Scientists and science enthusiasts can get exasperated by the conflation of definitions between the scientific conception of a theory and the colloquial definition. In the latter, a theory is sometimes considered no better than a guess, and at best what a scientist would call a hypothesis (an educated formulation of a mechanism or explanation). People will say things like “evolution is just a theory” as if that attests to some shortcoming of evolution. In the scientific conception, a theory is the gold standard. It is a set of inferences, explanations, predictions, and interpretations that bring together (sometimes disparate) data, evidence, and observations into a cohesive whole. Theories are what scientists use to make predictions in order to formulate new hypotheses and design new experiments. But what is the nature of a theory? And what is the ontological status of a scientific theory? In what way is a theory true?

First, we have to ask ourselves: what is the difference between a theory (in the scientific sense) and a fact? A fact is essentially a proposition, and in usual parlance is a proposition that also happens to be true (it is a state of affairs that obtains or once obtained in the actual world). Water is made from two hydrogens and one oxygen; it is currently forty-five degrees Fahrenheit outside; it’s 8:30 a.m. eastern standard time on Wednesday, February 16, 2022; the sky is blue; my grandfather begat my father; the weight of my coffee cup is dependent on how much coffee is contained within it; right now my coffee cup weighs roughly half a pound (I didn’t measure, but I’m guessing based on 1 cup of water being about 0.52 pounds); I drink coffee because I enjoy the flavor; I currently feel somewhat sleepy.

These are all facts. All of them were true when I wrote them. We can see that some facts, such as water being made of two hydrogen atoms and one oxygen atom, are universally true and will remain true at all times. Others, such as the time or temperature, are true only for a particular place and/or at a particular time (and are dependent on what metric we use to measure them; it wasn’t inevitable that our clocks use the same 60-second/60-minute/24-hour measurements and we know already that the temperature could be measured in Celsius or Kelvin).

The sky being blue has two interesting features: 1) it’s not eternally true (eventually the sky here on earth will no longer exist, and there was a time before it existed; it is not necessarily true when its cloudy or at night) and 2) it is subjective (the experience of the color blue requires that there be an experiencer). That my grandfather begat my father (assuming it is actually true) was, prior to the year 1952, untrue, but after that it will remain true for the rest of time (setting aside logical determinism about future contingents that says that propositions are true of future events before such events actually occur).

That the weight of my cup of coffee depends on how much coffee is contained within it is a somewhat more abstract fact. The (potential) variance of temperature says something about counterfactual possibilities: if my cup of coffee was, as I surmised, about half a pound, there are possible worlds in which it is some other weight. This is true of things like temperature, too, but my saying what temperature it actually is now does not invoke those possible worlds. Saying that X depends on Y is invoking those possible worlds by stating a proposition that can be formulated as a hypothetical: if there is Y amount of coffee in my cup, then it will weigh X.

This brings us to the fact about the actual weight of my coffee cup when I wrote the sentence (assuming my guess at the time was right). This is a fact that is grounded in another fact: the weight of my coffee cup is grounded in the fact of how much coffee is contained within it. Thus, we can think of facts as both the grounds of other facts and as grounded in other facts. This grounding-grounded relationship can exist in the other facts I’ve stated as well and will often be the case. Grounding can also sometimes be causal: I could say that there is coffee in my cup (and therefore has the particular weight it has) because I put it in there.

The penultimate fact I listed, that I drink coffee because I enjoy the taste, is a different sort of grounding or causality, because it refers to my mental states rather than physical, observable actions that I took. This makes it subjective and therefore difficult to test scientifically (at least without my testimony, a belief by others that my testimony is accurate and true, and that my actions correspond with my desire and my belief that my actions will satisfy that desire).

And finally, a fact like I feel somewhat sleepy is (in addition to being dependent on the particular place and time) purely subjective. Outside my testimony and doing a brain scan to determine the neural correlates of my consciousness, this fact is inaccessible to anyone besides myself. Indeed, even with testimony and brain scans, another person cannot actually feel or experience my sleepiness. These last two kinds of fact I will mostly be bracketing for our discussion because what I’m interested in here is facts in a scientific sense. And so, unless I specify otherwise, when I talk about facts I will be excluding these purely subjective sorts of facts.

