4 Perspectival modelling as modelling possibilities

The goal of this chapter and the next four ones is to carve out a positive role for perspectivism. I have dealt already with the charge of metaphysical inconsistency that has been levelled against perspectivism by laying out what I take to be the main argument for it (the Have-Your-Cake-And-Eat-It argument, or HYCAEI). I highlighted its additional and surreptitious premises and offered reasons to resist them. Perspectival realism should not be fazed by HYCAEI. For the culprit for the problem of inconsistent models is not the perspectival nature of the representation offered by models but instead an unduly demanding realist gloss on the representationalist assumption.

In Chapter 2, I hinted at a different way of thinking about the perspectival nature of the representation which I labelled perspectival₂. I stressed how I see these two notions (perspectival₁ and perspectival₂) as complementary. A scientific representation is perspectival in being both situated (from a vantage point or perspectival₁) and also in being directed towards one or more vanishing points (perspectival₂). Let me expand on this idea here. I’d like to think of perspectival models as offering perspectival₂ representations of the relevant target system, which—like the mirror in the Arnolfini Portrait—open up ‘windows on reality’. The realism I see as compatible with perspectivism is downstream from this exercise of perspectival modelling as opening up ‘windows on reality’. In this and the next four chapters (4.a–4.c and chapter 5), I unpack the artistic analogy with the Arnolfini Portrait.

First, though, there is still a question looming large here about what perspectivism may contribute to the long-standing debate about pluralism in science. Is perspectivism just another name for scientific pluralism? What (if anything) is distinctively perspectival about model pluralism? My answer develops in five steps:

Answer: because perspectivism captures a subset of model pluralism where models are best characterized as exploratory.

Answer: perspectival modelling enables a particular kind of inferential reasoning that proves fruitful when one wants to explore what is possible (instead of mapping-onto-what-is-actual).

Answer: of course, science is about finding out what is actual. But you should care about what is possible because, in the absence of a God’s-eye access to reality, knowing what is possible is an important (dare I say, it is the only) guide to find out what is actual. Like Marco Polo on his journeys into uncharted territories, we are not equipped with an ideal scientific atlas of the Realm-That-Is-Actual. We have to find it out for ourselves walking along inferential paths that resemble Jorge Luis Borges’s (1941/2000) ‘garden of forking paths’. Perspectival modelling guides epistemic communities over time across such a garden where at every twist and turn new paths can be explored and old ones left behind.

Answer: perspectival models, as I argue in detail in Chapter 5, guide communities across time along inferential paths by acting as ‘inferential blueprints’. From an epistemic point of view, perspectival-models-qua-inferential-blueprints deliver modal knowledge claims by inviting us to physically conceive particular scenarios. From a semantic point of view, perspectival-models-qua-inferential-blueprints support a particular kind of epistemic conditionals, namely indicative conditionals with a suppositional antecedent.

Answer: perspectival-models-qua-inferential-blueprints help a plurality of situated epistemic communities to navigate the inferential space of what is possible. Along the way, these communities come to reliably identify modally robust phenomena (more on this notion in Chapter 6). Often such an identification proceeds through data-to-phenomena inferences that are entirely perspectival. Each epistemic community may avail itself of experimental and technological resources for harvesting the data and of justificatory principles that are genuinely diverse and belong to different scientific perspectives (qua historically and culturally situated scientific practices as defined in Chapter 1). Thus, perspectival modelling (as I use the term here) is not narrowly confined to scientific models. It refers instead more broadly to the situated modelling practices of particular epistemic communities, including the way they use particular data to make inferences about phenomena of interest. As such, perspectival modelling is a defining feature of what a ‘scientific perspective’ is for. It captures how situated epistemic communities across a number of intersecting scientific perspectives come to know the world as being a certain way. Spoiler alert: the Realm-That-Is-Actual is nothing but the realm of modally robust phenomena displaying lawlike dependencies and inferred via perspectival modelling across a number of scientific perspectives (more on this in Chapters 5 and 6).

These questions will guide my journey into perspectival modelling in what follows. And I will have a lot more to say in Chapter 5 about the answers I have simply sketched here to Q4 and Q5. They will also pave the way to Part II of the book (Chapter 6 onwards), where the realist promise behind the title of my book is waiting to be delivered. But, for now, first things first: (1) Why is perspectivism not just another name for model pluralism?

What good is a plurality of models in any given area of scientific inquiry, anyway? The pluralist stance has long acknowledged that different models might accurately represent some aspects of the target system at the cost of distorting others. Inherent in this stance is a commitment to different models delivering incompatible, or even inconsistent, images for the same target system, a commitment that scientific pluralists by and large are happy to make. That there is pluralism about models is a fact about scientific inquiry. What good it is for remains debatable. Even more debatable is what perspectivism has got to do with it.

