Objections handled in the comments.
The following video serves as a good introduction to the uniformity of nature. The author ironically mocks the only worldview that can solve the problem whilst explaining the problem.
NYU defines the uniformity of nature as such: The uniformity of nature is the principle that the course of nature continues uniformly the same, e.g. if X is the cause Y, then Y will necessarily exist whenever X exists. In particular, the uniformities observed in the past will hold for the present and future as well.
Greg Bahnsen wrote:
Unbelievers claim: We only know things based on observation and experience. We only know things that are results of sense experience in the material world. But the problem arises: We have no experience of the future, for it has yet to occur. Therefore, on this experience-based scientific method, how can we predict that the future will be like the past so that we may expect scientific experiments to be valid? The unbeliever will attempt to respond: We know the future will be like the past because our past experience of the oncoming future has always been thus.‖ But this statement still only tells us about the past, not the approaching future we now must anticipate. Furthermore, you can‘t expect the future to be like the past apart from a view of the nature of reality that informs you that events are controlled in a uniform way, as by God in the Christian system. Even the renowned atheist philosopher Bertrand Russell (1872–1970) admitted the principle of induction (that we can take past experiences and project them into the future, that we can know the future by gaining knowledge of the past) has no foundation in observation, in sense experience. Therefore, it has no scientific foundation. Yet all formal science and all rational human experience assumes uniformity.
The problem of induction, which requires the uniformity of nature is defined by David Hume as - “instances of which we have had no experience resemble those of which we have had experience” The Problem of Induction. The original problem of induction can be simply put. It concerns the support or justification of inductive methods; methods that predict or infer.
As Christians we don't have a problem assuming the uniformity of nature. The uniformity of nature is perfectly compatible with the Christian worldview. The absolute, all-creating, sovereignly-governing God reveals to us in Scripture that we can count on regularities in the natural world. The Bible teaches that the sun will continue to measure time for us on the earth (Gen. 1:14–19; Eccl. 1:5; Jer. 33:20), that seasons will come and go uniformly (Gen. 8:22; Ps. 74:17), that planting and harvest cycles may be expected (Jer. 5:24; Mark 4:26–29), and so forth. Because of this God-governed regularity in nature, the scientific enterprise is possible and even fruitful.