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Mereologies Open Seminar: Round Table Discussion
26/09/2020
Architecture, Composition, Discussions & Conversations, Mereologies, Mereology, Open Seminars
Daniel Koehler, Mario Carpo, Emmanuelle Chiappone-Piriou, Giorgio Lando, Philippe Morel, David Rozas, Jose Sanchez, Jordi Vivaldi
University of Texas at Austin
daniel.koehler@utexas.edu
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Participants: Emmanuelle Chiappone-Piriou, Jose Sanchez, Casey Rehm, Jordi Vivaldi, David Rozas, Giorgio Lando, Daniel Koehler with questions from the audience including Mario Carpo and Philippe Morel.

Daniel Koehler: The talks of the symposium were diverse and rich but also abstract, and intentionally external to architecture. At such a point it can be asked if, how, and what role Mereologies can play in architecture? For the discussion we are joined by additional architects with unique angles on composition and part-thinking in their work. Casey Rehm, a computational designer, Jose Sanchez, who is working actively with digital models of participation and Emmanuelle Chiappone-Piriou, an ecological thinker, experienced in the history of architecture. 

José Sanchez: My first reaction to the presentations is controversial. I think it presents well much of the work that is happening in architecture at the moment showing an interest in Mereology and discrete architecture. However, looking at the issue of parts is fundamentally a project where the idea of composition and the idea of structure is relevant as well. Patterns organised by parts can potentially deal with different forms of value. So, in a way, I find a surprising rejection in some of the ideas. 
Mereology seems to be giving us a framework for many different positions to coexist, and I think that we did an excellent presentation of a much clearer advocacy for a form of relations that we might desire that has to do with pre-production, more like an agnostic framework that allows to give us a vocabulary. Are we interested in having advocacy, in having that intentionality, or are we more interested in what the ontology should be or the framework that we are going to work in?

Daniel: I have learnt something from Giorgio’s book that when we define Mereology, it comes in different notions and ranges. On the one hand, you can see it as a distinct theory, as a specific project that has its own agenda. But also, and more crucial in the first place: you can take Mereology as a larger framework to talk about the relations of parts to wholes – simply compositions. OK, but you might ask: why don’t we use the term composition directly? Because, composition has a specific connotation in architecture and refers to the Ecole des Beaux Arts, classical means of relating objects. It was rejected by the Bauhaus, which promoted a different form of composition with modern means. We could continue this through the history of architecture. In architecture, composition is a specific style but not a history. How could we compare those different modes of architectural composition? Can we think of something parallel to morphology or typology which would allow us to compare a plurality of relations between parts and wholes without defending a certain style? When the formal readings of parts turn into their own project, it might be quite valuable that one can figure a figuration without predefining its value by imposing a structure. That might be Mereology as a project. But first of all, the question is how can we intentionally speak about parts? That would be Mereology as a methodology.

