It has been pointed out earlier that the law of uniformity of nature and causation constitute the formal ground of induction.
Mill says that a principle of uniformity of nature is the formal ground of all inductions. For the leap from the known to the unknown, some to all is made possible by the presupposition of the law of uniformity of nature.
In case of scientific induction both the principles of causation and uniformity of nature form the formal ground of induction. By means of law of causation a causal connection is first established between two events.
But to generalize or extend this result further under the impression that the same cause will produce the same effect under similar circumstances we must seek the help of the principle of uniformity of nature. Law of causation is the discovery of a causal relationship between two events, states, processes or phenomena. But in order to arrive at a general proposition we need the help of the law of uniformity of nature.
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Thus for instance while to ascertain a causal connection between gravitation and falling of a particular stone to ground we need the law of uniformity of nature to establish the general proposition “all material bodies fall to the ground because of gravitation”.
In the conclusion it can be said that whereas the law of uniformity of nature is the ground of all forms of induction to bridge the gap of inductive leap the law of causation forms the basis of scientific induction. But both the laws constitute the formal ground of induction.
According to Mill the law of uniformity of nature is a formal ground of induction. It maintains that the same cause will produce the same effect under similar circumstances.
It also means nature behaves uniformly under similar circumstances. There are different departments of nature and each sphere is governed by uniform laws or regularities. The different laws or regularities constitute one system that we call nature. So nature is unity in diversity.
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When Mill reduces uniformity of nature to a form of induction there arises a paradox. Once the ground of induction is reduced to a form of induction, there will arise the fallacy of petitio prinicipii and other difficulties.