The Knight’s Song, or What is a [scientific] theory?

“Or else it doesn’t, you know. The name of the song is called ‘Haddocks’ Eyes.’”
“Oh, that’s the name of the song, is it?” Alice said, trying to feel interested.
“No, you don’t understand,” the Knight said, looking a little vexed. “That’s what the name is called. The name really is ‘The Aged Aged Man.'”
“Then I ought to have said ‘That’s what the song is called’?” Alice corrected herself.
“No, you oughtn’t: that’s quite another thing! The song is called ‘Ways and Means': but that’s only what it’s called, you know!”
“Well, what is the song, then?” said Alice, who was by this time completely bewildered.
“I was coming to that,” the Knight said. “The song really is ‘A-sitting on a Gate': and the tune’s my own invention.”
[Through the Looking-Glass, chapter 8]

Few words carry the weight that the Greek word theoria carries today. It is a word that applies to everything from politics to philosophy to mathematics, art, economics, psychology and of course, the natural sciences. Usually contrasted to another Greek word praxis, meaning practice or doing, it is the mental view one has of some aspect of the world. Beyond that, there is almost nothing in common with all uses of the term, especially now that it has been extended to apply to all of our general dispositions to observe and learn.

It comes as something of a surprise to me that the philosophy of science does not have a neat discussion I can locate of what counts as a theory in science. There are two general metalevel views – the traditional or “syntactic” notion and a structural or “semantic” notion – but these do not tell us what theories are, only what they entail in a more general philosophical sense. The syntactic notion holds that theories are logical theorems and their derivations, while the semantic view holds that theories are models that have real world interpretations. The slogan for the semantic view is

SEM: A theory is a collection of models (cf. McEwan unpublished)

There seems not to be an equivalent slogan for the syntactic view, but we can invent one:

SYN: A theory is an axiomatic system in some formal language

However, neither of these slogans make clear either what the difference between the two actually is, or what scientific theories, the things scientists take themselves to be using, making and testing, are. Instead we are dealing with logical objects – sentences, sets, classes and axioms. This is a dispute between philosophers (indeed, between schools of philosophy, the logical positivists supposedly holding SYN, following Carnap, and the post-positivists holding SEM (two originators of this view are Frederick Suppe and Bas van Fraassen).

SEM is about “model-theoretic models”, which is to say “an interpretation which satisfies some set of sentences (or sentential formulae). An interpretation specifies a set of individuals (the domain or universe of discourse) and defines of all the appropriate symbols (i.e., constant, function and predicate symbols) of the language on that set” (McEwan). SYN is a set of sentences in a formal (that is a logico-mathematical) language. Very roughly, a SEM theory is a structural representation of the world, while a SYN theory is a set of formal statements, each of which has some truth value. Both of these are highly abstract objects.

At the other end of the scale, we find scientists talking about theories as laws, prediction techniques, intellectual schemes, descriptions (sometimes) and even extended hypotheses. The Folk, on the other hand, treat “theory” as a special kind of guess. Creationists and other dissemblers regarding some science or other they object to play very strongly on these ambiguities and polysemies.

So I am left to wonder what a theory is (as opposed to how philosophers explicate theories in philosophy). We can consider a few senses for a theory in some domain of investigation:

  • The Mathematical Sense: A theory is some class of mathematical axioms and all their formal implications. This is sometimes called the axiomatic sense of theory – a theory, the real thing, is a class of mathematical theorems taken to be axioms.
  • The Interpretation Sense: A theory is a set of mathematical statements or structures together with rules for interpreting those statements.  If you have a mathematical equation that purports to describe how things fall, you need to know what to interpret the variables in that equation as referring to.
  • The Representation Sense: A theory is a description of the way things are in some domain. It allows the theorist to explain, predict, and manipulate those things.
  • The Worldview Sense: A theory is the set of beliefs that enables the theorist to engage with the world, structuring observation, action, reasoning and expression. This is effectively Thomas Kuhn’s notion of a “paradigm” or his later explication “exemplar”, some conceptual scheme that guides everything in the discipline.
  • The Practical Sense: It seems a bit odd to call a theory “practical” when it is usually contrasted with practice (praxis), but in this sense a theory is the set of conceptual commitments that the theorist employs to do things in the domain. So having a theory enables one to identify the relevant objects under study.
  • The Causal Sense: A theory is an explanation in terms of the causes of objects in the domain

Each of these senses appeals to some intellectual activity or state, but they vary greatly: the mathematical and interpretation senses involve mathematical equations or statements, the representation and worldview senses appeal to linguistic objects such as statements, sentences or logical formulae. The worldview and practical senses involve action-guiding stances. The causal sense is common but not universal. At best we can say they all involve beliefs (in the sense of mental stances, not faith statements necessarily). Of course, an actual theory may exhibit many or even all of these senses.