Giorgio Lando: I agree with Daniel that it is very important to distinguish various ways in which the word “Mereology” can be legitimately meant. In particular, the word “Mereology” stands in some cases for a specific theory of parthood and composition, and this theory may be such that structure has a role in it, or such that structure has no role in it. A historically important kind of mereological theory, Classical Mereology, is of the latter kind: it is deliberately blind to structure in providing existence and identity conditions for complex entities. In other cases, however, the word “Mereology” stands for an entire field of research, within which competing theories disagree about the role which structure should – or should not – play. If Mereology is seen as a field of research, then it is misleading to say that structure plays no role in it. This equivocation may explain some of José’s perplexities. 
However, some other perplexities are likely to persist even once we disambiguate the word “Mereology”, and we focus on Classical Mereology. Classical Mereology indeed includes some highly counterintuitive principles, and the usual reaction of the layman to these principles is to dismiss them rather quickly. For example, it might seem prima facie incredible that the order of the parts of something does not matter for the identity conditions of complex entities. However, this quick dismissal is usually determined by an equivocation: what is actually incredible is that the order of the parts of a building, or of a village, or of a car does not matter for its nature, for what that building, that village or that car is. However, this is not what Classical Mereology claims. What Classical Mereology claims is weaker and more reasonable: it says that the order of the parts does not matter for the identity conditions of complex entities, such as buildings, villages and cars. 
According to Classical Mereology, it never happens that there are two distinct entities which only differ because of their structure. Classical Mereology is not committed to the frankly incredible claim that structure has no impact on the nature of complex entities, but only to the more reasonable claim that complex entities are never distinct only in virtue of their structure. 
Moreover, this claim of Classical Mereology is restricted to single concrete entities. This might make the confrontation between Classical Mereology and other disciplines, such as architecture, troublesome, inasmuch as these disciplines are more interested in abstract types than in concrete tokens, more interested in repeatable entities than in their single, concrete instantiations. As far as I understand, when architects speak about the parts of a building or of a city, in most cases they are not speaking about a single piece of material and the way in which it is composed, but about a type of building and the fact that there are different types of buildings which result from the combination of the same types of architectural elements, differently combined. 
Once you move from this level of types and abstract entities to the level of concrete entities, the claim of Classical Mereology that structure has no role in the identity conditions of complex entities is much less incredible: consider a single, concrete building (not a type of a building) in a certain moment in time. In that moment, its parts are structured only in one way: the parts of a single, concrete building cannot be structured in two different ways at the same time.
Architects might legitimately retort that architecture is about repeatable types of buildings, about projects which can be applied several times. Given this approach, Classical Mereology is probably not the best tool for modelling repeatable types, and it is indeed desirable to look at different theories, which are not deliberately blind to structure. Mathematics is full of tools which can be employed to this purpose, including set theory and various kinds of algebras. Architects may legitimately wonder why philosophers focus on Classical Mereology instead, which is a serious candidate for the role of sound and exhaustive theory of parthood and composition for single concrete entities, but not for abstract types. The reason is probably a sort of deep-seated philosophical skepticism towards abstract entities, and the idea that fundamental reality consists of concrete entities, while abstract entities are less fundamental, or even a mere construct of the human mind.list or minimalistic inclinations
However, it is not the case that all the philosophers working on Mereology endorse the claims of Classical Mereology. In particular, in the literature of the last ten years, many prominent philosophers (such as Karen Bennett, Aaron Cotnoir and Katherine Hawley) have by contrast argued that Classical Mereology is completely misguided, and that we should also pay attention to structure within the realm of concrete entities. In my book I have defended the claim that, by contrast, Classical Mereology is a perfectly adequate theory of parthood and composition for concrete entities, but many other mereologists disagree with me. More in general, there is virtually no claim about parthood and philosophy about which every philosopher agrees! 

Mario Carpo: Giorgio, you have said that at some point Mereology merges with set theory. What exactly is here the overlay or intersection between Mereology and set theory? In reverse, where is Mereology separating itself from set theory, and where are the core differences?

Emmanuelle Chiappone-Piriou: Is there any way that relates Mereology to category theory?

Giorgio: For what concerns the relation between set theory and Classical Mereology (which, as we have seen, is a specific theory, which is mainly designed to characterise the realm of concrete entities and the way in which they are part one of another), the deepest difference consists in the transitivity of the relation: the relation of parthood in Classical Mereology is transitive, while the relation of elementhood in set theory is not transitive. Thus, if a first entity is part of a second entity and the second entity is part of a third entity, then – according to Classical Mereology – the first entity is part of the third entity. By contrast, it can happen that something is an element of a set, which in turn is an element of a second set, while that something is not an element of the second set. Sets are stratified: you have typically sets of sets of sets. In Classical Mereology, as a consequence of the transitivity of parthood, there are no stratified complex entities. 
While there are many interesting ties between set theory and Mereology, I am unaware of any connection between Mereology and category theory.

Mario: Can you give us maybe an example, like three inclusions in set theory and three inclusions in Mereology?

Giorgio: Consider the set of Italians. I am a member of this set. The set of Italians is also a member of the set of European people. However, I am not a member of this latter set, inasmuch as I am not a European people (I am not a people at all!). We thereby obtain a failure of transitivity of elementhood among sets. Nothing similar is admitted by Classical Mereology: I am part of the fusion of Italians, the fusion of Italians is part of the fusion of Europeans, and I am part of the fusion of Europeans as well.

Mario: So, in set theory, these don’t happen?

Giorgio: It does not happen in the sense that it does not always happen. There are indeed cases in which the same elements appear at different levels of the set-theoretical hierarchy, but this does not happen in general, and is not warranted by any principle of set theory. There are actually many varieties of set Theory, but in no variety of set Theory is elementhood transitive.

