Digital twins are a new paradigm for our time, offering the po ssibility of interconnected virtual representations of the real-world. The concept is very vers atile, and has been adopted by multiple communities of practitice, policymakers, researchers and innovators. A signiﬁcant part of the digi- tal twin paradigm is about interconnecting digital objects , many of which have previously not been combined. As a result, members of the newly forming digital t win community are often talking at cross-purposes, because they have different starting poin ts, assumptions and cultural practices. These differences are often due to the established philosophical world-view adopted within speciﬁc com- munities of practice. Therefore, in this paper we explore th e philosophical context which underpins the concept of digital twins. As part of this effort we offer a set of philosophical principles for digital twins, which are intended to help facilitate their further d evelopment. Speciﬁcally, we argue that the philosophy of digital twins is fundamentally holistic . We further argue that digital twins are recon- structivist , meaning they aim to reconstruct the behaviour of a physical twin by assembling multiple “components”, e.g. models, agents and data sets. Important ly, these digital twin components have the potential to capture emergent behaviours when they are dynamically assembled . Lastly, we discuss the following four questions (i) What is the distinction bet ween a model and a digital twin? (ii) What previously unseen results can we expect from a digital twin? (iii) How can emergent behaviours be predicted? (iv) How can we assess the existence and uniquene ss of digital twin outputs? Keywords: Digital twin, philosophy, modelling, complexity, systems , artiﬁcial intelligence Impact Statement Creating digital twins (or the process of digital twinning) is an concept of growing importance in a wide range of industries and technology sect ors. Digital twins can be used as a method to obtain value from data and as deployment platforms for AI and data-science techniques such as machine learning and statistical analysis. In many applications, d igital twins offer the means to integrate together multiple previously separate components in order to achiev e a speciﬁed objective(s). This type of in- tegration of digital components is based on a fundamentally holistic philosophy. This paper presents a philosophical framework for digital twins that considers h ow such a holistic integration can be achieved, including current questions of interest, and challenges fo r future research. 1 1 Introduction A digital twin is a virtual representation of a physical syst em (called the physical twin ) that enables a two- way coupling between the digital and physical domains, usin g some form of network-based connectivity. The digital twin evolves over time and is constructed from di gitised information such as recorded data and the output of computational models. Digital twins have been promoted as a way to accelerate our ab ility to understand engineering (and other) systems at previously unmatched levels of performan ce. This vision and aspiration was captured in the quote from Eric Tuegel and his coauthors (in the contex t of structural life prediction) in 2011 who stated that: “The digital twin is a reengineering of structural life pred iction and management. Is this science ﬁction? It is certainly an audacious goal that will r equire signiﬁcant scientiﬁc and technical developments. But even if only a portion of this vi sion is realised, the improve- ments in structural life prediction will be substantial” — T uegel et al. (2011). This is certainly a very exciting prospect, however, as engi neers we always need to be cautiously prag- matic and it is worth keeping in mind the observations of many experienced practitioners. For example, to pick just one related insight, even before the idea of digi tal twins was proposed: “Mete A. Sozen, Kettelhut Distinguished Professor of Struc tural Engineering at Purdue University, presented the 2002 Distinguished Lecture in Fe bruary at the EERI Annual Meet- ing in Long Beach, California. His lecture was entitled A Way of Thinking . Sozen was motivated in selecting his topic by the fact that at the prese nt time, ready access to versatile and powerful software enables the engineer to do more and thi nk less, which in his opinion makes it especially important to reﬂect thoughtfully on the role of analysis in design.” — Sozen (2002). Although it couldn’t be known at the time, Sozen’s observati on about software enabling engineers to “do more and think less” is relevant not just from the point of vie w of over-reliance on software, but also because the recent advent of large language models like Chat GPT (see for example Teubner et al. 2023), and other developments in artiﬁcial intelligence (AI), off er the prospect of a non-human AI doing at least some of the thinking for us as so-called "cognitive surrogat es" Leslie (2021). The aspiration for digital twins, particularly from commer cial vendors, seems to imply that the new technology will somehow capture and contain “the best of eve rything”, meaning models, data, AI meth- ods, processes, controls, decision, etc. in some optimal wa y. In addition, it is also often implied