In 1738 David Hume wrote of the “principle that the course of nature continues always uniformly the same.” (A Treatise of Human Nature, Bk I, pt iii, sec 6). In 1748 he wrote in An Enquiry Concerning Human Understanding:
When we have long enough to become accustomed to the uniformity of nature, we acquire a general habit of judging the unknown by the known, and conceiving the former to resemble the latter. On the strength of this general habitual principle we are willing to draw conclusions from even one experiment, and expect a similar event with some degree of certainty, where the experiment has been made accurately and is free of special distorting circumstances. (First Enquiry, Section 9, Footnote 1)
Hume is considered to be the first to use the term “uniformity of nature.” He described this as a “general habitual principle” since he justified it only via habit and custom rather than necessity. He stated that “even one experiment,” that is, a sample of one, is sufficient to enable us to draw conclusions and “expect a similar event” elsewhere or in the future because we judge that the unknown resembles the known.
The expression “the Uniformity of Nature” became familiar later from James Hutton in his 1785 Theory of the Earth and from Charles Lyell’s Principles of Geology in the 1830s. William Whewell termed this usage “uniformitarianism”.
I have written before (here) about how the principle of the uniformity of nature (PUN) was adopted by J.S. Mill in the 19th century for his explication of induction.
In 1953 Wesley C. Salmon wrote a paper on PUN with this abstract:
The principle of uniformity of nature has sometimes been invoked for the purpose of justifying induction. This principle cannot be established “a priori”, and in the absence of a justification of induction, it cannot be established “a posteriori”. There is no justification for assuming it as a postulate of science. Use of such a principle is, however, neither sufficient nor necessary for a justification of induction. In any plausible form, it is too weak for that purpose, and hence, it is insufficient. Since a justification which does not rely upon this principle can be given, it is not necessary. (Philosophy and Phenomenological Research 14 (1):39-48)
That is the position I have taken in this blog.