Philippe Morel: My feeling is that Mereology is a matter of “technicalities” about a relationship that exists in set theory. If you look at the inclusion as the property you are also looking for in Mereology, I don’t really get what Mereology brings on top of the purely mathematical “canonical” set theory. It gives me the feeling that Mereology is foremost a way (or a “trick”) for philosophers to take control of a theory that escapes them because it is a fully mathematical theory… So, this is why I have a bit of a problem with this notion because again, technically speaking, I still can’t make a clear distinction between the philosophical property and the mathematical property. It is like a layer of metaphysics that is brought on top of the mathematical theory and of course I can’t consider this as a great addition. My second issue is more of a general remark. Why don’t you speak about relational databases like SQL databases? At some point, to my understanding, it is a very practical implementation of what describes Mereology, because it is all about belonging, etc.
Though, I find the mereological approach interesting, especially if it prevents a reintroduction of composition, as I see a danger of bringing back this concept of composition in architectural discourse.

Giorgio: You are right: set-theoretical inclusion (i.e., the relation of being a subset) has precisely the same formal feature of mereological parthood. However, set-theoretical inclusion is not the fundamental relation of set theory: it is definable in terms of set-theoretical elementhood, while set-theoretical elementhood is not definable in terms of set-theoretical inclusion. Thus, the fundamental relation of set theory is elementhood and is not transitive, while the fundamental relation of Classical Mereology is parthood, which is transitive. 
There have been several attempts (for example in Parts of Classes, a book by David Lewis) to exploit the formal analogy between mereological parthood and set-theoretical inclusion in order to reduce set theory to Classical Mereology. The biggest obstacle for this project are set-theoretical singletons, i.e. sets with a single element. The relation between these single elements and their singletons is not easily reducible to Mereology: it is a kind of brute stratification (a form of structure), which has no place in Classical Mereology.
I agree with Philippe’s remark that Classical Mereology is nowadays a mathematically uninteresting theory, in spite of the fact that it has been originally elaborated by great mathematicians such as Stanisław Leśniewski and Alfred Tarski: it is simply a complete algebra without a zero object. The reason why philosophers discuss Classical Mereology does not depend on its alleged mathematical originality: some philosophers (including me) think that this very simple and unoriginal mathematical theory is the sound and complete theory of parthood and composition, at least in the realm of concrete entities. Thus, the reason to be interested in Classical Mereology is not its mathematical originality, but its plausible correspondence with the way in which parthood and composition really work.
As far as datasets are concerned, I think that it is prima facie preferable to construe them as sets rather than as mereological wholes. Indeed, the distinction between inclusion and elementhood is pivotal for datasets. This distinction characterises set theory, while there is no analogous distinction in Classical Mereology.

Daniel: I would like to extend on Giorgio’s point that Mereology offers mathematically an algebra without a zero object. Mereology starts with individuals without defining a set in the first place. In Mereology, you can’t have an empty set, a null set, a zero object. You can’t have a building without building parts. You need parts for thinking a building. This will become more dominant in future because with higher computing capabilities we are able to compute more and more without the need of abstract models. Take as an example the Internet of Things: a building environment where every building part has sensors and is connected. That means that very literally building parts can talk with each other. Such a building environment also participates, and will offer its own economy. Here, value begins with a building part as an active participant in the market. Already in daily BIM practice it is impossible to think of a building without its parts. So, we should also stop thinking of buildings as predefined sets.
To my understanding, a database is constructed on a very specific ontological worldview. Today’s databases take Composition-as-Identity. This principle says that everything is included in the distribution of data points. Nothing above the distribution of atoms exists, not any compound meaning. Whereas, compounds are fundamental to architecture. Just think of a typology; you can’t reduce a façade to windows. What does a courtyard actually exist of? This of course does not relate to math but to philosophy. It is controversial, otherwise it would not be philosophical. Every building is controversy, or call it multiplicitous, because architecture is pre-logical in a sense. We can’t reduce architecture to math. It is also the point where the discussions on beauty depart in architecture. With ease you can describe a building in the first instance through the distribution of its cells. You can describe a housing project just through the part-relation of a shared wall between two flats only. But how do you describe the mountain which Moshe Safdie designed by stitching together the shared walls of flats in such a way that their roofs turn into terraces? Architecture starts where it exceeds simplicity. Yes, we can design buildings with the use of databases with ease. We are able today to compute buildings without structures. But where are their compound meanings? It will be fundamental to find a way to compute what is common, what is collective between the parts. Therefore, I think we should be suspicious of databases or any kind of structural models which were thought without any compound meaning, so to say, without architecture in the first place.

