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Some people seem to use the words Sense and Intension (but also Denotation and Extension) without any distinction.

Are Sense and Denotation the same thing ? If not, how are they related ?

As I understand it :

Intension and Extension refer to how we describe a class of object.

  • In an Intensional definition, we describe a class of object by means of a property satisfied by all elements of the class.
  • In an Extensional definition, we describe it by enumering every elements. The extension is determined by the intension.
  • The Denotation of an expression is its reference, the object in the reality to which it refers to, what is interpreted. In formal logic, the denotation of "(True /\ False)" is False.
  • The Sense of an expression is how we interpret it, a way to obtain the denotation. In formal logic, the sense of "(A /\ B)" is A or B.

Is it right ?

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    Given your CS background from your profile, you might be interested in paultaylor.eu/stable/prot.pdf ("Proofs and Types", by J-Y Girard, et al), whose first chapter is "Sense, Denotation and Semantics". (And I'd guess you'd find the rest of the book pretty interesting, too -- and the price is right:) – John Forkosh Nov 4 '16 at 8:58
  • @JohnForkosh Actually, I'm currently reading Proof and Types. Then I saw the concept of "Intensional" and "Extentional". It seemed similar so I wanted to understand how it was related to Denotation and Sense. – Boris E. Nov 4 '16 at 21:54
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While the intension/extension distinction is ancient and unproblematic, the details of sense/reference (denotation) distinction are controversial, and are still evolving. I will suggest here a simplified version.

The sense/denotation distinction is similar to the intension/extension distinction, just that the intension/extension distinction applies to general names, predicates, expressions that purport to represent general types and properties.

For instance, the intension of “ship” as a substantive is “vehicle for conveyance on water,” whereas its extension embraces such things as cargo ships, passenger ships, battleships, and sailing ships. (Britannica)

While the sense/denotation distinction applies to proper names and definite descriptions, expressions that purport to represent particular objects.

The reference of 'evening star' would be the same as that of 'morning star', but not the sense. (Frege, On Sense and Reference)

In Frege's classical example, the two descriptions "the evening star" and "the morning star" were once held to apply to two different planets. In time, it turned out that the two descriptions applied to the same planet, Venus. One reference, two senses.

In an Intensional definition, we describe a class of object by means of a property satisfied by all elements of the class. In an Extensional definition, we describe it by enumering every elements. The extension is determined by the intension.

can be put

In an Intensional definition, we describe a property (or a general type). Its Extension is the class of objects that exemplify that property, exemplify the intension. The extension is determined by the intension.

We begin with the intension, which is a property, or type, and derive from it the class, the extension.

The Denotation of an expression is its reference, the object in the reality to which it refers to, what is interpreted. In formal logic, the denotation of "(True /\ False)" is False. The Sense of an expression is how we interpret it, a way to obtain the denotation. In formal logic, the sense of "(A /\ B)" is A or B.

can be put

The Denotation of an expression is its reference, the object to which it refers. The Sense of an expression is the aspect, or the description, under which the speaker refers to the object. It is something that the speaker knows, and that serves the speaker to fix the reference of the stated expression.

I would not use the term "interpretation" here, because it can imply that we hold the object in thought, as it were, and then interpret it. But the sense is the very way in which we "hold" the object in thought. We do not have a reference before we have sense.

I would also leave formal logic aside. Formal logic abstracts from all references, to concentrate on the form of expressions. There is no referring going on in formal logic.

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Regarding Sense and Denotation, you are right: the source is the philosophy of Gottlob Frege :

The reference (German: Bedeutung) of a proper name is the object it means or indicates (bedeuten), its sense is what the name expresses.

This approach is aimed at a "fine" analysis of what is usually named : meaning.

With reference to it, we may use denotation as synonym for reference.

But we have also another "traditional" distinction, due to J.S.Mill : that between connotation and denotation.


Regarding intension and extension, you can see the answer to the post : what are external properties?

