2 Contingent science and philosophy

2.1 Contingent science


To understand natural environments and predict their future, scientists and engineers build numerical models (e.g. Earth system models, the weather forecast models, the ecosystem models etc.). These models underpin various “what-if” scenarios to support management decisions. The language of the numerical models is typically based on mathematics and stories they tell are expressed in the form of data fields evolving through time.

The point I shall advocate in this section is that even in this, relatively simple case of natural systems, when we typically know what counts as an empirical evidence and must be able to test and rank these models against observations, even in this case we often do not know the true model and instead of a single, the only valid description of the environment end up with an ensemble of different but all plausible interpretations.

The situation deteriorates rapidly when we proceed beyond the realm of natural sciences and consider empirical evidence (observations) specific to different storied-worlds. The problem of choosing the right description in this case is exacerbated by the fact that we often do not know upfront what counts as an empirical evidence to test a particular storied-world. In different storied-worlds people designate different classes of objects to be real and, hence, amenable to observations. No agreement has been signed so far between a human kind and the nature (or the God) to specify what and under which circumstances must be considered an empirical evidence.

Scientific interpretations

Perhaps, sometime in the future when physicists succeed in establishing a theory of everything such that from a few basic principles one would be able to unfold all the past, the present and the future of the universe, all theories will converge to form a single true theory - an image of the reality applicable across all scales and dimensions. Some people believe this goal is achievable, others argue such theory is impossible to develop in principle. There are also those who doubt such theory (even if established) would be of any significant use in practice. Whoever is right, we do not have such theory today and may not have it in a foreseeable future. Instead, there are many theories and the corresponding models representing various phenomena at different scales and dimensions. Managers and scientists use these models on a regular basis in their practices - they need to solve problems today and cannot wait until the best and the only true unified theory is established to guide their decisions.

For some applications these patchwork theories and models are doing quite well, in other areas they are not so good. Applications where they perform particularly well are typically confined to narrow academic disciplines with established theories and practices customised to specific fields of the enquiry. The quality of predictions also improves when we move away from complex entities such as a human being or social systems towards more basic physical or chemical systems. We have proven theories in these disciplines and reliable models with established processes and parameters and a substantial record of successful applications.

If we step outside individual sciences and take a more holistic, multidisciplinary approach to the task of understanding and predicting reality, then the triumphal progression of science becomes less obvious. The desiderata for a multidisciplinary stance could be arising for a number of reasons including some pressing needs of environmental science and management dealing with increasingly complex Earth systems. The corresponding models are often built through the mechanistic coupling of relatively simple models, simulating different components of complex systems. For instance, physical, ecological and socio-economical models (each model with its own sources of the uncertainty) could be combined together to simulate the evolution of some environment (e.g. city, the fish stock in the ocean, forest etc). Data simulated by these models underpin management decision. The problem is that there are many sources of the uncertainty in such models undermining the quality of their predictions (e.g. unknown parameters and structure of the model, unknown boundary conditions, unresolved features, simplifying approximations etc).

Can we reduce that uncertainty and improve these models by fitting them to observations? To be specific, let’s take as an example uncertainty of the model due to unknown parameters. Assume all the key processes underpinning a particular ecosystem somehow have been captured by this idealised model, there are no errors in the boundary or initial conditions, and we have prefect observations of that ecosystem meaning no errors in data whatsoever. The only unknown in this model are parameters. Think of them as genes that define the behaviour of the model. Some combinations of these genes result in a poor agreement between model and observations, other combinations are doing better. We assume the only reason for the discrepancy between our idealistic model and observations are unknown parameters. We know there is the best set of parameters that gives a perfect match between the model and observations but we do not know exactly what is that set. Can we always find it?

Dimensionality curse
A short answer to the above question is that under certain conditions we may never be able to find the best set of the model parameters, even when such set exists. There is a fundamental epistemological constraint to our ability to find parameters of the model called “dimensionality curse”. The core of the problem is the exponential explosion of the number of scenarios one has to simulate in order to select the best configuration of parameters. When the number of parameters exceeds, say 100, the time required to simulate all relevant scenarios can easily exceed the age of the Universe. The interested reader is directed to the Appendix A for further details. The point to remember is that the problem is fundamental and cannot be solved by increasing the power of computers. Note, also, for the same reason any observation of the physical system which depends on 100 and more parameters is in general incomplete and statistically non-representative. Out of all possible states of that system, we always observe just a tiny fraction of these states and may have no idea how this system will behave under new, untested conditions.

Unknown metrics
Because of the dimensionality curse, we may never know the true description of the reality even if such description exists. The reason we do not know it, is just ridiculously small chance of finding it. Hence, in practice when we deal with such complex system there is always chance that we deal with some imperfect, approximate description of it. Since the truth is not known, we have not one but many different approximations. Can we always objectively rank these approximations and establish which one is if not true, then at least closest to the truth? A short answer to this question is that in some cases we may not. The problem here is that the choice of the metrics to compare the model to measurements and assess its quality is not unique. It might be a trivial task to assess the quality of the model that describes the movement of a ball attached to a spring. You just measure deflection of that ball from the equilibrium state and compare that number with the theoretical prediction. The situation becomes more convoluted when it comes to analysing the behaviour of complex multivariate, space-time resolving models. Consider, for example, two different models and different metrics to compare these models to observations. According to one metrics, one model outperforms another model in terms of predicting say salinity of the ocean at some places and at some time, and according to another metric, another model is better in terms of predicting, say, temperature of the ocean. Which metrics to use? Do we value more accuracy in temperature or accuracy in salinity, and which side of the ocean is more important – east or west? As soon as we bring in our discussion the notion of value, we have lost objective grounds for establishing the best model.

