Induction, whether primary or secondary, infers a general real proposition. It is a generalization with factual significance.
A generalization describes a relation of invariance between two things. It is like “all A’s are B’s”. If we say ‘all cows are ruminant’, ‘all men are mortal’, ‘no, bird is a mammal’ etc. we are marking generalizations.
In such a case the subject term denotes unlimited and uncountable individuals of that class. When an assertion of the sort ” All A’s are B’s” is made and A stands for a class of unlimited individuals, the description here is like a universal phenomenon of nature.
A universal phenomenon is a law of nature. When we say “all material bodies gravitate on earth” or “all living beings are mortal” etc. such descriptions are considered as universally true. It is not the case that known cases are true, but it signifies that all the cases of this sort are true.
It is not true here and now. But it is true everywhere and always as far as our experience goes. So on the basis of our experience of some A’s are B’s we make generalization that all A’s are B’s. That is all A’s are B’s always and everywhere.
Thus a generalization ranges over unobserved, unlimited and infinite number of cases. Our experience, however wide it may be, cannot exhaust all the cases covered by such a proposition. Hence an induction consists of a leap.
An inductive leap means a jump from some to all, from observed cases to unobserved cases, from the knowledge of a limited instance to the knowledge of all. But how is this jump justified? What is the basis for accepting the proposition “All A’s are B’s” always and everywhere on the basis of our experience of some A’s are B’s? This is the problem of induction.
Different attempts have been made by logicians to find out solution to this problems right from Aristotle. Aristole tried to solve this problem of induction unsuccessfully by deduction.
Aristotle who was the founder of the deductive procedure applied the deductive method in finding out a solution to the problem of generalization. For example, Aristotle justifies an induction by deduction-
Gandhi, Sankar, Buddha, Russell, Kant, Plato etc. are mortal.
Gandhi, Sankar, Buddha, Russell, Kant, Plato etc are all human beings.
\ All human beings are mortal.
This attempt to draw a conclusion covering a generalization is not sound. The premise, “Gandhi, Sankar, Buddha….. etc. are mortal” is not at all exhaustive for we cannot examine all human beings. While the conclusion is about all the members of a class, the premises are about some individuals.
In a valid syllogistic argument we cannot draw a conclusion covering all members of a class from the observation of some members of that class. From “Some A’s are B’s” it is not possible to deduce. “All A’s are B’s.
The very attempt to infer a conclusion with unrestricted totality from the premises of a limited number in a deductive manner is unsound. So by deduction we cannot arrive at a generalization from particular instances.
Therefore the leap remains, and since it is a problem of induction, this cannot be solved by any deductive procedure. Thus Aristotle’s attempt at a solution is not sound.
J. S. Mill holds that the solution to the problem of induction lies on our acceptance of two very fundamental laws called the law of causation and the law of uniformity of nature.
So far the law of causation is concerned it assumes that every event has a cause. Mill accepts the law of causation as a universal principle that can be the basis for inductive generalization. The law of uniformity of Nature assumes that nature is governed by uniform laws.
In other words nature functions in the same manner under similar circumstances. That is the way we have observed things in the past will also continue to happen in the future.
Since Mill holds that the problem of induction can be solved by these two laws if a causal relation is established between two phenomena in respect of some essential point, even one or two instances will be sufficient for a generalization. But unless a causal relation is ascertained hundreds of cases will not provide a basis for making a generalization.
So according to Mill the law of uniformity of nature and the law of causation form the basis to solve the problem of induction.
But Mill’s assumption that causal relation is absolutely certain which can be proved by experimental methods is misleading. First of all the experimental methods-that will be discussed in a laler chapter- do not conclusively prove a causal relation.1 Causal relation is an empirical relation but not a relation of necessity or implication. Further all inductive generalizations are not about a causal relation.
In some areas of knowledge a causal relation is required but in other areas no causal explanation is sought for generalizations. That is scientific explanation or induction is not to be restricted to a causal explanation. Science makes generalization on different grounds.
On the basis of statistical records, resemblance or analogical similarities generalizations are made. When a generalization is made it may be a hypothesis that needs gradual confirmation by deduction and observation. Thus Mill’s analogy to solve the problem of indication has not received universal acceptance.
In logic our purpose is to see how far a generalization is depenable. Logicians fix up standard to assess the veracity of generalization. Right generalizations are distinguished from illicit or unfounded generalizations.
What sort of evidences can provide a sufficient basis for a generalization and what sort of evidences are irrelevant to a generalization need to be distinguished. Since inductive generalizations are propositions with factual import, they cannot be conclusively established or proved. Rather they carry degree of probability with them.
Thus the problem of induction can be tackled at a pragmatic level. We go on discovering the secrets of nature, its exceptionalness regularities more and more by help of the inductive procedure.
That means the regularities of nature can be discovered by the inductive procedure as that constitutes the very objective of science. So whatever generalizations are made following the inductive procedure account for scientific explanation. That constitutes the rule-of-the scientific-game and its procedure.