  • Thanks for you answer but I'm not sure to understand. 1) So the intension is the set of attributes of an idea and the extension is the set of sub-concepts satisfied by all these attributes ? 2) I still don't understand how the two couples (Extension/Intension) and (Denotation/Sense) are related 3) Can we say that meaning = sense + denotation ? – Boris E. Nov 3 '16 at 10:40
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    @BorisEng - related but not coincident... It is easy to identify the reference of a name : Napoleon. It is easy to identify the extension of a concept : the individuals "falling under" it (the collection of Italians are is the extension of the concept "Italian"). But names ref to individuals and concepts to "universals"; thus we have no extension for a name. Sense partains to concepts (or descriptions) : have we also sense for names ? – Mauro ALLEGRANZA Nov 3 '16 at 10:46
  • Ok, thanks ! It's clearer. I guess you agree to my other questions ? – Boris E. Nov 3 '16 at 11:33
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    See Names : Sense Theories. – Mauro ALLEGRANZA Nov 9 '16 at 20:52
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    See also : Theories of Meaning. – Mauro ALLEGRANZA Nov 9 '16 at 20:57
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Boris, yes, those are good working explanations of the terms.

Similarly, as intensionality (not to be confused with intentionality) is intrinsic, it can be thought of as "analytic" and, as extensionality involves things in the world, extension can be thought of as "synthetic".

A more technical distinction per Searle:

"Intensionality-with-an-s is that property of statements, and other sorts of representations, by which they fail certain tests for extensionality. The two favorite tests are the substitutability of coreferring expressions without loss or change of truth value (sometimes called Leibniz's Law) and existential generalization. For example, the statement "Oedipus wants to marry Jocasta" fails the substitutability test, because together with the statement "Jocasta is identical with his mother" it does not permit the inference: "Oedipus wants to marry his mother." The statement is intensional with respect to substitutability. Statements that fail the substitutability test are sometimes called referentially opaque. The statement "Oedipus is looking for the lost city of Atlantis" does not permit the existential inference "There exists a lost city of Atlantis," for Oedipus may be looking, even if the thing he is looking for does not exist. So the statement fails the test of existential generalization. Intensionality is important for the subject of practical reason, because, among other reasons, statements of reasons for action are typically intensional-with-an-s."

You might enjoy these:

Gottlob Frege, "Sinn und Bedeutung"
Per the indtroductory note by Max Black, Cornell University:
Sinn translates to "sense"
Bedeutung translates to "reference" [for the process] or "referent" [for the object].
Note also modern translations of "sinn" and "bedeutung" from German to English include:
"sinn" => sense, meaning, mind, point, feeling, signification, inclination...
"bedeutung" => importance, meaning, significance, concern, definition, prominence, weight, bearing, implication, et cetera.

Bertrand Russell, "On Denoting"

P.F. Strawson, "On Referring"

See here also for a decent overview of the "Semantic / Pragmatic" distinction: "Pragmatics and Semantics" by Francois Recanati

If you are after an understanding of meaning, however, I suggest you read some Grice ("Meaning" as well as "Utterer's Meaning and Intentions") then consider what Professor Searle has to say in his article, "Grice On meaning: 50 Years Later", particularly:

"All the same, there is a difference between uttering the sentence and meaning it and uttering it without meaning it.
      In both cases, where I utter the sentence and mean it and I utter the sentence without meaning it, there is an intentional act on my part, the act of producing that utterance. The conditions of satisfaction of the intention in both cases include the condition that the intention itself should cause that utterance. I say “Il pleut” and if I say it intentionally, then that utterance, the occurrence of that very sequence of sounds, will be the condition of satisfaction of my intention to make those sounds. The distinction between making the sound intentionally, but without meaning it, and making the sound intentionally and meaning that it is raining, is that in the second case, the conditions of satisfaction of my intention are not only that an utterance be produced, but the utterance itself now has further conditions of satisfaction, in this case truth conditions to the effect that it is raining. That may sound complicated, but the idea is in fact very simple. The meaning intention consists in the intentional imposition of conditions of satisfaction (in the sense of requirement) on conditions of satisfaction (in the sense of things required)."

For example, if I am taking a shower and reciting French lessons repeating the phrase, "il pleut" this is not necessarily a comment upon micro-climate conditions. Likewise, if I am in despair and say, "Oh, why was I ever born?" offering upon an answer explaining why I was born is entirely beside the point of what was meant by the utterance. Lastly, if I say "I own this car" out of pride of ownership, rather than fact of it, demanding records in support of the claim is, again, irrelevant.

Hope that helps.

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