4 The structure and metaphysics of scientific theories
4.2 Reduction, replacement and the progress of science In showing that Kepler’s and Galileo’s laws were but special cases of more
general laws true everywhere and always, Newton not only explained why their laws obtained, he also undercut the basic metaphysical conviction that the realm of the heavens was somehow different than that of the Earth.
Along with Galileo’s telescopic discovery of the craters and other imperfec-tions of the Moon, Newton’s revolution had a profound intellectual influ-ence far beyond the formal derivation which he provided to unify physical theory. Moreover, the power of Newton’s unification was further sustained in the ensuing two hundred years as more and more phenomena came to be explained (or explained in more precise quantitative detail) by it: eclipses, the period of Halley’s comet, the shape of the Earth – a slightly squashed sphere, the tides, the precession of the equinoxes, buoyancy and aerodynam-ics, parts of thermodynamaerodynam-ics, were unified and shown to be “the same underlying process” through the derivation of laws describing these phe-nomena from Newton’s four fundamental laws. Moreover, none of these laws appealed to future goals, purposes or ends. Instead, all identify prior or present causes (position and momentum), and all except the inverse square law identify forces that act through physical contact as sufficient to explain
physical processes. As such, Newtonian mechanics allows us completely to dispense with purposes, goals and ends as properties that pre-Newtonian science invoked to explain the behavior of physical systems. The success of Newtonian mechanics thus encouraged a world-view, a metaphysical theory, according to which the physical universe is just a vast “clockwork” mechan-ism in which there is no teleology of the sort we discussed in Chapter 3. Of course Newton’s theory could not explain the behavior of living things, though some “mechanists” among scientists and philosophers held out the hope that it would eventually explain everything in terms of deterministic laws about position, momentum and gravity. Biology, however, remained a safe haven for teleological explanations long after it was eliminated from physical science. Kant, who as we saw in Chapter 3, argued that Newtonian mechanics was necessarily true of the physical world, held that its purely mechanistic picture of the physical world could never be extended to explain the biological realm. There will, he said, “never be a Newton for the blade of grass”. As with his claims about the necessity of Newton’s laws, this claim of Kant’s was also overtaken by events.
Newton showed how Galileo’s and Kepler’s laws could be derived from his own theories as special cases. Philosophers of science refer to this deriva-tion of the laws of one theory from the laws of another as “inter-theoretical reduction” or simply “reduction”. Reduction requires that the laws of the reduced theory be derived from that of the reducing theory. If explanation is a form of derivation, then the reduction of one theory to another explains the reduced theory; in effect, it shows that the axioms of the less basic theory are theorems of the more basic one.
So the scientific revolution of the seventeenth century appears to consist in the discovery and reduction of Galileo’s and Kepler’s laws to Newton’s, and the progress of physics from the sixteenth century onwards is the history of less general theories being successively reduced to more general theories, until the twentieth century when suddenly theories even more general than Newton’s are framed, which in turn reduce Newtonian mechanics by deriva-tion: the special and general theories of relativity and quantum mechanics.
Newton’s laws are deducible from the laws of these theories by making some idealizing assumptions, in particular that the speed of light is infinite or at least that all other attainable velocities are much, much slower than the speed of light, and that idealizing assumption that energy comes in continu-ous amounts and not in discrete but very small units or “quanta”.
According to one traditional view in the philosophy of science, the reduc-tion of theories to more fundamental ones reflects the fact that science is suc-cessively enlarging its range and depth of explanation as more and more initially isolated theories are shown to be special cases, derived from a smaller and smaller number of more fundamental theories. Scientific change is scientific progress and progress comes in large measure through reduction.
In fact, reduction is also viewed as the characteristic relation among disci-plines once they attain the status of sciences. Thus, in principle, chemistry
should be reducible to physics, and biology should be reducible to chemistry via molecular biology. Similarly, we should seek a psychological science composed of laws themselves reducible to the laws of biology. Of course the social sciences have yet to or never will uncover laws reducible to those of natural science, via reduction to psychological laws. Therefore, these disci-plines lack an important feature common to scientific theories – linkage via reduction to the most fundamental and predictively powerful of the sciences, physics.
We can now understand some of the attractiveness of axiomatization as an account of how a theory explains by uncovering more general underlying mechanisms that systematize and explain less general ones. If the universe reflects the neat picture of layers of causal laws, each of which rests on a layer of laws below it that logically imply these laws, and if the universe is com-posed of a small number of basic kinds of things that behave in a uniform way and out of which everything else is composed, then there should be a uniquely correct description of nature which will take axiomatic form because reality is a matter of the complex being built up out of the simple in accordance with general laws. The commitment to axiomatization as giving the structure of theory and the relations among theories is tantamount to a metaphysical claim about the nature of reality: at bottom it is simple in composition and operation, and all the complexity and diversity of more complicated and more composite things are the result of the simplicity at the bottom of things.
