Mathematics and logic deal with absolutes (within their fields of accepted axioms and rules of combination), and while science appeals to and conforms to mathematics and logic (as long as these are consistent with observations - they don't always appear to be), science is based on other guiding principles which, while not guaranteeing absolute truth, give us the best chances of getting things right*. The following paragraphs will deal with those principles.
Regarding induction, yes it is true that it is just possible, for example, that the sun will not rise or will not shine tomorrow. But let's say that there are some 10,000 years of recorded history. We have had more than 3.5 million days in which the sun has not failed to rise and shine. Let's say that ends tomorrow. What is the probability that it will? By pure mathematical probability theory, that is one in 3.5 million chance or less. Induction does not guarantee it, but it leads us, reasonably, on pure probabilistic grounds and nothing else, to think it is not going to happen.
Parsimony bears on the above. Parsimony is the principle that, if there are competing theories, hypotheses or notions, we should go with the simplest one that adequately accounts for the evidence. Does nature follow the same rules consistently? The parsimonious answer is, yes it does. There is no evidence that it does not. There is no reason in reason to think that it does not. If the rules did change, why would they change? We are speculating on something that has never actually happened, for reasons that do not exist. If, however, the rules do change, we will adjust our ideas. Such is the pragmatic nature of science. But unless and until they do, there is no reason for us to do so.
Nerd's note: Noether's theorem (which is a mathematical theorem, and not a theory) proves that the laws of conservation and of symmetry are two sides of the same coin. The relevance to the present discussion is that if the laws of physics were to be variable over time, breaking temporal symmetry, then the laws of conservation of mass and energy would be violated. See consistency/consilience, below.
Falsifiability and prediction are related scientific guidelines. If a scientific idea can be tested such that it might fail, it is regarded as (potentially) falsifiable. This idea is a little difficult to grasp. An idea may be true, but still be (potentially, before the conduct of a test) falsifiable. Think of it as "baptism of fire". The more we try to destroy a scientific idea, the more, if it survives our attempts, we can be convinced of its veracity. It doesn't guarantee it. There may be other tests it may fail, but we haven't thought of them or conducted them yet. Again, passing these tests does not absolutely guarantee that the idea is correct, but it does support the assessment that they are likely to be correct. Prediction is a related idea. It is not exactly "foretelling", but an examination of the implications of an idea. If an idea implies that some result must necessarily follow, and it does, it is a successful "prediction". If it does not follow, the idea is falsified.
Consistency/consilience: Another guiding principle of science is that nature is consistent. This is not fundamentally necessarily so, but it seems to be the case, and using the working assumption that it is produces results that appear to work. (Pragmatism at work again - if science discovers inconsistencies in nature, it will have to deal with them.) The more a scientific idea dovetails with others is regarded as evidence that it is on the right lines. The more disparate, independent lines of evidence we have that converge on the same conclusion, the more likely it is that that conclusion is correct*.
*Re. "right" and "correct". These terms need qualifying when used in the scientific context. I will go into this in a subsequent comment.
Tagging Michael Smit.
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