A word’s denotation is our conscious definition of it. You can think of this as the set of things in the world with membership in the category defined by that word; or as a set of rules defining such a set. (Logicians call the former the category’s extension into the world.)
Logicians also call the former “denotation”, and call the latter “intension” or “connotation”.
My, perhaps flawed, intuition is that “connotation” is what defines a concept from “outside” in that concept’s plane, “intension” is what defines it from “inside” in its plane, and “extension/denotation” is what defines it in another plane. So connotation is the net of independent concepts linked with the discussed concept, intension is the conceptual definition of that concept, and extension/denotation is what it refers to in (somehow conceived) reality.
I don’t understand the first sentence one bit, but agree with the second sentence. The use of “connotation” as a synonym for “intension” is horrible IMHO. Connotation already had an established usage before logicians ever used it; and that usage is both very different from and used in the same very specific area of discourse as this new definition. If definitions were trademarks, this would be a violation.
Connotation already had an established usage before logicians ever used it; and that usage is both very different from and used in the same very specific area of discourse as this new definition. If definitions were trademarks, this would be a violation.
You’re using ‘new’ in an interesting way here. This usage of ‘connotation’ was arguably first taken up by Mill in 1829. The word ‘connotation’ was first used by logicians in the 17th century, though it tended to mean something more like “the proper category to put something in”, and Mill was explaining he’d like to use the word more sensibly than that. The ‘common usage’ you refer to was possibly a bit earlier, 16th century if I’m to believe OED. And it was not a term of art.
According to Wikipedia. But I’ve never heard “connotation” used that way. “Intension” as set of rules, if such a set can be found; but most linguists would say that no such set of rules can be found for most categories that could actually define their intension. IMHO, in practice, the thing described by a set of rules is still more like the extension than the intension. That’s why I didn’t call it the intension.
It’s the usual way of explaining the distinction in intro to logic classes. I’m quite sure that Hurley uses connotation in that sense. Unsurprisingly, Enderton and Tarski do not touch upon the subject since their books are more mathematical/formal.
Logicians also call the former “denotation”, and call the latter “intension” or “connotation”.
Denotation is also called “extension”, with the obvious contrast to “intension”.
Maybe it would be clearer to use “associations” or “associative network” or some such, rather than “connotation”, for the pole opposite to denotation.
My, perhaps flawed, intuition is that “connotation” is what defines a concept from “outside” in that concept’s plane, “intension” is what defines it from “inside” in its plane, and “extension/denotation” is what defines it in another plane. So connotation is the net of independent concepts linked with the discussed concept, intension is the conceptual definition of that concept, and extension/denotation is what it refers to in (somehow conceived) reality.
I don’t understand the first sentence one bit, but agree with the second sentence. The use of “connotation” as a synonym for “intension” is horrible IMHO. Connotation already had an established usage before logicians ever used it; and that usage is both very different from and used in the same very specific area of discourse as this new definition. If definitions were trademarks, this would be a violation.
You’re using ‘new’ in an interesting way here. This usage of ‘connotation’ was arguably first taken up by Mill in 1829. The word ‘connotation’ was first used by logicians in the 17th century, though it tended to mean something more like “the proper category to put something in”, and Mill was explaining he’d like to use the word more sensibly than that. The ‘common usage’ you refer to was possibly a bit earlier, 16th century if I’m to believe OED. And it was not a term of art.
I was evidently using ‘new’ in an uninformed way.
According to Wikipedia. But I’ve never heard “connotation” used that way. “Intension” as set of rules, if such a set can be found; but most linguists would say that no such set of rules can be found for most categories that could actually define their intension. IMHO, in practice, the thing described by a set of rules is still more like the extension than the intension. That’s why I didn’t call it the intension.
It’s the usual way of explaining the distinction in intro to logic classes. I’m quite sure that Hurley uses connotation in that sense. Unsurprisingly, Enderton and Tarski do not touch upon the subject since their books are more mathematical/formal.