that digital twins will somehow overcome the fundamental challe nges and limitations related to modelling that we already have (e.g. limited computational resources , epistemic gaps), enabling beneﬁts such as improved ﬁdelity, trust and insight. But how exactly might t hat happen? When such questions are not satisfactorily answered, the conclusion for some is that th e whole idea is over-hyped, scepticism can become cynicism, and genuine scientiﬁc and technological p rogress can become stalled. We believe that part of the underlying issue is that because t he concept of a digital twin is so versatile and universally applicable it is open to a very wide range of i nterpretations — as evidenced by recent reviews Korenhof et al. (2021). Those interpretations come from a large number of different research and practitioner communities, which themselves have very wide -ranging cultures and practices built upon their speciﬁc world view. Typically these communities are d omain-speciﬁc, and have excellent reasons for their adopted philosophical culture, but are often oper ating in a silo, or at least only interacting with those who share a similar approach to themselves. However, a signiﬁcant part of the digital twin paradigm is ab out interconnecting these previously un- connected domains. For example, building socio-technical digital twins is a major ambition in this ﬁeld 2 — see for example Okita et al. (2019); Wang et al. (2020); Zhan g et al. (2021a); Savage et al. (2022); Yossef Ravid and Aharon-Gutman (2022). As a result, when con versations happen, people are often talking at cross-purposes, because they have different sta rting points, cultural assumptions, biases and motivations. Therefore, in this paper we seek to understand the philosoph ical context which underpins the concept of a digital twin. Firstly, in Section 2 a brief review of the h istorical and philosophical context of digital twins is presented. The role of modelling will be key to this d iscussion, and the distinction between models and digital twins, and the discussion related to this theme will be started in this section. Then in Section 3 we consider the types of complexity that occur in engineering systems, and how this might be represented in a digital twin. In Section 3.5 we brieﬂy con sider the role of human interpretations and bias. Then in Section 4 we introduce a philosophical framewo rk for digital twins. This includes a series of philosophical principles that underpin the concept of di gital twins, or the process of digital twinning . These principles are then used to suggest answers to four key questions relating to digital twins. Finally Conclusions are drawn in Section 5. 2 Philosophical context of digital twins The origins of the twinning concept is usually attributed to the work of NASA during the Apollo pro- gramme, where physical duplicates were used (Rosen et al., 2 015). The term digital twin itself ﬁrst ap- pears in work relating to product lifecycle management (see Grieves 2019 and discussion therein). The idea has received considerable attention since then in a wid e range of areas including product design, manufacturing, civil infrastructure, medicine, asset man agement, health/condition monitoring, energy networks, space structures, and nuclear fusion — to name jus t a few application examples. For those readers that might be interested in the history, developmen t and applications of digital twins there are multiple detailed descriptions of these (and many other) to pic areas in the growing number of review papers on the topic of digital twins including Ríos et al. (20 15); Negri et al. (2017); Kritzinger et al. (2018); Cimino et al. (2019); Enders and Hoßbach (2019); Boj e et al. (2020); Errandonea et al. (2020); Jones et al. (2020); Liu et al. (2020); Melesse et al. (2020); Wagg et al. (2020); Wanasinghe et al. (2020); He and Bai (2021); Huang et al. (2021); Jiang et al. (2021); Lo et al. (2021); Semeraro et al. (2021); Shahat et al. (2021); Korenhof et al. (2021); Niederer et al. (2021); Botín-Sanabria et al. (2022); Purcell and Neubauer (2022); Singh et al. (2022); Somers et al. (2022); Tao et al. ( 2022); Jafari et al. (2023); Liu et al. (2023); Sepasgozar et al. (2023); Thelen et al. (2023); Dale et al. (2 023). Although there has been much discussion on the potential deﬁ nitions relating to digital twins (see for example the review in Semeraro et al. (2021)) one area tha t has not received much attention is the philosophical underpinnings of digital twins1. We introduce this topic by ﬁrst reviewing the philosophy of modelling as applied to a wide range of scientiﬁc and engin eering domains. Models are very important for digital twins because they are one of the key components that make up a digital twin. In addition, many of the techniques previously applied to models, such as veriﬁcation, validation, calibration and prediction, are also functions that are often required of a d igital twin. The relationship between models and digital twins is a commo n source of confusion, and will be dis- cussed in more detail in Section 4.2. For now we note that mode ls and the philosophical concepts relating to models have a very important role for digital twins. There fore we start with a selected introduction to the philosophy of modelling. 