Scope of Foundations Laid
The Principia covered only set theory, cardinal numbers, ordinal numbers, and real numbers. Deeper theorems from real analysis were not included, but by the end of the third volume it was clear to experts that a large amount of known mathematics could in principle be developed in the adopted formalism. It was also clear how lengthy such a development would be.
A fourth volume on the foundations of geometry had been planned, but the authors admitted to intellectual exhaustion upon completion of the third.
Read more about this topic: Principia Mathematica
Famous quotes containing the words scope of, scope, foundations and/or laid:
“The scope of modern government in what it can and ought to accomplish for its people has been widened far beyond the principles laid down by the old “laissez faire” school of political rights, and the widening has met popular approval.”
—William Howard Taft (1857–1930)
“In the works of man, everything is as poor as its author; vision is confined, means are limited, scope is restricted, movements are labored, and results are humdrum.”
—Joseph De Maistre (1753–1821)
“Neutrality is a negative word. It does not express what America ought to feel.... We are not trying to keep out of trouble; we are trying to preserve the foundations on which peace may be rebuilt.”
—Woodrow Wilson (1856–1924)
“Under the wide and starry sky,
Dig the grave and let me lie.
Glad did I live and gladly die,
And I laid me down with a will.
This be the verse you grave for me:
Here he lies where he longed to be;
Home is the sailor, home from sea.
And the hunter home from the hill.”
—Robert Louis Stevenson (1850–1894)