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  1. How did 'ex/in-tēnsiō' semantically specialize to mean the logical meanings below?

  2. 'ex/in-tēnsiō' obviously share the same root, and differ merely in prefixes. Does the difference in prefix explain their meanings?

  3. Does the difference in prefix explain why 'ex/in-tēnsiō' didn't mean the opposite? Why didn't 'ex/in-tēnsiō' mean «in/ex-tēnsiō» respectively?

  4. To wit, why doesn't EXtension signify 'qualities or attributes that the term connotes'?

  5. Why doesn't INtension signify 'members of the class that the term denotes'?

Source: Hurley, P. A Concise Introduction to Logic (2014 12 ed, but ∃ 2017 13 ed). p. 92 Middle.

  The previous section of this chapter explored the cognitive meaning of language in general. The cognitive meaning of terms comprises two kinds: intensional and extensional. The intensional meaning, or intension, consists of the qualities or attributes that the term connotes, and the extensional meaning, or extension, consists of the members of the class that the term denotes. For example, the intensional meaning of the term “cat” consists of the attributes of being furry, of having four legs, of moving in a certain way, of emitting certain sounds, and so on, while the extensional meaning consists of cats themselves—all the cats in the universe. The term connotes the attributes and denotes the cats.
  The intensional meaning of a term is otherwise known as the connotation, and the extensional meaning is known as the denotation. Intension and extension are roughly equivalent to the more modern terms sense and reference, respectively. Also, note that logic uses the terms connotation and denotation differently from the way they are used in grammar. In grammar, connotation refers to the subtle nuances of a word, whereas denotation refers to the word’s direct and specific meaning.

Etymonline on 'intension (n.)' :

c. 1600, "action of stretching; increase of degree or force,"
from Latin intensionem/intentionem (nominative intensio/intentio) "a stretching, straining," figuratively "exertion, effort," noun of action
from past participle stem of intendere in its literal sense of "stretch out, strain" (see intend, and compare intention, which has the figurative sense).

[ OED : ] Etymology: < Latin intensiōn-em stretching, straining, noun of action from intendĕre to stretch: see intend n., intense adj., and compare intention n., which is etymologically a doublet of this.

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    The body of your question seems to be asking about why intension/extension are used. In that case, you should ask in one of the two English Stacks. – C. M. Weimer Feb 26 '17 at 4:11
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    I must concur with @C.M.Weimer. I am pretty sure (although I have no references at hand) that in/extensionality was first used as a term of the art of logic in English-language writings of R. Carnap, and this would set the terminus post quem for the term usage to 1935. If that's the case, the in-/ex- distinction is pretty much the same as that in the modern English language, and has probably nothing to do with its original nuances significant to the Roman mind. – kkm Feb 27 '17 at 3:58
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    This question seems to be about intension and extension, not about intensio and extensio. Therefore I agree with the others that it is off topic. Nevertheless, the question could be interesting for this site if you asked it from a Latin point of view (eg. comparing the English pair intension-extension with the Latin one intensio-extensio). – Joonas Ilmavirta Mar 13 '17 at 7:33
  • @JoonasIlmavirta Thanks! Do you mind editing my question please? This was your brilliant idea, so you ought get the credit! – Greek - Area 51 Proposal Jul 18 at 23:18
  • @Greek-Area51Proposal How does it look now? Questions often work best when kept concise and to the point. It would help if you could look into the dictionary definitions of these two Latin verbs yourself and specify what puzzles you. You can write a new paragraph of three sentences explaining that, but probably not more. The Etymonline quotes are mostly distracting; a simple link is enough. – Joonas Ilmavirta Jul 19 at 7:31

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