Is it possible to think of music theory as inverse composition?

Yes, of course it is possible, but that imprecision of expression in your Q allows me to state the bleedin' obvious and still remain coherent and true. That's precisely the problem with the premise you and your colleague were discussing likewise. (Ignoring that the inverse of composition would be decomposition, which would open up fatuous avenues uniquely their own.)

The fatal flaw in the whole rigmarole is to assume about *both* disciplines that they are moronically unidimensional. 'Theory' equals analysis and 'composition' equals construction. That is terminally naive, as well as paving the way for the premise you have put forward -- thankfully as one you wish to refute but are struggling for grounds for.

'Theory' as well as 'composition' are based in discipline -- 'rules' if you will -- which are fertilised by a host of satellite disciplines -- as both a musicologist and composer these are part of my daily life -- many of which coincide but rarely at the same instance. Even so these satellite disciplines have a crucial role to play.

Both are dependent on an intimate conversance with semiotics, historical practice, emotional acuity as a response to these preceding, and a number more, or 'Fingerspitzengefühl' for any will break down, upon which all depend to make sense as well as deliver real insight.. Not only do theory and analysis not equate -- and your interlocutor's assertion crucially depends on it that they do -- but the premise put forward to you which prompted the Q seeks to make you degrade them so. The construct is as plausible as it is seductive as it is false, for that reason.

I would also add, 'ins Blaue hinein', in my perspective as a practitioner of all these crafts, that your interlocutor has clearly never composed a note in his life 'in anger'. Had he done so, his folly would have struck him,.hopefully, sooner. For, the moment we compose, a further gaggle of satellites crowd in, among which would be rhetoric, more semiotics, sculpture and form, which cannot be analysed as to their *motivation* from a blank score of print, and for his thesis to hold true, they would have to be.

When I created the opening flourish to my clarinet concerto, containing the critical germ cell upon which the architecture of what follows depends, which, written to the person of my soloist, pitted stabbing chords from the tutti against equally stabbing multiphonic chords from the clarinet in quick-fire antiphony, its reasoning can only be explained by rhetoric, semiotics and my gloriously courageous colleague, capable sovereignly to pull this virtuosic madness off, for whom I wrote the work and who championed it like no other, cursing me roundly the while for my pains, while serving them incomparably... :-)

Let your colleague theorise *that* for *his* pains and get to the 'right' answer which he can then deconstruct and, moreover, by those means then attain a facsimile of my score of that work ultimately in result. I would await it with wry amusement.

His notion is as self-serving, as it is naive, as it is daft.

With my best wishes for the Season to you,

Certain elements of it are, yes. Basic composition skills are the end result of an understanding of musical theory, without theory there could be no composition. Although I would say this mainly applies to very strict composition unlike the works of composers like Debussy, who pushed the boundaries of the elements of composition, but then again theory does teach you the elements of chord structure and such. I'm not quite sure as to whether I've answered this question correctly, I don't exactly know if I've understood what you mean by 'inverse', sorry.

No...

Before Fromental Halévy composed the first piece to actually use 24-tet, it was simply a theoretical construct made in the middle east to describe their intervals in terms of 12-tet. Just one example where the theory came BEFORE the music, not after.

In other cases, yes, for example; the "rules" of counterpoint came after the music.

Only analysis is backwards composition.

I hope I explained it well enough.

Yes and no.

Ideas which we learn from composers are good,

but they are not readily reusable like kitchen recipes.

Is he suggesting writing a sonata movement with the themes recapitulated in reverse order,

like Mozart does in his D major sonata, K 311?

It works that way only if the themes which can fit into this so-called "mirror form."

Is he suggesting sticking an extra theme in the development, section,

like Mozart does in his F major sonata, K 332?

It works that way only if a development theme fits in the sonata movement.

Is he suggesting recapitulating the first theme in the subdominant key,

like Mozart does in his C major sonata, K 545?

It works that way only if a subdominant recapitulation can fit the thematic material.

i think i know what you are talking about, and I have probably done it before