Is there any known reason why Alonzo Church chose Greek $\lambda$ as the "binding operator" for the Lambda Calculus?



Why did Alonzo Church choose the letter $\lambda$ as the "binding operator"?
This question has been answered [on math.SE](https://math.stackexchange.com/a/64469/413) (as pointed out by Joel David Hamkins).
With a reference to *Lambda-Calculus and Combinators in the 20th Century* by
Felice Cardone and J. Roger Hindley, Handbook of the History of Logic
Volume 5, 2009, Pages 723–817, it is stated that “$\lambda x$” comes from “$\hat x$” in [*Principia Mathematica*](https://en.wikipedia.org/wiki/Principia_Mathematica).
Here is a quote from a [preprint](http://www.users.waitrose.com/~hindley/SomePapers_PDFs/2006CarHin,HistlamRp.pdf) of *Lambda-Calculus and Combinators in the 20th Century*:



> 
> By the way, why did Church choose the notation “$\lambda$”?
>  In [A. Church, 7 July 1964. Unpublished letter to Harald Dickson, §2]
>  he stated clearly that it came from the notation
>  “$\hat x$” used for class-abstraction by Whitehead and Russell, by first
>  modifying “$\hat x$” to “$\wedge x$” to distinguish function-abstraction from
>  class-abstraction, and then changing “$\wedge$” to “$\lambda$” for ease of
>  printing.
>  This origin was also reported in
>  [J. B. Rosser. Highlights of the history of the lambda calculus.
>  Annals of the History of Computing, 6:337—349, 1984, p.338].
>  On the other hand, in his later years Church told two enquirers that the
>  choice was more accidental: a symbol was needed and “$\lambda$” just
>  happened to be chosen.
> 
> 
> 


Assuming that “$\lambda x$” comes from “$\hat x$” in *Principia Mathematica*, let us look how it is used there.


In *Principia Mathematica* there are two ways the notation “$\hat x$” is used.
The first use is to write “propositional functions,” it is introduced in [Volume I](http://quod.lib.umich.edu/cgi/t/text/text-idx?c=umhistmath;idno=AAT3201.0001.001), in Chapter I of the Introduction, on page 15.
Here is a quote:



> 
> [...]
>  When we wish to speak of the propositional function corresponding to
>  “$x$ is hurt,” we shall write “$\hat x$ is hurt.”
>  Thus “$\hat x$ is hurt” is the propositional function, and “$x$ is hurt”
>  is an ambiguous value of that function.
>  Accordingly though “$x$ is hurt” and “$y$ is hurt” *occurring in the same
>  context* can be distinguished, “$\hat x$ is hurt” and “$\hat y$ is hurt”
>  convey no distinction of meaning at all.
>  [...]
> 
> 
> 


The second use is to write classes in a way similar to the modern “$\{\,z\mid\psi(z)\,\}$”, it is introduced in [Volume I](http://quod.lib.umich.edu/cgi/t/text/text-idx?c=umhistmath;idno=AAT3201.0001.001), in Section C of Part I, in definition \*20.01, on page 197.
Here is some quote:



> 
> [...]
>  But it is convenient to regard $f\{\hat z(\psi z)\}$ as though it had an
>  argument $\hat z(\psi z)$, which we will call “the class determined by the
>  function $\psi\hat z$.”
>  [...]
> 
> 
> 


