Was Ludwig Wittgenstein Jewish?

At the Times, philosopher Paul Horwich asks, Was Wittgenstein Right? His answer is that most philosophers vote no, and yet Wittgenstein's reputation is stellar.

We want to know, was Wittgenstein Jewish? Despite his extensive Jewish heritage, according to Jewish law, no, Ludwig Wittgenstein was a not Jew. He was a Catholic.

His mother and maternal grandmother were Catholic. Despite that, Wittgenstein rejected religion, yet at times claimed to be Jewish in spirit and thought. And some have speculated that he went to school with Adolf Hitler.

Wikipedia explains all of this.
Wittgenstein's mother was Leopoldine Kalmus. Her father was Czech Jewish and her mother was Austrian-Slovene Catholic—she was Wittgenstein's maternal grandparent and only non-Jewish grandparent, whose ancestry was Austrian and an aunt of the Nobel Prize laureate Friedrich Hayek on her maternal side. Ludwig was born at 8:30 pm on 26 April 1889 in the so-called "Wittgenstein Palace" at Alleegasse 16, now the Argentinierstrasse, near the Karlskirche. Karl and Poldi, as she was known, had nine children in all. There were four girls: Hermine, Margaret (Gretl), Helene, and a fourth daughter who died as a baby; and five boys: Johannes (Hans), Kurt, Rudolf (Rudi), Paul—who became a concert pianist despite losing an arm in World War I—and Ludwig, who was the youngest of the family.
The children were baptized as Catholics, and raised in an exceptionally intense environment...
Some speculated that W. went to school with Hitler.
There is much debate about the extent to which Wittgenstein and his siblings, who were of 3/4 Jewish descent, saw themselves as Jews, and the issue has arisen in particular regarding Wittgenstein's schooldays, because Adolf Hitler was at the same school for part of the same time. Laurence Goldstein argues it is "overwhelmingly probable" the boys met each other: that Hitler would have disliked Wittgenstein, a "stammering, precocious, precious, aristocratic upstart ...". Other commentators have dismissed as irresponsible and uninformed any suggestion that Wittgenstein's wealth and unusual personality may have fed Hitler's antisemitism, in part because there is no indication that Hitler would have seen Wittgenstein as Jewish.
Wittgenstein and Hitler were born just six days apart, though Hitler had been held back a year, while Wittgenstein was moved forward by one, so they ended up two grades apart at the Realschule. Monk estimates they were both at the school during the 1904–1905 school year, but says there is no evidence they had anything to do with each other. Several commentators have argued that a school photograph of Hitler may show Wittgenstein in the lower left corner, but Hamann says the photograph stems from 1900 or 1901, before Wittgenstein's time.
In his own writings Wittgenstein frequently referred to himself as Jewish, at times as part of an apparent self-flagellation. For example, while berating himself for being a "reproductive" as opposed to "productive" thinker, he attributed this to his own Jewish sense of identity, writing: "The saint is the only Jewish genius. Even the greatest Jewish thinker is no more than talented. (Myself for instance)." While Wittgenstein would later claim that "[m]y thoughts are 100% Hebraic", as Hans Sluga has argued, if so, "his was a self-doubting Judaism, which had always the possibility of collapsing into a destructive self-hatred (as it did in Weininger's case) but which also held an immense promise of innovation and genius."
In practice, W. rejected religion.
It was while he was at the Realschule that he decided he had lost his faith in God. He nevertheless believed in the importance of the idea of confession. He wrote in his diaries about having made a major confession to his oldest sister, Hermine, while he was at the Realschule; Monk writes that it may have been about his loss of faith. He also discussed it with Gretl, his other sister, who directed him to Arthur Schopenhauer's The World as Will and Representation. As a teenager, Wittgenstein adopted Schopenhauer's epistemological idealism. However, after his study of the philosophy of mathematics, he abandoned epistemological idealism for Gottlob Frege's conceptual realism.

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