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Inductive Reasoning, Miracles, and Examples from Number Theory

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It is an obvious fact that any empirical knowledge of physical laws currently possessed by human civilization arose, not from constant observation of the universe at all points in space at all instances in time, but rather through experiments conducted at specific points in space at specific instances in time. In fact, given the relatively small proportion of human beings who are engaged in science research, and given that even scientists do not spend every moment of their time performing experiments, it should be obvious to anyone that human beings are not constantly checking the laws of physics to prove rigorously that exceptions to known knowledge are not occurring. If one additionally considers the relatively short span of time modern human civilization has existed relative to the age of the earth, one realizes the great lengths of time that have passed with human beings not observing the universe. Nevertheless, the laws of physics are assumed to hold at all points in space and time. What then justifies this assumption?


Timothy Foo

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Graduate Student in Mathematics, Rutgers University -Newark