[AnimalMuppet]

Define "understand the fundamentals".

If you mean "the theoretical underpinnings", then, yes, we think we do. Turing machines and Church calculus provide solid theoretical underpinnings, that (as far as we know now) are complete. (Of course, the future could show us that they are incomplete. That's the problem with knowing whether your current understanding is proper - you don't know what gaps the future will reveal.)

However, if you mean "we know how to build programs so they work", there's massive empirical evidence that says that we don't. (That is, we can do it... sometimes. And sometimes we can do it after it takes five times as much money as we expected. And sometimes we can't make it work, ever. And we can't tell up front which will happen.) So in terms of this being engineering - as opposed to computer science - saying that we don't properly understand the fundamentals seems like an entirely reasonable statement.

[jng]

I quite agree with you, but not completely. It's true that Turing & Cburch fundamentals are complete, in that anything we describe in computation can be expressed in terms of those. But I think we are using a very small subset of all Turing-Church based computing, and refinements of this understanding will provide a qualitatively better algebra for the types of software we really create. This will make it easier both for engineers to create software, and for end-users to do things that nowadays only programmers can do.

Both ends you describe (computer science and software engineering) are to me part of the same continuum. We still have articulate most of it with a coherent theory.