What is a Theory

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A simple definition of "theory" is the statement that a theory is a scientific explanation. This definition, however, itself requires an explanation that we could explore for a lifetime and still never really fully answer. An academic discipline, the philosophy of science, is devoted to answering this question, and this essay will briefly review some of the answers to the question "what is a theory?" that have been presented from the origins of the philosophy of science until the modern age. The major issue in the philosophy of science is DEMARCATION; how can you tell science from non science.

We will begin our discussion with the logical positivists, a school of the philosophy of science that developed in Vienna late in the 19th century. I will present logical positivism as described by Carl Hempel and Paul Oppenheim (H&O) in an article entitled "Studies in the Logic of Explanation", published in Philosophy of Science, volume 15, pages 576-579. Note that this essay is my take on these issues, and is hardly any sort of last word.

H&O present a model suggesting that scientific explanations consist of two main parts; the EXPLANANDUM, the  sentence describing the phenomenon to be explained and the EXPLANANS, the group of sentences added to account for the phenomenon. The explanans consists of two parts, the  ANTECEDENT CONDITIONS and COVERING LAWS.

To be scientific, an explanation must satisfy CONDITIONS OF ADEQUACY, which can have logical and empirical conditions.

To quote H&O directly:
 

Logical Conditions of Adequacy:
(R1) The explanandum must be a logical consequence of the explanans; in other words, the explanandum must be logically deducible from the information contained in the explanans; for otherwise, the explanans would not constitute adequate grounds for the explanandum.

(R2) The explanans must contain general laws, and these must actually be required for the derivation of the explanandum. We shall not make it a necessary condition for a sound explanation, however, that the explanans must contain at least one statement that is not a law; for to mention just one reason, we would surely  want to to consider as an explanation the derivation of the general regularities governing the motion of double stars from the laws of celestial mechanics, even though all the statements in the explanans are general laws (I take this to refer to a explanation that includes no mention of antecedent conditions)

(R3) The explanans must have empirical content; that is, it must be capable, at least in principle, of test by experimentation or observation. This condition is implicit in R1, for since the explanandum is assumed to describe some empirical phenomenon, it follows from R1 that the explanans entails at least one consequence of empirical character, and this fact confers upon it testability and empirical content.  But the point deserves special mention because certain arguments which have been offered as explanations in the natural and in the social sciences violate this requirement.

Empirical Conditions of Adequacy
The sentences constituting the explanans must be true. That in a sound explanation, the statements constituting the explanans have to satisfy some condition of factual correctness is obvious. But it might be more appropriate to stipulate that the explanans has to be highly confirmed by all the relevant evidence available rather than it should be true. This stipulation, however, leads to awkward consequences. Suppose that a certain phenomenon was explained at an earlier stage of science, by means of an explanans which was well supported by the evidence then at hand, but which has been highly disconformed by more recent empirical findings (think of this when we go over Kuhn!). In such a case, we would have to say that originally the explanatory account was a correct explanation, but that it ceased to be one later, when unfavorable evidence was discovered. This does not appear in accord with sound common usage, which directs us to say that on the basis of the limited initial evidence, the truth of the explanans, and the soundness of the explanation, had been quite probable, but that the ampler evidence now available makes it highly probable that the explanans is not true, and hence that the account in question is not-and never has been-a correct explanation.
An abstraction of the model is as follows:
 
C1, C2, C3....Ck    Statements of general conditions
                                                                                \
+                                                                  Explanans
                                                                                /
L1, L2, L3...Lr      General laws

=

E                         Description of the empirical            Explanandum
                            phenomenon to be explained

Remember that H & O seek to describe how scientists explain things; trying to answer the question "what is a theory". H & O are philosophers, not scientists. They look at science, physical sciences in particular, and try to describe what scientists are doing when they prepare theories.

