Theories and Models in Sciences

2.1 Theories

The philosophy of science has proposed many theories regarding what is a theory. A general one has been offered by Morgan and Morrison (1999:13). For these authors, a theory is “a discourse used by scientists to express “principles that govern a group of phenomena.” Winther ads that “Effective scientific theories magnify understanding, help supply legitimate explanations, and assist in formulating pre­dictions” (Winther 2016).

A first one, proposed by the logical positivists (Carnap 1937; Reichenbach 1938; Hempel 1965; Nagel 1961) and traditionally called the “syntactic” view, sees a scientific theory as a collection of axiomatic statements and theorems.

Scientific theory is thus taken to be a syntactically formulated set of theoretical sentences (axioms, theorems, and laws) together with their interpretation via correspondence sentence (Winther 2016).

The second view of a theory is the “semantic view.” Here, the language of a theory must be mathematical (Suppes 1967). Or, to be more precise, as formulated by van Fraassen (1970:327), a theory is “always a mathematical structure,” but in which some interpretation, such as a Tarskian “model” for example, may define its semantics.

A model is called a model of a theory exactly if the theory is entirely true if considered with respect to this model alone. (Figuratively: the theory would be true if this model was the whole world) (van Fraassen 1989:218).

Though such views regarding theories have been widespread, they have been highly criticized (Winther 2016) for their limits and constraints.

This third view is grounded in the American pragmatism of Peirce, James, and Sellars and it has been influenced by Feyerabend, Hanson, Kuhn, Toulmin, Laudan, and Hacking. It is quite in opposition to the first two views. It has lately been renewed and reformulated by Rheinberger (1997), Giere (1999), Cartwright (1983), Morgan and Morrison (1999), as well as by many others.

According to this pragmatic view, most scientific theories are not formal and their explanation cannot be solely deductive or inductive. In fact, a theory is the result of complex cognitive processes that are points of view, perspectives, enquiry strategies regarding a phenomenon to be understood (Frigg and Hartmann 2012). And these perspectives are not just contextual (Scriven 1962). Such an under­standing builds specific theory structures:

To explain a phenomenon is to find a model that fits it into the basic framework of the theory and that thus allows us to derive analogues for the messy and complicated phe­nomenological laws which are true of it (Cartwright 1983:52).

In other words, as Winther says, a theory is constituted by a plurality of formal and informal components. For Cartwright (1983) and for Morgan and Morrison (1999), a theory of “a theory” must be more inclusive than what is proposed by the syntactic and semantic views, but without rejecting them. One way to achieve this is to approach the concept of theory through the concept of model. And models will become a dominant concept of the pragmatic view regarding theories.

2.2 Models in Science

The pragmatic view of scientific theories has underlined the role of models in science. For Cartwright et al. (1995), models should constitute the appropriate level of investigation to understand science.

Models are different from theories in that they focus more on the cognitive engagement of the scientific process than on the ontological commitment they may have with reality. In other words, models are not mini-theories in themselves. They are tools for the building of a theory. For Rheinberger (1997), models do not mainly serve to express what is known but mostly to “explore what is unknown.” Unfortunately, as Giere (1999) recalls, the relation between a theory and a model is not a well understood relation. There does not exist necessary nor sufficient con­ditions to identify which model satisfies a theory.

There are many senses of the term “model” in science, and these different kinds of modes serve distinct scientific ends (Giere 1999:1).

Naturally, as there are a multitude and a variety of possible points of view in a scientific enquiry, there will be a mosaic of models, as Baetu formulates so well:

Models anchor the diverse pieces of the mosaic of knowledge to a description of a phe­nomenon, on the one side, and to the methods and tools, experimental or theoretical, used to obtain each piece of the mosaic, on the other (Baetu 2013:2).

Each model being an approximation, a point of view, a perspective, etc., a theory appears as the background architecture that gives them their coherence. Points of view become comparable, and from this differentiability in models, coherence judgments emerge. This multiplicity and variety of models play an important epistemic role in the construction and in the value of a theory. Models are not just representations of observational data, they are constructions that, in their interac­tions, point to some “reality.” An anti-realist will focus on this constructivity feature of the models and will have to cope with the problem of explaining how, inter­actively, each partial model points to such reality. The realist will probably focus on models closest to observational practices and empirical verifications, but will, in turn, have to explain how other more conceptual if not physical models unveil reality.

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