Inductive Reasoning In Science

I’ve been debating with a friend about the nature of science, and he brought up the following argument:

1. All inferences from experience to conclusions about the future presuppose the principle that the future will resemble the past. (Principle of the Uniformity of Nature)
a. If we suspect that the course of nature may change and that the past is no guide to the future, then all experience becomes useless and does not support any conclusion about the future.
2. Therefore, no argument from experience can support the principle that the future will resemble the past.
3. No deductive argument can establish the principle that the future will resemble the past.
4. Therefore, the Principle of the Uniformity of Nature cannot be rationally justified.
5. If the Principle of the Uniformity of Nature cannot be rationally justified, then inductive reasoning in science cannot be rationally justified.
6. Therefore, inductive reasoning in science cannot be rationally justified.

Your thoughts?

The reply is at NeuroLogica.

However, one issue not discussed, probably as does not appear as one of the questions, but which is also often aired is that induction requires a leap of faith. Therefore science is no better than religion in requiring faith. In this case it is more revealing to look at mathematical induction, in which case it is necessary to start with one statement of fact then to show that a second fact is true, after which the method of induction proves the general case. Note firstly that induction is also used to prove the general case false, for example, in the proof that there are an infinite number of prime numbers we start off with the conjecture, or hypothesis, that there are only a finite number of primes. Secondly, induction requires that established facts are used to then drive the general case. In religion there are no such empirical facts and therefore is not subject to the method of induction, save as a metaphysical device to generate more metaphysical truths from initial metaphysical premises. In such cases religion has jumped off into faith well before the inductive steps.