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Formal Quotes - page 8 - Quotesdtb.com
Formal Quotes - page 8
So much of modern mathematical work is obviously on the border-line of logic, so much of modern logic is symbolic and formal, that the very close relationship of logic and mathematics has become obvious to every instructed student. The proof of their identity is, of course, a matter of detail: starting with premisses which would be universally admitted to belong to logic, and arriving by deduction at results which as obviously belong to mathematics, we find that there is no point at which a sharp line can be drawn, with logic to the left and mathematics to the right. If there are still those who do not admit the identity of logic and mathematics, we may challenge them to indicate at what point, in the successive definitions and deductions of Principia Mathematica, they consider that logic ends and mathematics begins. It will then be obvious that any answer must be quite arbitrary.
Bertrand Russell
It is urged in the first place that contempts cannot be crimes, because, although punishable by imprisonment, and therefore, if crimes, infamous, they are not within the protection of the Constitution and the Amendments giving a right to trial by jury, etc., to persons charged with such crimes. But the provisions of the Constitution are not mathematical formulas having their essence in their form; they are organic, living institutions transplanted from English soil. Their significance is vital, not formal; it is to be gathered not simply by taking the words and a dictionary, but by considering their origin and the line of their growth.
Oliver Wendell Holmes Jr.