I'm not sure what you mean by making a distinction between depth and
distance. Depth implies a distance--at least in the sense that most
people use the word--whereas distance does not imply depth (again, in
the sense that most people use the word). So in regards to the first
question it would seem that progess could be defined by both distance
and depth if progress is defined by depth. But the second question
seems to consequently raise the most important question. What are we
really talking about here? What is meant by this dichotomy depth or
distance?
But even before that question is considered, how robust is this
distinction between 'progress' and 'advance'?
(1) to advance: to go from one thing to another
(2) to progress: to return over and over again to a very few points,
in an effort to get involved with them and thus go into them even
deeper.
What is strange about (2) is that he defines the returning to the
point itself progress and that the effort 'to get involved with
them...' as only the purpose of that returning, but not itself
progress. This is strange because there is a reason that for example
we want to say that Mozart made progress when he 'returned to the
problem of harmony'. And it seems that that reason is because his
efforts to 'get into it even deeper' were a success--that is, he
actually DID go deeper. So the kind of returning he is talking about
doesn't seem to count as progress UNLESS it is successful ('goes
deeper').
I have to do my work, but the point I am trying to make is that this
distinction between progess and advancement is only apparently
robust. All he can really be saying with this is that when 'progress'
is made it is made by starting not at a new point, a new problem, but
at an existing point, an existing problem, and either solving the
problem or moving towards its solution. If you assume that he is
saying progress cannot be made by building off 'the depth' others have
made into a problem, that progress can only be made by starting with
the problem itself (although it can certainly read that way), you can
see where he is going with using the sort 'points' one starts as
criterial for the distinction between progress/advancement. But if he
is saying that, he is obviously wrong. What sort of advancement would
there be in science if everyone returned to only the actual problem
itself, with no regard for the 'points' that have already been formed
(e.g., Newtonian physics)?
I don't know if that is write or if I wrote that correctly. I need to
go back to work and I will try to make it clear what I am saying
later, but I would also like to know what is meant by this:
"Progress, in other words, would seem to be defined by either distance
or depth. Could it be both? Does one usually predominate?"
I don't know what you mean by this distinction.