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There are a few things to notice about the nature of facts. The first is that they are verifiable. Any person is, in principle, capable of finding out for themselves whether the proposition actually obtains. The second thing to notice is that there is little, if any, interpretation required. A person might not understand the words, or they might lack the requisite knowledge (e.g. knowing what an atom is is required to understand what is a hydrogen or oxygen atom; knowing that atoms can bond together in some way is required to know that water is composed of these atoms) or experience (e.g. someone who has never seen the sky) to fully grasp, but given an understanding of the language and background information, a person can come to know these facts without dispute.

There are, of course, facts which are disputed. What actually happened in the past is in a state of constant debate and revision among historians, lawyers, politicians, and other interested parties. But most reasonable people would not dispute that there are events in the past that actually obtained – there are true propositions that correspond with what actually occurred in the past, even if we don’t actually know which particular propositions actually obtained. These facts may in practice be unverifiable, but they are verifiable in principle (they were at one point in time verifiable). The only interpretation needed is in interpreting whether facts we do actually know entail that those disputed facts actually obtained.

When we step into interpretation, we then emerge into the realm of theory. Detectives (and historians, et al), when searching for clues and leads, come up with theories about what happened (e.g. during a crime). They use these theories to make predictions and formulate hypotheses. These hypotheses tell them where to search for more (factual) clues and who to talk to to search for more leads. This is the nature of a theory.

We thus come to the distinction between a fact and a theory: facts are concrete events, measurements, and/or verifiable propositions that actually obtained (even if we are ignorant of them). A theory is an interpretation of a set of facts – a Kuhnian paradigm. A scientific theory is underdetermined by the data. This means that there can be multiple theories that fit the data. But a theory is meant to explain the data and allow for inferences and predictions to be made in order to design more experiments. The success of a theory is how well it makes predictions about what new data one will find in future experiments and observations (or, if sticking with the detective analogy, predictions about where to search for more clues).

I’m sure there are plenty of ways to divide and categorize types of theories, but I will come up with my own. Theories, in my conceptualization of them, come in three varieties:

1. Historical Theories: these are the kind of theories that our historians, detectives, and lawyers are interested in. Given the facts that we have (archaeological, historical, material, testimonial, etc.) what can we say actually happened at some point or points in the past?
2. Procedural Theories: this is a theory that attempts to describe how certain phenomena are occurring. They essentially offer a narrative: think of something like the carbon cycle or reaction mechanisms or the theory of evolution by natural selection.
3. Ontological Theories: these are the kind of theories that are primarily within the purview of physics. Think of ideas like mass and energy causing a change in spacetime geometry or the many worlds interpretation of quantum mechanics. These theories purport to tell us something real about the mode in which reality itself exists.

These varieties of theory are not mutually exclusive. The different fields of inquiry that use these types of theory are not restricted to just one type. Historical Theories attempt to make inferences from available evidence to a most probable event or series of events in the past. Historical Theories are interested in retrodictions about past events and predictions about what evidence one will find (e.g. if person A is the murderer, then one could retrodict that they would be found at the scene of the crime at the time that it occurred and one could predict that they will find that person A‘s DNA matches that found beneath the victim’s fingernails).

Law itself is a type of procedural theory. Predictions that law might make is that prohibiting something will reduce its occurrence, or that carrying out trials in a particular way will lead to more convictions for people who are actually guilty and more acquittals for people who are not actually guilty. It may then even predict that such a way of doing trials will lead to reductions in crime. What we wouldn’t say is that the law (necessarily) has an ontological status. The law can be changed; it could even potentially be jettisoned altogether. When we put people on trial, we don’t posit any sort of substance or thing above and beyond the procedures being carried out to explain what’s happening.