When we look at actual theories, they typically involve formal models – equations, simulations, algorithms – but this is not true of some older theories prior to the flowering of mathematisation of all science. It is also often not true of theories in domains that lack well-elaborated accounts. For example, theories in psychology are often verbal. Darwin’s theories (I count seven of them) were not mathematical at all, although he clearly intended them to be filled out later (as they were, apart from his theory of heredity). Freud’s theories remain unmathematised. So it doesn’t follow that for something to be a theory, it must be a mathematical structure, even if the philosophical analysis of theories develops a mathematical view. The reason is that “theory” in philosophy is a different beast to “theory” in science, and the relation is more like the relation between “concept” in philosophy and my concept of a television, for example.

So we might entertain the heresy that there is actually no “natural kind” in science that answers to “theory”, or, if you like, there’s no such thing as a theory, just lots of individual and particular intellectual constructs that get called theories. P. D. Magnus has argued that the term “theory” is a “family resemblance predicate” in which there are multiple meanings that overlap and cluster, but which have no necessary and sufficient definienda for all theories (Magnus unpublished), in an analogy with my favourite term of science, “species”. I think that this is correct, but I would go one further, and say that “theory” (unlike “species”) is a term that lacks any substantial meaning in science, and is really an assertion of the sociological status that some ideas have attained in a discipline, which can be for programmatic, political, or educational reasons as well as explanatory. A good theory will exhibit the majority of the cluster properties, but it doesn’t follow that theory is a category that stands alone, as it were, from the psychological, historical and social aspects of science.

What gets called a theory depends on no unique set of inherent properties of the theories themselves. This has some deep implications for thinking about science, if correct. Let’s consider some of them: the scientific process, domain specificity, and theory-dependence of observation.

The scientific process

Scientists are introduced to their disciplines in various ways, but nearly all of them are taught at some point that there is a scientific method. This methodism is, however, itself indefinable. Some accounts introduce a cycle of conjecture, testing, formulation, further  testing and then publication as a law or generalisation. Others focus on the use of statistical adequacy. Yet others make consilience (abductive reasoning) a key virtue – many lines of investigation must coincide.

Nearly all of them work on conceptual elements: statements in ordinary, formal or mathematical languages. Some domains or disciplines are more formalisable than others, but independently of this, scientists work with “hypotheses”, which, when sufficiently well established, become “theories”. In short, a theory is what a hypothesis wants to be when it grows up.

If there is no common property for theories, apart from properties held by things that aren’t theories by any estimation, then this picture of science, while not false, is misleading. There can be no singular method, because there is no singular destination for scientific ideas (see Magnus’ paper for a good discussion about what count as scientific ideas). And as famously expressed by Feyerabend:

It is clear, then, that the idea of a fixed method, or of a fixed theory of rationality, rests on too naive a view of man and his social surroundings. To those who look at the rich material provided by history, and who are not intent on impoverishing it in order to please their lower instincts, their craving for intellectual security in the form of clarity, precision, ‘objectivity’, ‘truth’, it will become clear that there is only one principle that can be defended under all circumstances and in all stages of human development. It is the principle: anything goes. [Against Method pp27-28]

If there are no essential features for theories, then there are no essential methods for attaining them. On the other hand, I think that the simple view that anything is or can be science is equally mistaken. Feyerabend did not actually argue that anything goes, but instead that there is no fixed method; this is a reductio. He knew perfectly well that disciplines have canon of reasoning and methods, and that some methods are inadequate or unfruitful (no aid and comfort to creationists in this argument, at any rate).

Domain specificity

One assumption often made about science is that it is divided into fields of inquiry that are themselves more or less natural. We think, for example, of biology as a natural subset of natural processes where we do not think of medicine that way (because medicine uses techniques and ideas that also apply to veterinary science). One standard view about domains in science is that they are effectively defined by the best attested theory of the phenomena in the domain. As theories develop, and as some parts of a domain are explained by theories in other domains, the scope of the domain is refined and revised (consider how much biology has been relegated to organic chemistry, or psychology to neurobiology).

