Seeking a more elegant definition for Prog

To further explicate my views on this matter, I'd like to turn to the issue of categorization and propose prog as a radially structured category:

Figure one is a rough attempt at illustrating a proposal for a different approach to categorization. It's inspired by linguist/cognitive scientist George Lakoff – you can read more about radial categories and categorization in general in Lakoff's “Women fire and dangerous things – what categories reveal about the mind.” (University of Chicago press: 1987).

To accept prog as a radial category has a series of implications, the most important are:

a) Category membership (whether something is prog or not) is not a question of either/or – but a question of more or less.

b) Category membership is not determined by discovery of necessary and sufficient conditions or shared features but solely on the basis of degree determined by 'goodness of example' ratings.

The circles and numbers in the figure are taken to represent a center/periphery scale. The positions of the albums roughly (as in not thoroughly considered) reflect how central or peripheral I consider them relative to a prototypical understanding of prog (for example, “Tales from topographic oceans” is judged a 'very good example of the category prog'). It's simply a matter of asking yourself to what extend an album is central to a prototype. In this kind of category-establishment, you ask your informants (test-persons) to determine 'goodness of example' on a scale from 1 to 7, where 1 is 'very good example' and 7 is 'not a good example of [category]'. This has been done with the category furniture, and it showed that 'telephone' (6.80) is not a very good example of furniture, 'chair' (1.20) is a very good example and 'magazine rack' (3.40) is somewhere in the middle.* This may seem bizarre, but it severely challenges the classical view of categorization according to which something either is – or is not – a piece of furniture and a question to what extend something is a piece furniture is thus irrelevant.

A circle has both a vertical and horizontal dimension. The albums, in this case, are arranged randomly with respects to these dimensions, but one could imagine some principles of organization that utilize this multi-dimensional feature of the figure.

Following Rosch's prototype theory of categorization, prog, as a radial category, has a prototypical center that is taken to be independent; it has a cognitive status of it's own and doesn't occupy a place in a taxonomy. It follows that there are no certain features (elements, characteristics etc.) that an instance of prog has to have in order to be prog. To accept prog as a radial category requires you to abandon an idea of prog as a matter of either/or based on existence/non-existence of features and to accept that all music potentially is prog to some degree. If an instance of music has an average rating of 7, it follows that it's a very bad example of prog, not that it just isn't prog. This may seem very controversial.  

Figure 2 illustrates roughly what I mean by prog being independent. Each of the five circles are taken to be representations of the radially structured categories 'rock', 'jazz', 'classical', 'folk' and 'prog' - from prog's point of view, so to speak. It captures how prog relates to other music categories, while still having an independent status as category (the center of the inner circle).

All this leads me to one fundamental objection to your definition: it still has taxonomical traits in that it presents prog as something defined in terms of rock. I'd like to be more helpful in reaching a sufficient definition, but I'm not comfortable playing the role of a definer.  

I think characteristic is slightly better than element, but “Music either springing from or incorporating at least one distinctive characteristic of the rock genre while expanding beyond the traditional musical limitations and constraints of the genre” directs attention to a particular entity, namely a seemingly required minimum of at least one distinctive feature/element/characteristic of rock. That's somewhat misleading. I'd propose more tentativeness and awareness of prog as a radial category, and I carefully propose something along these lines: “prog is a genre of music which typically incorporates styles from other domains of music in an attempt to expand beyond the musical limitations of those domains” I'm not satisfied with this defintion, it's vague and imprecise and presupposes that other music styles have limitations. I'd still maintain that prog, really, is undefinable. Just like language is undefinable in linguistics.

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*Rosch, Eleanor (1975): Cognitive representations of semantic categories. Journal of experimental psychology: General 104: 192-233