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I study undergraduate philosophy. I enrolled in a semantics class this semester, which just held its first exam. One of the questions asked,

What is the extension, and the intension, of "I'm writing an exam right now."

I had thought that extension denoted referent of an expression, and that intension denoted the concept of an expression. But, is their a conceptual equivalent of "I'm writing an exam right now"? Is that expression really a concept?

So, what are the extension and intension of that expression?

Thank you.

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    Could they be one and the same in this instance? – James Grossmann Jan 23 '14 at 3:26
  • Yeah, someone asked that, and the professor told the class that they were not. – Hal Jan 23 '14 at 4:49
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    @Hal That's right, they're not. Here's a clue: All propositions can have one of two possible extensions (at least, on Frege's analysis). – P Elliott Jan 23 '14 at 8:51
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What Atamari said is actually not entirely correct. When indexicals are involved, there is an additional layer of meaning involved, called "character", following David Kaplan (1989).

The character is a function from contexts in intensions. An intension is a function from "circumstances of evaluations" (i.e. possible worlds, situations, etc.; depending on theory) in extensions.

Character =context=> Intension =situation=> Extension

For the example, let's assume the context is such that the speaker is Peter and it is Jan 23, 4pm. The for "I am writing an exam now", we have (in paraphrases):

Character: "The speaker is writing an exam at the utterance time"

Intension: "that Peter is writing an exam on Jan 23, 4pm"

Extension: "true" (if Peter is writing an exam on Jan 23, 4pm".

This is the basic idea of Kaplans theory of indexicala. See Zimmermann 2012 for an overview and technical details.

References:

Kaplan, David (1989): Demonstratives. In: Almond, J & Perry, J & Wettstein, H (eds.): Themes from Kaplan. OUP. 481-563.

Zimmermann, Thomas Ede (2012): Context dependency. Maienborn, C & von Heusinger, K & Portner, P (eds.): Semantics. de Gruyter Mouton. 2360-2407.

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Intensions are functions from contexts to extensions. The sentence contains two indexicals - I and now. What the extension is depends on the theory underlying the interpretation. On Frege's analysis, it's the truth value. In non-Fregean logic, it's a "situation", or "eventuality".

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