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The Wikipedia article about Wittgenstein says:

In Norway it was clear that Moore was expected to act as Wittgenstein's secretary, taking down his notes, with Wittgenstein falling into a rage when Moore got something wrong. When he returned to Cambridge, Moore asked the university to consider accepting Logik as sufficient for a bachelor's degree, but they refused, saying it wasn't formatted properly: no footnotes, no preface. Wittgenstein was furious, writing to Moore in May 1914: "If I am not worth your making an exception for me even in some STUPID details then I may as well go to Hell directly; and if I am worth it and you don't do it then—by God—you might go there."

Furthermore it says:

Despite this fame, he could not initially work at Cambridge as he did not have a degree, so he applied as an advanced undergraduate. Russell noted that his previous residency was sufficient to fulfill eligibility requirements for a PhD, and urged him to offer the Tractatus as his thesis. It was examined in 1929 by Russell and Moore; at the end of the thesis defence, Wittgenstein clapped the two examiners on the shoulder and said, "Don't worry, I know you'll never understand it." Moore wrote in the examiner's report: "I myself consider that this is a work of genius; but, even if I am completely mistaken and it is nothing of the sort, it is well above the standard required for the Ph.D. degree." Wittgenstein was appointed as a lecturer and was made a fellow of Trinity College.

How was it possible for Wittgenstein to get a PhD in philosophy without having a Bachelor's degree in philosophy? And how was it possible that his work satisfied requirements for a PhD but not for a Bachelor's degree?

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    $\begingroup$ Until recently (until 1980s, roughly speaking) the rules were much more flexible. I know several people (in mathematics) achieving the highest academic honors, and positions, some of them without Master degree, or equivalent, others without PhD. These things could happen in England, in Soviet union and elsewhere. $\endgroup$
    – Alexandre Eremenko
    Commented Apr 14, 2018 at 0:50
  • $\begingroup$ Further to Alexandre's comment, for example, the mathematician F. P. Ramsey, a friend of Wittgenstein who produced the first English translation of the Tractatus, only ever conferred an undergraduate degree. $\endgroup$
    – nwr
    Commented Apr 14, 2018 at 18:45
  • $\begingroup$ I think you're asking how to get a PhD without any Bachelor's. THere's no need to get all degrees in the same field. $\endgroup$
    – Carl Witthoft
    Commented Apr 16, 2018 at 11:58

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In the early and mid-20th century in Anglo-American higher education, exceptions of this sort occurred for individuals who showed that they could hold their own in elite academic circles. An example in addition to Wittgenstein and Ramsey is Garrett Birkhoff. After receiving a BA at Harvard in 1932 and then spending some time at Cambridge, he returned to Harvard and became an instructor in 1936, eventually retiring from there in 1981, after a long and storied career, as George Putnam Professor of Pure and Applied Mathematics. The BA was his only formal degree.

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  • $\begingroup$ Andrew Gleason was later also a professor at Harvard having on an undergraduate degree. Like Birkhoff (from 1933-36) he was in a "fellow" at Harvard before being hired as a professor, and this stage clearly operated in lieu of a formal doctoral stage. $\endgroup$
    – Dan Fox
    Commented Apr 19, 2018 at 8:00
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There was a lot of disruption to the education system during WWII. Apparently Wittgenstein wrote his notes for the Tractatus whilst serving in the Austrian Army. So this is one factor.

Wittgenstein also desperately wanted to be a philosopher of logic but did not know whether he had the talent and so he asked his hero Bertrand Russell to evaluate his philosophical talents.

Apparently Russell thought he was either an idiot or a genius. And then later revised it to genius. Who knows what later philosopgers might think. One philosopger recently told me that analytic philosophy was on the wane. So perhaps we may need to re-evaluate ...

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