What  H & O describe is what happens in most science, physical or biological. We can consider the example of some disease that someone investigated to determine whether or not the disease is a genetic disease. Genetic diseases have certain known properties; a sex-linked trait will show specific inheritance patterns, for example. To propose that a disease is a genetic disease, one must show that it conforms to some pattern of inheritance that characterizes genetic traits in general. The antecedent conditions in this case are the symptoms of the disease (the syndrome associated with the disease), the general laws are the "laws" of classical genetics that describe various inheritance patterns for genetic traits in general. Note that the law here is not restricted to just genetic diseases, but all genetic traits, and are laws to which the disease must conform in order to be considered as a genetic disease (a genetic trait). If the disease is distributed among generations of representatives of affected families in a manner that conforms to classical genetic "laws", an explanans can be generated explaining the explanandum (the disease). The explanans will relate the distribution of the disease among affected families and conclude that it conforms to genetic "laws" of inheritance, and thus the presence of the disease in some affected individual is the result of the inheritance of some genetic character(s) (gene(s)) from one or another or both parents. Note that there is no negative evidence generated. To conclude a disease is genetic, it must conform to some genetic pattern of inheritance, and if it does, we take that conformity as positive evidence that the disease is genetic.

Once we show conformity to classical genetics "laws", we can use such information to try to find the actual gene(s) that cause the disease. We would map the disorder to a certain region or regions of chromosomal DNA (under the "laws" that heritable traits like genetic diseases are "caused" by DNA). We would use positive evidence that showed that the disease did in fact map to a certain region or regions of DNA. We would then look for certain candidate genes and have to show which gene(s) caused the disorder, and how. In the end, we would have an explanation (a theory) describing the genetic disease, and we can do so in great detail. In all cases, we must use positive evidence that supports our theory at each step along the way. H & O thus describe what theories are quite well.

Two problems develop from logical positivism as described by H & O. Firstly, the "laws" must be "universal" and they must be "true". The difficulty here is that we have no perspective to state that any law is universal and we have no way to evaluate if a law is true. Laws describe regularities we observe, and provide an explanation that can be used to describe some class of regularities, like the inheritance of genetic traits, for example. A major problem here is that explanations for such regularities evolve, and what was "true" in one era is not in another. H & O spend a lot of time on this issue in the paper I quoted, however if, as Kuhn proposes, science has an historical aspect and a contingent aspect to it, then the process merely requires laws that are considered to be true for scientists to practice their craft. In the context of modern science, if we were to replace the word "law" with the word "assumption", the model of H & O would look very much like most modern theories.

The other problem is demarcation; what is science and what is not. This issue is actually the greatest problem for logical positivism, for pseudoscience such as Marxism and Freudian psychology emerged in the late 19th and through the 20th centuries, and the "laws" proposed by Marxism and Freudian psychology are such that they can explain any contingency. A logical positivist would simply state that Marxism and Freudian psychology are not scientific because the explanations are not derived from experiment, and cannot be subject to experimentation, because any experiment cannot fail. Such a proposition was in fact made by an individual from the logical positivist school, Karl Popper. H & O state that a theory is not valid because it can explain things after they happen, the theory must be able to predict what will happen. The problem with the Marxist theory of history and psychoanalysis is that they can only explain things after they happen, they are not inherently predictive.

Popper states, in a lecture given in Cambridge in 1953, and published in "Conjectures and Refutations: The Growth of Scientific Knowledge", by Karl Popper (1963), that he was concerned by the assertions that the Marxist theory of history, psychoanalysis (of Freud) and individual psychology (of Adler) were being presented as "scientific", when they were in fact not scientific. Why is it that scientists did not accept these explanations as scientific? What specifically is it about these theories that makes them unscientific? The simple answer is that these theories can never fail to explain anything. There is no way to test them, as they will pass any test. While the real philosophical (epistomological) problems, such as the manner in which the covering laws are related to observations by Marxists, for example (they change the "laws" to suit the given situation in any given case), Popper developed the idea of falsifiability as a means of excluding pseudoscientific explanations such as those proposed by Marx, Freud and Adler. Falsifiability is a simple concept; the test for any scientific theory must be falsifiable, that is, any test must include a very real means by which the theory can fail the test, and thus be falsified. Evolution, for example, predicts that the DNA of dogs will be more similar to the DNA of humans than will the DNA of frogs. This is an explicit test of evolution that the theory of evolution passes, although it need not have, despite the fact that the notion of relatedness among all organisms was proposed prior to the discovery of the biological function of DNA.

