In the SEP article on “Definitions,” Anil Gupta formulates the idea of “reduction” in the traditional account of definitions: “the use of a formula Z containing the defined term is explained by reducing Z to a formula in the ground language.” This struck me as strange, and got me thinking about the role of explanation in motivating and comparing between proposed reductions of a term.
Do we reduce a term to a base in order to explain the use of the term? I always thought that the main three reasons to reduce a term t were: (1) to increase the simplicity of the theories in which t occurs; (2) to demonstrate that (at least some well-formed) sentences containing t are contentful (or have a certain sort of content); and (3) to demonstrate that (at least some well-formed) sentences containing t do not lead to contradiction or paradox. I might have also have included (4) to demonstrate that a set of presuppositions (preferably minimal) are sufficient to make uses of t contentful (or contentful in a certain way, e.g., “cognitively”). There is no explicit mention here of explanation. Still, there is something like an explanatory bonus when a reduction satisfies (2)-(4). When a reduction demonstrates that sentences containing t are contentful, it also explains, or can later be used to explain, that same fact. Similarly for (3) and (4). Note that this really is a bonus, not the main purpose of the reduction. This is because we don’t, in general, try to explain some alleged state of affairs when we have real doubts whether it obtains, and (2)-(4) are good motivators only if we do have real doubts about the contentfulness, consistency, and theoretical baggage of uses of a term. So, in order to be strongly motivated, the sort of explanatory function of reductions that I have already described must be secondary.
I’m not sure what Gupta means when he talks about explaining the “use” of a sentence or formula. I thought that when we wanted to explain why a word (or a sentence containing it) has one use rather than another, we do etymology. Maybe we do some psycholinguistics to find out whether the word is an onomatopoeia, or why certain concepts are lexicalized and others aren’t. Reduction seems to be besides the point here.
Do reductions have some other explanatory role? Am I missing something?