Many realists would like to think of model pluralism as a ‘means to an end’: the end is realism about science; the means are as diverse as scientific practices typically are. There are two widespread attitudes to be found about model pluralism (the first especially among scientists, the second mostly among philosophers of science). Neither of them in my view captures what really goes on with perspectival varieties of model pluralism:

Some may think this is a common situation in science. Consider Galileo’s experiments with inclined planes. Through the medieval works of Abu’l-Barakāt, Oresme, and Buridan, among others, free fall was revealed as a kind of accelerated motion, rather than motion towards a natural place as Aristotle had maintained. Galileo went through several attempts at explaining the phenomenon in the Pisan treatise De motu antiquiora ca. 1590 (see Massimi 2010 for the historical details) before he hit on the best model that relates the distance traversed to the square of the time (as he eventually demonstrated it in Two New Sciences in 1638). Some scientific realists may argue that Galileo’s model pluralism was a typical example of ‘means to an end’: try out models until you find the best one (in this case, the one that matches experimental data). It is a default methodological stance that virtually any scientific realist would endorse.

However, this is not an example of a perspectival variety of model pluralism. Perspectivism is best seen as capturing a subset of model pluralism, where models are best characterized as exploratory, enabling a particular kind of inferential reasoning that explores what is possible. Galileo’s studies on free fall were aimed at finding out the actual nature of free fall by matching a number of hypotheses with the observed data. Of course, once the best model has been found, one might as well use it to give how-possibly explanations (Bokulich 2014; Verreault-Julien 2019) of how free fall works, how it might get replicated with bodies made of different materials and with different densities, how errors might be introduced, and so on. But providing how-possibly explanations is—in this example—downstream from finding the best model in the first instance. Common wisdom that actuality is a guide to possibility applies here. The kind of exploratory exercise that matters to perspectival modelling goes in the opposite direction: exploring what is possible to find out what is actual. And exploring what is possible turns out to be a lot more complex and nuanced than just trying as many models as one can think of until one hits on the best one.

But perspectivism is not just another name for there being ‘many points of view’. Nor is it a generic proxy for ‘there are as many models as there are epistemic communities with different research interests’. Perspectivism captures a well-defined subset of a larger family of model pluralism where the searches are exploratory in distinctive ways.

Thus, on my view, one can be a model pluralist but not necessarily a perspectivist. But one cannot be a perspectivist and not be a model pluralist of some sort. The charge of redundancy misplaces perspectivism in the wider landscape of scientific pluralism. There are significant areas of scientific inquiry where pluralism is a defining feature while perspectivism is absent. But using the term ‘perspectivism’ as if it were interchangeable with ‘model pluralism’ does a disservice to both.

Since I see perspectival models as exploratory, let me briefly do some more philosophical landscaping. First, I do not use ‘exploratory’ in the way in which it is sometimes used colloquially to denote something transient (e.g. exploratory talks). My usage bears family resemblances with the more recent literature on ‘exploratory experimentation’ (see Burian 1997; Elliott 2007; Peschard 2012; Steinle 2005/2016; Fisher, Gelfert and Steinle 2021, and related articles in this edited journal special issue, among others) as a way of studying phenomena, and their rules and laws, even in the absence of a fully fledged theoretical framework.

The exploratory nature of scientific models in general has only recently begun to attract attention. Axel Gelfert (2016, pp. 83–97) has presented exploratory models as fulfilling four distinct (not exhaustive) functions:

What I call perspectival models add to this list the specific task of modelling what is possible (rather than mapping-onto-what-is-actual). Conflating the exploratory role of perspectival modelling with its representational role is therefore like staring at the finger while pointing at the Moon. Representation is a means to an end, not the end itself. Despite being complementary, one should not confuse perspectival₁ representation (representation from a vantage point) with perspectival₂ representation (representation towards one or more vanishing points, as in the Arnolfini Portrait). To understand how a plurality of perspectival models can open up a ‘window on reality’, we should concentrate on how they fulfil their exploratory role, rather than on how the representational content might be affected by the vantage point from which the representation takes place.

Let me briefly articulate how the exploratory role of perspectival modelling relates more directly to its ability to model possibilities. I see this process not so much as situating a particular case within an already ‘given’ space of modal facts (the possibilities) but as figuring out what the space of possibilities looks like in the first instance.

Once in a seminar, philosopher of physics Tim Maudlin asked me why I was placing all this emphasis on modelling what is possible: ‘Is not science after what is actual rather than what is possible?’ Fair question. Science is after what is actual. Climate scientists want to find out what the global mean surface temperature is going to be in 50–100 years. Nuclear physicists around the 1930s–1950s were keen to find out what was responsible for observed isotopic abundances. And developmental psychologists are interested in finding out the specific pathways of language development in children.

