Yes, this is the second edition of the It Came From the Obvious Lagoon.

1) Natural disasters can change, mutate, and push ideas.

There are oh so many ways this can work.
A natural disaster that destroys a center of civilization (think big fucking volcanic explosion, or big fucking tsunami) can dry up a fertile source of ideas, or send survivors fleeing in waves to other places, bearing their society’s ideas with them. Stephen R. Lawhead uses this one to good effect in his Pendragon Cycle, where refugees from Atlantis carry some of their more advanced ideas to Britain.
A natural disaster could also be seen as punishment from gods/demons/insert power here, and that could cause a change in behaviors and attitudes that, given enough encouragement, might become permanent. This works especially well with plague in a society that doesn’t understand how disease works and doesn’t have ideas of hygiene fit to cope with the menace. When black plague is galloping around busily eating a third of your population, people may welcome military law. Or a small group which does have some idea of hygiene, perhaps as part of an archaic religious practice, could survive it more easily, and thus spread their ideas much more easily to the survivors.
Building on this, anyone who can help people recover from a crisis this overwhelming, or seem to guarantee some safety or rescue, might very well have a free hand. Thus a set of beliefs that would otherwise never have a chance gets to flourish in the sun. Got an incipient dictator who happens to live far enough outside the earthquake’s range to be able to fetch food and help—and soldiers—instead of fleeing for her life, and who’s quick-witted enough to act instead of react? She could quickly become the nucleus of a new regime. Got an ethnic or magical minority that’s immune to the plague? Well, they’ll almost certainly face danger from panicking majority members who want to know the “secret” of their survival or who rip into them in fear, but they might also have a chance to reshape the society that follows.
Then there’s deliberately engineered use of natural disasters, such as happened with some Spanish conquistadors in the New World, giving gifts of blankets to American tribes that had been rubbed with smallpox scabs. The European disease pool was fiercer than the American one, and the exchange of plagues nowhere near equal. (I think the only American disease that really managed to make an impact on Europe was syphilis, and that’s assuming it was a New World disease; some people think syphilis was Old World, and described anciently in Greece and the Middle East). If you have people—perhaps mages—in your fantasy world who use such weapons against their enemies, there may be civilizations crashing and burning, and dozens of religions, values, and beliefs going extinct inside a few decades.
It isn’t deliberately created, but, as an example of this kind of crashing and burning, Kim Stanley Robinson’s The Years of Rice and Salt asks what would happen if the Black Plague had been fierce enough to wipe out most of Europe, essentially destroying Christianity’s prominence as a world religion, and leaving the way open for other civilizations to make an impact.
If you need a sudden change in your society, there’s not much better than this.

2) Knowledge, including ideas, can be lost.

This is related to point 5 of the last essay, which talked about complicated beliefs arising from misunderstandings or misinterpretations (deliberate or not). Sometimes, it seems that no knowledge is ever really lost in fantasy worlds. A local group of people may know nothing of what happened to make their village so isolated, but along comes a wizard who does know, and can tell them, and just incidentally can reveal the blacksmith’s daughter as the hidden princess. I resent this when it happens, because it makes the fantasy world’s history seem frozen and stale. Unless the wizards in this world are actually immortal, let some things fade and be forgotten, without stories passing on from one generation to the next utterly unmarred by error, and transferring secrets the hero can use to destroy the villain or solve riddles. Sure, sometimes an author will compromise by saying no one remembers the purpose of the knowledge anymore, but it doesn’t suffice, because the stories are still word-perfect. Also, a copy of every necessary book in a fantasy world can always be found, and rocks that carry important information are never subject to weathering, and mysterious cave paintings always clearly show a skylark instead of “well, it kind of looks like a skylark, maybe.” (Also, documents and paintings that are hundreds of years old always seem to portray things that still exist. I like the idea of a fantasy hero figuring out that he needs a staff made of valkra wood, only to find out that, well, the last valkra tree was cut down a hundred years ago, ahahaha).
This is something Tolkien actually does pretty well, and he has immortal wizards. The One Ring goes out of sight and memory because no one knows what really happened to Isildur, who was its last known carrier—he’s shot in the dark by an orc—and, well, everyone has better things to do than search for it, like rebuild the kingdom. Then an utterly insignificant hobbit (Gollum) finds it, and everyone ignores it for more hundreds of years. Even when Gandalf starts suspecting, he doesn’t just recall some story that says this is the One; he has to go study and make sure of the signs and collect an enormous amount of information to try and reconstruct the tale of what happened. And why not? It’s been three thousand years since the Ring was lost. Middle-earth falters on the realism in lots of other aspects, but not that one. It does seem to have a living history, one that flows over and covers things, and doesn’t necessarily reveal them with a trumpet fanfare.
Come to think of it, much the same thing happens in The Hobbit. It takes the dwarves a while to figure out what door their key goes to, and they sit around arguing and wasting time on the side of the mountain because they cannot figure out the necessary clues. There, the solution is simpler, but they don’t know what to do automatically just because Gandalf is with them for part of the journey.
You can let ideas die. You can let knowledge pass, or get muddled and drift along in broken pieces. Really.

3) Ideas can support other ideas even when they don’t have anything directly to do with them.

