We were talking today at a "natural construction techniques" workshop about how to build a ceramics-firing kiln. We'd spent the weekend making adobe from materials found onsite and making buildings out of it.
A pottery kiln needs to withstand heating to at least 1050° for earthenware and bricks, and at least 1200° for stoneware or porcelain.
The most common way to build a kiln is apparently by lining it with kaolin-derived refractory brick. But there's no kaolin in the native dirt on site. What could be done about that, aside from going to the ceramics supply store to buy some kaolin?
Well, it might be possible to extract kaolin from glossy paper; it's one of the two minerals used to give common magazine paper its gloss, the other being calcite. Or it might be possible to mill porcelain to powder (known as "grog" when it's sand-sized, or "pitchers" when coarser) and then sinter the powder. But I think wet milled porcelain powder isn't going to have the plasticity of kaolin. You'd have to stick it together with something that will hold it in place until it fires.
My first idea for such a binder was salt, because I had the mistaken idea that sodium chloride didn't melt until 1500° or so. But in fact its melting point is only 801°. But kaolin won't sinter until 1200° or more. It's possible that the salt-binder idea might happen to work --- if the salt lets the porcelain chunks sinter at a lower temperature, but doesn't flux them enough for them to melt entirely at the temperatures the refractory must withstand --- but it's likely to fail one way or the other.
A somewhat more likely binder candidate is simply the other clays available. You'd mix a small amount of clay into a large amount of milled porcelain.
You might be able to press the milled porcelain into bricks using something like a compressed-earth brick press, then firing the bricks. This way, the porcelain particles are in direct contact with each other, and there's no possible flux in the way. Achieving porosity might be difficult, because I think you couldn't simply mix in sawdust, the normal way; its elasticity would force the porcelain particles apart when you took the brick press. Charcoal or carbon black might work.
Another possible alternative would be to make the refractory bricks from some other mineral found onsite. Quartz, for example, is abundant almost anywhere, and if you can purify it and get it to sinter, its melting point is 1670°; in theory, you could also turn quartz and alumina into kaolin, but I have no idea how. ("Chemical weathering of rock", says Wikipedia. But what reactions chemically weather quartz and corundum into dust?) Magnesium oxide (periclase) might work? It doesn't melt until 2852°, and you can presumably make it from electrolyzed seawater, but I don't know how to separate it out from dirt, or if it's common.
The traditional refractory used for gas lantern mantles is a mixture of uranium and thorium oxides, made from monazite, a common ingredient of sand. However, even if we could practically separate those out (separating the monazite should be easy because of its high density, but separating the rare earths involves lye and hydrochloric acid at above-boiling temperatures), people might complain that the furnace was too radioactive.
Calcium oxide (quicklime) doesn't melt until 2572° and would therefore work, and it's easily made by heating limestone to 825°, if there's limestone onsite, which there probably is. However, it's dangerously reactive with human bodies and other sources of water.
Magnetite is maybe the easiest mineral to separate out of sand. It oxidizes to hematite, ferric oxide, if heated with oxygen, and that doesn't melt until 1566°. I haven't heard of it being used for refractories, but it seems like it would work.