Daniel Nolan has a discussion of the term 'marriage'. The look at various things that get described as marriage in various cultures is interesting, but the argument of the paper suffers greatly, I think, from some false assumptions about how language works, and the most serious of these is a conflation of two things, extension of a term by analogy and metaphorical use of a term. These are not the same.
If I call you a 'pig' because of your sloppy eating, that is a metaphor, assuming, of course, that I am not simply deluded and actually think you porcine. We can explain my metaphorical use of the term by analogy: as a pig is supposed to be careless about eating, so are you with your eating. So we could consider the metaphorical use to be an extension by analogy in this sense. However, not all extensions of terms by analogy are metaphorical. If a German comes across an armadillo, not knowing what it was, and needs to refer to it, he may in the German way call it an 'armor-pig'. Is the use of 'pig' here a metaphor? The German language calls a lot of animals 'pig'; and the fact that an armadillo becomes a Panzerschwein is just an ordinary case of this. The idea is that this weird animal is classifiable as a pig-for-certain-practical-purposes. It could, of course, have begun as a metaphor and died, but using 'Panzerschwein' for an armadillo is certainly not a metaphor to later speakers; it is the name of the animal. Another example: when people in English call pandas 'panda bears' and koalas 'koala bears', are they speaking metaphorically? Neither of these animals is actually in any way a bear. But it's also the case that lots of people who use the phrases 'panda bear' and 'koala bear' have no inkling that they are completely different animals, so they are using it literally. If you press them on this, a lot of people will (rightly, as far as language goes) say, "Well, they're close enough," and won't be bothered by it, just as nobody is bothered by the fact that we call 'pandas' both giant pandas and red pandas, which are two different kinds of animal, and nobody is bothered by the fact that we call 'jade' both jadeite and nephrite, which are two different kinds of mineral. These are in fact all literal uses of the terms. We have to extend words; sometimes in extending the words, we are not actually engaging in metaphor, but are extending the term in a way that is literal.
The fundamental reason for this is that whether a term is being used literally or metaphorically is a matter of how you are actually using the term in a particular case relative to usual expectations about that term's use. Extension by analogy is entirely about how one kind of use of a term is related to another kind of use of a term, in terms of which is originary. If, knowing about human marriage, I come to think that mountains are actually formed by rocks marrying each other in pretty much the same way, I am extending a term that originally concerned a relationship between human beings to a relationship between rocks. This means that the term now covers more than it did. But, ex hypothesi, I am using the analogically extended term literally. Thus we have a term whose meaning is being extended by analogy to an unexpected use. But I'm not introducing any 'twist' into that use, no 'trope', and thus no metaphor. I'm just extending it to a new case on the basis of what I think I've learned about rocks, using the original paradigm (between humans) as a model for handling the new case (between rocks).
This plays a significant role in a number of areas of life. When we say that a body of people is a 'juridical person' or a 'moral person', the term 'person' is not usually being used as a metaphor; the whole point of the term is that this is classifiable as a person for certain legal or moral purposes. The term 'person' applies literally to corporations in those contexts (it's just what they're called in those contexts); but corporations are so only by analogical extension of the term. This contrasts with natural persons, which are literally persons and are person in the primary and most proper sense of the term. Both are necessary for the functioning of the term as it is supposed to function.
Let's take two examples Nolan uses: nuns marrying God and worshippers marrying gods. The case of nuns being married to God is without any question an extension of the term 'marriage' to a new kind of case by analogy. It's a very robust analogy, in fact; there are many similarities, many more than you might expect at first glance. It is also typically a metaphorical expression. But what makes it a metaphorical expression is not that it is an analogical extension, but that the term in its original use is fixed by the paradigm (Catholic sacramental marriage between man and woman) in such a way that to use it as a model for the relationship of a nun and God requires unfixing it -- there is no way to stretch the meaning so that it now includes the new extension. You just have to shift the word over to a new category, guided by the original case but not co-classifying them. It is a legitimate use (the Church approves of it, and it is commonly used), but it is a tropic use, a figurative use. But as Nolan in passing recognizes, you could have someone who did not realize that this was how everyone else was using the term; and this person might, by confusion, be using the term literally. In so doing, they would be using the term in one sense correctly (it does apply by extension) but in another sense not (the way in which they take it apply is not the one approved by authority and custom). But they would be both extending it by analogy and taking it literally. It would be like 'common law marriage', which is both undeniably a literal use of the term 'marriage' and very clearly an extension by analogy from formal marriage (which is how we got the term and why we would often qualify it with 'common law').
Now consider the case of religious rites in which worshippers marry their gods. Nolan is very concerned to argue, and rightly, that we should not assume that this is a metaphor. That will be a question of how the relevant word for 'marriage' typically functions in their language. But this is entirely irrelevant to the question of whether this is an analogical extension of the term 'marriage'. In many cases, the use of the term 'marriage' might well be literal, but we have excellent reason to think that the term in these cases is an analogical extension of the term's meaning. We have no evidence that the sacred marriages are the primary case; we have plenty of evidence that how a society with sacred marriage conceives of human marriage serves as a sort of template for how they think of sacred marriage, and that this is ongoing; it is not going to be the most common use of the term; we have no reason, given differences in rites and expectations, to think that they thought it was exactly the same as marriage between human beings. All of this points to its being an extension of the term by analogy even if the extended sense is a literal sense.
Nolan's conflation of the two has the effect of massively flattening the actual language we use with respect to just about everything. In reality, we can use a term metaphorically; we can extend it by analogy but use the extended term literally; we can extend it by analogy and use the extended term metaphorically; we can extend an extended term further and use it either literally or metaphorically; we can use a former metaphor literally but in such a way as to maintain the analogy with the original use of the term that was the root that became the metaphor. There's a lot of structure and scaffolding in most naming, and analogy is a lot of that, whether in any given case we are speaking literally or metaphorically.