether there is a top layer of entities, over which entities stop being interesting for urbanists and are at best interesting for other kinds of scholars, such as geographists.

Other principles concern composition (the other relation, which – together with parthood – is the subject matter of mereology). The principles about composition mainly provide existence conditions and identity conditions for composed entities. Existence and identity are in general two pivotal concepts in metaphysics, i.e. in the wider branch of philosophy to which mereology belongs. As far as composition is concerned, mereology asks whether, given some entities, there exists something which they compose (in answering this question, mereologists provide existence conditions for composed entities), and whether there may exist two or more entities composed by the same entities (in answering this latter question, mereologists provide identity conditions for composed entities). 

Thus, given some components, how many things do they compose? Consider Barack Obama’s nose, my left shoe and the Great Pyramid of Giza. Do they compose anything? Is there a spatially scattered object (a bit in Washington, a bit here, a bit in Egypt) they compose? 

Consider instead a building entirely made of bricks. Those bricks compose that building. Do the bricks compose only the building? Or do they compose also a different, less structured entity, which we might dub ‘heap of bricks’? Suppose that the building collapses: after the collapse – one might say – the building stops existing, while the heap of bricks continues existing. How can this happen, if they are identical, i.e. if the bricks compose only one entity? A single entity cannot both continue existing and stop existing.

The following are two examples of two rather popular (albeit controversial) mereological principles about composition (their usual label is indicated in the parenthesis):

given some entities – no matter how sparse and heterogeneous they are – there is at least an entity composed by them (Unrestricted Composition); 

given some entities, there is at most an entity composed by them (Uniqueness of Composition). 

Unrestricted Composition provides existence conditions for composed entities, while Uniqueness of Composition provides identity conditions for composed entities.

The Role of Structure in Mereology

In the above example of the brick building and of the heap of bricks, we have seen how the temptation arises to distinguish wholes according to their being structured or non-structured, or according to their being structured in different ways. In order to appreciate the role of structure in mereology, it is very important not to misidentify the subject matter of the philosophical controversies about this kind of example. 

Indeed, no mereologist doubts that, in order to compose a building, the bricks have to be in some mutual relations and that, more in general, not any heap of bricks is a building. There is no interesting philosophical controversy on the fact that the parts of many composed entities are arranged or structured in a certain way. 

The problem mereology is concerned with is different: does structure have any impact on the existence and identity of composed entities? Do some things need to be structured in a certain way (e.g. in a building-like way, or in a car-like way, or in a person-like way, or in a mountain-like way) in order to compose something? There is obviously a difference between the parts of a car on the one hand, and Barack Obama’s nose, my left shoe and the Great Pyramid of Giza on the other. The difference is that the parts of a car are in certain mutual relations and have certain designated functional roles. The relations among the parts of a car and their functional roles are constrained by the nature of cars in general, and by the project of that specific car model. The mutual relations among parts and the roles of the parts are roughly what structure consists in. 

To repeat: nobody doubts that the parts of a car have a kind of structure which, by contrast, disparate, sparse entities lack. Mereology is not about this. The mereological problem at stake is whether, on the basis of this difference between the parts of a car on the one hand, and Barack Obama’s nose, my left shoe and the Great Pyramid of Giza on the other, we should conclude that only the parts of a car compose something, while Barack Obama’s nose, my left shoe and the Great Pyramid of Giza do not compose anything. If this were the case, then, in contrast with the above principle of Unrestricted Composition, it would not be true that, given some entities – no matter how disparate and sparse they are – there exists something they compose: there would be nothing which Barack Obama’s nose, my left shoe and the Great Pyramid of Giza compose. 

Unrestricted Composition is a mereological principle according to which structures have no bearing on the existence conditions for composed entities. According to Unrestricted Composition, composed entities exist irrespective of whether and how their components are structured. 

Another mereological problem concerning structure is: does structure have any bearing on the identity conditions of composed entities? According to Uniqueness of Composition, given some entities there is at most one entity composed by them. Thus, there cannot be two different entities composed by the same entities. This entails that two composed entities cannot have exactly the same parts. If the composed entities are different, then they have a different part, and this different part is their difference maker. The fact that these parts are in different mutual relations and have different roles is not an admissible difference maker for composed entities. If Uniqueness of Composition is true, then the identity conditions for composed entities countenance only their parts, and not their structure. Thus, both Unrestricted Composition (for what concerns the existence conditions for composed entities) and Uniqueness of Composition (for what concerns the identity conditions for composed entities) exhibit a kind of deliberate blindness to structure.

