[Rudolph Eucken by Abel J. Jones]@TWC D-Link bookRudolph Eucken CHAPTER III 9/16
These premises may be in themselves general statements--how is their truth established? They may be, and often are, the generalisations of the empirical sciences, and must then possess the same degree of uncertainty that these generalisations possess.
Some philosophers have contended that certain general ideas are innate, but few would be found nowadays to accept such a contention.
At other times mere definitions of terms may serve as premises.
One might state as a premise the definition "A straight line is the shortest distance between two points," and the further statement that "AB is a straight line between A and B," and conclude that the line AB represents the shortest distance between two points A and B.In a manner similar to this Euclid built his whole mathematical system upon the basis of definitions and postulates, a system the complexity and thoroughness of which has caused all students of mathematics at one time or another to marvel and admire.
But, of course, a definition is little more than assigning a definite term to a definite thing.
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