There is an old dictum that ‘actuality is a guide to possibility’: if something is actual, it must also be possible, otherwise it could not be actual. But when it comes to scientific modelling, one needs first to find out what is actual. Actuality does not come served on a silver platter. Scientific modelling is the necessary scaffolding for getting at what is actual. My route to realism necessarily has to go through such scaffolding, or, to use a better metaphor, through the garden of forking paths (to echo Borges once more) that perspectival modelling qua modelling possibilities opens up. There is no shortcut to knowing what is actual. It is by moving along the inferential forking paths opened up by perspectival modelling broadly understood that epistemic communities gain over time ‘windows on reality’.

Scientific modelling aimed at exploring the space of possibilities has begun to attract attention in the philosophy of science literature. Models are said to probe what might be the case in given situations. For example, models can sometimes lead to understanding how certain processes might happen in nature. At other times a model can lead scientists to canvass possible economic situations (see Grüne-Yanoff 2009 and Grüne-Yanoff and Marchionni 2018); or gain knowledge via concrete artefacts (Knuuttila and Boon 2011), or help scientists figure out important details about what kind of material, shape, and structure might be more resistant for a bridge (Weisberg 2007). Sometimes models are built with the hope of finding new entities in nature (Hartmann 1999), or to provide how-possibly explanations for social phenomena like segregation in urban areas (think of Schelling’s model discussed in Verreault-Julien 2019). In yet other cases, the emphasis is on how engineered models in synthetic biology might be built (see Kendig 2016b; Knuuttila 2017; Knuuttila and Loettgers 2013, 2017, 2021); or how laboratory experiments might help in the understanding of ‘ecological possibility’ (Currie 2020; Kendig 2016a); or how to explain the way in which phenotypic traits in a population may optimize fitness (Rice 2015, 2019, 2021). The list is pretty much open-ended.

The modal aspect of scientific modelling has been presented in various ways. Sometimes it is articulated in terms of multiple model idealizations (see Weisberg 2007). Other times it is explained by appealing to counterfactual conditionals (Rice 2019); or how-possibly explanations (Bokulich 2014); or modal understanding (Elgin 2017; Grimm 2012; Le Bihan 2017; Potochnik 2017); or in more foundational domains, in terms of Lewisian possible worlds (Wilson 2020).

I share the spirit of all this existing literature in stressing the role of modality (and possibilities, in particular) for grasping what scientific models are really for. My specific task here is to carve out three distinctively perspectival varieties of model pluralism where ‘exploring the space of possibilities’ acquires a specific meaning. For the possibilities in question in perspectival modelling do not concern either

or

or

The possibilities of perspectival modelling have to do instead with modelling modally robust phenomena that could occur in more than one way and could be elicited via a number of perspectival data-to-phenomena inferences. It is this modal robustness over time and across domains that makes perspectival modelling distinctive as an exercise in modelling possibilities. I will have more to say on this ontological aspect of the view in Chapter 6. But here and in Chapter 5 my attention is on laying out perspectival varieties of model pluralism through which such modally robust phenomena are explored.

Therefore, I see perspectival modelling as enabling a variety of situated epistemic communities over time to collaborate—either within the same perspective or across a number of scientific perspectives—and make relevant and appropriate inferences to explore what’s possible (not knowing yet what is actual) about their object of study.¹ The view I shall defend is broadly inferentialist. But it departs in specific ways from traditional views where models have been seen as supporting inferences, or what is sometimes called ‘surrogative reasoning’.²

By and large, I do not see perspectival models as autonomous entities mediating between the theory and the experimental data along the lines of Morgan and Morrison’s (1999) ‘models as mediators’. I am operating with an inflated inferentialist view, whereby perspectival modelling (broadly understood) allows epistemic communities over time to make inferences from a number of datasets to what I call modally robust phenomena.

Consider the three examples to whose details I turn to in the following Chapters 4.a, 4.b, and 4.c. To start with, consider the atomic nucleus. Scientific knowledge of it is inevitably perspectival, subject to the specific technological, experimental, and theoretical resources that were available to different communities at different times. How did physicists gain knowledge of the nucleus, its nature and structure? In Chapter 4.a, I argue that such knowledge accrued via perspectival modelling that around the 1930s–1950s enabled a variety of epistemic communities to make inferences from data about the Earth’s crust and meteorites, among others, to relevant modally robust phenomena such as nuclear stability.

The flurry of nuclear models (especially shell, liquid drop, and odd-particle models around the 1930s–1950s) that accompanied such practices were all perspectival in being exploratory. They allowed atomic physicists, physical chemists, spectroscopists, et al. to collaborate, make inferences, and deliver knowledge about what is possible about the nucleus, the isotopic stability of some nuclides, the nature of nuclear rotational spectra, and so on. They offered perspectival₂ representations of the nucleus in that they jointly allowed scientists over time to gain a ‘window on reality’.