An evolutionary biologist would also be interested in making retrodictions about the past – what organisms existed and how did they behave or interact with their environment? What mutations occurred? What selection pressures did an ancestral species face that resulted in the features seen in current species? The evolutionary biologist will also be interested in making predictions about things like the kinds of fossils will be discovered (and what kinds will not be discovered at certain points in the fossil record – you won’t find a rabbit in the Cambrian period); the sorts of phylogeny that will be deduced (a newly discovered frog will be more related to other frogs than to squirrels, for instance); what diseases might emerge from the wild; how will organisms respond to climate change; and so on.

Evolution, however, doesn’t have an ontological status per se. There isn’t some substance (that we are aware of) causing mutations and bringing about selection pressures. That’s why the theory of evolution is not an Ontological Theory but a Procedural Theory that brings in many elements of Historical Theories.

Physicists, too, are often interested in making retrodictions, such as about what occurred in the early universe. They are interested in Procedural Theories, such as galaxy formation or stellar nucleosynthesis. But physics is the primary field of science that is interested in Ontological Theories.

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Ontological Theories tend to be slightly different and can be even more difficult to test for correspondence with reality. It is the nature of these kinds of theory that prompted me to make this post in the first place. I might subdivide Ontological Theories further into two types:

1. Mechanistic Ontological Theories (MOT): think of general relativity, where we say that mass and energy causes dynamic changes spacetime itself. This is a mechanism that explains why we observe the data that we do – the change in path of light around massive objects, gravitational waves, and so on – by appeal to a kind of substance (sometimes called the “fabric”) of spacetime.
2. Interpretive Ontological Theories (IOT): think of interpretations in quantum mechanics. In the Copenhagen interpretation, it is not positing a causal mechanism for how the wavefunction collapses, but merely giving an interpretation of what’s happening during a measurement; in the many worlds interpretation it is not positing a mechanism for how new universes come into existence, but merely giving an interpretation of what is actually happening during a measurement; the pilot wave interpretation says that the wavefunction is something that sort of pushes the particle around; and so on.

MOT tends to be less controversial because such theories appeal to our intuitions. Indeed, this often characterizes such theories: the bending of some “fabric” in response to a disturbance (e.g. by mass or energy) is something most humans can grasp, even if the mathematics of general relativity aren’t understood. But what is the ontological status of this “fabric” of spacetime? And what is the causal mechanism by which mass and energy disturb this “fabric”? Nothing in Einstein’s field equations demands that we make this disturbed/bending/flexible “fabric” interpretation of the underlying mechanisms explaining the data.

Similarly there is quantum field theory. What is the ontological status of a field (quantum or otherwise)? Do these fields actually exist in some ontological sense, or are they mathematical objects that only function in an epistemological sense as opposed to an ontological sense?

I think MOT fits in well Thomas Kuhn’s idea of the paradigm. A paradigm is a proposed mechanism and/or substance that appeals to our intuition in some way. The Newtonian view of gravity posited a sort of force between objects. Gravity says that it’s not a force as we tend to understand it, but in fact the curving of spacetime. But this picture of a “fabric” curving in response to matter or energy, not being necessarily entailed by the Einstein field equations, could some day be overturned, even if the current data continues to be tested and verified. This makes one wonder how much stock we put into the curving spacetime “fabric” way of thinking about gravity and spacetime.

The same goes for the quantum fields. If they are simply mathematical tools (similar to the Lagrangian, which don’t have a direct physical interpretation) used as more of an epistemological framework, thereby lacking any ontological status, a new paradigm could come about to replace it. Indeed, once general relativity and quantum field theory are reconciled, we might end up with some completely new paradigm to explain the mechanism of the fundamental forces.

IOT can be more controversial. Copenhagen interpretation, collapse interpretations, many worlds, pilot wave, and so on are all competing ways to interpret the wavefunction and measurement problem of quantum mechanics. But we could see how IOT applies in other areas, such as the fine-tuning argument, where the appearance of fine-tuning in our physical constants is interpreted as either emerging from the multiverse, being just a happy accident, or as evidence of an intelligent designer.

The hallmark of IOT is that it permits the “shut up and calculate” approach to doing physics. What the wavefunction actually is, or what actually happens to it when measured, don’t matter, according to this view. All that matters is that the theory makes accurate predictions and can be useful. The same goes for the fin-tuning: who cares how the constants got their values, this view says, all that matters is that they do have the values and we have been able to measure them.

