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Human reasoning works two ways, one by induction and one by deduction. Induction starts from particulars and moves to general claims and deduction starts with general principles and moves to particular claims.
Inductive reasoning normally works by examining multiple examples and discovering common features. For example, if you examined many individual dogs and found they all had four legs, you would then conclude that dogs were quadrupeds.
Much of scientific discovery proceeds by induction. For example, the astronomer Edwin Hubble used observation of the redshift of the spectrums of many distant galaxy to calculate that the universe was expanding; this is induction because he derived a general principle (the expansion of the universe at a fixed rate known as "Hubble's constant") from many different individual pieces of data, namely the redshifts and distances of many galaxies.
There are two types of arguments - inductive and deductive. In simple terms an inductive argument is when the claim in the conclusion goes beyond the information in the premises. The premises do not contain sufficient information to guarantee that the conclusion is correct.
Therefore induction is much like an assumption based on information we have and examples, but an assumption we have not proven.
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