If, however, we find that there are no such privileged conceptual constructs as theories, what does this mean for domains? How do we anchor domains (like biology) in natural ways? We can always give institutional arguments for domains, like saying that there is a Biology faculty in universities, or a course of educational requirements in schools. Or we can argue that it is easier to teach techniques when bundled together (microscopy, field observation, etc.) but it may just as easily have turned out a different way. Arguments about “what is “life”, for example, presuppose the naturalness of that domain (as do the NASA attempts to locate evidence of “life” elsewhere than earth), but if there is nothing that ties life together but human practical considerations and a collection of theories that are not entirely connected or commensurate, why bother? Why not just further divide the domains into groupings that are natural? Why, for example, does biology consider both evolution by natural selection and biochemistry, the Krebs cycle and ecology, behaviour and biogeography?

Attempts to formulate ontologies of domains also typically derive from the theoretical commitments of the domain (atoms are part of the domain of physics, while pain sensations aren’t); so if the theoretical commitments are sui generis to the domain because the nature of “theory” in that domain is unique also, we have a problem of ontological relativity, which may or may not be a problem, depending on how you think ontologies should be handled.

This is, in effect, an argument for a descriptive pluralism. Pluralisms are often thought of as some kind of failure or postmodern relativism, but I see them rather differently. We start our investigations of things based on the phenomena that present themselves to our inspection. Since we have prior sensory, social and conceptual commitments which may or may not be reliable guides to the structure of the world, we very often have to revise our concepts to fit what we learn by investigation. So, “fish” no longer means any thing that lives in water and moves of its own accord, and humans are now apes. Pluralism is a necessary aspect of discovering that the world wasn’t structured the way we naively thought it was. It is a recognition that words matter less than the world they describe.

But this indicates something about science that is so obvious as to almost not need saying: evidence – observation, measurement and experiment – takes priority over theory. That is perhaps a dumb thing to say, or perhaps it is so dangerous as to be obviously false, depending on what you think about our ways of knowing and explaining (theoretical constructionists would take the latter tack). But I think that theories, and domains demarcated by theories, are definable solely in terms of their being something other than evidence. In short, a theory is what evidence isn’t. That leads naturally to the next point.

Theory dependence of observation revisited

I have previously discussed the “theory-dependence of observation thesis (TDOT)” in detail, so I will be brief. If theory itself is not a natural kind, the claim that observation relies upon it falters. Of course our conceptual furniture affects how we observe – this follows from the mere existence of trained observers – but the nonexistence of Theory (that is, as a natural kind) means that the sting of the TDOT is largely removed. It resolves down to the view that we observe things that we have learned to observe. This is not, I think, so deep as the TDOT5 claim defended by Kuhnians at one time. It certainly does not license the sorts of claims that are sometimes made that science is a self-contained hermeneutic bubble just like any other world view.

Conclusion

I think this is significant in part because it helps up to understand how science really proceeds. The notion of “law” in science has been deprecated recently amongst philosophers (e.g., Cartwright et al. 2005); it is time to deprecate “theory” also.

It also means that what we call a theory and how we talk about the notion of theory is not unlike the Knight’s song. We often refer to philosophical accounts of representation, explanation and formalisation when we discuss “theory” (excluding the terminological arguments amongst other philosophical traditions, like Marxist or phenomenological schools) when we should be talking about the ways scientists use the terms, and then, and only then, consider the philosophical implications. And if “theory” lacks the sort of reality it is sometimes held to have, if it simply is whatever in science is not evidentiary or probative, then we should be more empiricist in our philosophy.

I take this line, of course, to defend the claim that one thing science often does is, independently of theory, classify the world as a way to investigate it. If theory is not a natural kind, then it becomes clear that we can do this, only what we rely upon, our conceptual commitments that make a trained observer a better systematist, is more complex than “theory” suggests it would be.

Cartwright, Nancy, Anna Alexandrova, and Sophia Efstathiou. 2005. Laws. In The Oxford Handbook of Contemporary Philosophy, edited by F. Jackson. New York: Oxford Univ Press:792-818.

Feyerabend, PK. 1975. Against Method. New York: Verso Editions.

Magnus, P. D. Unpublished. What SPECIES can teach us about THEORY.

McEwan, Micheal. Unpublished. The Semantic View of Theories:Models and Misconceptions.

31 thoughts on “The Knight’s Song, or What is a [scientific] theory?

  1. None of this comes as a revelation to folks who do science in “messy” realms like biology, where concrete, here’s-the-edges definitions are just invitations to exceptions. A LOT of the terms are very loosely defined, which must be frustrating for structured thinkers (the edges are firmer in physics and chemistry), but it’s just the, pardon the expression, Nature of the Beast.

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