Principle of uniformity of nature is a principle that is derived from two claims:
- Space and time are relative and therefore aren't perceivable states of objects.
- There are exceptionless laws of nature which determine future perceivable states of objects solely based on past and present states of objects.
Kant calls the first principle 'the first analogy of experience' and the second principle 'the second analogy of experience'. In James Clerk Maxwell's formulation the principle says the following: laws of nature are uniform regardless of our position in space and time.
NOTE 1: Carl Friedrich von Weizsäcker noticed an interesting link between Noether's theorem and Kant's 'first analogy' (here). As another user pointed out, there is a deepconnection between certain consequence of Noether's theorem and "Uniformity of Nature".
NOTE 2: It is important that we speak in this formulation of states or properties, i.e. ways in which various objects, situations etc. can resemble eachother. If we speak of mere sets or classifications of objects, there are infinitely many, arbitrary ways in which we might draw the distinction, and this leads to what Nelson Goodman calls "The New Riddle of Induction", the inability to infer anything about the future from claims about the past, cf. N. Goodman, Fact, Fiction and Forecast.
The argument that Kant uses to establish these principles is a transcendental argument: he says that if these principles weren't true, certain features of our perception of time couldn't be made, in his words, 'objective'. This means, for example, that we couldn't have an intersubjective account of which event follows another temporally. In other words, he posits that these principles are conditions of possibility of experience.
NOTE: The principles themselves are called 'analogies' because they establish analogies between what happens in time and pure time-determinations (persistence, successivity, simultaneity). But the reasoning itself isn't an analogy.
This only establishes, however, as Kant is aware, certain heuristics regarding formulation of scientific theories which cannot be definitely proved or disproved by any finite amount of data. Kant's word for it is: 'regulative principle'. The argument also relies, very explicitly in fact, on a view of time associated with Newtonian physics that has been later challenged by quantum mechanics.
Indeed, a big problem appears if we deny that there are indeed exceptionless laws of nature or when we posit retrocausality (future states affecting past states). There are viable interpretations of quantum mechanics which make these changes to our view of the world. Other interpretations say that the very states aren't determinate before measurement takes place. In fact, according to results like the famous Bell's theorem, one of these disjuncts has to be true, i.e. either the results of measurements aren't defined before the measurement takes place, there are causal connection from the future to the past or the principle of locality (in a huge simplification: "law of causality") is violated. Although the idea is intact, Kant's original formulation is impossible to preserve.
Further reading:
- Ian Hacking, The Emergence of Probability
- Ernst Cassirer, Determinism and Indeterminism in Modern Physics