1Though see Korenhof et al. (2021) for one notable exception. 3 physical system model interpretationobservations model making output assumptions improvements Figure 1: Schematic diagram showing the typical method of ma king a model of a physical system. The physical system can be a process or a material obj ect 2.1 A selected introduction to the philosophy of modelling In order to try and understand the philosophical context, we ﬁrst consider the method via which a model2 of a physical system is typically made in an engineering cont ext. An example of a model making process is shown schematically in Figure 1. The ﬁrst stage of the meth od in Figure 1 is to make observations from a physical system3. These observations are then used to make a model based on a se t of assump- tions. The subsequent output(s) from the model are then inte rpreted, and in many cases, this leads to improvements being made to the model, and the process is repe ated as often as deemed necessary. There are several important philosophical viewpoints that can be understood in the context of Figure 1 that will be important for our later discussion on digital twins. The ﬁrst is objectivism which can be deﬁned as the belief that there is an objective tr uth represented by the behaviour of the physical system that our model is tryi ng to represent. In this worldview, the modeller and modelling process are separate from the physic al system of interest, and do not have any direct inﬂuence on it. In addition, the “objective truth” is the same for all observers. Objectivism relates closely to the Newtonian scientiﬁc worldview, which will be described shortly. In contrast, the idea of subjectivism is the belief that the process of making observations is not objective and actually any time an observation is made, then an interaction with the physical system takes place. This relates to the idea of relativism4in the sense that the “truth” (or experience) is affected by and/or not the same for all observers. For example, as was f amously shown to be the case in the early 20th century physics — see for example Greiner (1994); Rovel li (2016). Regardless of whether the objective or subjective view is ta ken, real-world physical systems are typically complicated5, and can often be (conceptually) decomposed into “simpler" parts in order to be more effectively studied. The philosophy that supports thi s approach is the idea of reductionism which assumes that the physical system can be reduced to something simpler, and that by studying the reduced version, useful information about the complete system can b e obtained (Heylighen et al., 2007). For the purpose of this discussion we will consider two prima ry forms of reductionism. The ﬁrst is 2The review is not intended to be comprehensive in any way, and readers are referred to Oberkampf and Roy (2010) for a comprehensive overview of modelling in the scientiﬁc and e ngineering domains. Note also that the word ‘model’ in this context is used to mean a representation of the physical syst em on interest. It could be any type of model used in the contex t of engineering practice depending on the context. However, a point we return to later is that models can be made of both processes andmaterial objects . 3This obviously assumes that there is already a physical syst ems in existence, which is often not the case in engineering when we are asked to design something not previously built. S ome discussion on this is given in Wagg et al. (2020), but for now we assume that the physical system is available for obser vation. 4And also perspectivism (Giere, 2019). 5The distinction between complicated and complex systems wi ll be discussed in Section 3. 4 component-based reductionism which involves dividing the physical system into separate p hysical (e.g. geometric or process) components, and if required dividing these components into smaller and/or simpler parts, as required. The second is physics-based reductionism , which is to simplify, approximate or even neglect entirely some part of the physics. Physics-based re ductionism can be applied to the whole system or to sub-components of the whole system after component-ba sed reductionism has been carried out. In Figure 1 the reductions are encoded as a set of assumptions . The reductionist philosophical ap- proach has come to dominate scientiﬁc and engineering pract ices over time, and has been used to great effect. Reductionism has become associated with a Newtonia n world-view, and Newton himself said: “We are to admit no more causes of natural things than such as a re both true and sufﬁcient to explain their appearances. To this purpose the philosoph ers say that Nature does nothing in vain, and more is in vain when less will serve; for Nature is pleased with simplicity and affects not the pomp of superﬂuous causes.” — Isaac Newton, Principia: The Mathematical Principles of N atural Philosophy (Newton, 1686). Here the idea of avoiding “superﬂuous causes” and the idea th at “Nature is pleased with simplicity” has been taken as an argument for reduction to enable simpliﬁcat ion. There is also the interpretation that nature intends or prefers simplicity, which is related to th e idea of parsimony which is discussed later. However, it was not just Newton who contributed to what has be come