Note also it is not only the fitness of the model to observations that we value in the model but also its predictive powers. We use historical data to improve predictive skills of the model, and only in this context historical data have value for us (at least in the ecosystem example). We call true models those which not only reproduce the past but also predict the future. The problem, however, is that the future states are often designed rather than merely predicted, which, again, brings a subjective element into our discussion. What is the desired future state of the ecosystem? How we define a healthy ecosystem and what are trade-offs between the ecosystem health and, for example, industrial needs? Who must take the burden of paying for carbon emissions, current or future generations, wealthy or poor countries, those who contribute now or those that will contribute in the future, how values are assigned between human beings and other species, etc.? You will have to answer all these questions prior to assessing the quality of the model and there is no way you can answer them objectively.

Fundamental lack of predictive theories
Another fundamental reason for observations not being able to single out unique description of the system, is the lack of predictive theories in some areas, including such complex systems as a human being or social systems (see Popper’s “The poverty of historicism” for more details). However accurate fit between our model (which predicts, for example, new scientific discoveries) and historical data, that calibrated model does not help us to predict future innovations (i.e. new discoveries), because if it does, then the prediction is wrong (i.e. the discovery which is meant to happen in one year, has happened today).

Similar comments go for any statistical treatment of the problem (e.g. Bayesian inference), except that instead of propagating forward in time individual states of the system, we now propagate its probability distribution function.

Irreducible uncertainty
Another kind of the indeterminacy arises in probabilistic models (e.g. Schrodinger equation) which predict probability distributions rather than a single solution. These models answer the question of “how the world can be?” rather the question of “how it will be?”. Analogously, deterministic chaos models predict ensemble of trajectories rather than a single solution. Irreducible errors in observations (e.g. turbulent fluctuations, or Geiger counter, Heisenberg uncertainty principle) contribute to the uncertainty of all these models.

To summarise key points of this section, I shall highlight that even in natural science we have applications where observations (empirical evidence) do not provide sufficient grounds to discriminate between different descriptions (interpretations) of complex systems. This indeterminacy problem cannot be solved by improving the quality of observation or through the deployment of more powerful computer machines. There are fundamental constraints which make unique description of complex multidisciplinary systems impossible (e.g. dimensionality curse, irreducible lack of predictive theory, non-unique metrics of quality, stochastic nature of the system). As a result, we have, instead of a single description of complex systems, a number of interpretations, sometimes called ensemble of models. Examples of such indeterminacy can be found in various branches of science including environmental sciences (e.g. weather forecast ensemble prediction, ensemble of climate models, earth systems), fundamental physics (quantum mechanics, multiverse theories). Note that, analogous irreducible indeterminacy is pertinent to philosophy theories (rationalism-empiricism, pragmatism, realism-antirealism, existentialism, positivism, structuralism etc).

An interesting question that follows is about the meaning of this indeterminacy of the description? Do we have many Indian Oceans, each ocean representing a sample from the corresponding probability distribution function (pdf), or there is one real Indian Ocean and the manifold of our descriptions is just due to observational errors? One line of reasoning in answering this question is that it does not make much sense to talk about the true Indian Ocean as long as errors are irreducible and we never have access to truth but only to imperfect observations. The notion of a single Indian Ocean could be a misconception based on a stereotype we inherited from being used to deal with relatively simple well-defined objects.

The sceptic may argue that the kind of contingency we considered here is specific to models. If we go beyond models and consider theories and scientific laws, there is much less uncertainty in this area. The laws of physics are unique. My response to this argument is that, first, history shows that theories may not be immutable. Second, until the theory is proven, it is just a hypothesis (opinion). To test this hypothesis and prove it wrong or right, one needs to run models and test them against empirical evidence (except, purely mathematical theories, proved through the inference rules defined within the math itself). Hence, models do matter – our trust in theories depends on the quality of the corresponding models. The problem is that in many interesting applications the quality of the models is irreducibly poor. Subsequently we cannot single out one true descriptions of the simulated system.

Both models and observations are instrumental to the quality of simulations. So far, we focused on models to show that the choice of the model, often, is not unique. We also assumed that the notion of “observation” is well defined and unambiguous, however, this is not always the case (in fact in stats it is appropriate to talk about observation-models thus emphasising a heuristic nature of observations). In the next section we will take a closer look on the notion of observation itself.

Contingent observations

Complex multidisciplinary systems of natural science often are represented by an ensemble of models, each member of the ensemble simulating a particular behaviour of the system. In some cases that ensemble has a minor spread of the trajectories, the solutions are close to each other and we talk about approximately unique description of the system. In other cases, the spread of the ensemble is sufficiently high to comprise disparate images of that system (e.g. the weather forecasting system predicting either rain or sun with 50 by 50 chances). An assumption underlying ensemble interpretations is that each member of the ensemble represents some potential state of the system. Each of these states, in principle, can be assigned a probability value to be evaluated through the comparison of the model with observations. The later (called also an empirical evidence) is considered to be true and objective indicator of how things actually are.