This “shut up and calculate” approach could be used in many parts of physics. We certainly don’t need the curving “fabric” of spacetime in order to use Einstein’s field equations to calculate predictions about how matter and energy will move through space and time. One could perhaps even say that the distinction between MOT and IOT is that MOT has interpretations that appeal to human intuition where IOT does not.

These questions I’ve been considering have to do with what is known as scientific realism and scientific anti-realism (or instrumentalism). The scientific realist says that the putative “fabric” of spacetime or fields in QFT are real entities. Indeed, a popular argument by scientific realists is that it would be a miracle if our predictions were so exquisitely true if these things did not exist in some important way (known as the no-miracle argument or NMA). Meanwhile, scientific anti-realism says that these proposed objects are just useful (instrumental) ways of talking about these things. It is the “shut up and calculate” view of quantum mechanics, meaning that we shouldn’t waste our time discussing what the ontological nature of the wavefunction actually is. This is popularly framed in what is known as pessimistic induction, which essentially says that every sort of ontological entity that has been postulated in the past has been shown to be wrong and we have no reason to think that our current entities (spacetime “fabric,” quantum fields) won’t go the way of the luminiferous aether and phlogiston. Scientific structuralism attempts to bridge the gap between realism and anti-realism, although structuralism in science has itself split between the schools of ontic structural realism (the structure exists and is the ground of reality, e.g., it-from-bit) and epistemic structural realism (the structure exists but is realized by some deeper entities not accounted for in our theories, e.g., it-from-bit-from-it).

The ontological status of Ontological Theories, whether MOT or IOT, has been examined by people like Rudolph Carnap and W.V.O Quine. Carnap talked of linguistic frameworks, whereby the ontological reality of a theory is an invalid attempt at and external view of the theory.

Are there properties classes, numbers, propositions? In order to understand more clearly the nature of these and related problems, it is above all necessary to recognize a fundamental distinction between two kinds of questions concerning the existence or reality of entities. If someone wishes to speak in his language about a new kind of entities, he has to introduce a system of new ways of speaking, subject to new rules; we shall call this procedure the construction of a linguistic framework for the new entities in question. And now we must distinguish two kinds of questions of existence: first, questions of the existence of certain entities of the new kind within the framework; we call them internal questions; and second, questions concerning the existence or reality of the system of entities as a whole, called external questions. Internal questions and possible answers to them are formulated with the help of the new forms of expressions. The answers may be found either by purely logical methods or by empirical methods, depending upon whether the framework is a logical or a factual one. An external question is of a problematic character which is in need of closer examination.

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From the internal questions we must clearly distinguish external questions, i.e., philosophical questions concerning the existence or reality of the total system of the new entities. Many philosophers regard a question of this kind as an ontological question which must be raised and answered before the introduction of the new language forms. The latter introduction, they believe, is legitimate only if it can be justified by an ontological insight supplying an affirmative answer to the question of reality. In contrast to this view, we take the position that the introduction of the new ways of speaking does not need any theoretical justification because it does not imply any assertion of reality. We may still speak (and have done so) of the “acceptance of the new entities” since this form of speech is customary; but one must keep in mind that this phrase does not mean for us anything more than acceptance of the new framework, i.e., of the new linguistic forms. Above all, it must not be interpreted as referring to an assumption, belief, or assertion of “the reality of the entities.” There is no such assertion. An alleged statement of the reality of the system of entities is a pseudo-statement without cognitive content. To be sure, we have to face at this point an important question; but it is a practical, not a theoretical question; it is the question of whether or not to accept the new linguistic forms. The acceptance cannot be judged as being either true or false because it is not an assertion. It can only be judged as being more or less expedient, fruitful, conducive to the aim for which the language is intended. Judgments of this kind supply the motivation for the decision of accepting or rejecting the kind of entities.

