Ontology is the philosophical discipline concerned with questions of existence: What actually exists? How does it exist?*
One of the most important distinctions in ontology is the distinction between reductionism and holism. These are both relatively recently-coined terms, but the distinction has been there since the beginning of Eurasian philosophy, and it's pretty important to get it right. (It's much more complicated than the way I'm presenting it here, but this is a simple summary.)
To a lot of people, reductionism means simplification. Anthropologists in particular - who think of themselves as 'holistic' thinkers, even when they aren't - use the word 'reductionist' primarily as a slur, and those who don't (like, say, Dan Sperber) are greeted with confusion when they use 'reductionism' in a positive sense.
Reductionism doesn't mean simplification. What it means is the idea that the properties of a thing - say, a table - reduce to the properties of the things that make it up. Tables consist of atoms, and there isn't a property that the table has that doesn't reduce to the atoms that make it up. Its weight, density, tensile strength, and shape are all properties that reduce to the combination of atoms that make it up. The table isn't anything more than the atoms that compose it, and we might even say that the table doesn't exist (a position called eliminativism), and that only the atoms do, because the table is nothing more than the atoms.**
This saves us a lot of trouble when it comes to philosophical problems (as you'll see), but obviously you can't live as if the table you're sitting at doesn't exist, and if you really believed it, you'd have a hard time buying furniture for your kitchen. This is because humans are natural holists; they are used to treating the large objects they perceive as independent entities, with properties that are in some way independent of the things that make them up (that's what holism is). A table, to the human mind, is something more than the atoms that compose it, which is a holistic idea. This is a necessary feature, because actually the properties of tables change all the time, and thinking of everything as atoms would be impossible for your brain to compute. But holism certainly leads to problems, and it seems a lot like magical thinking. I'm tempted to say that holism is the idea that, given any situation, something is going on other than what is actually going on.
Take the paradox of the heap. This is a paradox that results from holistic thinking (as many paradoxes do). The paradox is as follows: You have a heap of sand. It consists of a certain number of grains of sand - say, a million. You take a single grain of sand from the heap. Is it still a heap? Sure - it's only one grain less, a barely perceptible difference. So, you take away another grain. Is it still a heap? Sure.
Keep doing it, and you'll eventually get rid of all the grains, despite the fact that no single grain's removal made the difference between heap and non-heap. There is no single point at which the heap stopped being a heap.
This is an important problem in logic, and actually goes all the way back to ancient Miletos, in Anatolia, as a mind-bending logic problem. But it is an equally important problem in ontology, because it asks the question: just which things actually exist? How can the heap be said to exist if it is such a vague object?
A reductionist view - or an eliminativist view - is that there is no heap, and that the removal of each grain isn't changing the properties of a single object, a heap, but is instead a much simpler act, and consists of nothing more than moving the grain from one place to another. The heap doesn't change because there is no heap. This is a simple and elegant solution, but it isn't intuitive: we can see the heap and feel it and so on, and we all seem to agree on the notion of what a heap is. That's not really a problem, though; it seems as if the way we naturally think isn't necessarily the way the world actually is.
Only a holistic view presents any problems. If you treat the heap as being an independent object whose properties do not wholly reduce to the grains, then the removal of each grain shouldn't necessarily make a difference. But clearly it does, and clearly the heap isn't something more than the grains that compose it. It's merely useful to treat the heap as a single entity. It's computationally convenient for human brains. Treating composite objects - all objects apart from elementary particles, I suppose - as whole, independent objects makes things easier for your brain. This actually makes holistic thought considerably simpler than reductionist thought, despite the tacit claim, made frequently by anthropologists, that reductionism is simplistic and holism embraces complexity.
In social science, there are two features that we can think of in reductionist/holist terms. One is the ontology of society, in which the fundamental question is, 'how does society/how do social facts exist?' The other is explanation - of, for instance, the rise of agriculture or urban civilisation or whatever else.
In the ontology of human society, we often come up against a holistic brick wall. Human society has to be a natural thing, it has to somehow obey the laws of physics and somehow exist in a world consisting of elementary particles. But it seems so difficult to find a path from atoms to human institutions. If we locate human institutions in individual human acts (the only naturalistic position) and simultaneously accept that societies and social facts exist, then we have a problem, just like the paradox of the heap, when the people themselves don't follow the dictates of the institutions that their minds create and accept. If one person doesn't accept the institution, then how can it be an institution if institutions depend on individuals accepting them? The answer is, surely, that institutions are not things, not independent entities. Their properties have to reduce entirely to mental states with nothing left over. Societies are not more than the things that compose them - humans, human thoughts, and human acts.
It is easier to think of 'societies' and 'systems' rather than the specific mental states of individuals to which these societies and systems have to reduce. We find it very, very hard to conceive of society as reducing to individual humans and their mental states. But that's just because we're generally not very good at thinking. It's not because societies and social facts don't reduce, because actually there's very little that humans do that can't explained with recourse to their mental states (it just so happens that the mental states we need to ascribe are more complex than we usually think, and can consist of recursive loops of beliefs about beliefs about beliefs).
