What do you really mean by Paradox of Induction?

The law of uniformity of nature is a formal ground of induction according to Mill and others. It is the foundation or the basis of all inductive generalisations.

Unless we believe this principle we cannot pass from some to all, known to unknown, from past to present and then to distant and unknown future.

In other words the law justifies or guarantees the leap from particular cases to a general law. Neither can we generalize nor can our generalization be proper unless we believe that nature will behave in the same way under similar circumstances. This law, therefore, is the very basis or ground of induction.

But quite contrary to this above view Mill also held that the law of uniformity of nature is the result of induction. Even he called it the result of induction per simple enumeration. Induction is justified by the law of uniformity of nature. But the law of uniformity of nature itself is the result of induction per simple enumeration.

In other words from experience we gather cases of particular uniformities like fire always accompanies smoke, water flows downwards, magnets attract iron and so on. Since we do not come across any contrary experience we are gradually led to believe that everywhere in nature things behave in uniform manner, or nature, as a whole, is uniform.

This uncontradicted experience of ours gathered year after year forms the very basis of our understanding of nature. In short, according to Mill the law of uniformity of nature is the result of induction per simple enumeration. This is the manner in which the law of uniformity of nature is established as the ground of induction.

So for Mill what is the ground or foundation of induction is also the result of induction. This is known as the paradox of induction. But Mill’s paradox of induction is subject to criticism for the following reasons-

First, Mill’s argument involves the fallacy of petitio principii because he argues in a circular way. He says that the principle of uniformity of nature is the ultimate basis; the major premise of all inductive generalizations and again he says; hat this principle is the result or conclusion of induction.

But can the uniformity of nature be the major premise and conclusion at the same time? If it is the ground or very basis of induction it cannot be its result at the same time. Mill is trying to prove uniformity of nature by induction and again he is trying to prove induction by uniformity of nature.

This is like proving A by B and B by A. But this is not tenable for he is arguing in a circular manner. He assumes the law and again tries to prove it.

Secondly according to Mill the conclusion of induction per simple enumeration has lesser degree of probability. If the principle of uniformity of nature be the result of induction per simple enumeration it will have less probability too.

In that case it cannot be the basis of all inductions. But in scientific induction the conclusion has a higher degree of probability. What is less probable cannot be the basis of what is highly probable.

Thus uniformity of nature cannot be reduced to a form of induction per simple enumeration. Since it is the basis of all inductions, it itself cannot be reduced to a form of induction. Certainty can be the basis of probability, but probability cannot form the basis of certainty, j

Mill, as an empiricist, accepts the law of uniformity of nature as an empirical y derived assumption. His problem is, he takes induction, particularly scientific induction, as absolutely certain.

An absolutely certain generalization cannot be founded on an empirically derived assumption, that too which is a product of induction per simple enumeration. So he tries to make the law of uniformity of nature as the major premise of all inductions and draws generalisations from it to make induction as absolutely certain.

He seeks logical or formal certainty in case of induction. That means to provide analytical or formal certainty to scientific induction he seeks justification for the law of uniformity of nature on the basis of experience of facts. That leads him to fall to the problem of paradox of induction.

But any generalization, even scientific generalization, cannot enjoy formal certainty for inductions are about facts of the world. Any proposition that enjoys formal or analytical certainty cannot have factual significance. Any factually significant assertion cannot enjoy logical, formal or analytical certainty. To mix formal certainty with factual certainty is a conceptual confusion.

Further in case of factual certainty there are also differences. The statement that at present there are thirty districts in the state of Orissa is a particular proposition whose truth can be conclusively ascertained by verification.

In case of particular propositions, its truth or falsity can be ascertained by verification with the help of observation or experiment of facts. But a general proposition like all material bodies gravitate, no crow is a mammal etc. is a generalization with unlimited numbers. Such propositions can have probability but not certainty.

Since we have verified such cases under numerous and varied situations we accept them beyond doubt as uniform occurrences. But such generalisations cannot enjoy formal or analytical certainty, for no factually significant proposition possesses it.

Mill’s confusion of two stands leaves him in a paradoxical position. But a paradox is an absurd position somewhat self-contradictory or self-defeating. Mill as an empiricist tries to find justification for the law of uniformity of nature and has taken experience as its basis. He, therefore, infers it like an induction.

On the other hand he ascribes analytical certainty to induction thereby making the law of uniformity of nature as the major premise of all inductions. For if it would be the ultimate major premise of all inductions, generalisations thereby can be absolutely certain.

So he fails to a perplexing position by making the law of uniformity of nature as the basis of induction and the law as a product of induction. But in fact no paradox would be there once it is understood that inductive generalisations are factually true and cannot, unlike analytical propositions, enjoy absolute certainty.

Thus it is absurd to accept the law of uniformity of nature as the ground of all inductions and again make itself a result of induction. But this paradox can easily be avoided.

For if the law of uniformity of nature is taken as the ground of all inductions, the empiricist position that the law of uniformity of nature is the result of an inductive procedure should be given up. And if the law will be taken as a result of induction per simple enumeration, then the idea that it is the ultimate ground of all inductions should be abandoned.