Jose: I’ll re-bring some of the points that Jordi made to the conversation. Jordi, you brought up Graham Harman’s concept of a radical present. I find it kind of controversial that it seems to eradicate a form of speculation, a form of potential, a form of endless abstractness. If we’re moving from the classic Mereology towards a more abstract sense, I think that a lot of architecture production that we discuss especially with discrete projects – that has to do with parts – has to do with potential encounters of entities in that list and is not purely defined by the actual instantiation of the actual encounter of entities. So, we evaluate and design, also thinking that encounters might never happen. So, under the umbrella of that radical present, I wonder what do you see in them?

Jordi Vivaldi Piera: I would say that the term “potential” is misleading. Its meaning generally refers to its capacity to produce other realities, but at the same time it undermines the possibility of novelty because it assumes that an object already contains what it will become. In this sense, I emphasise radical presence in order to understand which object’s “actualities” permit the production of novelty, rather than understanding which are the hypothetical novelties that it contains and therefore at the same time undermines. In this sense, I interpret potentiality as a particular type of actuality.

Casey: I was interested in Daniel’s point; it reminds me of a recent article by Luciana Parisi called “Reprogramming Decisionism”, where she’s talking about machine learning, neural networks and that these technologies in essence assemble. With this, fact is accumulated, which says that something is probably something else. I’m interested in this relative to Mereology and also the statement that a human deals with abstraction but a machine deals with simple facts. How does the mereological project deal with probability? Is that something probably something rather than not? How does the part, certainly something like, you know, the models that you have shown us rely on clear logic? As I nearly understood there is a kind of model that you’re describing, but how does Mereology deal with improbability? I think it is also something that is going to face the design profession in relationship to the kinds of machines which deal with things. 

Giorgio: As far as probability is concerned, I do not envisage any specific, direct problem stemming from the interaction of probability and Mereology. A mereological claim can have a certain degree of probability, and the probability at stake can be either objective/statistical or subjective. In neither case are there specific problems: mereological claims are, from this viewpoint, on a par with other claims. 
While probability is not directly troublesome, there are some potential problems in the vicinity: Classical Mereology does not countenance the hypothesis that an entity is part of another, but only at a certain degree. Consider a cloud in the sky: the water molecules in the centre of the cloud are definitely parts of the cloud, and the molecules far away from the cloud definitely are not parts of the cloud. However, there seems to be a grey zone of molecules, which are neither definitely within the cloud nor definitely out of it. 
These scenarios can be treated in various ways, and the approach depends on the adoption of a certain theory of vagueness. According to the so-called epistemic theory of vagueness (set forth for example by Timothy Williamson), the fact that we are unable to identify the boundaries of a cloud depends on our epistemic limitations (we are unable to identify the boundaries of the cloud, but this does not show that the cloud has in itself no definite boundaries). According to the semantic theory of vagueness (in the version adopted for example by David Lewis), there are actually myriads of clouds and each cloud has precise boundaries; however, our discourses about the cloud are semantically underdetermined, inasmuch as we have not decided which among the myriads of clouds in the sky we are speaking about. Both the epistemic theory of vagueness and the semantic theory of vagueness are perfectly compatible with Classical Mereology, because they locate vagueness in our language or in our epistemic practices and not in reality: in reality, given two entities, either the former definitely is part of the latter, or the former definitely is not part of the latter.  
However, recently also the so-called ontological theory of vagueness (Michael Tye is one of the most ardent advocates of this approach to vagueness) has gained some traction. According to the ontological theory of vagueness, vagueness is in reality, and this happens also in the mereological case of the cloud: the molecules at the periphery of the cloud are neither definitely parts nor definitely non-parts of the cloud. The adoption of the ontological theory of vagueness indeed requires a revision of Classical Mereology. According to Classical Mereology, for example, two complex entities are identical if and only if they have the same proper parts (the proper parts of something are those parts of it which are not identical to it): but this principle is not applicable to entities which have no definite domain of proper parts. According to the ontological theory of vagueness, this is what happens in the case of the clouds and in similar cases. To sum up: probability and various theories of vagueness (such as the epistemic theory and the semantic theory) do not require any departure from Classical Mereology; only the ontological theory of vagueness requires a departure. 