Popper does not reject confirmation as a means of supporting a theory, however the confirmatory evidence is only acceptable if the experiment from which is was derived included the possibility of falsification. For our genetic disease, the original tests to see if the disease conformed to genetic "laws" could have indicated that the disease does not conform to genetic laws, falsifying the explanation that the disease was genetic. This point, however, does not reject the tradition of the logical positivists.

Logical positivists such as Popper championed deduction as the means by which scientists reason, as opposed to induction. We will first look at induction. Induction is "inference based on many observations" to use the words of Popper. Popper sees induction as a process where explanations mysteriously "pop" into the head of an investigator as the result of intense study of the system in question (after making many observations). Popper suggests that scientific advances do not come as the result of induction, but rather deduction (applying known "rules" (rules are more or less the "laws" of H & O, as far as I can see) of critical argument, along with luck and ingenuity).

A simple way to differentiate induction from deduction is as follows:

Induction:
An investigator makes a large number of observations and develops generalizations to connect them.
Deduction:
One develops theories by connecting groups of observations using known rules.
While induction is probably impossible to account for logically at this time, the fact is that deduction requires pre existing rules. The hypothetico-deductive model of "the scientific method" that is presented in most elementary accounts of science requires an initial hypothesis that is to be tested, and it begs, as does Popper's argument, for the origin of any initial hypothesis. Popper states that such initial hypotheses are conjectures, that scientists "jump to conclusions, sometimes based on one observation", which still begs the question! Popper's idea of falsification and his concept of deduction are widely accepted because they are easy to understand, despite their inadequacies, and the fact that they are essentially logical positivism in any event.

I see Popper as having a problem with induction moreso than logical positivism. One cannot dispute that scientists more often than anything else work to generate positive evidence to explain a phenomenon. Science is not a process of falsificationism. It also seems to me that Popper was more concerned about excluding certain philosophies from science because they were not predictive. However, even prior to Popper, such philosophies were not considered as science because they do not offer general explanations with predictive power but rather seek to explain single events independently, after the fact. Popper does, however, offer a very elegant means of demarcating science such as to eliminate most pseudoscience. Unfortunately, falsificationism also limits science itself, because not all theories are falsifiable.

Popper himself suggests that "Confirming evidence should not count except when it is the result of a genuine test of the theory; and this means that it can be presented as a serious but unsuccessful attempt to falsify the theory." Yet Pickett, Kolasa and Jones, (PKJ) the their book, Ecological Understanding, The Nature of Theory and the Theory of Nature (Academic Press, 1994), claim that falsificationism, which they attribute to Popper, requires that "observations never confirm any general theories, but only refute or fail to refute them." What is meant by "general theories" is difficult to understand, as it is not well defined, but something like the periodic table of the elements is accepted because it does explain how atoms interact with each other. It is a good theory because it makes risky predictions, predictions that could falsify the theory. It is, however,  mainly a good theory because it does in fact explain a lot about how atoms react with each other. I find it interesting to note that on page 77, PKJ claim that logical positivism is a failure because it views theories as a series of statements joined by deduction alone, while Popper in the work I cited is concerned about the large role of induction in logical positivism. Popper's main problem with induction is that it cannot be logically explained.

Popper also has problems with the idea of covering laws. Popper is concerned that we cannot ever know for sure if any covering law is true; thus Popper has difficulty accepting verification, because such verification requires that the covering laws involved be true. In our genetics example, if we conclude that a disorder is autosomal, recessive and that the gene involved is at a particular point on chromosome 7, we are assuming that what we know about genes and disease is true, that classical genetic laws of inheritance are true and that what we know about molecular biology is true (the role of DNA and the central dogma of molecular genetics, for example). Popper might argue that we don't know for sure if all these explanations (theories) are true, but it's what we have to work with, and we do follow the covering law model when we use these theories to explain genetic diseases. When we map a gene, we don't falsify the mass of possible locations other than where it is, but we use methods to generate positive evidence as to where it is. Popper did, howeve, point out the problems with logical postitivism and present solutions. Logical positivism, as described by Popper, is the most widely accepted model of a scientific theory

A last point on the nature of theories is that the mark of a good theory is elegance; the more you can explain with fewer sentences, the more elegant the theory. More elegant theories explain things at a higher level than less elegant theories. H & O use the example of the more inelegant gas law that predicts the expansion of a gas with rising temperature, but so does the more elegant kinetic theory of heat. Gas law explains only gases, but the kinetic theory of heat explains many more phenomena, including what is explained by gas law. The kinetic theory of heat subsumes gas law.