Principles of Structure Obliteration

Before considering how it is possible to argue in favour or against this blindness to structure, it is useful to be a bit more precise on how structure is construed in this context. A theory of parthood and composition can countenance or obliterate various aspects of structure. This depends on whether, in a certain theory of parthood, certain principles of structure obliteration hold or not. We will consider four principles of structure obliteration.[1] These principles are interesting because they are of help in distinguishing various aspects of structure. These aspects of structure are obliterated in the identity conditions for composed entities, if the respective obliteration principle holds. They are by contrast countenanced in the identity conditions for composed entities, if the respective principle fails. 

The first principle is Absorption and claims that the repetition of parts is not a difference maker for composed entities. If Absorption is true, then the repetition of parts has no impact on the identity conditions for composed entities. Absorption can be formalised as follows (Σ is an operation of composition, whose inputs are the components and whose output is the composed entity; the formula expresses the fact that the multiple occurrences of the inputs – expressed by the multiple occurrences of the variables x and y in the left part of the formula – make no difference for the identity conditions of the output): 

Absorption: ∑ (…, x, x, …, y, y, …) = ∑ (…, x, …, y, …)

The second and the third principles are Collapse and Levelling and jointly claim that the stratification and the groupings of parts at different levels are not difference makers for composed entities (i.e. they have no impact on the identity conditions for composed entities). 

Collapse: ∑ (x) = x

Levelling: ∑ (…, ∑(x, y, z, …), …, ∑ (u, v, w, …), …) = ∑ (…, x, y, z, …, …, u, v, w, …, …)

The fourth principle is Permutation and claims that the order of the parts is not a difference maker for composed entities (i.e. it has no impact on the identity conditions for composed entities).

Permutation: ∑ (…, x, …, y, …, z,…) = ∑ (…, y, …, z, …, x, …)

This approach manages to differentiate various theories of parthood, according to their degree of blindness with respect to structure. What is usually called (for historical reasons) Classical Mereology abides by all the above four principles of structure obliteration and is, as a result, deliberately blind with respect to the repetition, to the stratification, to the groupings at different levels and to the order of the components in a composed entity. Only the parts matter for the identity conditions of composed entities, according to Classical Mereology. By contrast, the ways in which the parts are arranged/structured (e.g. repeated, stratified, grouped or ordered) do not matter. 

It is noteworthy that the four principles of structure obliteration are mutually independent. If you adopt a Non-Classical Mereology, you are not thereby forced to reject all the four principles as a single package. You can reject one or more of them, while keeping the others. In so doing, you sometimes end up adopting a theory which is no less well-established than Classical Mereology. For example, suppose that you think that the stratification and groupings at various levels of parts matter for the identity conditions of composed entities, while their order and repetition do not matter. What you obtain is Set Theory, a well-established theory, with a pivotal role in the foundations of mathematics.

Controversies in Mereology (and How to Argue About Them)

How should we argue about the formal features of parthood and composition? What reasons can be brought in favour of or against the mereological principles which attribute formal features to parthood and composition? And what reasons can – in particular – be brought in favour of or against the principles we have introduced above, such as Transitivity of Parthood, Unrestricted Composition, Uniqueness of Composition and the four principles of structure obliteration? 

Mereologists mainly proceed either by analysing and assessing alleged counterexamples to the mereological principles, or by analysing and assessing a priori arguments in support of or against them. As far as counterexamples are concerned, let us focus on Uniqueness of Composition and on its radical blindness to structure (i.e. – as we have seen in § 3 – blindness to repetition, stratification, groupings at different levels and order of components in a composed entity). One might be tempted to dismiss Uniqueness of Composition rather quickly, on the basis of the fact that some prima facie unavoidable counterexamples might seem fatal to it. 

Consider the components of the sentence ‘Gina loves Mario’: the words ‘Gina’, ‘loves’ and ‘Mario’. The same components can also form the sentence ‘Mario loves Gina’. ‘Gina loves Mario’ and ‘Mario loves Gina’ might seem two composed entities with the same components, in contrast with Uniqueness of Composition. The order of words (an aspect of structure, which belongs to the subject matter of syntax in linguistics) in sentences seems to matter for the identity conditions of sentences, in contrast with Uniqueness of Composition and with Permutation. 

Consider also a very small village, composed by a square, two streets and four buildings. It seems prima facie plain that Uniqueness of Composition fails for those components: the disposition of the streets with respect to the square, and the location of the buildings with respect to those of the square and of the streets (in general: the way in which the components of the village are arranged) would seem to matter for the identity of the village. 

