I reverted the changes introduced by black. It should work as intended now.

This is pretty close. I really only have two concerns with it:

• I would prefer that this leverage the Initializer() logic if at all possible: that logic standardizes how we process arguments to Component constructors so that (hopefully) all Components / arguments behave the same.
• (and this is the bigger issue): this PR breaks backwards compatibility. That is, older models (including the tests in test_sets) no longer work with this change. Although The Book is ambiguous as to the signature that IndexedSet.validate should take, the fact that there are examples / tests that exercise the old convention makes me uneasy about breaking it. I think we should update this PR to either
  1. Work (silently) with either syntax
  2. Expect the new syntax but accept the old syntax (issuing a deprecation warning)

I am happy to work on a patch for this, but it will take me a little while to get to it.

This is pretty close. I really only have two concerns with it:

* I would prefer that this leverage the `Initializer()` logic if at all possible: that logic standardizes how we process arguments to Component constructors so that (hopefully) all Components / arguments behave the same.

* (and this is the bigger issue): this PR breaks backwards compatibility.  That is, older models (including the tests in `test_sets`) no longer work with this change.  Although The Book is ambiguous as to the signature that `IndexedSet.validate` should take, the fact that there are examples / tests that exercise the old convention makes me uneasy about breaking it.  I think we should update this PR to either
  
  1. Work (silently) with either syntax
  2. Expect the new syntax but accept the old syntax (issuing a deprecation warning)

I am happy to work on a patch for this, but it will take me a little while to get to it.

As you say, the book is vague about this and it led me to think Sets behaved exactly like Parameters. Once I realised that they did not, I raised this issue. Only recently did I find the time to come up with a solution. Therefore, the Initializer() approach makes sense but I never looked into it.

On the subject of backwards compatibility, the adjustments needed are minimal and by design: all that is needed is to add the index to the arguments (it is always the last argument) and ignore it, which is what I did in some of the tests. Issuing a deprecation warning seems reasonable.

This PR has been superseded by #3338 (that PR includes all commits here plus the rework of the Initializer and restoration of backwards compatibility [with deprecation warnings]). I am closing this PR to ease some of the burden on the CI system.