Observations are often contrasted to models in a sense that they are unique, while models are not. The reason observations are unique is because they point to real things. There is one object and one pointer to that object – an observation. If there were two pointers, e.g. one pointer saying that an object is green and another pointer saying that an object is red, then either they point to two different objects or one of the pointers is false. Because observations are unique and point to real stuff, they provide a reference point to rank a manifold of subjective models (interpretations).

In the rest of this section we will have a closer look on what we usually call an observation but before we commence this analysis, I shall note that by no means our investigation will be exhaustive and complete. My very modest goal at this stage is to highlight the problem by showing that the definition of an observation is not a matter of discovering some objective truth about the nature - there is a significant normative (subjective) component inherent to this task.

To kick off this investigation, let us check a few definitions of the word “observations” as available from online dictionaries. The Oxford dictionary, for example, defines “observation” as
  1. the action or process of closely observing or monitoring something or someone
  2. the ability to notice things, especially significant details
  3. the act of taking the altitude of the sun or another celestial body to find a latitude or longitude.
  4. a statement based on something one has seen, heard, or noticed
The MacMillan dictionary defines this word as
  1. the process of watching someone or something carefully, in order to find something out
  2. a written or spoken comment about something that you have seen, heard, or felt
  3. the ability to notice things
  4. the practice of obeying a law, rule, or custom
First of all, as we see, according to these definitions, the word “observation” could be considered as both the verb and the noun. The verb ”observation” refers to “the action or process of closely observing something”, “the practice of obeying a law, rule, or custom”, “the act of taking the altitude of the sun”. The noun “observation” is understood as a collection of data sets or knowledge produced by the process of observation (“a statement based on observation”, “a written or spoken comment about something seen”, etc).

Observation as a process
The verb “observe”, according to the Oxford dictionary, means a capacity to
  1. notice or perceive (something) and register it as being significant
  2. watch (someone or something) carefully and attentively
  3. take note of or detect (something) in the course of a scientific study
  4. make a remark
  5. fulfil or comply with (a social, legal, ethical, or religious obligation)
  6. maintain (silence) in compliance with a rule or custom, or temporarily as a mark of respect
  7. perform or take part in (a rite or ceremony)
  8. celebrate or acknowledge (an anniversary)
Another dictionary defines the verb “observe” as a capacity
  1. to see; perceive; notice - we have observed that you steal
  2. to watch (something) carefully; pay attention to (something)
  3. to make observations of (something), esp scientific ones
  4. to make a comment or remark - the speaker observed that times had changed
  5. to abide by, keep, or follow (a custom, tradition, law, holiday, etc.)
  6. comply with, keep, follow, mind, respect, perform, carry out, honour, fulfil, discharge, obey, heed, conform to, adhere to, abide by - Forcing motorists to observe speed restrictions is difficult.
A hint we are getting from these definitions is that the process of “observation” typically is a structured and organised process. To observe something, is to follow certain protocols, to comply with customs, to obey the law. More generally, as long as we talk about the capacity of doing something, the conditions that underpin that capacity must be satisfied first. To observe a trajectory of the elementary particle on a film, you will have to have access to the experimental facility and conduct an experiment in agreement with a certain protocol. To observe an apple on the table, you may need to switch the lights on and, at least, open your eyes. To produce new knowledge about real things, the process of acquisition of that knowledge must follow very specific instructions, a protocol, which makes this observation valid.

Rules and protocols are important ingredients of the definition of the word “observe” (even though they are often only implicitly present in the aforementioned definitions being hidden behind the word “capacity”) but they do not exhaust it. Another key element of that definition is an action itself. Consider, for instance, the definition of the word “observe” such as “follow the rule”. The second term in this definition is the rule (an algorithm, tradition, custom, protocol, law etc.) that guides a particular action. The first term (“follow”) is referring to the action itself. Think of it as a computer code and the simulation of that code. The code itself (the protocol, the rule, etc) does not deliver results unless it is implemented (e.g. it cannot predict the temperature in the Indian Ocean). It is only through the combining those two (the code and the simulation) that you are able to achieve the goal. To summarise, an observation of something involves both (a) a protocol, a rule, which tells us how to observe (or measure) something, and (b) an act of observing itself (running experiment, simulation, action, practice).

Observation as knowledge - Empirical evidence
The term “observation” can refer not only to the process of the acquisition of data sets, but also to the data sets (or knowledge) themselves. When we say the model was tested against observations, we highlight through this word (“observations”) close connection between the data and the process of their acquisition. The data sets have been acquired through the very specific process of observation - we have neither invented them ourselves nor asked an astrologist to predict them.

The outcomes of observations are often called “empirical evidence”. This evidence is typically obtained through the direct sense observation or an experiment. It highlights close links between the data and the process of acquisition of that data and is often used to describe physical experiments. The empirical evidence sometimes is contrasted to the realm of math and logic in a sense that empirical evidence is never perfect and the corresponding knowledge always has some uncertainty built in while the math objects could be known exactly. When the experimental element and the use of instrumentation become significant part of the process of observation, the observation itself as well as the empirical evidence produced by it could be called measurements. Measurements sometimes are contrasted to the capacity of a human being to observe something directly with his own eyes, ears, or feel something or have some other private experience.