Thus it is clear that the acceptance of a linguistic framework must not be regarded as implying a metaphysical doctrine concerning the reality of the entities in question. It seems to me due to a neglect of this important distinction that some contemporary nominalists label the admission of variables of abstract types as “Platonism.” This is, to say the least, an extremely misleading terminology. It leads to the absurd consequence, that the position of everybody who accepts the language of physics with its real number variables (as a language of communication, not merely as a calculus) would be called Platonistic, even if he is a strict empiricist who rejects Platonic metaphysics.

Internal questions can say nothing of the ontological status of its subjects. External questions can only pertain to the utility of a theory, not to its actual ontological status. This view has always struck me as the “shut up and calculate” approach to science. In quantum mechanics, the Schrodinger equation, for example, gives the linguistic framework for answering internal questions – what is the probability of getting a particular result? – and the external question is whether or not these predictions are useful for whatever it is that we want to apply quantum mechanics. To even ask whether it’s a pilot wave or a split in the universe is invalid because these things are outside the linguistic framework and do nothing to tell us about the utility of quantum mechanics. Carnap was famously a logical positivist (aka logical empiricist) and so had no patience for such navel gazing sorts of questions as what things actually are (i.e. what is there ontological status).

Quine, on the other hand, talked about ontological commitment:

The locus classicus for Quine’s criterion is “On What There Is”. Quine writes:

A theory is committed to those and only those entities to which the bound variables of the theory must be capable of referring in order that the affirmations made in the theory be true. ^[2] (Quine 1948: 33)

To illustrate: if a theory contains a quantified sentence ‘∃x Electron(x)’ [read as “there exists x such that x is an electron”], then the bound variable ‘x’ must range over electrons in order for the theory to be true; and so the theory is ontologically committed to electrons. (For an introduction to the logic of quantifiers and bound variables, the basics of which are presupposed in this article, see Shapiro (2013).)

Talk of “commitment” has an unfortunate connotation: it applies more naturally to persons than to theories. But Quine’s criterion should be understood as applying to theories primarily, and to persons derivatively by way of the theories they accept (Quine 1953: 103). It would be more perspicuous to speak simply of the existential implications, or ontological presuppositions, of a theory. But ‘ontological commitment’ is well entrenched, and it would be pointless to try to avoid it.

Or, to oversimplify, if your theory requires that some entity or substance exist in order for the theory to work, then you are committed to the ontological existence of that entity or substance; you are not committed to any entities or substances that do not alter the sorts of predictions your theory makes (i.e. don’t add unnecessary entities or substances to your theory). This works well for MOT, but perhaps not always for IOT. But even applying it to MOT we are shying away from the question of whether something (say, the “fabric” of spacetime or quantum fields) actually exists as real entities or substances. Just because we need to commit ourselves to its existence for the theory to fully work says nothing about its actual existence.

It’s possible that neither Carnap nor Quine would say that there is not some fact of the matter, some truth value to, say, the proposition that “spacetime is a substance X.” But what they both might say is that, at best, such questions are unhelpful and unknowable. Some might see these attitudes as defeatist and even unhelpful – thinking about such questions of “what is there?” can potentially lead to progress in science that would not be possible by taking the “shut up and calculate” approach. Others might see it as useful because people won’t waste their time pondering unanswerable questions.

My own view is informed by my pragmatist approach. Theories, or Kuhnian paradigms, must be accepted for practical reasons, but the hope is to find something more accurate. Theories, like everything in science, are an attempt at being as close to what is real as possible. The ontological status of a theory has to be judged on three things, which I talked about in my post about science and God:

What we can say for our purposes, however, is that we want to weigh evidence and formulate theories to explain the data that are A) parsimonious, B) falsifiable, and C) give data that is in principle equally accessible to everyone (hence why science prefers to study phenomena that are quantifiable and measurable, because 1 kilogram is 1 kilogram for everyone, regardless of where and when they were born).

I might clarify here that, under the falsifiable criteria, the theory can be judged on how accurate its predictions are.

With my stance there is still no way to really know what the ontological status of scientific theories, specifically MOT and IOT type theories, is. That doesn’t make discussing and thinking about such things a waste of time, in my opinion. I am not in the “shut up and calculate” camp. But I do wonder if humans are even capable of ever understanding the universe at that level.