A reductionist view is a complex and difficult view to take, which is why most explanation in social science depends on treating some things as independent entities whose properties aren't necessarily the same as the component parts. Marriage alliance isn't usually explained in terms of specific mental states, but rather in terms of models that take for granted the existence of clans and lineages. We have to be holists when explaining social institutions and so-called 'social action', despite the clear advantages of a reductionist ontology. What we need is the ability to use holistic models while accepting that they necessarily reduce to the properties of other things. We do this all the time - we find it trivially easy to accept the existence of a heap of sand while simultaneously knowing that it consists entirely of sand grains - but for some reason, there has been a bit of resistance to, or disdain for, reductionist theories of human society in social science, as if there is something toxic about the idea of reductionism (or, more likely, the word 'reductionism', as most things described by anthropologists as 'holistic' are anything but***). But there isn't, and I see no reason to accept any holistic view of human life - or anything, for that matter - and holistic explanations can only ever be tools we use when we can't break the thing down into what it fundamentally consists of. Holistic explanations always leave a little left over that isn't accounted for. Explanation of marriage alliance in terms of rival clans won't account for individual marriages created by the idiosyncrasies of the individuals concerned, because those clans entirely reduce to the mental states of the individuals that constitute them, and taking them for granted leaves gaps. That is true of all systems-based thinking, however; the continents don't really exist, as their properties are determined by the particles that constitute them with nothing left over, but it is incredibly useful - and it produces accurate, powerful, interesting models - to think of them in a holistic way. So social scientific models aren't undermined by reductionism. They're just put on a different base.
The approach of reducing human society to individuals' mental states is represented by, among others, John Searle (who deliberately avoids using the term 'reductionism' in his books and articles on the topic; see Making the Social World, Oxford: OUP, 2010, or any of his works since the mid-1990s) and Michael Suk-Young Chwe, a game theorist who also doesn't seem to mind much that his explanations are reductionist. They seem to take it as a matter of course that fundamental explanations depend on reducing complex phenomena to their component parts. For some reason, this is not the state of affairs in most of social science - or it is (perhaps), but labelling it as 'reductionism' seems to be seen as distasteful.
Jared Diamond is someone who has been accused of 'reductionism' by anthropologists who see his ideas as simplistic. But his explanations are reductionist. Diamond looks at all the possible factors in play - for instance, he examines the effects of the Central Asian dust cloud on agriculture and carrying capacity on islands in the Pacific (the further the island is from mainland Asia, the less dust it receives, reducing soil fertility and variation). This seemingly minor effect is surprisingly important, and it is one of many variables involved in understanding just why one group of humans might prosper more than another. What anthropologists are objecting to about Diamond's models isn't the reductionist aspect - it's the holistic side, the part where, for ease of understanding, groups of people and ideas are lumped together simplistically. But this seems to be entirely necessary, and there's little objectionable in principle about Diamond's views (on the other hand, there are a few empirical problems, especially with regard to the farming/language dispersal hypothesis).
Similarly, the anthropologist Keith Hart has claimed in a comments thread that Emile Durkheim - an arch-holist and believer in the independent existence of social facts and society with properties above and beyond those of the people and thoughts that make them up - was actually a reductionist, because his explanations 'reduce' phenomena like suicide to 'the social'. This is actually simplification and 'explanation' (if it can be called that) through holism, not reductionism. Durkheim isn't taking anything apart to see how it works. He's seeing how things relate to other things, taking for granted the existence of wholes and treating them as independent entities. Just because he appears to be simplifying the problem, it doesn't mean that he's reducing it. And that does make a lot of difference.
So a lot of anthropologists, in particular, are using the word 'reductionism' in ignorance. It really doesn't mean what they think it means. It does refer to scientific explanations, or at least most scientific explanations are reductive (in principle), but it doesn't refer only to simplifying or simplistic theories, and it shouldn't be used as an insult. I would like to see ontology become part of social science curricula, because almost none of its key terms are used correctly by many social scientists (including the word 'ontology' itself), and because it is a very important topic, not to mention an easily misunderstood one.
*This is a different subject to the one I was going to tackle. But it's an important one, I think.
** I don't see anything wrong with this idea and it has plenty of defenders, including the philosopher Trenton Merricks, whose Objects and Persons (Oxford: OUP, 2003) is in part devoted to defending it.
*** Most, but not all. Some social scientists are quite aware of the holism/reductionism distinction, and use it well. Recent work on, for instance, pre-imperial trade networks in the Indian Ocean has taken a deliberately holistic position, using the word entirely correctly. This is because Indian Ocean trade is complex (and it is, by the way, an incredibly fascinating topic) and breaking it down into its constituent parts, viz, reductionism, would make it difficult to unravel. See, for instance:
Beaujard and Fee. 2005. The Indian Ocean in Eurasian and African world-systems before the sixteenth century. Journal of world history. 16(4): 411-465.