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Are enumerative definitions necessarily extensional?
Intuitively, it seems natural to use the expression "enumerative definition" about both enumerations of objects and of types of objects. What makes a definition enumerative is, in my opinion, that it gives a disjunction of sufficient criteria. If you define "farm animal" as "horse, sheep, pig, chicken etc." we would have an enumerative definition, but not an extensional.
The first sentence is clear. The rest baffles me. I see only:
farm animal — horse, sheep, pig, chicken, etc.
This would be a non-Aristotelian claim, lacking both genus and differentia. What is here is a (necessarily) partial enumeration of subtypes of farm animal. There is no definition in sight, unless we are reduced to undistinguished equivalents. A semantically equivalent statement could be:
'There are several sorts of things that we generally take to be things that we call "farm animals". These sorts of things include horses, sheep, pigs, and chickens. These things might be animal things, because we we see that "farm" modifies "animal" in the erstwhile definiendum.'
Unfortunately, this merely exposes the need to define the terms 'animal', 'horse', 'sheep', 'pig', and 'chicken'. — Belastro (talk) 02:17, 31 July 2013 (UTC)