The idea of describing it as a non-constructable set as in language arts is to express the idea that Raga cannot be dissected or reduced by the ideas of Western music. Perhaps a better term might be irreducible, but if you look at papers on Linguistics and non-constructibility I think you may see that the comment is not meaningless.
The problem is that defining a Raga as "a set of notes", and "a motif", and "a framework for the musician to ..." blah, blah, blah, is that this reduction is a completely Western Philosophical view applied to an Asian tradition. Raga is more than that. It does not express the full idea of what Raga means to say that a musician is noodling around on the Dorian mode (which is one of the Carnatic Scales). Raga includes cultural ideas. In some sense one can compare it to language where we have a vocabulary, then we have cultural ideas expressed in idioms. English, Canadians (for the most part), Australians, etc. speak English, yet they don't always understand each other. Not because of accent but because of idioms, euphemisms, vocabulary not in common use across all English speaking regions. This is not reducible like the base roots of language. A great deal of meaning is conveyed by tone of voice and other things like body language. Yet we remove that when we try to describe "language" as a rule set.
Raga is often mapped to a complete human experience, not just some notes that are played with. Phrasing, and other attributes are taught as part of the Raga. Some examples are Morning Raga, Evening Raga, etc. Musical ideas that are supposed to invoke in the listener the feeling that most people have when they wake up, or start slowing down in the evening and stop working. You can't write this is Western sheet music. In fact we cannot even express the full gamut of Western experience this way. I seems to me that the entire Westernized way of looking at music evolved from the development of orchestras and multi voice harmony. Not all musical languages follow this tradition and are not describable in these terms.
In the Indian culture Yoga and chakras are an integrated idea that permeates art and music. Not everyone in India practices this or believes in it but it has roots that are thousands of years old and hence is an integral part of everyone's common experience. That being said, many Raga ideas map to chakras, moods, etc. We have some of this in western music in that minor modes usually convey negative moods, and major positive moods, etc. But that is a far cry from saying that this collection of musical motifs (a Raga) stimulates sexual desire, or produces a calming effect. Again, I am not stating that there have been double blind studies that verify this, but the idea is deeply rooted in the Raga tradition. To simply reduce it to "up scale", "down scale", "etc". Misses the entire point of Raga, and ignores the cultural ideas contained within the Raga.
I'd recommend reading the following (Wikipedia is not always a good source if info).
The Raga-ness of Ragas by Deepak Raja
Classical Music of India by Subramaniam and Subramaniam
Nuances of Hindustani Classical Music by Hirlekar
And listen to some of these classic Ragas like The Morning Raga, etc. I have a box set I got in India more than 10 years ago called 50 Glorious Classical Years that has examples of every kind of Classical Indian music performed by the great musicians of India. The Western view of music is not all encompassing yet it doesn't stop us from trying to fit every thing in our box. To really get a Raga you need to learn it the traditional way, from a master in person. All the subtle nuances are transmitted by oral tradition.