There are regularities in nature and discovery of them advances human knowledge from our varied experience when we notice some regularity and have explanation we make generalization.
For example we find living beings die, birds lay eggs, iron water flows downward, cats catch mice, matter gravitates etc.
There are also irregularities in nature. We find some boys are intelligent but some are not, some mangoes are sweet but some are not, some birds sing but some do not, good harvest does not follow every etc. But science seeks exception- less regularities of nature.
These are like invariable generalizations. Generalizations are most significant in the sphere of human knowledge for they are the very basis of all positive sciences. Not only in science in our practical life are generalizations very much helpful without which we cannot regulate our life.
When a generalization is made it comes within the scope of induction. Inductive logic examines the conditions for appropriate generalization. Theoretically it explains basis and structure of a sound generalization. By formulating the criteria for generalization it distinguishes sound generalization from the illicit ones.
When a generalization is made, it makes a universal proposition covering unlimited instances. When, for example, we say living beings are mortal, bird’s lays eggs, all quadruped animals are mammals, no bird is a mammal, etc. each such proposition is about a class of unlimited members. To .say that all men are mortal is to make a general proposition unrestricted generality for it not only covers known cases, it includes a vast number of unknown cases.
Any such above proposition covers a large number of unobserved inst; too. To say that ‘No bird is a mammal’ includes all birds of past, present and future. It covers unlined cases.
Since every physical science makes empirical generalization, a question may well be raised regarding the basis of such generalization. It is found that our observation is the basis of our generalization.
From our experience we find that birds are not man but lay eggs. On the basis of this regular experience we make the generalization that all birds are non-mammals. On the other hand we observe from nature that cows, dogs, cats – all quadruped animals – are mammals.
In case of such animals the female animal gives birth to babies and feeds them with milk from her body. Here the premises are based on verifiable or observable instances and are true. On the basis of particular experiences a generalization is made. Thus in induction there is generalization on the basis of actual observation of facts.
But a genuine general proposition with unlimited totality cannot be established by experience. Experiences falsify a general proposition in face of observation of a contrary instance, but experience cannot justify the truth of a general proposition.
We cannot individually verify every quadruped to be a mammal and then make the generalization that all quadrupeds are mammals nor can we individually verify every bird and then make the statement that no bird is mammal.
Since in these cases the conclusion is a general proposition with unlimited members it is beyond the scope of actual verification. But for all practical purposes we have no doubt on the veracity of these generalizations.
Thus in induction the conclusion is a real inference as on the basis of our observation we pass to a general truth of similar cases. Here there is a leap and every genuine from of induction carries a leap.
A leap is a jump from the observed instances to unobserved cases, from some to all or from known cases to unknown cases of unlimited totality.
This process of jumping from some to all, from limited cases to a generalized theory is said to be the “inductive leap”. This characteristic of having a leap is an essential feature of inductive reasoning. An inductive inference is worth the name by virtue of its having the inductive leap.
Since the generalization in induction is based on observation of particular cases the conclusion is probable in nature.
The premises only lend support to the conclusion. The presence of the inductive leap makes the induction probable. Of course probability is a matter of degree; it may be very high or low depending upon the verifiable facts and their link with the conclusion.
An induction however certain it may be lacks absolute or logical certainty. A logical certainly is a conceptual relation but induction is a factual relation. In case of a genuine induction there may not be any contrary evidence, but the possibility of having any in future cannot be completely ruled out. Of course in an induction if the inferred characteristic is a structural feature of the class of which it is inferred then the degree of probability will be very high. More and more confirmation increases more and more the degree of probability.
It the generalization is not an isolated theory but linked with other theories and laws at a fundamental level then its degree of probability will be high. But the significant point is that the support of the premises for the establishment of a generalized fact can never be complete.
It can enhance the possibility of the conclusion but will never be final. Even the uniformities of nature established by some developed sciences are not totally free from the possibility of a modification or revision in future in face of new facts. Thus the very basis of an inductive generalization is only probable in nature.
Any generalization extends our knowledge, therefore induction has novelty. What we observe and finally what we infer are factually significant. And what is factually significant must have novelty. For it widens our knowledge and extends our information about the physical world.
Indications are also very much essential for practical purpose of life. By induction we imagine the course of events to take place in future.
Thus inductions are very useful from the scientific as well as practical point of view. Therefore there must be a theoretical study to formulate rules and fix up some criteria for valid generalization. That is what is done in inductive logic. Inductive logic provides a criteriological basis to study the different procedures of induction and examine the reasonableness of inductive generalization.