While H & O explain what a complete theory is, they fail to explain the process of science. Theories describing many phenomena are incomplete. We understand a lot about why blood pressure rises and falls, but we cannot accurately predict who will suffer from hypertension and why. There are too many variables, including the effect of the environment. We have some covering laws, we know the renin-angiotensin system quite well. We know of many alleles that affect blood pressure, but we still do not have the full picture of all the factors that affect blood pressure and how they interact. This type of problem is typical in biology, and atypical for the physical sciences. Yet we know a lot more about biological phenomena than previous generations, and we continually add knowledge, and as we add knowledge, the way we describe biological phenomena changes. New technologies and new information allow for the design of different methods of making observations and analyzing data. Thus biological theories, more than those of the physical sciences, are subject to constant revision. Such revision creates great difficulty for a hard core logical positivist, as covering laws also changes, thus changing the way phenomena are described. The fact remains, however, that even though the covering laws change, the nature of the explanations remains the same. The only deficiency in the logical positivist description of scientific explanations is the assertions that the covering laws must be true; they are not necessarily true, and even if they are, we certainly have no way of knowing if they are universally true. The covering laws of the day are the basis for the methodology of the day, when the covering laws change, the methodologies change. Kuhn calls such changes scientific revolutions, and calls the methods of the day, as well as the covering laws upon which they are based paradigms. We will review Kuhn is more detail later in this course to better understand science as a process.

Next I will discuss the structure of a theory as described  by PKJ. I use this description because it applies to the biological type of theory decribed in the preceeding paragraph; a theory that grows over time as opposed to a theory that is some sort of final statement with respect to some phenomenon or phenomena.

PKJ suggest that the main goal of science is the development of understanding. They define understanding as "an objectively determined, empirical match between some set of confirmable, observable phenomena in the natural world and a conceptual construct.". This is essentially a match between theory and reality; the match between what hings actually are and what we think they are.

A key component to this definition is the conceptual construct. A conceptual construct is what we think something is. For example, consider a tree. We have an idea, a conceptual construct of what a tree is, but that concept is really not what a tree actually is. At best, all most of us can do is recognize a tree when we see it; we know what it looks like relative to something else, like a car or a lawn chair. We don't, however, really know what a tree is. In fact, the information as to what a tree actually is is probably beyond the comprehension of a single human, but probably within the grasp of human knowledge in general. A forester has one conceptual construct of a tree, a plant physiologist another and a plant ecologist yet another.

We have conceptual constructs to describe all natural phenomena. PKJ present theories as the "braiding" of conceptual constructs into a "pillar of understanding".

The empirical content is/are the observable phenomena, which are related to representative conceptual constructs by "tools". The tools facilitate a dialog between the observable phenomena and conceptual constructs within a domain. PKJ seem to me to be fairly vague on what is represented by "domain", but their definition of domain is "the set of objects, relationships and dynamics occurring on specified spatial and temporal scales that are the subject of scientific inquiry". I see the domain as the discipline or subdiscipline involved. For example "plant physiology" might be a reasonable "domain" for a theory about the differences between sun and shade leaves in oak trees.

The tools are causal explanation, generalization, and testing. Remember again that these tools are connecting our conceptual constructs to observable phenomena, we are relating what we think things are to what they actually are under the assumption that we never have a complete understanding of the phenomena in question.

A major issue in the philosophy of science is objectivity. PKJ require an objective match between theory and reality. The general consensus is that an individual scientist cannot be objective. PKJ suggest that the scientific community can be objective. Observations that are matched to conceptual constructs must be repeatable by others, where repetition of an experiment by others negates the bias of individual researchers. This is not really what happens, as almost all researchers follow ruling paradigms, including prevailing "laws" and modes of application of laws, and thus there is a collective bias that is only overthrown when a scientific revolution occurs.

So we have the community of science providing objectivity, our observations are the empirical content, that must match our idea of what the phenomenon is, it must match our conceptual construct. If there is not a match, we must recognize that the problem is with our conceptual construct, not with the observable phenomenon.

