In a nutshell, Church asserted effective computability by saying "look what you can do with the lambda calculus". Turing took the philosophical approach saying

In a nutshell, Church asserted effective computability by saying "look what you can do with the lambda calculus". Turing took the philosophical approach saying "this is what it means to compute". To Godel, Church's argument was incomplete. Turing provided the direct argument. Godel was convinced.