On the Vienna Circle: Eight of Eight

 

Let us finally say something about two deaths: the murder that justifies the title of the book we have been discussing, "The Murder of Professor Schlick," and four decades later the mental-illness driven death of the mathematician/logician Kurt Godel.  

On the morning of June 22, 1936, Schlick was due to present his final lecture of the semester to his class at Vienna University. He took Tram D and arrived at the University at 9:15. He walked through the iron gate, down the hall, and turned right onto a staircase. Students in Room 41 were waiting for him. 

He must have walked right past Johann Nelbock on his way. Nelbock, a mentally unhinged student, had become extremely agitated by a lecture Schlick had given on immortality earlier in the semester. (For the positivists, there was a puzzle as to whether the claim of immortality was even meaningful.)  

After Schlick walked past him, Nelbock ran forward to get ahead of Schlick, turned around and fired four bullets at him. As he did this, he apparently shouted, "Now you damned bastard! Have at it!"

Schlick died, of course (two of the bullets passed through his heart), and Nelbock waited patiently for the arrival of the police. There wasn't much material for a whodunnit here. 

The following month, an article appeared in the journal PHILOSOPHICAL REVIEW about the principle of verification. The author defended that principle against some of its critics. 

This author was ... the newly deceased Moritz Schlick. And the article uses an example from that lecture earlier in the year, mentioned parenthetically above. The posthumous article says there is a puzzle about whether the statement "After my death I will continue to exist" is meaningful. But Schlick concludes that it IS meaningful, because it is in principle verifiable. "I can easily imagine, e.g., witnessing the funeral of my own body." 

Whether he survived in that sense or not, his departure from this embodied life had a devastating consequence for the Circle -- it had lost its center. Edmonds tells us that Waismann soon thereafter visited Wittgenstein's younger sister Gretl, to see if she could persuade Ludwig to return from the British isles to Vienna. "The idea" Edmonds says, "seems to have been that he would replace Schlick." Gretl apparently told Schlick that her family would never "let itself be used like that."  

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I want to conclude this, though, by speaking of Godel. I first encountered him as one of the stars of Douglas Hofstadter's book, Godel, Escher, Bach: An Eternal Golden Braid.

Godel (1906 - 1978) is best known for the "incompleteness theorem" in mathematics, the proof that there are limits to provability in all formal axiomatic systems. There will always be truths that cannot be proven. One sensible extension, contrary to Vienna Circle notions, is that since there will always be unproven truths,  it is unwise to tie together too closely the ideas of truth and of proof -- perhaps it is even less wise to tie together meaning and verification. 

Godel proved his incompleteness theorem by making an innovative use of the Liar's Paradox. Remember, in the standard version the Cretan is imagined to say,"This is a lie." We are then expected to ask ourselves, is THAT a lie, or is it true? 

Godel shows that it is possible to code that sort of statement into arithmetical form. He coded into that form the following statement: "This statement is unprovable." If that statement is provable, it is false. If it is false, it cannot be provable. The only way to escape paradox is to regard the statement at issue to be, in fact, true. Given the assertion it codes, this implies that is is also unprovable. So there is at least one true-but-unprovable statement in any system for which this coding can be accomplished.   

As we mentioned earlier in this discussion, VC member Tarski proposed banishing the troublesome underlying paradox by creating a formal language with a strict hierarchy, so that a self-referential statement of the sort in question can never be made.

One way of understanding Godel's showing is that Tarski's banishment isn't so easily accomplished as all that. The hierarchies tend to become tangled as they are elaborated, and the paradoxes find a way to recur.  

As to the Vienna Circle, Godel seems to have attended a lot of the meetings, and to have kept his own counsel. Schlick's view of mathematics and logic was a logicist one, in accord with his admiration for Russell: they are both collections of tautologies. Edmonds said that Godel silently disagreed with this notion, but that he did credit the VC with helping to awaken his interest in the foundations of the subjects.  He published his incompleteness theorem in 1931, after having submitted it for his doctoral thesis at the University of Vienna. By 1940 (when he arrived in New Jersey as a refugee) he was famous ... in the world of mathematicians and logicians. 

The story of HOW Godel and his wife got to New Jersey is itself fascinating, but I leave it aside for your own researches. He happily became there a neighbor and a friend of a hero of his: Albert Einstein. 

Godel's later life, and his death, tug at my heart strings.  Einstein's death in 1955 was a great blow to him. Godel became ever more reclusive, and more paranoid, after that, in a decline both physical and mental that lasted 23 years. In 1977 his wide Adele had to go to the hospital for an operation. When she returned, she found him both paranoid and dangerously wasted away. He had not been eating, convinced someone was trying to poison him. Godel was taken to the hospital but continued to deteriorate. He died in January of the following year. His death certificate describes the case of death, "malnutrition and inanition, caused by personality disturbance," Edmonds reports.

So Godel's death was only quite recent when Hofstadter made his name one of the three building blocks of his title (1979). 

We have now covered all the material that I aspired to cover from Edmonds' fascinating work. I have only to say that a few closing words. 

The Circle seems in retrospect like a stone fortress that, once habitable and defensible, stood grandly on a tidal island.  The erosive power of the tides eventually brought it down, and made it not only uninhabitable but unfathomable. Still ... beneath the waves of the contemporary world a lot of treasure, along with a lot of dross, lies buried from the days of this old Viennese fortress. Mining the treasures may properly engage adventurous minds for decades to come.