I think that λ-calculus is about as difficult to work with as Turing machines. I think the reason that Turing gets his name in the Church-Turing thesis is that they had two completely different architectures that had the same computational power. When Church proposed that λ-calculus was universal, I think there was a reaction of doubt, and a general feeling that a better way could be found. When Turing came to the same conclusion from a completely different angle, that appeared to verify Church’s claim.
I can’t back up these claims as well as I’d like. I’m not sure that anyone can backtrace what occurred to see if the community actually felt that way or not; however, from reading papers of the time (and quite a bit thereafter—there was a long period before near-universal acceptance), that is my impression.
Actually, the history is straight-forward, if you accept Gödel as the final arbiter of mathematical taste. Which his contemporaries did.
ETA: well, it’s straight-forward if you both accept Gödel as the arbiter and believe his claims made after the fact. He claimed that Turing’s paper convinced him, but he also promoted it as the correct foundation. A lot of the history was probably not recorded, since all these people were together in Princeton.
It’s also worth noting that Curry’s combinatory logic predated Church’s λ-calculus by about a decade, and also constitutes a model of universal computation.
It’s really all the same thing in the end anyhow; general recursion (e.g., Curry’s Y combinator) is on some level equivalent to Gödel’s incompleteness and all the other obnoxious Hofstadter-esque self-referential nonsense.
I think that λ-calculus is about as difficult to work with as Turing machines. I think the reason that Turing gets his name in the Church-Turing thesis is that they had two completely different architectures that had the same computational power. When Church proposed that λ-calculus was universal, I think there was a reaction of doubt, and a general feeling that a better way could be found. When Turing came to the same conclusion from a completely different angle, that appeared to verify Church’s claim.
I can’t back up these claims as well as I’d like. I’m not sure that anyone can backtrace what occurred to see if the community actually felt that way or not; however, from reading papers of the time (and quite a bit thereafter—there was a long period before near-universal acceptance), that is my impression.
Actually, the history is straight-forward, if you accept Gödel as the final arbiter of mathematical taste. Which his contemporaries did.
ETA: well, it’s straight-forward if you both accept Gödel as the arbiter and believe his claims made after the fact. He claimed that Turing’s paper convinced him, but he also promoted it as the correct foundation. A lot of the history was probably not recorded, since all these people were together in Princeton.
EDIT2: so maybe that is what you said originally.
It’s also worth noting that Curry’s combinatory logic predated Church’s λ-calculus by about a decade, and also constitutes a model of universal computation.
It’s really all the same thing in the end anyhow; general recursion (e.g., Curry’s Y combinator) is on some level equivalent to Gödel’s incompleteness and all the other obnoxious Hofstadter-esque self-referential nonsense.