Emmanuelle: It appears we are navigating and combining different sets of discourses that may or may not be consistent with one another, nor with Mereology as it appears here to be merge into a compositional paradigm: we are simultaneously addressing materiality and formal systems, social coherences and principles of governance, all at once.
I believe that, as in the 1950s and 1960s, architecture faces the risk of talking itself into an impasse, by resorting to certain languages and positions that may induce, and reproduce, a reification of social patterns. 
In this context I often think of a remark from Michel Ragon, the French architecture critic who wrote about and promoted experimental architecture in the 1960s. Looking back at those projects, twenty years later, he asked himself how a “life-like” macro-structure could be designed in advance, and if it could be designed at all, considering life is “rightly made of chance and unpredictability”. This remains a valid and important question, which is updated by our resort to instruments that allow us to think of, and manipulate, the world in terms of particles and parts. Quantum physics teaches us that there is irreducible uncertainty in our physical existence, an inherent contingency, and that there is a fundamental limit of precision with which you can actually measure a particle, hence a limit to the precision with which you can grasp the world. How is it that this uncertainty can be taken into account when dealing with matter or with information; and, when dealing with parts, how can we do so without first defining them? How can we account for interactions and relationality? How is it that we can account for change, for performance and transformation, all at once?
This brings me to a second point that stems from this a priori impossibility to capture the image of life without “to some extent captur[ing] life itself” (Ragon). I understand that Mereology makes a claim for exhaustibility and generality. But what if we take this claim into the architectural project? Do we think that we can actually design a system, a structure or a whole whose formal principles allow for it to be exhaustive? Following Gödel, I understand that you either have exhaustibility or consistency, but not both. 

Mario: Can I go back to the branch of theoretical philosophy to cover things? We more or less know why we in the design profession became interested in particles, and the relation between particles, in recent years. It seems he (Daniel) came across the term Mereology. He hijacked it and imported it into the architectural discourse. Like we always do. We take a more refined tool which comes from another discipline, and then we appropriate it and give it another meaning which means nothing to you (Giorgio). This we have been doing for a long time. This part of the story we know. The part of the story that we don’t know, that you can tell us in two lines is, does this happen with Mereology? Can you give us an outline of the history of analysis of Mereology in contemporary philosophical discourse? Because when I was a student nobody mentioned Mereology, and now everyone does? When did that happen? Where does this come from? And from a distance, from a critical point of view, why is it that you right now are talking about Mereology while many years ago nobody talked about it?

Giorgio: The word ‘Mereology’ is rather new and was made relatively popular by Stanisław Leśniewski at the beginning of the 20th century (according to Leśniewski, Mereology was more properly a branch of logic). However, philosophers (and in particular metaphysicians) have always used the notion of part and set forth theories about it. Plato’s theory of parthood has been recently analysed and defended by Verity Harte, while Aristotle’s theory of parthood is considered by several neo-Aristotelian metaphysicians a viable option in the contemporary mereological debate.

Mario: But, in math, there are fractions, proportions, modularity. These are all today discussed as mereological questions.

Giorgio: An important difference between many past theories of parthood (in particular in Ancient and Medieval philosophy) and contemporary Mereology concerns the expected domain of application: Plato, Aristotle, Abelard and Ockham were for example mainly interested in the parthood relation which connects a property with an individual instantiating those properties, or two properties one with another. These instances of parthood were important within metaphysics itself, for example when a theory of ideas or universals was elaborated. By contrast, contemporary Mereology is more focused on the concrete, spatio-temporal parts of concrete entities.
However, no matter what the original domain of application of the parthood relation was, the theories of parthood became progressively more abstract and formal: in some works of Leibniz (17th century), for example, it is possible to find a formally complex and highly abstract theory of parthood, whose principles are expected to hold irrespective of the domain of application. This is also the case of the theory of parthood developed by Bernard Bolzano in the 19th century. Thus, in spite of the fact that the word ‘Mereology’ became popular only in the 20th century, contemporary Mereology has solid roots in the history of philosophy. 
Nonetheless, it is true that – for example – forty years ago Mereology was much less popular than nowadays. This may have depended on the alternating fortunes of metaphysics (the wider branch of philosophy to which Mereology belongs) in analytic philosophy. Forty years ago analytic philosophers, in continuity with logical positivism, often despised metaphysics as an obsolete leftover from the past. This has changed dramatically in the later decades, thanks to the influence of thinkers such as David Lewis and Saul Kripke, and metaphysics is now back at the centre stage of contemporary analytic philosophy. The renewed popularity of Mereology is an aspect of the renewed popularity of metaphysics in general. This also depends on the fact that contemporary metaphysicians often attach great importance to the concepts of existence and identity. Classical Mereology has the ambition to provide existence and identity conditions for every complex entity. This makes Classical Mereology highly interesting for contemporary metaphysicians. 

