‘The entire body of the sciences may be regarded as an ocean, continuous everywhere and without a break or division, though men conceive parts in it and give their names according to their convenience.’
‘The phenomenon of a relatively autonomous theory becoming absorbed by, or reduced to, some other more inclusive theory is an undeniable and recurrent feature of the history of modern science.’
-- Ernest Nagel
‘A new and more comprehensive theory reduces an older theory just in case the new theory, when conjoined with appropriate correspondence rules, logically entails the principles of the older theory.’
-- Paul Churchland
The minimal commitment of reductionism holds that the facts of a whole (its structure and its properties) are fixed by the facts of its parts. Accordingly, if one wanted to build an exact replica of an organism, one could do so using only knowledge of the most fundamental parts that constitute that organism. By specifying the parameters of these ontological basics, one could expect the replica to instantiate all of the higher-level features of the original -- structural, metabolic, and even phenomenal if the original organism had a mind.
In-line with the quotes given above, the strongest claim of reductionism is that our sciences (biology, psychology, geology, marketing, and whatever other domains turn out to be fit for scientific inquiry) can all be collapsed to and absorbed within whatever scientific theory describes the goings-on of the most fundamental constituents of reality. If one imagines our theories as parsing nature into different levels of analysis, there is a fundamental theory describing the lowest-level at the bottom, and from this theory can be derived all the theories occupying the higher levels. For a reductive physicalist, this penultimate bottom theory is the theory of physics, naturally.
While echoes of the desire to integrate disparate pieces of knowledge can be found in Francis Bacon, Descartes, Kant, and Leibniz, it was Ernest Nagel who codified the idea into a rigid, formalized prescription for unification in his 1961 The Structure of the Sciences. Contemporary arguments of reductionism revolve around questions in the philosophy of mind. In these philosophical circles, the thesis statement is something like the following: the description of the mind provided by psychology / cognitive science, and the description of the brain provided by neuroscience, are simply descriptions of the same thing told in two different languages.
There are, naturally, several opposing views, one of which is emergentism.
Emergentism is a view holding that a whole is in some sense more than just a sum of its parts, or that an emergent property does not consist in any collective or organizational feature of its parts. In some versions, this view is one in which there are top-down causal influences (in other words, wholes may have causal relations in nature that are not just the propogation of the causal relations between their parts). Aside from philosophers talking about the relation of consciousness to the brain, some systems biologists hold this view, using examples of eg the protein folding problem (namely, just knowing the details of a particular protein tells us nothing about that protein’s shape or how it fits within the entire biological system).
Returning to our picture of levels of analysis above, an emergentist holds that the theories occupying the higher levels are describing causal relations between objects which are not captured by a theory at the more fundamental level.
Another opposing view is essentially a linguistic view. If the strong view of reductionism is that our scientific theories can be reduced to, collapsed within, and absorbed by some more fundamental theory, the linguistic anti-reductionist view simply denies this claim. For the linguist, the problem here is one of translation. The language of theory A could not be adequately translated into the language of theory B without some explanatory remainder, and thus one could not be reduced to or derived from the other. On this view, the languages of the social sciences, for instance, are said to be incommensurate with the languages of the physical sciences, or the design sciences, or what have you.
Finally, there are many views which attempt to deny reductionism by way of denying physicalism. Among these are epiphenomenalism (thoughts are caused by brain states but do not in turn cause brain states), property dualism (physical things have both physical and mental properties), platonism (in addition to physical objects, there also exist certain abstract objects which exist outside of space, time, and the realms of physical things), and plain old substance dualism (there are both physical and non-physical things outright). All these views conclude that a purely physical description of the world leaves out information about the world (namely, information about mentality (or mathematics, in the case of platonism)), and thus reject at least the physicalist variety of reductionism.
Join Plato’s Cave philosophers as we consider reductionism, the unification of the sciences, and whether such a unification entails an explanatory or predictive remainder. Be sure to check the Plato’s Cave discussion board and files section where you can read, post and download documents that are relevant to this topic.
I’ve linked several articles from the Stanford Encyclopedia of Philosophy below. In addition to these, there are tons of articles available on wikipedia which should serve as introductory reading.