User blog comment:Ikosarakt1/Ideas of going past psi(K)/@comment-24509095-20140618004924/@comment-1605058-20140618064215

But we don't use Turing machines to compute ordinals in general. For example, think about this: What is $$D_D$$? Intuitively, it's $$D$$-th element of sequence D_1,D_2,...D_\alpha,... . But what does "$$D$$-th" mean, if $$D$$ is not even a number, if it's just a mere symbol for our notation?