PKJ make the distinction between understanding and explanation. PKJ present explanation as a process and understanding as a result. Explanation is supported by general laws. PKJ suggest also that explanation occurs by the decomposition of phenomena into phenomena at lower levels, giving the example of photosynthesis as a process explained in terms of biochemistry and physiology. I see this as no different that using general laws, as one simply uses the laws of biochemistry and physiology to explain photosynthesis. In any event, PKJ suggest the term general explanation for explanations that generate an understanding of broad domains and causal explanation for the act of putting specific events into the context of laws. Photosynthesis would be a generral explanation that is derived from a series of causal explanations of things like the generation of oxygen and ATP during photosynthesis. I see this as the difference between gas law, that PKJ would call a causal explanation and the kinetic theory of heat which PKJ would call a general explanation. While there is to me just a difference in elegance between the two explanations, PKJ use the distinction to describe the development of understanding.

Getting back to the tools of explanation, generalization is making some statement as to a pattern among observations. Generalization requires the collection of a series of observations that are thought to be related.The aspects of the phenomena describe then must be boiled down to the elements relevant to the generalizations; this boilng down process is called ABSTRACTION. Following abstraction, a statement of some idealized form of the observations must be made, with this idealized form called an IDEALIZATION.

The periodic table of the elements, for example, requires first knowledge of how various elements interact followed by the observation of some pattern with respect to those interactions. Elements need to be presented in a form that is boiled down to only those aspects important for the generalization and an idealized description of elements must be prepared that is again relevant to the periodic table. Thus we have elements described as entities with protons, neutrons and electrons. We then relate the numbers of protons in the nuclei and the number of electrons in outer shells of the different elements to create the periodic table.

Causal explanation is an accounting of the mechanisms, interactions and conditions that result in the pattern or phenomenon in question. In my experience, we use quantum theory to explain the periodic table, which works as far as that goes. My understanding is, however, that quantum theory is accepted because it works, and there is no causal explanation for quantum theory.

Finally, we have to test the notion that our causal explanation that unites our observations into our proposed generalization is valid. A key aspect of testing is PREDICTION. To me, this is the key element of a scientific explanation. It is not enough to tell us why something happened in the past, you must be able to predict something in the future. Tests involve predictions. This is the essence of what makes a scientific explanation. The theory has an expectation of the natural world that must match the expectation, or the theory is invalid.

A test of a theory is performed to determine if the theory explains the phenomena in question. If the  theory does effectively explain the phenomenon, then it should be able to predict some aspect of a system associated with the phenomenon. We should be able to predict how hydrogen and oxygen interact in a given system, for example from the periodic table of the elements. We can test the predictions the periodic table makes. If hydrogen and oxygen interact as the periodic table predicts, then such a test is confirmatory evidence that supports the periodic table. If hydrogen and oxygen do not interact as the periodic table predicts, our test is contrary to the periodic table of the elements. One failed test does not, however, refute a theory like the periodic table. One positive test does not "prove" the periodic table. Theories grow over time and require a great deal of testing, involving aspects of testing such as experiment, comparison and correlation. The degree to which a theory explains a phenomenon generally grows over time, with theories restated, subsumed and completely refuted by higher level theories. In general, the pattern is likely simple theories to explain simple phenomena that are then collected into higher level generalizations; in terms of PKJ, causal explanations are subsumed by general explanations.

In short, PKJ see theories as collections of conceptual constructs that are inter related by the theory. The theory is in a sense, a generalization that is supported by causal explanations which must be tested and either verified or refuted.

We really do not have a full understanding of natural phenomena. In science, one does not use this as an excuse to retreat into supernatural explanations, but as a challenge to be met by the development of better theories. We really can't prove anything, but we can show things to be consistent with nature. It is not a matter of rhetoric. There is no proposition opposition and resolution (there is never really resolution), but rather better and better understanding. No other philosophy has come even close to developing the understanding of the natural world that has been developed through science. Science challenges philosophies that do not have such a strong compoent of objectivity; science does not tell us what we want to know, but rather it tells us what we can know. The natural phenomena are independent of us, and we can develop an understanding if we wish, but we cannot make them out to be as we wish, regardless of sociopolitical desires.