In what follows I will use the term “empirical evidence” to refer to the results of the observation. The words “measurements” and “observations” could be referring to both the process of the data acquisition and the result of the observation. In sentences where the meaning of these worlds could be obscured by this uncertainty I will add further clarification in brackets following the word (e.g. measurement (process), or measurement (data)). The meanings of both the “empirical evidence” and the “observation” (process) will be further refined and enriched through this chapter.

Entanglement of empirical evidence with interpretations
Observations (empirical evidence) could be referring to either observational data as such (e.g. numbers, images, words produced by the process of observation) or to the knowledge about some parts of the observed object which integrate these data into a meaningful construct. The data sets by themselves are meaningless unless they are integrated into some context which defines an observing system and the object of the observation. In other words, if we refer to observations as just data without any reference to the broader contextual framework, we talk about symbols (numbers, images, words) which have no meaning. Observations always imply some new knowledge about the object under consideration. That knowledge may not be unique which in turn would translate into a number of different interpretations.

Not only results of the observation (the knowledge) are loaded with an interpretive part, but the process of observation itself involves a fair bit of interpretations. For example, to measure temperature we may use some scaling relationship between the mercury column and the degrees of centigrade. Another example provides remote sensing data which rely on atmospheric correction models to come up with the meaningful data.

While any observation involves some interpretation, when we talk about real objects any of these interpretations typically are amenable to further empirical verification (at least in principle). This empirical evidence (observation of the interpretational part of observation) in turn will have some interpretive component which itself could be a subject of observation. This cycling of observations and interpretations can go forever. In practice, we just cut it at some level and call all the lower levels of the iteration as pointing to subscale processes believed to be real.

Observation of what we think is real
Dictionary definitions of observations, as presented earlier, do not discriminate between observations delivering true or false descriptions of the phenomena. For instance, “a statement about something based on our experience” is considered an observation regardless the truth value of that statement. The meaning that we are after is more constrained. We are interested only in those observations that we think deliver truth so that we can use them, for instance, to rank our hypothesis. While someone can notice something on a tree (an apple, a ghost, a Santa Claus), we are interested only in those observations that we believe point to real objects (and thus deliver new knowledge called empirical evidence). If we do not believe in ghosts, then having observed a ghost on the tree does not count as a valid observation.

The question that follows is which objects we call real? Intuition tells us that real objects must be observable because observations provide empirical grounds that support existence of these objects. If we never observe something, then there is no empirical evidence for that something to exist, and we shal call it not real but a fiction, a made up construct, the product of imagination, hypothesis, theory etc. “The real thing” does not exist unless we can observe it. On the other hand, the word “observation” does not make sense unless there is a “real thing” to be observed. We ran the full cycle here – to define “observation” we need to know what is “real” and to define “real” we need to know the meaning of the term “observation”.

If we knew what counts as an observation, then we can tell what is real and what is not; and vice versa if we knew what is real then we know what is observable and what is not. It does not follow from this, though, that “observation” (i.e. empirical evidence) and the real thing are the same objects. You may observe only some parts of the real thing, the rest being represented by interpretations. Despite the fact that you have observed only parts of that object, you may still call it real.

In what follows, we take it for granted that the notion of observation is closely related to the notion of real. Second, we lump together these two terms into one big word “observation-of-real-object” meaning observation delivering new knowledge. And finally, we will appeal to our intuitive understanding of the notion of observation and the notion of real in order to build a plausible definition of that new term “observation-of-real-object”. To start with, let us see what kinds of objects are amenable to observations? In other words, what kinds of objects we typically assume to be real?

Examples of real (i.e. amenable to observations)

Apart from material objects made out of particles and voids, people call and have called real many other things. Some people argue that mathematical constructs and, more generally, idealised forms (e.g. Platonic forms) are not least real than the material objects and in fact are the only real things that exist - the rest being just a shadow and imperfect imitation of that reality. For others, a private experience of certain states and feelings is of a paramount significance underlying their definition of the reality. Remember Descarte’s “I think, therefore I am”. I had an experience of the God, love, pain and that experience provides the most compelling evidence of the existence of these entities. I can be confused and mislead about anything else but never have doubts about feelings that I had and states I have experienced. Hence, what I felt must be real. Take another example - a character type or a person. Some would argue that the notion of a “samurai” conceived as an experience of one’s own biography is referring to an entity, which is not less real than, for instance, the notion of an “electron particle”.

People normally not only declare certain objects real but also tend to provide some justifications for their claims. To justify something is real they show it fits the definition of the real. These definitions are considered as impersonal truth-holders which generalise certain claims and function as the source of an objective authority (i.e. something is real not just because I will it, but because it fulfils certain criteria and those criteria are more stable and reliable than my will). Plus, such definitions, based typically on induction from the set of examples, are helpful in allocating new objects into one or another class. Over the course of the history quite a remarkable effort has been made towards establishing such rules. Some of these are listed below In the next few sections I shall have a closer look on some of these definitions and will elaborate some other dimensions of the notion of “real” relevant to our discussion. The point I would like to emphasise is that there are many definitions of real objects, each of these definitions has arguments for and against it but there is no one single definition that stands out as the winner. But before we go further investigating definitions of “real”, we need to clear the road for our enquiries and move aside a big obstacle in our journey called physical reductionism.