Philippe: Let’s make a comparison with the discipline of architecture. In architecture, this last trend could be compared to what happened with Christopher Alexander, or before with Mies and then Peter Eisenman. The challenge for me is that I don’t consider Mereology an uninteresting philosophy in architecture, I just see it as a highly modernist theory.
My question is the following. According to you (Giorgio), in the field of philosophy, do you consider Mereology as a modernist philosophical trend or something that has nothing to do with philosophical modernism? Because in architecture, my feeling is that it directly corresponds to a highly modernist attitude, and the fact is that this modernist attitude is highly reductionist. It is defining what is the most elemental aspect of things, so it’s pure reductionism, and it’s still based on some concept of – maybe not order, but at least some attempt at bringing order into things (though sometimes “unpredictable order”).
For me, that is super modernist and my feeling is that we are living in a world built on this reductionist modernity. Right after this reduction – and we already had it in some form a hundred years ago –, let’s say after 1950 we were already going into the opposite direction: an explosion of models… That one is now based on statistical methods, on big data, as related by Mario in his book. So again, I’m not saying Mereology can’t be an important or at least a useful platform for debate, I am just wondering about the inherent nostalgia of going backward in the ordering of reality – in History. Maybe we can – and should – just accept absolute chaos and trillions of trillions of terabytes of data as a fact, without trying to put some order into that. So, my question finally on a purely philosophical level is: do you consider Mereology as modernist, or maybe as a new modern or late modern philosophical theory, or as something which has nothing to do with that?

Giorgio: There is indeed a modernist component in Mereology: the deliberate blindness to structure, which characterises Classical Mereology, is motivated by a form of “taste for desert landscapes”, which in turn might be seen as the outcome of a modernist appetite for order. However, it should also be considered that Classical Mereology includes either as an axiom or as a theorem (according to the way in which Classical Mereology is axiomatised) the principle of Unrestricted Composition, according to which – given some entities, no matter how sparse and gerrymandered they are – they compose something. Due to Unrestricted Composition, Classical Mereology is committed to the existence of all sorts of awkward entities, such as the fusion of my left arm, Barack Obama’s nose and the Great Pyramid of Giza!
On the other hand, a rather “modernist” thesis, which is often associated with Classical Mereology, is the thesis of Composition as Identity. According to the thesis of Composition as Identity, any whole is strictly speaking identical to its parts and is – so to say – no addition to being, with respect to them. This mereological thesis is expected to warrant a form of ontological economy, and can be seen, as a consequence, as the outcome of an appetite for order. 
However, Composition as Identity is not derivable from Classical Mereology, and is a highly problematic thesis in itself. A whole (for example, a chair) and its parts (the four legs, the back and the seat) are mutually discernible, inasmuch as – for example – the chair is one entity, while the four legs, the back and the seat are six entities. If they are discernible (i.e., if they have different properties), then it is not easy to make sense of the claim (entailed by Composition as Identity) that they are identical.

Casey: I think you have covered everything I want to say. Based on this I don’t think there is anything suggestively reductive about composition. I think that it is a ridiculous idea that unrestricted composition suggests that this property could be part of something.
My colleague Daniel is doing the mereological project, but it is certainly nothing reductive. I think it’s more that there is a very explicitness and straightforwardness about the roles and function of the thing, i.e. the function isn’t the exclusive part of the composition, especially according to the kind of lectures we saw today.