However, the evaluation of these alleged counterexamples is not as easy as it seems, and Uniqueness of Composition should not be dismissed so quickly. Why? Because whether two composed entities (two sentences, two small villages) can be different while having the same parts and whether they can – as a consequence – be different only in virtue of their structure depends on a controversial identification of the entities at stake. 

In the case of the sentence, it depends on whether the entities at stake are linguistic tokens or types. Consider only single concrete tokens or inscriptions of ‘Mario’, ‘loves’ and ‘Gina’: sequences of sounds, stains of ink or groups of pixels on a screen. These concrete tokens are always in a single, specific order. Some of these inscriptions are ordered in a way such that ‘Mario’ is the first inscription (counting from the left) and ’Gina’ is the last inscription (this is the case of the word inscriptions in ’Mario loves Gina’). Others of these inscriptions are ordered in a way such that ’Gina’ is the first inscription (counting from the left) and ’Mario’ is the last inscription (this is the case of the word inscriptions in ’Gina loves Mario’). It never happens that the same inscriptions are arranged in two ways and thereby compose two different wholes. The initial impression that it is clear that two sentences can be different simply due to the arrangement of their parts (even if they have exactly the same parts) depends on seeing words not as tokens but as abstract word types, which occur in many different sentence types. 

Consider also the case of the small village. Given a specific small village, at a specific time, the square, the two streets and the four buildings are arranged in a single way (they have a single structure). There are not two small villages composed by that square, those streets and those buildings at that time. 

These considerations about the sentence and the small village can, as a matter of fact, be generalised. Whenever we are tempted to dismiss those principles of Classical Mereology which express its deliberate blindness to structure, it turns out that the temptation depends on a controversial characterisation of the involved entities.[2]

Please note that the philosophers objecting to Uniqueness of Composition might refine their counterexamples, and the defenders of Uniqueness of Composition might refine their analysis in order to deal with these counterexamples: the purpose of the above analysis is not to resolve the philosophical disputes about the role of structure in mereology in favour of blindness to structure, but to exemplify the way in which philosophers argue one with another about mereology and structure. The exemplifications are also meant to suggest that these controversies are unlikely to be easily solvable by adducing counterexamples: the analysis of these counterexamples is often arduous and depends on controversial assumptions. 

Finally, I would like to discuss an example of the second main way of arguing about mereological principles, the one which involves general, a priori arguments in support of or against mereological principles. Let us focus in this case on Unrestricted Composition. Suppose that you deny Unrestricted Composition. This denial will be based on the intuition that there is a patent difference between – say – the parts of a car on the one hand, and Barack Obama’s nose, my left shoe and the Great Pyramid of Giza on the other. What does this difference consist in? In order to obtain an alternative to Unrestricted Composition, this difference should correspond to a general condition which a plurality of entities should satisfy in order to have a fusion. 

We might try to extract this general condition from the examples, e.g. by observing that the parts of a car are spatially close one to another, while Barack Obama’s nose, my left shoe and the Great Pyramid of Giza are not; or by observing that there are causal links among the parts of a car (e.g. a movement in the steering causes a movement in its anterior wheels), while Barack Obama’s nose, my left shoe and the Great Pyramid of Giza are in no direct causal connection. On this basis, one might propose the following criteria for the restriction of composition: only mutually close entities compose something; only entities which move together (or act together) compose something. However, these criteria are unavoidably vague. There is no such thing as being definitely close in space or as being definitely causally connected. Every two parts of the universe are at some distance and have some kind of more or less remote causal connection. 

How is it possible to fix a threshold, i.e. a minimal degree of proximity or of causal connectedness? The threshold should be such that: entities above that threshold compose something; entities below that threshold do not compose anything. For example, we should determine once and for all at which maximum distance some buildings should be in order to contribute to compose a certain town, instead of belonging to two different towns. Any such threshold would be arbitrary, and would risk making arbitrary our existence claims about composed entities (such as towns) as well. 

A famous argument in support of Unrestricted Composition is based on the thesis that existence claims cannot be either vague or arbitrary. This means that no compelling motivation for restricting composition can be satisfied, and that, as a consequence, composition cannot be restricted. Thus, composition would be unrestricted. 

The general idea behind this famous argument for Unrestricted Composition (of which I have presented a simplified version)[3] is that existence conditions for composed entities should not be constrained by structural considerations about the mutual unity of parts. Why? Because it is arbitrary to delimit the domain of what is unitary. Every plurality of entity can be seen as unitary (or as non-unitary) according to certain criteria and/or from a certain standpoint. This is a general motivation why classical mereology is deliberately blind to structure: because the attribution of roles to structure risks introducing arbitrary and hardly justifiable thresholds. Thus, also, when mereologists proceed by analysing and assessing a priori arguments – as much as when they proceed by analysing and assessing counterexamples, as we have seen above – the problem whether structure has any role in mereology is pivotal, and has no easy solution.


