To quote Bertrand Russell, "My Philosophical Development", Simon and Schuster, N.Y., 1959, p. 86:

I used to know of only six people who had read the later parts of the book [Principia Mathematica]. Three of these were Poles .... The other three were Texans ...

Jan Woleński in "Polish Logic", Logical J. of the IGPL 12 (2004), 399-428 (reprinted in "Historico-Philosophical Essays", Copernicus Center Press, Krakow, 2012), suggests two of the 3 Poles were Chwistek and Leśniewski.

Leon Chwistek wrote about theory of types, got positive reference from Russell while applying for a professorship in Lvov, and is referred to in the introduction to the 2nd edition of "Principia Mathematica", so he is one of the Poles without doubt.

Who were the remaining 2 Poles and 3 Texans?

Perhaps another strong contender is Tarski.

Stanisław Ignacy Witkiewicz (a friend of Chwistek) mentions "Principia Mathematica" in his novel "Nienasycenie", but it is doubtful whether he had really read it, and not being a mathematician or logically inclined philosopher, he, probably, does not qualify.

Update January 6, 2015.

As was noted by JHD, the full Russell quote continues as follows:

... Three of these were Poles, subsequently (I believe) liquidated by Hitler. The other three were Texans, subsequently successfully assimilated.

Indeed, neither of the 3 strong contenders (Chwistek, Leśniewski, Tarski) was "liquidated by Hitler". I believe Russell is just wrong in that respect, for two reasons: First, at the time of writing this, his interests, for a long time, shifted far away from (mathematical) logic. If he was no longer interested in the subject, it is natural to assume he was also not much uptodate about the fate of its practitioners. Second, since so many Poles, and Polish mathematicians in particular, perished during WWII, it was, probably, natural to assume, not knowing the details, that any particular person "was liquidated by Hitler" than otherwise (btw, as far as I know, Chwistek died in Russia under strange circumstances, so it is quite possible that he was "liquidated by Stalin" instead of Hitler, but this will move us far away from the initial question).

Still, I am in full ignorance about Texans (and why and how they were "assimilated").

• Russell says of the Poles that they were “subsequently (I believe) liquidated by Hitler”. (op.cit p.66) This completely rules out Tarski. Leśniewski died of cancer in May 1939, several months before the German invasion of Poland. Chwistek died near Moscow in 1944. Neither was “liquidated by Hitler”, although perhaps Russell mistakenly believed that they had been. – MJD Jan 5 '15 at 17:01
• In “Principia Mathematica in Poland” (The Palgrave Centenary Companion to Principia Mathematica, Griffin N. and B. Linsky, eds., ch 3), Woleński says (p55) “Can we identify three Poles who read the later parts of PM…? I am afraid not. Chwistek, Zawrirski and Tarski quoted the second volume, but none of them was liquidated by Hitler; Chwistek died on Moskva in 1944, Zawirski in 1948 in Kraków and Tarski in 1983 in the USA. Russell probably never heard of Sleszyński….” – MJD Jan 5 '15 at 17:19
• The title of this thread sounds like the start of a 'walks into a bar' joke. – dotancohen Jan 6 '15 at 12:34
• @MJD: Thanks for the comments and for putting properly Polish diacritics. I will augment the question. – Pasha Zusmanovich Jan 6 '15 at 15:35
• I find it impossible to believe that Russell could have been thinking of Tarski. At the time that Russell wrote about the "three Poles" (1959) Tarski was alive and well, active in the logical and mathematical communities, and had been at Berkeley for nearly twenty years. The Woleński essay I mentioned relates that someone once asked Russell who the three Texans were, and his answer was vague and suggested that they were graduate students nobody now would remember. – MJD Jan 6 '15 at 16:10

One of the Poles was Emil Leon Post, who discussed the incompleteness of Principia.

From Wikipedia:

While at Princeton, he came very close to discovering the incompleteness of Principia Mathematica, which Kurt Gödel proved in 1931.

In his doctoral thesis, Post proved, among other things, that the propositional calculus of Principia Mathematica was complete: all tautologies are theorems, given the Principia axioms and the rules of substitution and modus ponens. Post also devised truth tables independently of Wittgenstein and C.S. Peirce and put them to good mathematical use. Jean Van Heijenoort's well-known source book on mathematical logic (1966) reprinted Post's classic article setting out these results.

• You should try to include some references to back up your claims. How else should we know whether to trust what you're saying or not? – Danu Oct 21 '15 at 12:57
• Post lived until 1954, so he was clearly not "liquidated by Hitler", as the question says. – HDE 226868 Oct 22 '15 at 1:08
• Post's 1994(1941), Absolutely Unsolvable Problems and Relatively Undecidable Propositions, Solvability, Provability, Definability: The Collected Works, ed. Martin Davis, Boston: Birkhaeuser, p.375-- is probably what this answer is referring to. It was written 1921--1922 but part of the paper was submitted to journals and rejected then so Post never sent full the paper out to journals again until 1941 --- when again Weyl rejected it. This time because it was no longer a new idea. So it remained unpublished, only discussed. – Guido Jorg Oct 28 '15 at 21:22

Even as a Polish-trained mathematician with active interests in philosophy and history of mathematics and science (who took two courses from Prof. Woleński, among others), I am hard pressed to think of three mathematicains/logicians/philosophers who would have good motivation for reading Principia and were “liquidated by Hitler”.

