2.1. How should we judge the Hubble system?
As Sandage points out in the superb introduction to the Carnegie Atlas of Galaxies , successful classification systems can lead to enormous advances in science. Perhaps the best example of this phenomenon is the periodic table, which played a direct role in the development of models for atomic structure.
The central idea in any physically motivated (as opposed to merely descriptive) classification system is that of ranking, in the belief that this ranking reflects an underlying order in the basic physics of the system, rather than merely reflecting the natural tendency of the human brain to impose order and organization on randomness in order to facilitate communication and memory. The choice of features upon which the ranking is defined is, in the first instance, completely subjective. In this stage of the process intuition, experience, and inspiration are paramount (see the books by Sandage  and van den Bergh  for insight into the creative processes through which galaxy classification systems are developed). But once the system is in place, subjectivity should drop away as the system is tested against the underlying physics. Therefore in my view an ideal classification should have three characteristics:
(a) physical significance: The ranking imposed by the classifier should track important underlying physical processes.
(b) completeness: There should be no gaping holes in the system, ie. the vast majority of objects should slot naturally into the system somewhere.
(c) objectivity: The system should be sufficiently well-defined that classifications made independently by well-trained observers should be very similar.
These are the metrics we will use when judging the success of the Hubble system in the latter part of these lectures. My own verdict will be given in Section 2.6.