To take just one example: The nineteenth century is sometimes called the Golden Age of Atheism, because of the sudden spread and flourishing of it in Britain—and possibly the rest of Europe, though I’ve only looked closely at Britain—during that time. Part of the reason, though certainly not the whole of it, had to do with the growth in scientific theories. This doesn’t mean science was inherently atheistic, or that theology could receive no support from science whatsoever. It does mean that the conflict between science and theology weakened some of the mental supports for Christianity in some people’s minds, and when certain theories were formulated, especially evolutionary theory, atheists could escape some of the intellectual problems that had hampered them so far, like “How do you explain the variation in life if no God exists to create that variation?” People could accept evolution without becoming atheists, but hey, if they already were freethinkers and the idea appealed to them, then they had firmer ground to stand on.
Recent developments of older ideas helped, too. For example, what happens if you take tools of criticism invented for other documents and turn them on the Bible? What happened to Mary Ann Evans, George Eliot, was a shaking of her faith so severe that she never really got it back, and so one of her ruling themes in her novels became exploration of secular morality, and how one lives ethically in a world bereft of God.
And, of course, the same ideas can have negative consequences, as well. Some of the worse sides to evolutionary theory include its application to Social Darwinism and racism, and, later, eugenics. Likewise, environmentalism has an unfortunate tendency to get tied to fascism, a state that can impose social limits, “back-to-nature” attitudes, and population control.
Don’t necessarily plot just the growth of whatever belief is most central to your society. Know what would affect it, too, and what would support it, and what might let it down.

4) Include different kinds of reasoning.

I noted in the rant on keeping magic mystical that there don’t have to be scientific explanations for everything that magic does, and neither does everyone have to shrug tamely and say “That’s the way it is” (except for the protagonist who turns out to be the one curious person in the story and discovers the truth, of course). You can use mythological explanations.
And you can use mythological explanations to support your world’s ideas, too. Not every argument the character makes has to be supported by Western ideas of reason and logic. In fact, if the world is deliberately low-tech and low-magic, with no written language, no academies, no monasteries, no mysterious orders of mages, and no means to exchange information with people thousands of miles away—your central characters might not even know those people exist—what are they doing with concepts of philosophical thought that need a whole literate leisure class talking with each other to develop? Why don’t proverbs, oral narratives, myths, traditions, observed experience, ancestors’ experiences recounted by parents to children, also support wisdom?
This is one way to get at giving your world a really different history of ideas: know the matrix by which those ideas form and disseminate. Some parts of that matrix might resemble Western science. Other parts might be very different. Just because the empirical is such a dominant mode of thought in our own world doesn’t mean that it has to automatically take over in another.
One reason I remember liking Sean Russell’s Moontide and Magic Rise duology was that it portrayed the rise of empiricism and natural history as technology increased, rather than assuming that everyone in the books’ world already thought that way. (And then, when these empirical characters had to confront actual tribal taboos and magic that obeyed no scientific rules, they were scared out of their minds—as well as they should have been). I’m also enjoying it in the book I’m reading currently, Chris Wooding’s The Weavers of Saramyr. One character sneaking into another’s house meets no one on the way, but rather than just thinking it coincidence, she attributes it to the favor of the god of luck. And several different systems of thought are shown coexisting in the book’s empire: science resulting in astronomy; theology; traditional loyalty to the throne that keeps the Imperial Guard loyal while one family rules and then encourages them to serve the new one just as faithfully; and dog-eat-dog, where the nobles have to deal with a kind of magic they really hate in order to keep abreast of each other.

5) Tie the ways your people think about “common” things to that world, not ours.

I will use this example because I recently used it myself, and then it started bothering me. This is war. The most common attitude I’ve encountered in fantasy is, “War is hell.” I think some of it is Tolkien’s influence, but a good part of it must also come from authors’ own convictions. At the same time, even while most fantasies condemn the horror of war, horrible actions in war are considered to be necessary: “This is war.” (At least, they’re considered necessary if it’s the heroes doing them). So even while the characters know they’re plunging into hell, they also have to do horrible things, then steel themselves and go on. Anyone who believes anything different, including the fresh-eyed recruits who think of war as honorable, is very soon taught differently.
However, is that kind of philosophy about war the one that would actually flourish in your fantasy world? If the only wars that have ever been fought there are tiny skirmishes over territory or game, how would a character instinctively know that a bigger conflict would be horrible? If suicide is considered a sin, would a soldier captured by the enemy automatically kill himself rather than give up information? If battle is supposed to be fought only with certain kinds of weapons, would a commander adopt a new kind without a qualm? (A situation something like that prevails for part of Marion Zimmer Bradley’s Darkover series, where the Compact forbade distance weapons, so that if someone wanted to kill someone else, he had to face him close at hand). How much of these ideas is truth, and how much is ingrained repetition that sounds like truth?
Watch this. I think it’s very easy to give characters certain basic attitudes and ideas, especially towards things like war, because we assume that such things are “common sense.” They may not be. Consider what the historical experiences and priorities of your world are, as well as its other ideas, as in point 3. Does it really make sense for your characters to do these things, or would their “common sense” consist of something else?
(No, it is no coincidence that this kind of thing leads to more complicated and more alien ethical situations. Why do you assume that anything I suggest which leads to those is coincidence?)
I think there will be another part of this, because I had a few more ideas, but I forgot them.