In The Logic of Scientific Discovery, Karl Popper outlines what he calls 'the problem of induction'; a 'problem' first demonstrated by David Hume. Induction (in the scientific sense of the word) is the method of generalising a (universal) law or principle after numerous observations and tests have been carried out. For example, every single time I have dropped an object it has fallen towards the centre of the Earth (as the observations). Therefore all dropped objects will always fall towards the centre of the Earth (as the law). What this is saying is that given a large number of observations of X, and if all known Xs are Y, then all unknown Xs are Y as well. Using the term unknown says exactly what the problem is - we do not know! An example from everyday life might be, "I have watched a lot of cricket test matches and as such all cricket balls known to me are red. Therefore all cricket balls unknown to me are red as well." Thus an inductive conclusion is reached; but as soon as I personally witness a one-day match (where the ball is white) I would see this to be false. Popper saw induction as attempting to establish a universal statement from a singular one, or indeed many singular ones. How can we believe something to be universally true when we can only show it to be true a finite number of times? Even a very large number of singular statements or events will not prove a universal one. The only way to prove a universal statement is by testing it an infinite number of times, which is impossible.
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