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## Principia MathematicaFor Isaac Newton's 1687 book containing basic laws of physics, seePhilosophiae Naturalis Principia Mathematica.
The types: a set has a higher type than its elements and one can not speak of the "set of all sets" and similar constructs which lead to paradoxes (see Russell's paradox).
The The questions remained whether a contradiction could be derived from the Principia's axioms, and whether there exists a mathematical statement which could neither be proven nor disproven in the system. These questions were settled, in a rather disappointing way, by Gödel's incompleteness theorem in 1931. ## Reference- B. Russell, A. N. Whitehead:
*Principia Mathematica*, Cambridge, University Press, 1910-1913
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