Theory Construction vs Model Building Theories and Models

Theory Construction vs. Model Building

• Theories and Models • Semantic vs. Syntactic Approaches to Theories and Models • A Case Study: Darwin’s Theory of Natural Selection • Models and Theories in Evolutionary Biology

• hypothetico–deductivism, treated theories in all the sciences as sets of assumed or unproved axioms from which theorems are derived. • axioms, the underived, basic laws in theory, are usually expressed in terms that make no reference to observations and so cannot be tested directly. • Axioms are couched in observational terms • difficulties with this axiomatic approach. • deriving narrower theories from broader more basic ones, • the difficulty of providing a satisfactory account of the meaning(fullness) of theoretical terms.

Definition of model • Model in mathematics: meaning an interpretation of an abstract axiomatic system. • Model in science: • • the planetary model of the atom, the billiard ball model of a gas, Mendelian models of genetic inheritance, the Keynesian macro-economic model.

• second of our two problems for the axiomatic approach is the very idea that a theory is an axiomatized set of sentences in a formalized mathematical language. • 1937 John Maynard Keynes published The General Theory of Employment, Interest and Money. • a set of three linear equations, the so-called Keynesian model, • [aggregate income = consumption + investment + government spending] • [consumption is a function of income] • [investment is a function of “the marginal efficiency of capital”]

• none of the components of the Keynesian model is really to be understood as a robust contingent truth of the sort that figures as the axiom of some logical system. • Now the reason we call these definitions models is that they “fit” some natural processes more accurately than others • they may still be useful calculating devices, • Often a model advanced by a scientist is true by definition: e. g. an ideal gas is by definition just what behaves in accordance with the ideal gas law.

• The empirical or factual question about a model is whether it “applies” to anything closely enough to be scientifically useful—to explain and predict its behavior. • A theory is a set of hypotheses claiming that particular sets of things in the world are satisfied to varying degrees by a set of models that reflect some similarity or unity.

The “semantic” account of scientific theories • theories, according to which they are sets of models • claims about what things in the world satisfy these definitions, • contrast it to the axiomatic account the “syntactic” account for two related reasons: (a) it requires derivation of empirical generalizations from axioms in accordance with rules of logic, (b) the derivations which logical rules permit operate on the purely formal features— the syntax—of the axioms, and not the meaning of their terms. • the semantical approach has of course is that it focuses attention on the role and importance of models

• it is hard for the axiomatic analysis to accommodate the formulation of models known from the outset to be at most false but useful idealizations. • as an empirical generalization about real objects to be derived from axioms of the kinetic theory of gases, • When we try to frame theory of natural selection into an axiomatic system, the result is often rejected by evolutionary biologists as failing to adequately reflect the full richness of Darwin’s theory and its latter day extensions.

• Recall one of the metaphysical attractions of the axiomatic approach: its commitment to axiomatization as an account of how a theory explains by uncovering underlying mechanisms. • semantic approach makes no commitments to any underlying simplicity or to the reducibility of less fundamental theories (i. e. sets of models) to more fundamental theories • to the semantic approach’s indifference to the controversy surrounding realism. • construction of models as the fundamental task of science • Both the success and accuracy of science demands an explanation

• the realist will argue, the semantic approach shares with the axiomatic account a commitment to the existence of theories distinct from and different from the models on which it focuses. • A theory is the set of definitions that constitute the models plus the claim that there are things that, exemplify these definitions sufficiently well to predict their behavior • like the axiomatic account, the semantic approach is committed to the truth of general claims in science. • Whether theory (or a model) explains data as the realist holds, or only organizes it as the instrumentalist holds, theory can do neither without recourse to claims about this realm of unobservable things, events, processes, properties that an empiricist epistemology makes problematic.

A Case Study: Darwin’s Theory of Natural Selection • problems of testability and confirmation - adaptation as the result of purely causal processes • Darwin did not lay out theory of natural selection as a set of assumptions

Why do giraffes today have long necks? 1. Reproducing populations increase exponentially. 2. The capacity of any region to support any reproducing population is finite. Therefore: 3. There will always be a struggle for survival and reproduction among competing populations. 4. There is variation in the fitness of members of these populations and some of these variations are heritable. 5. In the struggle for survival and reproduction, the fittest variants will be favored and, therefore, 6. Adaptive evolution will occur.

• 1, 2, and 4 as axioms • 3, 5, and 6 as theorems. • Statement 1 to Thomas Malthus, a nineteenth-century economist who held that human populations increase geometrically while the food supply increases only arithmetically • By contrast to physical theories, every member of a species is different from every other member in some way or other;

• Natural selection as a passive filter that removes the unfit elements in a population shows that the purely mechanical vision of nature associated with Newton’s theory can be extended all the way through the life sciences, leaving no room for a teleological or purposive view of any part of nature. • sets of laws, theory of natural selection makes a number of hypothetical claims: if there is variation in heritable traits and if these variants differ in fitness, then there will be adaptational change. • For that conclusion we need initial conditions: • the assertion that some things reproduce, that • their offspring’s traits are inherited from their parents, and that these traits are not always exact copies, but • do in fact vary from parent to offspring and among offspring.

• evolution by natural selection requires reproduction with heritable variation, it is silent on how reproduction takes place, and tells us nothing about the mechanism of heredity: how traits are transmitted from parent to offspring.

Models and Theories in Evolutionary Biology • a Newtonian-style axiomatization is inadequate to capture one or another of the processes evolutionary biologists would describe as Darwinian evolution. • Richard Lewontin • 1. There is always variation in the traits of whatever it is that replicates or reproduces. • 2. The variant traits differ in fitness. • 3. The fitness differences among some of the traits are heritable.

• it is far too abstract to be applied to explain evolutionary processes or outcomes, and • its key-concepts—traits, fitness, replication/reproduction, heritability are open to interpretations that make theory false in some cases, and irrelevant to evolution in other cases. • is silent on the blindness of variations

• two simple Lotka–Volterra equations that model the cyclic relations between populations of predators and prey, parasites and parasitized • Lag • Of course there are cases where the equilibrium breaks down, for well-understood reasons. These are domains in which the model doesn’t work. • equilibrium modeling is even more characteristic of the centrality of models in evolutionary biology

• Herbert Spencer, “the survival of the fittest, ” • PNS: Given two competing populations, x and y, if x is fitter than y, then in the long run, x will leave more offspring than y • For heritable variations in fitness among reproducing entities won’t lead to changes in the distribution of traits without making a difference in reproductive rates. • “fitness” is a theoretical term, like “positive charge” or “atomic mass. ”

• But why are these the problems that an organism must solve to be fit? • How do they combine into over-all fitness? • How do we compare organisms for fitness when their abilities to solve any one of these problems differ?

(a) the problems the environment presents an organism with are ones whose solution increases the organisms chances to survive and reproduce, (b) we can calculate the degree to which organisms solve these various problems by measuring the organisms’ number of offspring, (c) two organisms are equally fit no matter how differently they deal with environmental problems, provided they have the same number of offspring.

• On the semantic approach a scientific theory is really more than the set of the models that take its name. • set along with the assertion that things in the world realize, satisfy, instantiate, exemplify these definitions sufficiently well to enable us to explain and predict their behavior • the semantic approach is committed to the truth of some general claims

• Unless we find ourselves at the end of inquiry when no further explanations of the fundamental laws of nature can be given, there will have to be some underlying mechanism or process which is shared among all the different things that realize the same settheoretical definition, an underlying mechanism which explains why the predictions we can make employing the model are confirmed