To be sure, Leon Chwistek is the strongest contender. He worked on theory of types and corresponded with Russell, who (successfully) recommended him for the chair of logic at the Lwów University in 1928. Mark Kac, a student in Lwów in 1930s, wrote the following words about Chwistek in his autobiography “Enigmas of chance”: “Rumor had it that he was the only one who, except for the authors, had read all three volumes of Principia Mathematica (pp. 42-43).” However, Chwistek died of a kidney failure in Moscow in 1944 (there were rumors about his poisoning).

As noted by other participants in this discussion, several strong candidates cannot be counted because of when and how they died. But it is still worth recalling some of the evidence of their reading Principia, along with a little of biographical information, since not all are household names.

Jan Sleszyński (1854-1931), a Pole who was first a professor in Odessa (under the name of Ivan Sleshinskii), then in Kraków, started out working in number theory and analysis, later turning to logic. His lecture notes in proof theory, published in Kraków by the Mathematics and Physics Student Circle in 1925-29, discuss extensively the history of logic up to (and including) the contributions of Russell and Whitehead. (see the book by Roman Murawski, Philosophy of mathematics and logic in the inter-war Poland). According to A. Hoborski, O Śleszyńskim, wspomnienie pośmiertne [On Śleszyński, an after-death reminiscence], Wiadomości Matematyczne, 36 (1934), he sought to eliminate any hidden rules from deductive reasoning, which prompted him to study Principia Mathematica (private information from Lidia Obojska).

Zygmunt Zawirski (1882-1948) was a philosopher with some mathematical background, a student of Kazimierz Twardowski. In 1937 he became a professor in Kraków. He was interested in application of logic to natural sciences. He had hoped that Russell’s theory of types would help eliminate logical antinomies arising in quantum physics (this information after Irena Szumilewicz-Lachman: Zygmunt Zawirski. His life and work. With selected writings on time, logic and the methodology of science. Kluwer Academic Publishers, 1994).

Of course, the names of Alfred Tarski and Stanisław Leśniewski are much better known among mathematicians. Regarding whether Tarski read Principia, one can note that he considered the concept of membership and in a lecture in 1966 he quoted Principia Mathematica to support his view that it is a logical notion:

“Using this method [of Principia Mathematica], it is clear that the membership relation is certainly a logical notion. It occurs in several types, for individuals are elements of classes of individuals, classes of individuals are elements of classes of classes of individuals, and so on. And by the very definition of an induced transformation it is invariant under every transformation of the world onto itself” (quotation after Stanford Encyclopedia of Philosophy, http://plato.stanford.edu/entries/tarski/).

Tarski’s PhD advisor Leśniewski tried to provide foundations for mathematics in a very unique manner, bypassing the set theory and the type theory. He referred to Principia Mathematica at least by criticizing its terminology, which he found confusing (“Foundations of a General Theory of Sets I”, 1916; after http://plato.stanford.edu/entries/lesniewski/).

My personal bets (if speculation is allowed), besides Chwistek, are Władysław Hetper and Witold Wilkosz.

Hetper was a student and coauthor of Chwistek (and a close friend and roommate of Mark Kac in their student days), who received his PhD in 1937 and his habilitation in 1939. He was imprisoned by the Soviets and executed by them, probably in Kharkov in 1941.

Wilkosz was a professor of mathematics in Kraków, Banach’s high school classmate, a PhD student of Giuseppe Peano in Turin, and a polymath with multiple interests, including logic. Not quite ”liquidated”, he died in 1941 (during the German occupation of Poland) of natural causes, but the time he spent in German prison in 1939 and subsequent wartime deprivation made his condition worse. Wilkosz explicitly referred to Russell and his arguments with Peano when discussing equivalence relations in the paper “O definicji przez abstrakcjȩ” [On defining through abstraction], Kwartalnik Filozoficzny 14 (1938), 1-13 (see Murawski’s book cited above). Hetper in his work credited some unpublished results of Wilkosz.

All three (Chwistek, Hetper, Wilkosz) died during WWII. Russell either did not know the details of their death (in the cases of Chwistek and Hetper, these are still not fully confirmed and were not public knowledge in communist Poland) or else he was reluctant to blame the Soviets.

There was also Stanisław Bilski, a graduate in mathematics and a doctor in philosophy (from the Jagilellonian University in Kraków) in 1926, whose thesis title was “A priori knowledge in Bertrand Russell’s epistemology”. he was a communist activist in Poland, subsequently liquidated in the USSR in the Great Purge of 1934 (hence again by Stalin, not by Hitler). But his name was rather unknown.

Finally, a popular account in Polish of Russell’s antinomy was written in 1927 (Przegla̧d Filozoficzny, vol. 30, issue 4, pp. 291-292) by the Lwów mathematician Lucjan Emil Boettcher, who worked mainly in iteration theory. He died of natural causes in 1937, before WWII and German occupation.

The only sure conclusion of all this is that Russell’s works were studied by Poles (and in Poland, when it was reborn in 1918) before 1939.

• Hi Margaret, and welcome to this site. Note that (tex?) commands like \l do not render when used in plain text, on this site. – Danu Dec 25 '15 at 8:28
• I did note, but how do I fix this? Putting text between backticks does not seem to work. – Margaret Friedland Dec 26 '15 at 1:38
• If you have a Mac, holding down the letter key you want accented gives you the ability to accent the character. The editor will also take unicode so ń is &#324; ó is &#243; You can search for other Unicode characters here: unicode-table.com/en – AMR Dec 27 '15 at 6:52