Reductionism

According to physical reductionism, everything is reducible to physics. All mental constructs and other sentiments supervene on underlying materialistic substrate. The whole world is divided into the realm of the real substructure and the realm of the ephemeral superstructure. We may find it convenient to talk about the superstructure as if it has its own ontological foundation but in reality all these talks are just a roundabout talk about the material stuff. The reason we focus on physical reductionism is that (a) it underpins the scientific vision of the world and (b) it is relevant to our talk about storied worlds in a sense that if everything is reducible to physics, then all our storied-worlds are just imaginary constructs. We may talk about these worlds to entertain ourselves but at the hard-rock bottom the reality is represented by material particles and forces in between and nothing else is real. On the other hand, if the world is not reducible to one language (i.e. the language of physics), then many other languages make sense.

Before we start exploring justificatory grounds of the reductionism, it is worth making explicit some contextual settings that will guide our enquiry. When we ask the question of whether some, say mental constructs, are reducible to physics, what we implicitly take for granted is an assumption that we ask about the truth value of that proposition. We are interested in truth because it gives us more accurate description of the reality and we care about accurate description of the reality because, for instance, this way we have more chances to predict the future and hence avoid some unpleasant surprises. Those who can predict the future win. However, if for some reasons, we cannot single out truth out of many other possibilities (e.g. cannot say for sure whether everything is reducible to physics or not) then the notion of truth becomes less relevant to our project. In this case, instead of the truth talk, we might better talk about the well-being and the quality-of-life as the guiding principles for choosing the right answer. But before we switch the context of our enquiries to that of the well-being and the quality-of-life it makes sense to see arguments for and against reductionism in the context of its truth value.

First, we need to clarify our subject matter. It will be sufficient for our purposes to distinguish between two different interpretations of the term reductionism: epistemological (or theoretical) and ontological. Ontological reductionism tells us that everything consists of a bunch of particles and those particles are real, while aggregate entities, such as for example our bodies, are just linguistic constructs – the tag we attach to the collection of particles. The focus of the enquiry is on finding these elementary particles and establishing their properties. Epistemological reductionism, on the other hand, is more concerned with different ways we may describe some subjects or phenomena and the ways these descriptions may morph one into another. It may tell you, for example, that there is some special language (e.g. math) which expresses all our knowledge in the most concise way and, perhaps, introducing the least number of basic entities, whatever these entities could be. The focus here is on different ways of expressing knowledge. The basic entities of that special language could be referring to some abstract forms rather than smallest parts of aggregate entities (as in the case of the ontological reductionism).

In what follows we will treat ontological reductionism as a sub-species of the epistemological reductionism. We say that whenever we talk about ontology we talk about our knowledge of the ontology and on these grounds we reduce ontology to epistemology. Instead of asking whether something is real, we ask “how do we know that something is real?” What makes us to believe that we have knowledge about this or that statement? How can we justify the belief that we know truth?

It makes sense also to distinguish between mild forms of the reductionism which restrict the scope of the reductionism to some specific fields of science (e.g. equations of chemical reactions are reducible to physics; certain physical theories under the limit of low speed are reducible to classical mechanics, etc.), and radical reductionism which extends these claims over the whole science and beyond. It is the radical reductionism that is the main subject of our enquiry in this section.

There are several interpretations of the epistemological reductionism (http://www.iep.utm.edu/red-ism/). One of those takes the task of the reductionism as that of translation. There are two languages (say the language of physics and the language of social sciences) and the task is to translate one language into another. In other words, the goal is to express all statements of the social sciences in terms of the movement of particles (or chemical reactions). An austere version of such reductionism is the project of reducing all our knowledge to the laws of physics. More relaxed version of the reductionism is the task of reducing all the manifold of different languages to a single language which may not necessarily be the language of physics. Historically the key motivation behind such projects were driven by the concerns about diversity of the science and the feeling that in order to understand all branches of science we have to comprehend it at the level of individual persons. The notion of coherence truth is integral to these concerns - if we are to understand different languages of sciences, we must map them into one universal language that makes sense across disciplines. Key points defining this form of reductionism can be found in Rudolf Carnap’s “The Unity of Science”(1995).

Another interpretation of the reductionism is based on the idea that one theory is reduced to another when the later (the larger one) can be derived from the former (the smaller one). Since the larger theory will have terms not present in the smaller one, to map small onto the large you will have to define new items of the large theory in terms of the items of the reduced theory. Such mapping was dubbed as “bridge laws”. The key figure drawing on these insights is Ernest Nagel (“The Structure of Science”, 1979).

One more interpretation of the reduction is that of two theories explaining the same set of observations but with different theoretical luggage. We say that one theory is reduced to another if the later provides some economy of terms and definitions as compared to the former (Kemeny and Oppenheim, 1956).

The main focus of our discussion in this section is on a particular version of the reductionism, physicalism, which claims that there is only one language, the language of physics, and all other languages are reducible to it. The idea is that if we understand the behaviour of particles, then we understand the behaviour of the whole world. To be specific, we assume that the term “understand” means that we have the right set of equations governing behaviour of particles. The claim of reducibility now is understood as the claim that having the right equations for parts we can simulate and predict the whole. In this sense the whole is reducible to parts.

