When it comes to the subject of classification, a conventionalist view might at first blush seem quite welcoming. After all, many classificatory systems are in place for our convenience, and as such we should be free to change them if a new system seems to be doing a better job (given our needs). As examples one might take the many differing library classification systems, or The Harmonized Commodity Description and Coding System (HS) of the World Customs Organization – probably the most ambitious classification system ever created, as anything that might cross borders will have a place within the HS. The thing with such systems of classification is that we build them out of whole cloth; they are in no sense “found in the world”. So, here our intuitions might guide us to be conventionalists about classifications. They are things we impose on the world.
So, are all classificatory systems like HS or the Dewey Decimal system? Lewis Carroll provides us a reason to doubt this in his poem The Hunting of the Snark, where the map that the Bellman has provided is described thus:
“What’s the good of Mercator’s North Poles and Equators,
Tropics, Zones, and Meridian Lines?”
So the Bellman would cry: and the crew would reply
“They are merely conventional signs!
“Other maps are such shapes, with their islands and capes!Carroll 1876/1999, 683, emphasis in the original.
But we’ve got our brave Captain to thank”
(So the crew would protest) that he’s bought us the best–
A perfect and absolute blank!”
To Carroll’s eyes, if a system is not based on something real, it might as well not exist. How can we navigate the seas (or do mathematics for that matter) based on convention? Carroll overshoots the mark, as no conventionalist worth their salt would say that a map lacking “such shapes, with their islands and capes” would be of any use, only that the choice of zones and meridian lines is quite arbitrary. Still he does raise a worry: can all things be classified by mere convention?
A realist would answer: “no, some classifications are natural and we find them through careful study of nature”. The realist can of course say that anyone is free to use some other classificatory system than the natural one, but such systems are built, not found. Natural systems include (says the realist) the system of elementary particles, the periodic table of elements, and the classification of taxa in biology.
Take biological classification as an example. Although biological classification started more or less as an exercise in sorting similar looking organisms in the same families, it has now for a long time been based on evolutionary relations between organisms – relations that can (at least for extant organisms) be supported by genetic similarities. And it is not only that taxonomy is based on testable evolutionary relations, but biological classifications also allow for inductive generalisations. For instance, if you happen to know that a thus far unknown (at least to you) critter is in the family Felidae you will be able to surmise that it, among other things, will be a carnivore and will lack the capacity to digest (or taste!) sugars. Could such knowledge be gained from mere conventions?
Here the conventionalist will interject: “But of course! We choose our conventions to aid us in navigating the world, and as such we would expect such success in these matters.” The realist will have none of it: “Such success is – must be – an indication that our classifications are tracking the structure of the world. So, insofar as there is success, there is a natural system of classification.” Here the conventionalist will point out that conventions such as the Dewey decimal system allow for inductive generalisations – upon encountering a Dewey decimal for a previously unknown (at least for our investigator) book, if its code starts with an 8, one will be able to infer that it is a work of literature, and if with 88 a work of Greek literature and so on. The realist will retort that this is a case of deduction rather than inductive generalisation. To which the conventionalist will reply: “is then not the case with Felidae also a case of deduction? In turn the realist will point out that success of non-natural systems is predicated in knowing the intent of the purposes of the system in question, an idea that plays little role in, say, biology or physics. And so it will go on, with thrust and parries, feints and ripostes, both sides claiming points and victories.
For once I will leave things in as much disarray as I found them. I have no way of brokering peace between the realist and the conventionalist. But perhaps the whole question of “is x real or a product of convention?” is not a good question. (Compare: is x real or socially constructed?) Maybe we should only care about what we can do with x, with what role it can play in our investigations?
 Lewis Carroll was the nom de plume of the mathematician Charles Dodgson, who was quite opposed to conventionalism in mathematics and logic.
Carroll, Lewis (1876/1999) The Hunting of the Snark, in The Complete Lewis Carroll, Hertfordshire: Wordsworth Editions, 1999, 680–699.