Induction and deduction work together for knowledge

[Michael Stuart Kelly]

I made the following post in another thread. What has not been clear in recent discussions of induction is how it is only half the picture, and how deduction is only half the picture. The two work together in gaining knowledge. One without the other is practically useless.

David Kelley and William Thomas are very clear in the following post about how this works.

One of the most refreshing things I have read (besides Roger's posts) on induction was just now in The Logical Structure of Objectivism (beta version) by David Kelley and William Thomas.

Early in the Introduction, there is mention that epistemology is concerned with identifying the factual base of knowledge, i.e., what the features of knowledge are and the method for structuring it. Then there is a wonderfully clear section called "Induction and Deduction." Here is a partial quote. I removed the example, but anyone can read the whole thing by clicking on the link.

The logical processes by which we build up the structure of our knowledge are of two broad types, which logicians call induction and deduction. Although a technical discussion of these two processes could fill a book in itself, understanding their role in the structure of Objectivism requires only that we differentiate them on the basis of essentials.

Induction is the process of drawing general conclusions from the observation of particular cases. For instance, we notice that all people age and die, that their bodies are fragile and can be fatally damaged. We generalize this observation as: All people are mortal. Deduction is the process of drawing out the implications of the general knowledge we already possess, usually by applying generalizations to specific instances of a type. Continuing our example, each of us knows that we will die some day by deducing it from the fact that all human beings are mortal.

Since our knowledge is hierarchical, resting on the base of perceptual observation of concrete things in our environment, it would obviously be impossible for us to build up our knowledge by deductive inference alone. Where would we get the generalizations on which deduction depends? For those generalizations we need inductive inference. Above the level of perception, all of our knowledge depends in one way or another on induction. In a sense, induction is like earning money: it is the process of acquiring new information. Deduction is like spending money, because it allows one to get the most out of one’s store of inductive information. In most cases, our conclusions depend on both inductive and deductive procedures used in combination, just as we normally obtain economic goods by a combination of earning and spending money. A point of particular importance is that there can be inductive support at any level in the structure of our knowledge.

. . .

Thus deduction and induction could not function apart from each other. Understanding the world in terms of generalizations allows us integrate large amounts of information in a compact form. Induction is the process of forming generalizations from the data we are aware of, but our generalizations would be useless if we failed to employ deduction to apply them to particular cases. Furthermore, deduction and induction must be employed together if we want our thinking to be robust against error. Inductive confirmation is not always necessary to establish the truth of a proposition: a conclusion that one has correctly deduced from true premises is itself true. However, when we deduce from a broad abstraction . . . to a more concrete principle, . . . there is a danger that something essential to the more concrete case may have been left out.

. . .

By looking for direct inductive evidence of the conclusions we deduce from our generalizations, we can check to make sure nothing has been overlooked or incorrectly integrated.

On the other hand, accurate abstractions, connected by deductive inferences, can put an enormous amount of information at our disposal in a concrete form.

The next section is called "Context" has some comments I cannot resist quoting either.

A common source of error in generalization is a failure to base one’s conclusions in the full context of evidence. Our knowledge is contextual in virtue of its hierarchical nature. It does not consist in isolated bits of data, each with its own, self-contained meaning, each with its own separate relationship to reality. The meaning of any conclusion, and its relationship to reality —i.e. its truth or falsity— depends on its relationship to the network of other knowledge by which we derived it. Hierarchical knowledge is contextual because each item of knowledge is grounded in some particular evidence, in the awareness of certain types of things, a certain range of experience. In this sense, the context of knowledge is like the different places that the pylons of a building’s foundation come to earth: the structure depends on many sources of support coming together. As the support changes, the superstructure of knowledge may change as well.

The meaning of a principle, in the Objectivist view, is determined by tracing the process by which it connects to reality. This means, among other things, establishing the context that a person integrates by means of concepts. A failure to attend to this is one reason why people discussing abstract ideas often “talk past” each other: they are using the same words, but they don’t mean the same things.

. . .

The contextual nature of knowledge is also significant because one’s context of knowledge changes over time. As individuals we become aware of new evidence and facts. Even the cognitive context of society as whole expands with exploration and new scientific discoveries. As one’s context changes, the meaning of one’s principles can change as well. For instance, in the 18th century, generalizations about “fish” integrated information about all creatures that swam, including whales and porpoises. This categorization was not a mistake: there are valid reasons for regarding swimming creatures with fins as similar. However, by the 20th century, marine biology was better understood, and the term “fish” came to be applied to a more narrow class of animals. The old knowledge about “fish” was not false; it is still true in terms of aquatic creatures. But now we have knowledge about fish, e.g. that fish are cold-blooded, that would not have applied to the old manner of classification.

Because one’s knowledge is contextual, it can be expanded to apply to a wider range of circumstances as one actively expands it by investigating new evidence and information. One model of the development of knowledge from one context to the next is the transition from Newtonian to Einsteinian physics. Newton’s mechanics accurately described the motions of bodies moving at low velocities relative to the speed of light, which was the context of evidence to which Newton had access. Centuries after Newton, Einstein was aware of a broader context of evidence, including improved astronomical observations, and the discovery that the relative velocity of light was constant from all perspectives. Einstein’s theory addresses that broader context, but in addressing Newton’s original context, it replicates Newton’s findings. Newton was not falsified by Einstein in the context in which his laws were solidly confirmed, indeed, he could not have been. On the other hand, the common assumption of the 18th Century, that Newton’s mechanics would describe the motions of all objects at all times in all places, turned out to be in error.

As can be seen here, if we can get past the verbiage and efforts to prove that Popper trumps Rand (or vice-versa), we can see that they both actually have quite a lot in common.

That was a wonderful phrase about people talking past each other because they ignore each other's respective contexts: "they are using the same words, but they don’t mean the same things."

Ain't that the truth?

Michael

[John Dailey]

Mike:

~ Worthwhile points to quote, definitely. Ntl, re the subject of 'induction', I have a prob with it's not being clarified as being more than merely (simplistic) 'general'izing.

LLAP

J:D

Edited October 1, 2007 by John Dailey