The meaning of the word “right” in this definition we can define through the reference to the capacity of these equations to reproduce historical features and to predict future events. If we can neither reproduce the history nor predict the future with these equations, then they are likely to be wrong. Note, however, in general, having the right set of equations does not necessarily entail reproducibility or predictability of the system. For example, we may know the right set of governing equations upfront but may not be able to predict a specific trajectory because of the stochastic nature of that system (unless, of course, we have a capacity to operate with distributions rather than individual trajectories that may not always be the case) or because of some other unknown factors we may not be able to predict in principle (e.g. unknown boundary conditions associated with the light from a distant star which has not reached our planet yet). Hence, having the right set of equations does not necessarily imply predictability or reproducibility. The reverse is true, however. If we can reproduce and predict with a particular set of equations, then we have the right set of equations.

In the light of these considerations, to prove reductionism we have to show that equations governing individual parts of the system define unequivocally the history and the future of the whole system. Note that the failure to prove reductionism does not imply the reductionism is wrong – we may not be able to prove it for some other reasons. Having said this, if we succeed in showing that we cannot prove reductionism, then, I think, even without proving it wrong, we have enough justificatory grounds to reject reductionism.

Except some artificial cases when we know upfront the right set of equations, in real life we typically gain the knowledge about the quality of the equations through the process of validation - by testing these equations against observations and showing how well they reproduce past or predict the future. To justify our claim that we have the right set of governing equations, and hence that we understand phenomena, we have to show that these equations work. If for some reasons we cannot reproduce the history and predict the future, then we do not know that we have the right set of equations even if we have (i.e. we do not know that we know).

Having these reservations in mind, I suggest the following definition of reducibility: The whole system is reducible to parts, when we can reproduce the history and predict the future of that whole from the equations that describe parts.

To be sure there are vague terms in this definition that require further clarification. What do we mean by saying “reproduce” or “predict”? How accurate this prediction must be, or for how long we must be able to predict the future? Or what is that whole we are going to reproduce? How do we know we have the right equations for parts? I will clarify some of these questions in the following section dealing with arguments for and against reductionism.

Note, again, with our definition we might be able to prove reductionism but cannot disprove it. Rather than trying to prove it right or wrong, our strategy will be to illustrate arguments bearing on plausibility or improbability of the reductionism.

Arguments in support of reductionism
  1. I believe, the main argument for the reductionism is that there are quite a few examples of the successful reduction in physics, chemistry, some biology and psychology. Thermodynamics is a large-body approximation of the statistical mechanics, one can explain some chemical reactions in terms of the underlying physics, we can produce certain behavioural responses by stimulating certain parts of the brain. In fact, physicists today are busy building Theory Of Everything (TOE) which is meant to provide a set of fundamental equations to describe all physics and, ideally, the rest of the sciences.

Arguments against reductionism
  1. One major argument against reductionism, I think, is that as a matter of fact at present we do not have a single language that speaks all sciences let alone everything beyond science. Past projects to streamline, for example, social sciences with physics have failed (e.g. logical positivism). Recent developments in physics aiming at TOE have their own problems. No one takes seriously the prospect of resolving some social conflicts, say between two nations, on the grounds of predictions made by physics. Furthermore, an assumption that we may have such predictions and they can help us to resolve social conflicts is pregnant with contradictions. There is no doubt that discoveries in natural sciences may resolve some environmental issues fuelling social tensions and this way physics can be instrumental to relieving these tensions. However, it is hard to believe that math can help us to settle a dispute between people who believe the sweetest songs are those sung in one or another language.
  2. The hope that examples of the successful reduction in specific areas of science could be extrapolated over the whole science and beyond is based on induction and as any conclusion based on induction will always be looked upon with a suspicion.
  3. Let’s assume the world is reducible to physics and physicists finally have succeeded in establishing a system of governing equations (let’s call it TOE) such that from the knowledge of the location and velocities of all particles in the Universe they can predict exact location of these particles at any time in the future and in the past. The world is locked in the chain of the cause and effect relations. The present defines the future and the past. Shall we believe in this vision? For a number of reasons, I think, we better do not.

    Firstly, the idea of TOE is pregnant with a contradiction - if we know the future of everything, then we can change that future thus spoiling the prediction. The physicist may argue that TOE may predict only stuff we cannot change, but then it does not predict everything, and the world is not reducible to physics. Don’t confuse TOE with a conventional forecasting system predicting a subset of the Universe. We can interfere with the prediction made by such a conventional model without violating the logic. Analogous intervention in the case of TOE introduces a contradiction because the TOE is meant to predict everything including our own intervention.

    Secondly, according to modern physics there are reasons to believe that the nature is inherently stochastic. In this case the truth value of our hypothesis concerning TOE, will be expressed in terms of the probability for this hypothesis to be either true or false. In a stochastic world the probability of the true TOE can never reach 1 (since we never have enough samples to prove a particular distribution of probability for all particles in the Universe starting from the Big-Bang). In other words, there will be always a degree of uncertainty attached to this hypothesis.

    Thirdly, to prove TOE physicists will have to test it against observations. To avoid problems with unknown boundary conditions and initial settings they will have to simulate the whole universe starting from the Big-Bang. To prove it into the future, they will have to simulate infinity. Since no one can simulate infinity, at some stage they will have to rely on induction to claim the truth of the TOE. Claims based on the induction are never watertight.

