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Goal Quotes

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Goal Quotes

“Inanimate objects can be classified scientifically into three major categories: those that don't work, those that break down and those that get lost. The goal of all inanimate objects is to resist man and ultimately to defeat him, and the three major classifications are based on the method each object uses to achieve its purpose. As a general rule, any object capable of breaking down at the moment when it is most needed will do so.”

“The goal of a definition is to introduce a mathematical object. The goal of a theorem is to state some of its properties, or interrelations between various objects. The goal of a proof is to make such a statement convincing by presenting a reasoning subdivided into small steps each of which is justified as an "elementary" convincing argument.”

“. . . the membership relation for sets can often be replaced by the composition operation for functions. This leads to an alternative foundation for Mathematics upon categories -- specifically, on the category of all functions. Now much of Mathematics is dynamic, in that it deals with morphisms of an object into another object of the same kind. Such morphisms (like functions) form categories, and so the approach via categories fits well with the objective of organizing and understanding Mathematics. That, in truth, should be the goal of a proper philosophy of Mathematics.”

“I wish my life and decisions to depend upon myself, not on external forces of whatever kind. I wish to be the instrument of my own, not other men's, acts of will. I wish to be the subject, not an object...I wish to be somebody, not nobody; a doer - deciding, not being decided for, slef-directed and not acted upon by external nature or by other men as if I were a thing, or an animal, or a slave incapable of playing a human role, that is, of conceiving goals and policies of my own and realizing them.”