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  • formal explanation:

I can't supply this off the top of my head. Something like: a function from X to the set of worlds in which X is the case.

  • informal explanation:

The Sense (as opposed to Reference) of a word.

intensional contexts

Logical contexts that shift from one world to another, e.g. believe shifts from the world in which the believer does the believing to the worlds in which the beliefs are true. I'm sure someone can explain this better. --And Rosta

--And Rosta

Given the regularity with which this is thrown around, I would expect a clearer exposition. I can't derive enough understanding from these hints above. --xod

Google is your friend:

INTENSIONAL/EXTENSIONAL CONTEXTS (or REFERENTIALLY OPAQUE / REFERENTIALLY TRANSPARENT CONTEXTS)?this is primarily a distinction between types of sentences. A sentence is said to constitute an extensional context if the following two conditions hold
(a) co-referring expressions can be substituted for one another in the sentence without changing its truth value (e.g. if "Mary loves John's best friend" is true, and John's best friend is Fred, then "Mary loves Fred" is true)?the technical term for this criterion is intersubstitutivity salva veritate; and (b) the sentence entails the existence of the entities it mentions (e.g. if "Mary loves Fred" is true then "Fred exists" is true)?the technical term for this criterion is that such sentences support existential generalisation. Conversely, a sentence is said to constitute an intensional context if both these criteria fail of it (e.g. "Mary believes that Father Christmas lives in the North Pole" does not entail that "Mary believes that Santa Claus lives in the North Pole" (for Mary may not know that Father Christmas and Santa Claus are meant to be one and the same) and nor does it entail that "Father Christmas exists"). Importantly, sentences describing PROPOSITIONAL ATTITUDES form intensional contexts. Whilst they are related, it is important not to confuse intentional-with-a-"t" and intensional-with-an-"s".

Executive summary:

  • In extensional definitions, you define something by enumerating everything there is to it. In intensional definitions, you give some sort of definitions in words instead.
  • An extension of a meaning is the set of the things in the world it means. It's specific to the actual world we're in: no hypotheticals or subjective judgements allowed. An intension allows hypotheticals, and judgements; so it maps a meaning, not to the set of things in this world, but to the possible worlds in which it means something. For example, "I believe you are human" maps the sentence to the possible worlds in which you are human. In some possible worlds, you're not, but a robot, or something. The possible worlds selected are the worlds in which my subjective judgement actually turned out to be correct. That's because "believe that" allows some doubt; you don't know it's true in all cases. On the other hand, "You are 25 years old" doesn't allow any doubt, and is not subjective or hypothetical; it's either true or false. So it has an extension, not an intension.
  • The connection between the two is that, if you're enumerating the things an expression means, you're certainly limiting yourself to the real world, and yes-or-no membership. To capture hypotheticalities, you can no longer enumerate the things in this world involved -- because you don't know for a fact that you're right. You need the words (the intensional definition), not just the enumeration (extensional definition), to capture what you're trying to refer to.
  • Intensional contexts are the contexts in which intensions arise: the contexts in which hypotheticality is an issue. "believe that", "doubt that", "necessarily true that", etc.

Extension is hard-core, take-no-prisoners, yay-or-nay. Intension... lets in the human stuff. :-)

extension = reference = denotation = se sinxa

intension = sense = connotation = smuni

  • Is that intended as a definition or as a question? The extension/intension distinction is analgous, but not equal, to the reference/sense distinction, while I don't see the relationship with denotation/connotation (I'd have to check some textbooks to see what technical meaning the term 'connotation' ever has). As for the Lojban equivalents, smuni and selvla might suffice for intension/sense, but so might se sinxa. --And Rosta
  • It is an explanation. ordnet has the following:
    1. reference, denotation, extension -- (the most direct or specific meaning of a word or expression; the class of objects that an expression refers to; "the extension of `satellite of Mars' is the set containing only Demos and Phobos")
    1. intension, connotation -- (what you must know in order to determine the reference of an expression)
  • So while there may be differences in technical uses and exact definitions, extension, reference and denotation all have the same general meaning on a sufficiently high level of abstraction, as do intension, sense and connotation and the former correspond to Lojban se sinxa whereas the latter correspond to Lojban smuni, both of which are a bit more general than any of those English words. At lange'u, nitcion talks about the sense (smuni) and reference (se sinxa), so I really thought that assigning those meanings to those gismu was a settled matter. -- Adam