A uniformity principle says, What is true of some is true of all. This is usually applied to nature: What is true of some of nature is true of all of nature. Or, What happened in one experiment will happen if the experiment is repeated by anyone else. Since J.S. Mill this principle of the uniformity of nature (PUN) has been considered necessary for science. That is, science reasons as follows:
Proposition P is true of some.
What is true of some is true of all. (The uniformity principle)
Therefore, proposition P is true of all.
This syllogism is completely logical and thoroughly outrageous. Yes, it allows something which science needs: that an experiment done on Monday in Australia is just as valid if it were done on Tuesday in Africa. But it allows far more.
A uniformity principle is the presumption that things unobserved were, are, and will be similar to those observed. But what things? Under what conditions? What suffices to make things and conditions similar enough? Is it the color? The size or shape? Generally, no. What makes things and conditions similar enough? There’s the rub.
A uniformity principle would allow a sample of one or a minuscule amount of X to represent all the X. But if we know anything it is that what is true of some things is not necessarily true of all things. Does a sample of one white powder represent all white powders? Is everything that is true of some rocks true of all rocks? Does everything that happens on Mondays happen on Tuesdays, too? No, no, and no.
Now it’s true that a sample of any amount of copper represents all copper. But that begs the question: what is copper? If something looks like copper, is that enough? No, its chemical structure must be that of copper. But how did chemists find out what the chemical structure of copper is? After experimentation, chemists defined copper by a certain chemical structure. That was the real inductive step.
We can reasonably say: In some cases, what is true of some is true of all. But what cases are those? There is where the real work of science takes place. No PUN intended.