Editing Lambda calculus (section)

=== Origin of the ''λ'' symbol ===
{{anchor|Origin of the lambda symbol}}
There is some uncertainty over the reason for Church's use of the Greek letter [[lambda]] (λ) as the notation for function-abstraction in the lambda calculus, perhaps in part due to conflicting explanations by Church himself. According to Cardone and Hindley (2006):
<blockquote>
By the way, why did Church choose the notation "λ"? In [an unpublished 1964 letter to Harald Dickson] he stated clearly that it came from the notation "<math>\hat{x}</math>" used for class-abstraction by [[Principia Mathematica|Whitehead and Russell]], by first modifying "<math>\hat{x}</math>" to "<math>\land x</math>" to distinguish function-abstraction from class-abstraction, and then changing "<math>\land</math>" 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.
</blockquote>
[[Dana Scott]] has also addressed this question in various public lectures.<ref>Dana Scott, "[https://www.youtube.com/embed/uS9InrmPIoc Looking Backward; Looking Forward]", Invited Talk at the Workshop in honour of Dana Scott's 85th birthday and 50 years of domain theory, 7–8 July, FLoC 2018 (talk 7 July 2018). The relevant passage begins at [https://www.youtube.com/embed/uS9InrmPIoc?start=1970 32:50]. (See also this [https://www.youtube.com/watch?time_continue=1&v=juXwu0Nqc3I extract of a May 2016 talk] at the University of Birmingham, UK.)</ref>
Scott recounts that he once posed a question about the origin of the lambda symbol to Church's former student and son-in-law John W. Addison Jr., who then wrote his father-in-law a postcard:
<blockquote>
Dear Professor Church,

Russell had the [[iota operator]], Hilbert had the [[epsilon operator]]. Why did you choose lambda for your operator?
</blockquote>
According to Scott, Church's entire response consisted of returning the postcard with the following annotation: "[[eeny, meeny, miny, moe]]".