Abstract
Views of theory structure in philosophy of science (semantic and syntactic) have little to say about how theories are actually constructed; instead, the task of the philosopher is typically understood as reconstruction in order to highlight the theory’s essential features. If one takes seriously these views about theory structure then it might seem that we should also characterize the practice of building theories in accordance with the guidelines they set out. Examples from some of our most successful theories reveal nothing like the practices that conform to present accounts of theory structure. Instead there are different approaches that partly depend on the phenomena we want to account for and the kind of theory we desire. At least two strategies can be identified in high energy physics, (1) top down using symmetry principles and (2) bottom up strategy beginning with different types of models and gradually embedding these in a broad theoretical framework. Finally, in cases where methods and techniques cross disciplines, as in the case of population biology and statistical physics, we see that theory construction was largely based analogical considerations like the use of mathematical methods for treating systems of molecules in order to incorporate populations of genes into the theory of natural selection. Using these various examples I argue that building theories doesn’t involve blueprints for what a theory should look like, rather the architecture is developed in a piecemeal way using different strategies that fit the context and phenomena in question.
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Notes
- 1.
For an extended discussion see da Costa and French (2003).
- 2.
What this suggests, then, is that as philosophers our first concern should be with the exact specifications of theoretical structure rather than how the models used by scientists are meant to deliver information about physical systems.
- 3.
But once this occurs the state-space models take on a linguistic dimension; they become models of the theory in its linguistic formulation. Similarly, in Suppes’ account, when it comes to specifying the set theoretical predicate that defines the class of models for a theory, we do need to appeal to the specific language in which the theory is formulated. And, in that context, which is arguably the one in which models become paramount, they cease to become nonlinguistic entities. But as long as no specific language is given priority at the outset, we can talk about models as nonlinguistic structures.
- 4.
We can axiomatize classical particle mechanics in terms of the five primitive notions of a set P of particles, an interval T of real numbers corresponding to elapsed times, a position function s defined in the Cartesian product of the set of particles and the time interval, a mass function m and a force function F defined on the Cartesian product of the set of particles, the time interval and the positive integers (the latter enter as a way of naming the forces). A realization or model for these axioms would be an ordered quintuple consisting of the primitives \({\text{P}} = < {{\text{P}},{\text{T}},{\text{s}},{\text{m}},{\text{f}}} >\). We can interpret this to be a physical model for the solar system by simply interpreting the set of particles as the set of planetary bodies, or the set of the centers of mass of the planetary bodies.
- 5.
The notion that these are different theories is typically characterized in terms of the difference between forces and energies. The Newtonian approach involves the application of forces to bodies in order to see how they move. In Lagrange’s mechanics, one does not deal with forces and instead looks at the kinetic and potential energies of a system where the trajectory of a body is derived by finding the path that minimizes the action. This is defined as the sum of the Lagrangian over time, which is equal to the kinetic energy minus the potential energy. For example, consider a small bead rolling on a hoop. If one were to calculate the motion of the bead using Newtonian mechanics, one would have a complicated set of equations that would take into account the forces that the hoop exerts on the bead at each moment. Using Lagrangian mechanics, one looks at all the possible motions that the bead could take on the hoop and finds the one that minimizes the action instead of directly calculating the influence of the hoop on the bead at a given moment.
- 6.
Displacement also served as a model for dielectric polarization; electromotive force was responsible for distorting the cells, and its action on the dielectric produced a state of polarization. When the force was removed, the cells would recover their form and the electricity would return to its former position (Maxwell 1965, 1: 492). The amount of displacement depended on the nature of the body and on the electromotive force.
- 7.
For a more extensive discussion of this point, see Morrison (2008).
- 8.
His attachment to the potentials as primary was also criticized, since virtually all theorists of the day believed that the potentials were simply mathematical conveniences having no physical reality whatsoever. To them, the force fields were the only physical reality in Maxwell’s theory but the formulation in DT provided no account of this. Today, of course, we know in the quantum theory that it is the potentials that are primary, and the fields are derived from changes in the potentials.
- 9.
The methods used in “A Dynamical Theory” were extended and more fully developed in the Treatise on Electricity and Magnetism (TEM), where the goal was to examine the consequences of the assumption that electric currents were simply moving systems whose motion was communicated to each of the parts by certain forces, the nature and laws of which “we do not even attempt to define, because we can eliminate [them] from the equations of motion by the method given by Lagrange for any connected system” (Maxwell 1873, Sect. 552). Displacement, magnetic induction and electric and magnetic forces were all defined in the Treatise as vector quantities (Maxwell 1873, Sect. 11, 12), together with the electrostatic state, which was termed the vector potential. All were fundamental quantities for expression of the energy of the field and were seen as replacing the lines of force.
- 10.
This section draws on work presented in Morrison (2000).
- 11.
In order to satisfy the symmetry demands associated with the SU(2) group and in order to have a unified theory (i.e., have the proper coupling strengths for a conserved electric current and two charged W fields), the existence of a new gauge field was required, a field that Weinberg associated with a neutral current interaction that was later discovered in 1973. For a discussion of the difficulties surrounding the neutral current experiments, see Galison (1987) and Pickering (1984).
- 12.
I should also mention here the importance of symmetry and the eightfold way in predicting the existence of particles.
- 13.
For a longer discussion of this case see Morrison (2002).
- 14.
I would like to thank the Social Sciences and Humanities Research Council of Canada for research support and the editors for helpful comments and suggestions for improvements.
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Morrison, M. (2018). Building Theories: Strategies Not Blueprints. In: Danks, D., Ippoliti, E. (eds) Building Theories. Studies in Applied Philosophy, Epistemology and Rational Ethics, vol 41. Springer, Cham. https://doi.org/10.1007/978-3-319-72787-5_2
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