Whitehead and Russell published their monumental work
Principia Mathematica in which they attempted to put mathematics on a logical basis using arithmetic defined using set theory. The appears problems with their theory before it was even published.
Gödel later proved that what they wanted to do, specify a formal symbol system (that included arithmetic) that was both complete and consistent was not possible.
Part of their attempted fixes were using a theory of "
types" as in "
typed sets". This did not resolve the paradox named the "
Russell Paradox". Similar issues appear to be in Whitehead's ideas that became known as "
process theology" in that one can use it to show anything true or false as desired.
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Details are left as a future topic.
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