known as Newtonian (or classical) mechanics. There are (at least) two other key phi losophical components that are important for our current discussion. First, the idea of a rules based mechanistic world view, leading to a set of “laws” that could be relied upon to apply “universally”. A major con tribution came from Descartes who said that: “...reliable rules which are easy to apply, and such that if o ne follows them exactly, one will never take what is false to be true or fruitlessly expend one’s mental efforts, but will gradually and constantly increase one’s knowledge till one arrives at a true understanding of everything within one’s capacity.” — René Descartes: Rules for the Direction of the Mind (see reprint: Descartes, 1985, ﬁrst published 1701). In addition to reduction (i.e. simpliﬁcation) and laws, the re is the idea of determinism which (has come to mean) that the state of something in the future can be d etermined entirely from it’s current state. This idea is generally attributed to Laplace (see rep rint: Laplace, 2012, ﬁrst published 1795) who also made key contributions to the ideas of probability and “ ignorance” (i.e. lack of knowledge), both of which we return to later. Classical mechanics has been bui lt on these principles of a reductionist, mechanistic and deterministic approach, with huge success , and the plethora of models of this type are typically deﬁned with a high degree of mathematical rigour. However, it has also been long recognised that reductionist models, by deﬁnition, cannot capture the entire physical behaviour of the physical system, and th e difference between a model output and an observation is described as the error oruncertainty related to the model — see for example Smith (2013). In particular, in the case when a deterministic mode l cannot capture the observed behaviour of the physical system, the model is often considered to be “missin g” some important part of the physics. The missing knowledge is the model inadequacy of the reduced model, and is often deﬁned as the epistemic uncertainty. In other words, this type of uncertainty repre sents the lack of knowledge (e.g. our ignorance of) of the real-world physical system. In addition to this, observations of physical systems will a lways exhibit time varying ﬂuctuations, and the more precisely one tries to make an observation, the g reater (typically) these ﬂuctuations grow. These ﬂuctuations are often referred to as “noise” or “distu rbances” and are typically considered to be 5 an inherent part of the physics and observation processes6. Collectively they are known as aleatory uncertainty — see for example Hughes and Hase (2010). In contrast to reductionism is holism where the physical system is not reduced, but treated as a who le. In the engineering domain, this philosophy has been develop ed primarily through the ﬁeld of systems engineering7(and the related, overlapping subjects of cybernetics (see e.g. Ashby 1956), systems science (see e.g. Edson et al. 2016), operations research (see e.g. H illier and Lieberman 2001), complexity science (see e.g. Waldrop 1993) and artiﬁcial intelligence (see e.g. Russell and Norvig 2010). Systems engineering uses a hierarchical landscape of systems inclu ding the “closed” (relatively simple) systems that can be modelled using deterministic (Newtonian) mathe matical models such as those for the motions of point masses (e.g. like billiards), which we call classic al (linear or nonlinear) dynamics. There is also the possibility of closed systems-of-systems, when many de terministic systems can interact with each other. Beyond this are “open” complex systems (such as livin g organisms or social systems) where closed, mechanistic models can fail to sufﬁciently represe nt the complexity of the underlying processes. Open systems, are critically dependent of their environmen t and the interactions they have with outside effects, such as other systems. In the case of complex interacting systems, the occurrence o femergent behaviours can be induced by interactions between different parts of the overall syst em. Crucially, the emergent behaviours cannot typically be anticipated just from a knowledge of the parts o f the system. Often such interacting systems contain intricate hierarchies or interdependencies, and e mergence (e.g. self-organisation) can happen within a part, or across the entire system (see e.g. Bedau and Humphreys 2008). Systems engineering recognises that systems exist within an environment , and that systems can interact with each other to create systems-of-systems. An ongoing challenge with the s ystems engineering approach is how to rep- resent the boundary between the system and its environment o r other systems.8For instance, the choice of where to draw boundaries around a system is inherently a fr aming decision which inﬂuences what is included and excluded from analysis. This framing can be inﬂ uenced by various values and cognitive biases, such as the researcher’s theoretical commitments, interests, and goals (e.g. the perceived value of knowledge or insights to be derived). We will say more about t his later in the paper. Emergent behaviour has also been studied using complexity theory9which (typically) uses coupled systems of dynamic mod- els acting as “agents” to create models