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Recently, I am very interested in Russel's paradox in set theory, and I knew that "Type Theory" is one solution to cope with such paradox in (naive) set theory.

However, in a book "Incompleteness: The Proof and Paradox of Kurt Gödel" by Rebecca Goldstein, I some how felt that she referred Type Theory is makeshift of naive set theory. It sounds like Type theory is not a common view.

Regarding this, I'd like to ask about the academical status of Type Theory. Does that theory believed to be common wisdom? Replacing all naive set theory?

Thank you all for your answer.

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    $\begingroup$ The Stanford Encyclopedia of Philosophy has a very nice article about type theory. $\endgroup$
    – MJD
    Commented May 12, 2017 at 14:56
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    $\begingroup$ For a very nice "modern" textbook on TT, see : P.B. Andrews, An Introduction to Mathematical Logic and Type Theory: To Truth through Proof, 2nd ed, 2002. See also: William Farmer, The Seven Virtues of Simple Type Theory, 2008. $\endgroup$ Commented May 12, 2017 at 18:54
  • $\begingroup$ @MJD Thanks for your help. I thinks it's a better document about Type Theory than Wikipedia. $\endgroup$ Commented May 13, 2017 at 3:55
  • $\begingroup$ @Mauro ALLEGRANZA Thanks for your recommendation! I was truly finding for good books about Type Theory! $\endgroup$ Commented May 13, 2017 at 3:57
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    $\begingroup$ It's worth clarifying your question that you're specifically interested in Russell's type theory, rather than how type theory has developed since. $\endgroup$
    – user14972
    Commented May 13, 2017 at 4:06

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