Since I've been musing about fiction recently, here's another thought that crossed my mind.

Fantasy fiction often has a magic system involving spells cast in spoken language. But what language? Why does that language work and not another? Or would another language work? Would it depend on the spell? On the caster? On the location? It seems to me that there are quite a few plausible ‘cosmologies of magic’ which would cause different answers to those questions, many of which have specific examples in existing fiction, and I wonder if there are any more I've missed out.

A special Language Of Magic embedded in the universe. In this model, there is some particular language (or language-ish thing – at any rate, producible by human vocal apparatus), to which the underlying nature of the universe responds or resonates directly. So spells must obviously be cast in that language, or they won't work; and the language of magic won't (typically) correspond to any normal human language, but will instead be an extra one that mages have to learn. Examples: the Logrus magic in Roger Zelazny's later Amber novels, Patrick Rothfuss's ‘The Name of the Wind’.

Magic consists of asking a powerful entity to do something. In this model, a ‘spell’ is nothing more than a particular kind of request or prayer. So you must use whatever language is acceptable to the entity you're entreating to help you. (Though in some cases it might speak all languages, and not care.) Examples: David Eddings's ‘Elenium’, Katharine Kerr's Deverry novels, and surely a great many examples involving summoning of demons.

Magic words are just a way to get into the right kind of concentration. In this model, the real means of casting the spell is just a matter of being in the right frame of mind; the act of mumbling strange words is indirectly helpful in achieving that frame of mind, but not directly relevant to the spell working. So here the language you use for magic is a property of the caster, not of the spell or the universe: different casters will quite likely find that different languages (or plausible-sounding non-language mumblings) happen to work best for them. Examples: Stephen Donaldson's ‘Mordant's Need’.

Magic depends on the intent behind your speech, not the words themselves. In this model, it doesn't matter what language you use, but you do have to speak something in your chosen language that you recognise as a meaningful expression of your magical intent. I can't think of an example in which this is specifically stated in the text, but I always have the impression that Neil Gaiman's magic for one gravitates towards this mode; I think it's a natural sort of model to be implicitly intended by authors who didn't care very much about this sort of detail.

Magic words are totally at the whim of the caster. It doesn't matter a bit what language or word you choose, but for some reason there has to be a word. Pick anything you like and it'll work just as well. Examples: David Eddings's Belgariad.

Magic is a function of large numbers of people. In this model, words become magical by virtue of lots of people using them, or caring about them, or believing in them, or similar. So the language of magic is not an inherent property of the universe itself, but neither is it completely up to the caster to choose it: instead, it's determined by the population who gave rise to the magic, and you might find that different languages or wordings are needed in different localities with different supporting populations. Examples: Kate Griffin's series of Matthew Swift books, and the Artifice in Juliet E. McKenna's Einarinn books.

Magic spells are originated by specific people. In this model, every spell works by virtue of some originating mage in the past having created it somehow (presumably using some deeper order of underlying meta-magic), and arranged for it to work for all mages henceforth. So the language used for a given spell will be at the whim of the mage who originated that particular spell, just as the language used for a given computer program is at the whim of its author. I don't know of any definite examples of this model, but any system in which spells are named after people (e.g. D&D's ‘Bigby's Crushing Hand’) strongly suggests it. Also, in my head this really ought to be how the Harry Potter universe works, because it would so neatly explain why all the spells are in bad Latin – clearly they were originated by past wizards who had paid about as much attention to their Latin lessons as their modern counterparts pay to other Muggle subjects :-)

The author never bothered to work it out, or wanted to keep the magic mysterious. Of course there has to be one Doylist explanation in this list, to go alongside all the Watsonian ones. Sometimes the nature of magic and its relationship to language just didn't strike the author as an important aspect of the story, or they felt it would have specifically gone against what they were trying to achieve with having magic rather than technology in their universe in the first place. Examples: Lord of the Rings (‘naur an edraith ammen!’), and surely many universes in which magicians are simply described as ‘incanting a spell’ or similar, without it ever being mentioned what words are being used.

So, what have I missed?