    To summarise the aforementioned points, however strong arguments for TOE physicists will furnish, there will be always room left for a doubt.

    Can we design a weaker definition of the reductionism, the definition that acknowledges finite spatial and temporal scales and degrees of accuracy of the prediction? I guess, we can and special sciences provide examples where they may work (e.g. chemistry being reducible to physics). However, such weak, localised definitions of the reducibility will have little bearing on our project of studying and designing SWs. The fact that chemical reactions are reducible to physics has little to do with the reducibility of the whole world to the equations of physics.

    If we had proved that all our interpretations are reducible to physics that would have strong implications to our project. Fortunately, it looks like we cannot prove such general statement. Maximum the reductionists can afford is to believe that they knows the true model of the universe; others might be equally justified to believe that they do not.

    Now, the reader may argue that even if we do not believe into epistemological reductionism (that we know the right set of equations), we may still have this ultimate set of equations but for some reasons not be aware of it (e.g. because we cannot test it for all the future events). So, the epistemological reductionism might be true, but we may not be aware of it. And I agree, this might be the case, but knowing that we do not know does not help us to make rational choose between these two perspectives. We cannot prove nether positive nor negative statement, but there are arguments for and against reducibility, and, I think, arguments against it are strong enough to justify one not believing reductionism.

    The reader may argue we do not believe reductionism because cannot predict the future, but it may still be the case that nothing apart from particles and forces is real. What we know about the world and how it is by itself are two different things. Epistemological non-reductionism does not necessarily entail ontological non-reductionism.

    I would argue that this conclusion is wrong. To talk about ontology in isolation from epistemology, I think, makes no sense. Someone famous said that “he does not need reference to the divine in order to explain any phenomena in the world”. In other words, cause-effect relations between material objects are sufficient to explain any changes in the material world. However, it is because we think that we know that cause-effect relations between material particles are sufficient to explain all the observed phenomena, that we make conclusion that there is no place left for a divine or any other metaphysical intervention in this universe. But as we just discussed the premise “we know that cause-effect relations between material particles explain all material phenomena” may not be true - we do not have sufficient evidence to prove this statement. There are chances that we are not able to explain every material phenomenon in the world with a given set of governing equations. And if we can’t, then the statement that there is no divine intervention is false (because we cannot prove it). Epistemic non-reductionism entails ontological non-reductionism.

    In what follows, I shall outline additional, more exotic and yet still valid, arguments against physical reductionism.

  4. Cartesian scepticism
    As mentioned earlier, on the nominalistic account, the fundamental microscopic particles may not exist at all. They could be representing just linguistic constructs people have invented in order to talk about macroscopic phenomena.
    5. There are arguments suggesting that we live in a simulated reality. Computational power of modern computers nowadays is close to that of the human brain and some day we may simulate artificial intelligence (check out Human Brain project). Once we can simulate intelligent beings, we may extend these simulations to artificial societies and civilisations as well. Imagine a student of the history class in the future, assigned with the task of simulating human society. We may leave in such simulated reality. Now, if they can simulate us and we will be able to simulate others, who in turn might be able to simulate others, then perhaps there is an infinite cycle of hierarchically nested simulated beings, where beings from the higher level of the hierarchy simulate beings from the lower level.

    Another argument in support of this idea is that all elementary particles of the same type are exactly the same (i.e. one electron has exactly the same properties as another). Such identities are typical to idealised theoretical constructs rather than real particulate things.

    It makes sense to assume that space is discrete and the smallest cell of that discrete space could have just two states, zero or one (filled or empty). With such basic material one can build a computer and simulate everything that is there.

    Finally, given how miserable our lives from time to time could be, I think, it makes sense to suggest that this world has been created by a lazy student rather than by an omnipotent benevolent God.

    Now, the simulated reality argument does not quite object the idea of reducibility, but it provides a context which shifts the focus of the enquiry. The whole idea of the fundamental level of the description which is independent of anything and channels all macroscopic developments becomes somewhat slack and obscure if we can see a shadow of the history student behind the computer who can just unplug the power cord.
  5. Consciousness loop. Physics tells us that at microscopic level there are no particles per se but rather some strange objects we can describe with math that predicts the probability for a particle to be observed at one or another place. Until we observe it, the particle does not exist as something occupying a particular spot in space, but rather is smeared around some area with different degrees of probability to be observed. There are different interpretations about what happens with that smeared distribution when we make an observation. According to the mainstream interpretation, when we observe a particle that smeared distribution collapses into one particular location where we find the particle. Another interpretation is that of the Everet’s multiverse, which says that the distribution is made up out of the ensemble of universes with different allocation of particles and the act of observation amounts to observing a particle in one of these universes. Finally, according to Eugene Wegner’s theory, an integral part of the observation is consciousness. It is because of the interaction between consciousness and particles that we are able to observe these particles. In this last interpretation we have a loop connecting particulars with abstract entities. In order to observe elementary particles, we have to have something else which may or may not be reducible to these particles, and some people may argue that consciousness belongs to the realms of mental rather than material constructs.
  6. Mathematical Platonism. Microscopic particles have very strange behaviour which often defies our intuitions (e.g. wave-particle dualism). The only guiding principles we have in that world are rules of math. If the micro-world speaks math, looks like math and behaves like math, then perhaps it is math. Maybe math is the most fundamental level of being, a kind of Platonic form which underpins everything we know? There are scientists who believe this statement is true (e.g. Max Tegmark). This and some previous arguments show that there are many different forms of reductionism, and they may not necessarily agree with each other.
  7. Vague separation from mental and sentimental. We have never seen an electron particle but have a theory for such particles which works. There are other entities we never seen but can describe them and use in our practices (e.g. traditions, Gods etc). Why do we hesitate to call them real? Or why we do not call real some feelings and dispositions, or more general states of affairs (e.g. biographies, lifestyles, cultures, ecosystems, arts, etc)?
  8. Multiple relaisability. This argument against reductionism, which says that for the same super (e.g. pain) we can have different subs (e.g. injuries) producing that super, is one of the most often cited in literature, but, I believe, it has little relevance to our discussion because it addresses one particular form of the reductionism. Pain could be caused by different physical factors (and hence, in general, is not reducible to a single physical factor), but in every individual case it may still be reducible to that particular factor. This argument does not address the kind of reductionism we are interested here.

