Lumping and splitting refers to a well known problem in any discipline which has to place individual examples into rigorously defined categories. The lumper/splitter problem occurs when there is the need to create classifications and assign examples to them, for example schools of literature, biological paleo-species and so on. A "lumper" is an individual who takes a gestalt view of a definition, and assigns examples broadly, assuming that differences are not as important as signature similarities. A "splitter" is an individual who takes precise definitions, and creates new categories to classify samples that differ in key ways.
In history lumpers are those who tend to create broad definitions that cover large periods of time and many disciplines, whereas splitters want to assign names to tight groups of inter-relationships.
Each approach has its well known problems. Lumping tends to create a more and more unwieldy definition, with members having less and less mutually in common. This can lead to definitions which are little more than conventionalities, or groups which join fundamentally different examples. Splitting often leads to "distinctions without difference", ornate and fussy categories, and failure to see underlying similarities.
For example, in the arts, "Romantic" can refer specifically to a period of German poetry roughly from 1780-1810, but would exclude the later work of Goethe, among other writers. In music it can mean every composer from Hummel through Rachmaninoff, plus many that came after.
Language families with lumper-splitter controversies include Ural-Altaic, Altaic itself, Austric, Nostratic, and Joseph Greenberg's similar Eurasiatic, his Amerind languages, Indo-Pacific, and Nilo-Saharan, and above all Merritt Ruhlen's Proto-World.
Splitters regard reconstruction of a common ancestor (protolanguage) via the comparative method as the only valid proof of relationship, and consider genetic relatedness to be the question of interest. American linguists of recent decades tend to be splitters.
Lumpers are more willing to admit techniques like mass lexical comparison or lexicostatistics, and mass typological comparison, and to tolerate the uncertainty of whether relationships found by these methods are the result of linguistic divergence (descent from common ancestor) or language convergence (borrowing). Much long-range comparison work has been from Russian linguists like Vladislav Illich-Svitych and Sergei Starostin. In the US, Greenberg's and Ruhlen's work has been well publicized. Some well-known earlier American linguists like Morris Swadesh and Edward Sapir also pursued large-scale classifications.
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"Lumpers and splitters".
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