Mario: I have a suspicion. I see one main point of this symposium is that in the theory of parts of  today’s computation the parts we are dealing with are new in the history of architecture theory because they don’t need rules of application. These parts are different from Alberti’s or Eisenman’s because for the first time ever in the history of humankind or the history of design we can deal with parts without any rules or orders in them whether it is proportions, fractions, modules, geometrical symmetry, proportional symmetry, etc.
In the history of design, all these tricks and tools were needed to make sense out of parthood. We had to invent structures, like reductionism or data compression, to put some order into the chaos generated by the random accumulation of parts–to make order out of chaos; to manage parts in a “rational”, ie intelligible way: a way that made sense for the limited data-management skills of our own mind.  And now for the first time ever in many practical instances we are getting particles just as they are. We can put them flat on the table and each one of them stands, and that is all that we need. This the nobility of the parts that you’re dealing with. This is the novelty: parts without anthropocentric reduction and human-made intelligibility. 

Casey: Do you say that there are no rules for these parts or is it just that the rules are inherited in the parts and not applied to the total? I’m suspicious of saying that (the former) in dealing with parts. And again, we still have rules because we have generated something that is mereological. There are still rules but the rules are in the parts rather than trying to be imposed on them. And so actually, it is just where the rules are located in the design process. 

Mario: There must be rules of some sort somewhere, but the main difference, and again, I follow my suspicion, we no longer need rules to manage the accumulation of parts beyond the limit of computational (ie machinic) retrieval.  We don’t need to structure them in symmetrical parthood or any other strategy for part retrieval. We always needed some superposition over the structure to reduce the complexity of what was so big that we couldn’t deal with it. Now when dealing with something so big, we can just let the machines deal with it.  The generation process must have some rules somewhere, but my suspicion is these are no longer needed for any practical human purpose. Now we are capable of managing any messy random heap of disconnected parts–because if fact we don’t have to deal with that mess any more: we have machine to do it in our stead.

Emmanuelle: One simple question would be: what kind of parts are we dealing with? Are they not themselves wholes composed of other parts, entering into larger or different wholes? Are we talking solely about human-made parts, which designers can generate, craft and master, or we are considering opening up these wholes to other domains; thus, to what degree and within which limit are they potentially extendable?
You’ll excuse me for coming back to my previous point, regarding the notion of uncertainty and how it can be taken into account, and let’s hypothesise the wholes we consider are governmental ensembles. The researcher in philosophy of law Antoinette Rouvroy identifies how uncertainty and unpredictability are systematically considered as risk. She analyses how the cybernetic and algorithmic order that underlie our contemporary forms of governance attempt to systematically and preemptively tackle risk in order to eradicate it. On the other side, there is a reverse relationship to risk that, against risk management, consists in exploiting it and profiting from it, as you can see in high frequency trading. Risk here appears to be the motor of speculation, it plays with the asymmetric distribution of information within a system.
But if you consider chance, and hence uncertainty and unpredictability, as being not epistemic – as in both aforementioned cases – but objective, and furthermore, if you consider it to be at the source of all life in the biosphere – as Biology Nobel Prize Jacques Monod showed – how can it be taken into account and integrated in the elaboration of hybrid parts and wholes? Embracing this objectivity could allow us to conceptualise a commonality based on an open, decentralised notion of whole that is not subjected to social constructivism.

Giorgio: I owe an answer to Emmanuelle about unpredictability. Unpredictability can be either an epistemic phenomenon (it happens when some human subjects are de facto unable to foresee how things will go, and their inability to do so might be due to their contingent cognitive limitations), or a metaphysical phenomenon (there is metaphysical unpredictability when something is objectively indeterminate, independently of any fact concerning human subjects). If unpredictability is seen as an epistemic phenomenon, then it does not require any modification of Mereology: the fact that some human subjects are unable to determine whether x is part of y has no impact on the circumstance whether objectively x is part of y
The philosophical consequences of quantum indeterminacy are hard to interpret: according to some interpretations, it is indeed a kind of objective, metaphysical indeterminacy. However, as far as I can see, quantum indeterminacy does not concern mereological relations. Thus, it seems to me that neither epistemic nor metaphysical unpredictability have any specific bearing on Mereology.

Daniel: Unpredicted and indeterminant like a good building, it seems to me that Emmanuelle and Giorgio overcame the boundaries of the round table. I would like to use the moment to thank you all for your insights, contributions, and round up the discussion with an open ending.

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