Theories

Scientific theories have been at the heart of modern philosophy of science from its beginning. And although the philosophical interest for understanding the nature of theories has not diminished, there has been a substantial shift towards the study of scientific models as they are more accurate units of analysis of scientific practice.

Examples of scientific theories abound in scientific and non-scientific literature:

evolutionary theory in biology, relativity in physics, transition state theory in chem-istry, just to mention a few. Now, what exactly a theory encompasses is still the subject of many discussions among scientist, historians, sociologists, and, naturally, philosophers. The problem is that the concept of scientific theory is elusive, making it difficult to pinpoint what exactly it stands for, and what it includes in its scope.

Take as a simple problem the temporal validity of scientific theories: Ptolemaic interpretation of the planetary movement was valid even when the Copernican in-terpretation was already available. This means that the Ptolemaic theory included phenomena that, at a certain moment in history, the Copernican theory did not account for.

My interest here is not about scientific progress; it is not about delimiting a scientific theory from a pseudo-scientific theory; and it is certainly not about a thorough analysis of the nature of scientific theories. Rather, it lies in the historical grounds behind the evolution of the notion of scientific theory. When did it all begin?

One is more or less justified in setting the beginnings of philosophy of science as

we know it today with the Vienna Circle. Although the philosophical interest of the members of the circle were diverse, they all shared a fierce opposition to the use of metaphysics for the sciences as well as an overstated confidence in the use of logic for the natural sciences. The rejection of any intromission of metaphysics for conceptualizing the world along with a twentieth century marked by several important achievements in mathematics, logic, and theoretical science, boosted the confidence of the Vienna Circle. The theory of relativity by the great Albert Einstein became the cornerstone for the members of the Vienna Circle. Kurt Gödel and Hans Hahn in logic and mathematics, Richard von Mises in economics and political theory, and Otto Neurath in political economy also played a central role in the construction of a logically structured and metaphysics-free philosophy of science.² In the philosophical community, the members of the Vienna Circle later became known as ‘the logical positivists.’

The logical empiricist, a relative and successor of logical positivism, took scien-tific theories in a language-oriented way.³ Theories then became linguistic entities in the form of an axiomatic system, related by deductive calculus and consisting of an abstract formalism, axioms of the theory, and correspondence rules that provided the necessary interpretation for theoretical terms.⁴

The search for scientific terms with fixed and precise meanings lead the empiricist to take the language of a theory as divided into two classes: a non-logical class, known as theobservational vocabulary (VO) which defined the terms in the theory by empirical means (i.e., by means of observation, experimentation, and measurement);

and a theoretical vocabulary (VT), that is, the class of terms of a scientific theory have not been defined by means of empirical operations.⁵ For instance, if a theory includes in its formulation the term ‘thermometer,’ then this term refers to a thing in the world since a thermometer can be touched, manipulated, used for measuring, and so forth. Now, if the theory includes a more abstract term such as ‘density’

and defines it as the division between ‘mass’ and ‘volume,’ then the theory will be meaningful only if these latter two terms are empirically defined. In other words, only if atomic terms used in a theory (such as ‘mass’ and ‘volume’) are empirically defined, can the notion of ‘density,’ and in turn the entire theory, be meaningful.

The first of our terms, ‘thermometer,’ belongs to theobservational vocabulary (VO), whereas the second term ‘density’ belongs to thetheoretical vocabulary (VT) until it is empirically defined.

The distinction between unobservable and observable, a distinction which grounds the dichotomy of the two vocabularies, presupposes that a term inVT can be ‘moved’

into VO when given the right conditions. Indeed, what is unobservable at one

mo-ment in time becomes observable at another, as science progresses. The term ‘elec-tron’ in the pre-Thomsonian era belonged toVT until Joseph J. Thomson developed his famous experiment.⁶ Now, to the empiricist’s mind, it is important to reduce the number of terms inVT to make an impact on the scientific interpretation of theories.

The question was, therefore, how can a term in VT be moved to VO? The answer came with ‘operationalism,’ a theory that defined theoretical terms by means of concrete scientific procedures, such as observation and measurement. For instance, the theoretical term ‘volume’ is defined by measuring the quantity of a liquid in a marked container. Thus understood, operationalism defines a term by relating it to one specific procedure.⁷ The problem was that a change of methods entailed a change in the definition of a term. In this sense, there were as many notions of

‘volume’ as scientific procedures available.

After enjoying a certain success, the logical empiricist view of theories came un-der intense attack. There were problems everywhere, including the unsatisfactory operationist approach. In fact, the root of most criticism was at the heart of the distinction between observational and theoretical vocabularies. Willard Van Orman Quine wrote a fundamental piece of work which criticizes this distinction, along with the traditional distinction between analytic and syntactic.⁸ Similarly, Karl Popper strongly objected to the observational and inductivist based scientific method pro-moted by the logical empiricist. In its place, he proposedfalsificationism as the only valid scientific method.⁹

These attacks had a very positive effect for the young philosophy of science, for they virtually forced philosophers to diversify the problems into subtopics, such as theories of scientific progress, the notion of scientific method, as Popper himself de-fended, or against scientific methods, as Paul Feyerabend did.¹⁰ Research programs, scientific realism, and scientific explanation,¹¹ are also part of the subjects in the new philosophy of science. It is no exaggeration to say that the logical positivist and his successor, the logical empiricist, set the agenda for the philosophy of science as we know it today.

The semantic view of theories emerged as the only decent rival to the logical empiricist. Theories were no longer understood as linguistic entities but identified with a class of set-theoretic structures (i.e., scientific models). Indeed, the proponent of the semantic view removed the syntactic peculiarities in the formulation of a scientific theory and, instead, focused on its underlying structure. In this vein, Isaac Newton’s own formulation of classical mechanics in the Principia, modern Lagrangian formulations, and modern Hamiltonian formulations are all variants of the same underlying theory, that is, of classical mechanics.¹² Theories became,

then, families of set-theoretic models that represented more accurately the complex relationships between theories, data, and phenomena.

Over the years, various versions of the semantic view of theories have been de-vised, and although they eventually suffered from heavy criticism, modern philos-ophy of science owes much of the introduction of models to the semantic view of theories.¹³

Now, a pervasive objection to the semantic view was that it made models highly dependent on theories.¹⁴ Indeed, the semantic view demanded that models be true of the theory, that is, that the relation between them was one of deriving the model from the theory. Proponents of an alternative conceptualization claimed that models not only do not depend on theories in the way suggested, but sometimes models do not hold any relationship to theories at all.¹⁵ Newton Da Costa and Steven French conceive this issue in the following way:

according to the Semantic Approach theories are families of mathematical models; if this approach is an adequate representation of scientific practice then any scientific model should feature as a member of such a family; how-ever, there are models which do not so feature, since they are developed inde-pendently of theory; hence the Semantic Approach is not an adequate repre-sentation of scientific practice. (Da Costa and French, 2000, 120)

Mary Morgan and Margaret Morrison, Mauricio Suarez, and others¹⁶ believe that the philosophical study of models must focus on their design, construction, and function in the context of scientific practice. The basic claim is that modelsmediate between theory and phenomena, and that neither of the relationships are deductive.

On the contrary, a model is ‘autonomous’ in the sense that it is not always clear how it relates to higher level theories or to phenomena.

In the remainder of this work I take the idea of ‘model as mediators’ as fundamen-tally correct. In the following section I analyze in more detail these considerations about scientific models.