tractatus 5

The two principles, those of Piety and Virtue, are seen to extend to algebra. Some insist that the primary foundation of algebra is Aristotelian, the identity that N=N. Independent of all other numbers, many take this truth for the beginning of the numerical science. What folly! Such asserts that if an egg have a crack, and if the egg can remain itself without a crack, that the crack can exist without the egg! The two principles I have delineated more satisfactorily resolve the foundation. The four basic relations of algebra comprise addition, multiplication, exponentiation, and logarithms. These relations comprise a minimum of two numbers, as an opened fruit yields at least two pieces, else the fruit is whole. For logarithms, I shall say that they tell the mathematician how long something may mature given a rate of growth. For exponentiation, I shall say that it makes growth observable. For multiplication, I shall say that it distributes itself among its parts. For addition, I shall say it is simplistic.