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4. Herschel-Mill's theory of induction
Herschel, in his Preliminary Discourse on the Study of Natural Philosophy (1830) suggested ten rules of philosophizing. These are rules for discovering and confirming causal relations which can explain the given phenomena (we will see some of these rules later). According to him, the objectives of scientific inquiry are described as follows:
(Q10) The first thing that a philosophic mind considers, when any new phenomenon presents itself, is its explanation, or reference to an immediate producing cause. If that cannot be ascertained, the next is to generalize the phenomenon, and include it, with others analogous to it, in the expression of some law, in the hope that its consideration, in a more advanced state of knowledge, may lead to the discovery of an adequate proximate cause. [sect. 137]
The relation of cause and effect is, according to him, an invariable connection, i.e. the same cause always produces the same effect (unless, of course, prevented by some counteracting cause). Notice that, thus characterized, there is no room for probability in the relation of cause and effect.
Herschel's ten rules are modified and reorganized by Mill as his Five Canons of Induction.
(1) Method of agreement
(2) Method of difference
(3) Joint method of agreement and difference
(4) Method of residues
(5) Method of concomitant variations
The essence of these canons is that they enable us to eliminate hypotheses which are incompatible with given data and the law of universal causation (which says, roughly speaking, that every event has a cause).
Let me explain such a process of elimination by a simple example. Suppose that, after our family dinner, my wife and I began to feel a strong stomach ache but our two daughters were all right. In order to identity the cause of our pain, you may analyze the situation in this way: What did they eat during the dinner? They all had steamed rice, beefsteaks, greenbeans, and a melon for dessert. Since only the parents feel the pain, its cause must be in some conditions which are satisfied by both of them, but not by the children; now the parents like beer, and they had a glass of beer, whereas the daughters didn't; therefore, that beer must be the cause of the stomach ache. In this reasoning, both methods of agreement and of difference are used; and these somehow succeeded in eliminating many factors from the candidates of cause.
Thus you may think that Mill's method is quite close to Holmes's method of elimination. But we have to see whether or not Mill's method can capture all features of Holmesian reasoning.
Mill emphasized the role of induction as a method of (empirical) proof. This is clear from his distinction between Deductive Method and Hypothetical Method (what we call hypothetico-deductive method corresponds to the latter, not the former). The former consists of three steps: induction, deduction, and verification. By means of induction, we ascertain causes or laws involved in a given case; next, we combine these causes and laws and calculate their effects, i.e. we deduce concrete consequences from them; and finally, we verify whether or not such consequences hold in the actual case. Hypothetical Method differs from this, in that the step of induction is absent. We merely assume such causes or laws, deduce particular consequences from them, and try to verify whether or not they hold (notice that, according to Mill, even a logical or mathematical truth must be verified ultimately by referring to experience). Hypothetical Method lacks any proof of causes and laws by means of induction.
Herschel is not as strict as Mill on this point. But it is clear that Herschel also aims at some sort of proof by means of his ten rules; so that he claims that we can obtain certainty in the field of physics. He distinguishes theoretical certainty and practical certainty, and admits that the former can be attained only in such fields as mathematics or geometry. However, he is never in doubt that in many fields of physics we have attained the latter, practical certainty; and he has a strong belief that our knowledge by means of scientific inquiry can be certain in that sense.
Then a question arises: Does Holmes share such a belief in the certainty of scientific knowledge? We will come back to this question after we give a brief look at what Whewell said about induction.
June 21, 1998; last modified, April 16, 2006. (c) Soshichi Uchii
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