of emergent behaviou rs (typically in a deterministic sense — see for example Jensen 2022), although a non-deterministic fra mework can also be adopted10. More broadly, the role of humans is important in this discuss ion (more details are given in Sec- tion 3.5), because humans are imperfect, and they make decis ions and assumptions based on their own worldview (or lens). Furthermore, communities and organis ations can adopt and develop their own bi- ases based on a range of factors, and perpetuate these over lo ng periods of time11. Often this results in current views and approaches that have been “inherited” fro m previous generations without being appro- priately examined (a phenomena known as social learning (Hoppitt and Laland, 2013)). For example, 6In control engineering, the a disturbance is considered to b e an input that acts on the underlying dynamic system deﬁning the plant, and noise is the unwanted corruption of the measur ed output signal. 7For a discussion of how systems engineering relates to the di gital twin concept see Madni et al. (2019). Recent discus- sions regarding the principles and hypotheses that underpi n systems engineering can be found in Watson (2019); Watson e t al. (2019). 8This challenge is one area in which societal values enter int o scientiﬁc theorising and engineering design choices.Lon gino (1990) 9An excellent overview of the philosophical relationships b etween classical reductionist science, systems thinking a nd complexity theory is given in Heylighen et al. (2007). The to pic is discussed further in Section 3. 10Note the terminology of “agents” and “environment” used her e is not to be confused with deep reinforcement learning, which also uses this terminology — see for example Graesser a nd Keng (2019). 11The interplay between science and society, and the roles of b oth scientists and laypersons is also relevant here — see for example Kitcher (2011). 6 in science and engineering, the type of model iteration proc ess shown in Figure 1 happens repeatedly, often over many years, or even decades and involves multiple humans during that time. It is perfectly possible for people to be working on a model for which they did not do any model making, and therefore be unaware of the philosophical approach used in developing the original version of the model or the encoded assumptions within the model that are inherited by s uccessive generations of practitioners (e.g. a choice to use one "standardised" measurement scale over an other). In many domains (engineering being one) the separation of pr actitioners from the model making process (and the associated assumptions) is increasingly t he case as modelling becomes more frequently integrated into sophisticated software tools. This leads t o the obvious questions of (i) is the model being computed correctly in the software? (veriﬁcation) and (ii) does the model output correctly represent the behaviour of the observed physical system? (validation)12. These are important questions that naturally can be extended to digital twins, and to which we will return l ater in Section 3.5. 2.2 The role of knowledge in model making It will be argued here that a primary useful purpose of a model is to gain (or enhance, extend, and/or clarify) knowledge. Once additional knowledge is gained, i t can be used (exploited) to create value , for example by supporting decisions. For the purpose of this dis cussion we focus on the process of gaining knowledge rather than exploiting it. We return to the topic o f decision making in Section 5.3. There are a multiple theories of knowledge relating to scien ce that have been developed over many centuries13. One of the most important is the idea of empiricism which is the epistemological idea that knowledge can only be obtained by physical observations (e. g. the sensory experience of the observer). In the scientiﬁc context, during the 19th Century, empirici sm led to what has become known as the scientiﬁc method where physical observations are made and used to test a speci ﬁchypothesis , primarily using statistical models to assess whether the hypothesis c ould be proven or not (see e.g. Lehmann et al. (1986)). An example of a this type of hypothesis-based model making pr ocess is shown schematically in Figure 2. Here the model-making process of Figure 1 is expand ed to show (very simplistically) the role of knowledge in this type of model making. The ﬁrst step is to e stablish a research question. Next (or often as part of the ﬁrst step) a review of existing knowledge that is relevant to the research question is carried out. From there, a testable hypothesis needs to be cr eated, after which an experiment that can actually test the hypothesis needs to be designed and then pe rformed. After the experimental outputs have been reviewed, the process can be improved. All these st eps require expert knowledge of the speciﬁc application and the wider context. Multiple judgem ents are needed if the results are to be of use at the end of the process. The scientiﬁc method is still used extensively, but two sign iﬁcant developments in the 20th Century have had a major inﬂuence14. Firstly, following the development of quantum mechanics, the philosophy of science underwent a major shift in perspective (see for ex ample, the discussion and