In this case, the ‘window’ on the nature of atomic nuclei required modelling what is possible about a number of modally robust phenomena (e.g. nuclear stability, slow neutron capture, nuclear fission, nuclear rotational spectra) identified over time through data-to-phenomena inferences that were perspectival every inch of the way. By ‘being perspectival’, I mean that the specific epistemic communities involved in each of these data-to-phenomena inferences proved remarkably diverse, ranging from petrology to cosmochemistry, from spectroscopy to atomic physics.

My second case study concerns climate modelling. This is also an example of exploratory modelling because the task is to explore both that global warming has historically occurred compared to the pre-industrial era and how it might accelerate in the future unless action is taken to cut greenhouse gas (GHG) emissions. Climate scientists need to model the multifactorial phenomenon called ‘global warming’. This is another example of what I call a modally robust phenomenon, which can be reliably studied through a plurality of perspectival data-to-phenomena inferences from dendroclimatology, geothermal physics, and palaeoclimatology, as I reconstruct in Chapter 4.b.

Knowing the past global temperature of the planet and how it has changed over the past 100 years is only the first step in this process. To make future climate projections that can inform climate policy, a distinctive type of perspectival model pluralism is adopted by the Intergovernmental Panel on Climate Change (IPCC) in the so-called Coupled Model Intercomparison Projects (CMIP). A plurality of models is required to make robust climate projections under a range of conceivable GHG concentration scenarios. Here again possibility is our guide to actuality. To find out what the climate will be like in 100 years, climate scientists have to model a plurality of factors concerning land surface temperature, changes in glaciers, and ocean heat content, among others, under the suppositions of various GHG scenarios.

And to give a third example, consider language development in children. To learn how to read and write, children develop a range of subskills and go through different learning stages as they move from the pre-school years to primary and secondary school. A child who displays difficulties with reading at the age of, say, 8 does not necessarily remain an underperforming reader at the age of 13 if early educational interventions are put in place. The phenomenon of what I shall call ‘difficulties with reading’ is another example of a modally robust phenomenon in that it might occur for a number of different reasons, and it is of interest to diverse epistemic communities, including cognitive psychologists, educationalists, and neurobiologists, all trying to study and explain dyslexia.

To this end, developmental psychologists Uta Frith and John Morton have articulated what they call developmental contingency modelling (DCM) for dyslexia. DCM is another example of perspectival modelling in that it models possible causal pathways for language development setbacks across different domains (i.e. neurobiological, cognitive, behavioural, and environmental). A child who displays difficulties with reading at the age of 8 might be a child who could develop successful compensatory strategies by the age of 13. Being able to perspectivally model the relevant phenomena is key for effective school interventions in early years and vital to giving each child the best educational opportunities.

To sum up, there are specific contexts in which modelling possibilities matters and the model pluralism in those contexts is perspectival in that it is designed to be exploratory. Or better, the perspectival nature of the representation is best understood along the lines of perspectival₂. Cognitive neuroscientists do not build developmental contingency models for dyslexia because they want to represent dyslexia, or the mechanisms thereof from a specific vantage point. They build those models because they want to explore how breakdown points might contingently occur in the long journey of developing language skills during the early years. The function of those models is to provide a framework that covers all possible contingencies and may facilitate diagnoses and appropriate educational interventions at different stages and across different natural languages.

The nuclear physicists who came up with models of the nucleus were not primarily interested in ‘representing’ the nucleus from a particular point of view. They aimed to explore instead how a range of phenomena might be related to one another: for example, how patterns of isotopic abundances might be related to the phenomenon of slow neutron capture.

And the climate scientists who build ensemble models and run CMIP for refining and improving the robustness of global warming projections over the next 50–100 years do not do so because they want to ‘represent’ climate change from the point of view of different GHG scenarios. They want to tackle instead climate change by offering to policymakers and politicians actionable points that are informed by evidence, state-of-the art modelling techniques, and a plurality of perspectival data-to-phenomena inferences (from tree rings, corals and boreholes, among others).

These are examples of situations where modelling what is possible is a necessary step to find out what is actual. If the goal is to find out how global warming will evolve over the next 50 years; or how the nucleus will behave in radioactive chains; or how reading skills acquisition will be hampered in particular cases, modelling possible long-term GHG concentration scenarios, possible nuclear reactions, or possible language development paths, respectively, is the way forward.

In handling situations that involve dynamic change over time and across domains, the modelling in question is bound to be perspectival, that is, pluralistic and exploratory. This is a distinctive kind of modelling possibilities, very different from other examples in the existing literature on scientific modelling. How to better characterize this exploratory exercise in each case and how it does provide us with a ‘window on reality’ is something I explore in more detail in the three following case studies of Chapters 4.a, 4.b, and 4.c.