[1] These principles have been originally presented in K. Fine, "Towards a Theory of Part," The Journal of Philosophy, 107, 11 (2010): 559-589.

[2] 2 See G. Lando, Mereology: A Philosophical Introduction (London: Bloomsbury, 2017), chapter 8, for other applications of this defense strategy for classical mereology.

[3] The argument had been originally presented in  D. Lewis, Parts of Classes (Oxford: Blackwell, 1991) and has been later refined in T. Sider, Four-Dimensionalism: An Ontology of Persistence and Time (Oxford: Oxford University Press, 2001). See D. Korman, D. The Argument from Vagueness” Philosophy Compass, 5, 10 (2010), 891–901 for an overview of the literature on this argument.

Suggest a Tag for this Article
Application of the Hyperumwelt concept in an urban proposal, Blockerties, 2018. Image: Junyi Bai, Anna Galika, Qiuru Pu, RC17, MArch Urban Design, The Bartlett School of Architecture, UCL, 2018, photograph by Rasa Navasaityte.
Synthesising Hyperumwelten
Architecture, Building, City Architecture, Computational Design, Hyperobjects, Mereologies, Mereology
Anna Galika
University College London
Add to Issue
Read Article: 1314 Words

Object-oriented programming in blockchain has been a catalyst for philosophical research on the way blocks and their nesting are perceived. While attempting a deeper investigation on the composition of blocks, as well as the environment that they are able to create, concepts like Jakob von Uexkull’s “Umwelt”[1] and Timothy Morton’s “Hyperobject”[2] can be synthesised into a new term; the “Hyperumwelt”. The Hyperumwelt is an object that is capable of creating its own environment. By upscaling this definition of the Hyperumwelt, this essay describes objects with unique and strong compositional characteristics that act as closed black boxes and are able to create large scale effects through their distribution. Hyperobjects are able to create their own Umwelt, however when they are nested and chained in big aggregations, the result is a new and unexpected environment: the Hyperumwelt. 

In his book Umwelt und die Innenwelt der Tiere (1921) Uexkull introduced the notion of subjective environments. With the term “Umwelt” Uexkull defined a new perspective for the contextualisation of experiences, where each individual organism perceives surrounding elements with their senses and reinterprets them into its own “Umwelt”, producing different results.[3] An Umwelt requires two components: an individual and its abstracted perception of its surroundings. Based on this process and parameters, notions of parthood and wholeness in spatial environments, and the relations that they produce with interacting elements, become relevant.

Space as a Social Construction

For Bill Hillier and Julienne Hanson these two parameters related to society and space, writing that “society can only have lawful relations to space if society already possesses its own intrinsic spatial dimension; and likewise space can only be lawfully related to society if it can carry those social dimensions in its very form.”[4] What Hillier and Hanson argue is that the relation between the formation of society and the space is created by the interaction between differing social environments. Hillier and Hanson essentially make use of a mereological definition of the environment that states that parts are independent of their whole, the way that society is independent from its space, but at the same time societies contain definitions of space. Space is therefore a deeply social construction.

As Hillier and Hanson outline, our understandings of space are revealed in the relations between “social structure” and “spatial structure”, or how society and space are shaped under the influence of each other. Space is a field of communication. Within a network of continuously exchanged information, space can be altered as it interacts with the people in it.[5] However, this approach can only produce limited results as it creates environments shaped by only two parameters, humans and space. At this point is where Hillier and Hanson’s theory fails, as this way of understanding the environment relies only on additive information produced by interactions. If we were to expand this theory into the kind of autonomous learning mechanism that is mandatory for processing today’s computational complexity, we would end up with a slow, repetitive operation between these two components. 

Hyperobjects to Hyperumwelt

Another perspective that is elusive from Hillier and Hanson’s understanding of the environment is how social behaviour is shaped by spatial parameters. Timothy Morton’s object-oriented ontological theory contradicts this anthropocentric understanding of the world. In The Ecological Thought (2010) Morton presents the idea that not only do we produce the environment but we are also a product of it. This means that the creation of things is not solely a human act non-human objects cannot partake in, but rather an inherent feature of any existing object.[6] For Morton, complexity is not only a component of society and space, but extends complexity to an environment that has objects as its centre and thus cannot be completely understood. He calls these entities ‘Hyperobjects”.[7]

While Morton uses the term Hyperobject to describe objects, either tangible or intangible, that are “massively distributed in time and space as to transcend spatiotemporal specificity”.[8] The term can be reinterpreted to describe an environment, rather than an object, which is neither understandable nor manageable. This environment – a Hyperumwelt – is the environment constructed by Hyperobjects. A Hyperumwelt is beyond comprehension due to its complexity.

