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Wednesday, July 22, 2009

Induction and Scientific Reasoning

In this post I argue that enumerative, or "simple" induction (henceforth "induction")* does not play a significant role in scientific discovery. I construct this argument within a framework of epistemological behaviorism.

I. The Meaning and Value of Science

As I understand it, knowledge is another word for ability. Scientific knowledge is predictive ability, which is the ability to organize our behavior in accordance with the unfolding of nature.** In other words, science is the process of learning how to predict what is going to happen in new situations. Scientific knowledge is demonstrable in so far as the abilities it engenders are demonstrable and reliable.

Science is not the process of describing what has already happened, nor is it the process of describing what is happening at any given moment. Of course, science can help us understand what has already happened and what is happening right now. But the focus of science is always on the future, not on the present or the past.

Facts, not theories, are representations of the world. Theories are tools for constructing representations of the world. The theory/fact distinction does not refer to some distinction that exists beyond our discourse. The distinction between theories and facts helps us understand the relationship between knowledge and action. The meaning of a theory is in its ability to generate facts, and the meaning of a fact is determined by its relationship to our behavior. Knowledge, as such, does not exist as information stored in the brain, or on paper, but rather in the way information relates to behavior.

Scientific theories do not approximate extra-theoretic truth. There is truth in science in so far as science works; which only means that scientific practice engenders abilities to predict how things in the world will behave. In other words, scientific theories help us regulate our own behavior more effectively and in new ways. Truth is thus defined in terms of human behavior. When we say a scientific theory is true, it is quite like when we say of an accomplished archer that his aim is true. For example, quantum mechanics provides a formal method (or set of methods) for regulating our behavior in specific domains--domains which were not open to us before quantum mechanics was established.

II. Induction and Observation

Theoretical/experimental frameworks precede observations. There could be no observation of quantum entanglement before there was a theoretical framework that provided a mathematical model for it. The observations make sense because we have a way of understanding them.

Consider: There are observations in quantum mechanics we still cannot explain, such as what some call "wave/particle duality." When we say scientists observe duality, what we mean is that their observations cannot be explained by a single model, but indicate the need for two apparently incompatible models. Thus it is more accurate to say that we are not sure what scientists are observing, because we lack a unified theoretical framework to make sense of the behavior.

Could induction help us solve this problem? Can we resolve the issue of wave/particle duality by inductive means?

We might say that, because we consistently observe wave/particle duality, wave/particle duality is a fact of nature. Thus, we now have a scientific theory which says wave/particle duality is true. But all we have done here is moved from a situation in which we lacked a unified framework for interpreting our observations to a situation in which we claimed that our intitial, confused interpretation of our observations is true. What understanding would be gained by this move? How could it be called scientific?

If science were to proceed in this way--if this was how scientific theories were built--science would be a hopelessly circular enterprise. We would end up saying, "of course we observe wave/particle duality, because that is what our theory predicts!" This is to mistake an observation for a theory. Fortunately, science does not work this way.

A scientific theory does not simply say "wave/particle duality is true, because we have observed it to be true." Rather, scientific theories provide frameworks for making new predictions. They are not limited to what has already been observed. This is what makes them testable. It is how they open the horizons of human behavior in unexpected ways. This is where the value of science is had.

Inductive reasoning does not tell us anything beyond what we have already observed; it only attempts to account for our observations by defining them as instances of a general rule. But this is no accounting at all. It is not science.

III. Is there any role for induction in science at all?

There are two possible places to look for an answer to this question: in the production and in the testing of hypotheses.

First, consider whether induction could play an important role in coming up with testable hypotheses. Charles Sanders Peirce, the American pragmatist, claimed there is a different sort of reasoning which we use to come up with scientific hypotheses. He called it abductive reasoning. This is the process whereby we construct theories to account for facts which do not fit into our prevailing interpretive framework. Yet, it is not clear that this process follows any rules, methods, or principles. In any case, the suggestion that it depends upon induction is unwarranted. In fact, induction cannot play a pivotal role here.

If we observe a number of cases of X, but we have no explanatory framework for understanding X, how could induction help us produce a theory for explaining X? Induction only produces the claim that X is a rule or law of nature. This is not a scientific hypothesis, because it makes no novel predictions. Thus, in the formation of hypotheses, induction has nothing to offer.

Let us instead consider whether induction might play a role when we test hypotheses against observation. Are we using inductive reasoning to generalize from our observations? For example, the conservation of momentum has been supported by a great deal of experimental data. Does that mean that, after X number of trials, the meaning or relevance of the theory was finally established?

Clearly the meaning of the theory was not induced by the observations. The hypothesis preceded the experimental results. Was the relevance of the theory induced? Relevance to what, exactly?

We might say that, after a theory has been corroborated by a number of tests, its relevance to humanity has been established. But this is not induced. The relevance of the theory is deduced from the fact that the theory works.

Or, we might say that the relevance is not to humanity, but to the universe itself. But what relevance could a theory have to the universe, apart from the relevance it has to humanity?

Theories are relevant in so far as they engender ability. Their meaning and value is defined in terms of behavior, after all. So there is no sense in trying to define relevance to the universe as a whole, apart from the contexts in which the theories are used.

I think we can conclude that the meaning or relevance of a theory is never induced from observation.

It may be claimed that the meaning of the observations requires induction; that, in order to claim that the observations have some relevance beyond their particular time and place, we must use inductive reasoning. Yet, we should not forget that the interpretation of an observation already requires that it have meaning beyond the particular event it represents. For an observation to be regarded as such, it must make sense within some theoretical framework. Thus, we cannot claim that the meaning or relevance of an observation with respect to a theoretical framework requires induction without also claiming that the meaning of the theoretical framework requires induction. But this has already been shown to be incorrect. The meaning of a theoretical framework is not induced from observations or particulars.

IV. Conclusion

The search for a role for induction in scientific reasoning seems to lead us in circles. It might indicate a real problem for philosophers, if we had some reason to think that induction just has to play a role in scientific reasoning. Fortunately, we do not. There is no reason to think that induction plays a significant role in scientific reasoning. So I think we can let the matter drop.


* The Stanford Encyclopedia of Philosophy's entry on the problem of induction indicates that this usage of the term "induction" is somewhat antiquated, and that the term is now sometimes taken to refer to a large range of synthetic or contingent judgments, or perhaps even to all contingent judgments. This seems to confuse the language and makes it impossible to identify what the term "induction" is supposed to mean. In any case, the so-called "problem of induction" is quite specifically about enumerative induction, and it is with respect to this historical debate that I am writing. I see little reason to extend the term "induction" to other cases. In fact, I suspect that the confusion surrounding contemporary uses of the term indicate conceptual confusions within philosophy; I thus would prefer sticking to the traditional usage, if only as a lifeline when trying to navigate those murky waters, until I find a compelling reason to abandon it.

** In retrospect, I would make an important distinction here. Predictive abilities are not the only abilities which organize our behavior in accordance with the unfolding of nature. There are more basic anticipatory abilities. Prediction requires language. More p
rimitive forms of anticipation require less sophisticated forms of representation. [This post was edited to include this footnote.]