Of course, this picture must be substantially complicated. To begin with, the notion that the laws of one theory may be directly derivable from those of another is too simple. Scientific progress involves the correction and improvement of a theory’s predictions and explanations by its successors. If the successor theory merely “contained” the original reduced theory as a logical consequence, it would incorporate the errors of its predecessor. For example, Galileo’s law of terrestrial motion implies that the acceleration of bodies falling towards the Earth remains constant, while Newton’s laws recognize that accelerations must increase owing to the gravitational force between the Earth and bodies approaching it. For predictive purposes we can neglect these slight increases in acceleration, but we must correct Galileo’s terrestrial mechanics, adding gravitational force, if it is to follow from Newton’s laws. Similarly, Mendel’s laws of genetics should not follow directly from laws in contemporary molecular genetics, for we know that Mendel’s laws are wrong. Phenomena like genetic linkage and gene cross-over falsify these laws. What we want of any reduction of Mendel’s laws to more fundamental laws of molecular genetics is an explanation of where Mendel’s laws go wrong as well as where they work. This suggests that reduction usually involves deriving a “corrected” version of the theory to be reduced from the more fundamental reducing theory.
But the requirement that the reduced theory must sometimes be “cor-rected” creates problems for the axiomatic view of theory change.
Some-times, one theory supersedes another not by reducing it, but by replacing it.
Indeed, replacement seems characteristic of a discipline’s becoming a “real”
science. For example, before the work of Lavoisier in the late eighteenth century, combustion was explained by “phlogiston” theory. Phlogiston was hypothesized to be a substance which escapes from things when they burn, but which owing to its character could not be directly observed. One trouble with phlogiston theory is that careful measurements revealed that burning a substance increases its weight. Therefore if phlogiston is liberated in com-bustion, it must have negative weight. Since weight depends on mass and on the strength of the Earth’s gravitational force, which presumably remains constant when things burn, it would seem that phlogiston has negative mass. This is something hard to reconcile with Newtonian physics. For this and other reasons, chemists were dissatisfied with phlogiston theory despite some of its apparently satisfactory explanations of chemical experiments in combustion. Lavoisier advanced a new theory, which hypothesized a quite different unobservable substance, which he termed “oxygen” which is incor-porated by substances when they burn and so, among other things, need not have negative mass.
Lavoisier’s oxygen theory did not reduce the older phlogiston theory of combustion. It replaced the “ontology” – the kinds of things phlogiston theory was about: phlogiston, dephlogisticated air, etc., and its alleged laws, by providing a completely different kind of thing, oxygen, which could not be linked up to phlogiston in ways that would enable this latter concept to survive in Lavoisier’s theory of combustion. Attempts to define phlogiston in terms of the concepts of Lavoisier’s theory of combustion will not enable us to derive the phlogiston theory from Lavoisier’s theory. And of course, Lavoisier’s theory is the beginning of modern chemistry. Accordingly, scien-tists say that there never was any such thing as phlogiston.
By contrast, when a theory is reduced to a broader or more fundamental one, the “ontology” of the reduced theory – the kinds of things it makes claims about – is preserved. The reason is that reduction is a matter of deduction of the law of the reduced theory from those of the reducing theory, and such derivation is possible only when the terms of the two theo-ries are connected. You can’t derive the laws of Mendelian genetics from those of molecular genetics unless the Mendelian gene can be defined in terms of nucleic acids. For it is assemblages of DNA which molecular genet-ics are about and Mendelian genes which Mendel’s laws are about: a law about all As being Fs will only follow from a law about all As being Bs if every B is identical to a C and every C is identical to an F. Indeed, a large measure of the achievement of reduction is the formulation of these identi-ties. For example, the reduction of the thermodynamics of gases to statistical mechanics turns on the identity we noted above:
3k/2 [T in degrees Kelvin]⫽(mv2)
Whether we treat this identity as a definition or a general law relating tem-perature and kinetic energy, its formulation was the crucial breakthrough that enabled physicists to reduce the behavior of gases to the behavior of the molecules which compose them.
It seems a characteristic feature of reduction that it unifies observable phenomena or at least unifies the generalizations that report them to more and more fundamental, more and more accurate regularities which are more and more observationally inaccessible. Having begun with cannonballs and planets, physics succeeds finally in explaining everything in terms of unde-tectable microparticles and their properties. So, it seems to make explana-torily basic what is epistemically most problematical – hardest to acquire knowledge of. While the official epistemology of science is empiricism – the thesis that our knowledge is justified only by experience, that is, experiment and observation – its explanatory function is fulfilled by just those sorts of things that creatures like us can have no direct experience of. Indeed, the microparticles of modern high-energy physics are things no creature like us could have acquaintance with. And this fact raises the most vexing questions about the nature of scientific theories.
4.3 The problem of theoretical terms and the things