We have presented quite a few arguments against reductionism which, I believe, provide us with sufficient grounds to move on in our discussion. Note that none of these arguments is watertight. It turns out that almost all interesting problems in philosophy are of the same type. Arguments in support or against such problems are often ampliative, that is deductively not valid but capable of offering good, though not conclusive, support for their conclusions.

Apart from the physical reductionism (the focus of our discussion in this section) there are other types of reductionism which, if proved, will undermine the thesis of plurality of the worlds advocated in this manuscript. The strategy I shall take with this line of attack is to let the proponents of the reductionism to prove their point. Unless such proofs are furnished, the case of the reductionism is considered inconclusive and as such not valid argument against the multiverse theory.

In the rest of this chapter I will again elaborate on the question of “what is real?” or, in other words, “what entities we can observe?” I have already sketched a few possible answers to these questions earlier. In what follows I will take a more systematic approach to addressing this issue by presenting more or less established philosophical and scientific schools of thought concerning this issue. I shall start with an overview of the branch of philosophy called metaphysics.

Irresponsible reifications

Before proceeding with metaphysics, let me consider one more argument for reductionism referring to irresponsible reifications. According to this argument, the non-reductionist vision of the Universe is ontologically redundant - it is conducive to introducing artificial objects that we claim to be real when, in fact, they are not. For example, as Rawl puts it there is no such thing as a university but a collection of buildings, departments, programs and people, which for the sake of convenience we call a university. Split it in half and you have two smaller universities.

It might be hard to consider a fly split in half as two smaller flies, but this is not my point. I think, the notion of “irresponsible reification” is a meaningless term unless there is a framework that defines the notion of “irresponsible”. Which vocabulary we use to define the word “irresponsible”? Why the reification might be called irresponsible? Is it because the reified items are surplus to our needs in a sense that we can know truth and build on it without reference to such objects? But as we discussed earlier we may not know truth. Or is it because there is no empirical evidence that supports the existence of such entities? But as we seen the definition of the empirical evidence is not unique and to a large extent it is up to us to decide what counts as evidence and what is not depending on our beliefs? And in a more general sense, why do we seek that correspondence to observations? Isn’t it because when we do not have it, we find it difficult to believe in such entities? And why do we need to believe in them? To answer this question, we have to ask: What is the goal of the game? Is our ultimate goal to make a prediction or to achieve some qualities related to our well-being? If the ultimate goal is a well-being (and perhaps sustainable well-being), then any reification must be called irresponsible when, and only when, it is inconsistent with that goal. The goal of consistency between interpretations and observations is subordinate to the goal of being able to believe that interpretation, which in turn is subordinate to the goal of achieving a sustainable well-being. If you believe in something and that belief sustains your well-being, then you may not need to require it to correspond to observations at all. The problem is that it might be hard to believe in something unless it forms a cohesive network integrated into a more or less coherent whole that you believe is true. But again, the correspondence to observations, while important element of the network, is just only means for achieving some other more fundamental goals. If you are able to cut across and get to the point straight, then you may not need to take on board at least some of these intermediate steps.

The protagonist of the observational truth may argue that you can believe whatever you like, but if your belief is not consistent with observations your well-being may not last long. To answer this charge, it would suffice to note that many generations of people used to believe and still believe in entities which have no conventional observational support and nevertheless it is not obvious, at all, they have lived less fulfilled lives than those who did not believe in anything. We talk more about this in the next chapter.

Another point on this issue is that, I believe, one of the reasons for the negative attitude toward the “reification” comes from the fear that through the reification one can claim the discovery of a true and unique nature of the subject under consideration which makes any other possible interpretation obsolete and surplus. For instance, the claim for a true human nature always is looked upon with a suspicion of attempting to narrow down the conversation about the human nature to the established single and the only valid interpretation of that nature. One may claim, for example, the only true and the only right way of a conduct is the way of samurai - all others must follow, because it is imprinted in the human nature. However, if we leave the door open, and let many other distinct human natures to co-exist then I cannot see any fundamentalistic harm coming from the reification. To avoid confusion, perhaps, we should not use the term human nature in this case but be more specific saying, for instance, the human nature of a samurai thus enabling other definitions of the human nature to coexist.