---
created_at: '2016-02-04T23:03:15.000Z'
title: Why Church chose lambda (2009)
url: http://www.wisdomandwonder.com/link/3022/why-church-chose-lambda
author: networked
points: 56
story_text: 
comment_text: 
num_comments: 9
story_id: 
story_title: 
story_url: 
parent_id: 
created_at_i: 1454626995
_tags:
- story
- author_networked
- story_11037982
objectID: '11037982'
year: 2009

---
Todd
[asked](http://list.cs.brown.edu/pipermail/plt-scheme/2009-May/033320.html)
“Why \[did Church choose\] lambda and not some other Greek letter?”.
Here are three
answers:

### 1

[Matthias](http://list.cs.brown.edu/pipermail/plt-scheme/2009-May/033321.html):

> The story is that in the 10s and 20s, mathematicians and logicians
> used ^ as a notation for set abstraction, as in ^i : i is prime.
> Church used ^\` (i.e., a primed version of this symbol) for function
> abstraction, because functions are just sets with extra properties.
> The first type setter/secretary read it as λ and Church was fine with.
> True or not? I don’t know but it’s fun.

### 2

[This
paper](http://www-maths.swan.ac.uk/staff/jrh/papers/JRHHislamWeb.pdf)
(link provided by Dave Herman
[here](http://list.cs.brown.edu/pipermail/plt-scheme/2009-May/033322.html)):

> (By the way, why did Church choose the notation “λ”? In \[Church,
> 1964, §2\] he stated clearly that it came from the notation “xˆ” used
> for class-abstraction by Whitehead and Russell, by first modifying
> “xˆ” to “ˆx” to distinguish function abstraction from
> class-abstraction, and then changing “ˆ” to “λ” for ease of printing.
> This origin was also reported in \[Rosser, 1984, p.338\]. On the other
> hand, in his later years Church told two enquirers that the choice was
> more accidental: a symbol was needed and “λ” just happened to be
> chosen.)

### 3

[This
paper](http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.26.7908)
(link provided by Dave Herman
[here](http://list.cs.brown.edu/pipermail/plt-scheme/2009-May/033322.html)):

> We end this introduction by telling what seems to be the story how the
> letter ‘λ’ was chosen to denote function abstraction. In \[100\]
> Principia Mathematica the notation for the function f with f(x) = 2x +
> 1 is 2xˆ +1. Church originally intended to use the notation xˆ .2x+1.
> The typesetter could not position the hat on top of the x and placed
> it in front of it, resulting in ˆx.2x + 1. Then another typesetter
> changed it into λx.2x + 1.