Figure 1 – Qualities of the Hyperumwelt forming at the urban scale, Blockerties, 2018. Image: Junyi Bai, Anna Galika, Qiuru Pu, RC17, MArch Urban Design, The Bartlett School of Architecture, UCL, 2018.

The term Hyperobject is insufficient as it retains its own wholeness. This means that all components inside a  Hyperobject cannot be seen (as it acts like a black box of information) but can only be estimated. Morton described the Hyperobject as a whole without edges. This stems from Morton’s point of perception, as he puts himself inside of the object.[9] This position makes him unable to see its wholeness and thus it leaves him adrift of its impact, unable to grasp control of it. Here, also, the discussion opens about authorship inside the environments and what Morton suggests is that Hyperobjects have their own authority and there is nothing that can alter them or specify their impact on the environment.[10]

Figure 2 – Elements creating distributed patterns of information, creating their own environment, Blockerties, 2018. Image: Junyi Bai, Anna Galika, Qiuru Pu, RC17, MArch Urban Design, The Bartlett School of Architecture, UCL, 2018.

A Tree in a Forest

Yet there is also no need for the Hyperobjects to be clearly understandable. In terms of the Hyperumwelt, Hyperobjects can remain vast and uncomprehended. What is now needed are the implications of distributing nested Hyperobjects, seen as black boxes, inside an environment. An Umwelt is an environment constantly altered by the perceived information. This makes the Hyperumwelt a whole with porous edges that allows the distribution, and the addition or subtraction, of information. Another difference is the external position that the Hyperumwelt is perceived from, meaning that there is no need for it to be part of the environment. Since what is important is the distribution of the objects within the Hyperumwelt, a distant point of view is needed in order to detect the patterning of the distributed objects. While it will remain difficult to decipher and discretise the components, the patterns that are created can be seen. 

Figure 03 – Zooming in on patterns to recognise familiar qualities that provide a better understanding of the composed whole, Blockerties, 2018. Image: Junyi Bai, Anna Galika, Qiuru Pu, RC17, MArch Urban Design, The Bartlett School of Architecture, UCL, 2018, photograph by Rasa Navasaityte.

While the Hyperobject is a closed whole of parts that cannot be altered, a Hyperumwelt is an open whole of wholes that uses objects as its parts. So, while the Hyperobject gives us no authority over its consequences, the Hyperumwelt bypasses this in order for its wholeness to be controlled. Yet what is important for the Hyperumwelt is not the impact of one object, but the impact of multiple objects within the environment. This synthesis and merging of objects and their relations produces a new reality which may or may not be close to the reality of the single objects. A Hyperobject is looking at a black box – say, a tree – and knowing there is a pattern – such as a forest – and a Hyperumwelt is looking at the tree and knowing the impact that it has on the forest and the impact that the forest creates in the environment. 

Figure 4 – Application of the Hyperumwelt concept in an urban proposal, Blockerties, 2018. Image: Junyi Bai, Anna Galika, Qiuru Pu, RC17, MArch Urban Design, The Bartlett School of Architecture, UCL, 2018, photograph by Rasa Navasaityte.

[1] J. von Uexküll, Umwelt und Innenwelt der Tiere (Berlin: J. Springer, 1909), 13-200.

[2] T. Morton, Hyperobjects: Philosophy and Ecology After the End of the World (Minneapolis, Minnesota: University of Minnesota Press, 2013).

[3] J. von Uexküll, Umwelt und Innenwelt der Tiere (Berlin: J. Springer, 1909), 13-200.

[4] B. Hillier and J. Hanson, The Social Logic of Space (London: Cambridge University Press, 1984), 26.

[5] Ibid.

[6] T. Morton, The Ecological Thought (Cambridge, Massachusetts: Harvard University Press, 2010).

[7] Ibid, 110.

[8] T. Morton, Hyperobjects: Philosophy and Ecology After the End of the World (Minneapolos, Minnesota: University of Minnesota Press, 2013).

[9] T. Morton, Being Ecological (Penguin Books Limited, 2018).

[10] Ibid.

Suggest a Tag for this Article
Subscribe To Prospectives To Automatically Receive Curated Issues By Our Advisory Board Twice A Year!