An Anecdote of Carnap’s

In 1953-54 , my first year of teaching at Princeton University, Carnap[1] was on leave at the Institute of Advanced Studies (also in Princeton, but not connected to the University), and I went to talk to him frequently, and found him not only impressive intellectually (as goes without saying), but also friendly and charming and free of any trace of “Herr Doktor Professor-ism”. One day he told me the following anecdote. When I recounted it to a friend a few days ago, I realized that Carnap may never have written it down, and that by publishing it here I could make sure it is on the record.

In 1918, after a few years as a student at the University of Berlin, Carnap enrolled as a graduate student at the University of Jena to obtain a Ph.D. in physics. As Carnap explained it to me, his plan was to formalize Einstein’s theory of relativity using notations from Principia Mathematica  (although the notation that figures in this anecdote is older, from the “algebra of relations” of Peirce and Schröder). Using the notion of the square of a relation­ – that is the product of a relation[2] with itself – Carnap found that he could write the statement that the relation T, “earlier in time than”, is transitive and dense simply as T=T².  When Carnap went to his professor’s office to discuss his plan (here Carnap imitated the professor’s pompous voice) the professor said,

“It seems to me that if T=T², then either T=1 or T=0”.  Carnap explained that T was not a symbol for a number but rather for the temporal precedence relation, etc., etc., etc., and at the end the professor said, “It still seems to me that if T=T², then either T=1 or T=0. Young man, you had better try the philosophy department.”

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[1] Carnap’s wife Ina and all his friends called him simply “Carnap”. As far as I know, absolutely no one used his first name.

[2] The product of a relation R and a relation S is “R of an S of”, e.g., the product of brother of and father of is “brother of a father of”, i.e., paternal uncle of. The square of a relation R is “R of an R of”, e.g., the square of parent of is grandparent of.