http://www.3ammagazine.com/3am/on-the-nature-of-truth/
Volker Halbach: Usually declarative sentences are about objects. Some sentences – such as the preceding sentence – are about sentences; and one of the sentences may be that sentence itself. Some sentences are only about themselves. The best-known sentences of this kind are liar sentences. For instance, [the sentence in square brackets is not true] is about itself, and it says about itself that it is not true.
Sentences in arithmetic are about numbers. We can assign to each sentence of arithmetic a number, for instance, by listing all sentence in alphabetical order and then numbering them. Then there is a first sentence, a second sentence, and so on. If a sentence of arithmetic is about the number 12122, then it is about the 12122th sentence. Gödel showed how to construct a sentence of arithmetic that is about itself in this indirect way and that says about itself that it is not provable. There are many other sentences in arithmetic that make claims about themselves. The Henkin sentence, for instance, says about itself that it is provable.
That’s the idea at least. However, it’s not very clear what it means for a sentence to be about something. Linguists, philosophers of language, and logicians have struggled with the notion of aboutness. It is a very elusive notion. Consequently it is not very clear what self-reference is, not only in arithmetic. However, even if it’s difficult to come up with a general definition of self-reference, there are paradigmatic self-referential sentences.
What interests me is the following: For a given property there may be different sentences ascribing to themselves the property and these sentences may have very different properties. For instance, a sentence may say about itself that it is true and be true; another sentence may also say about itself that it is true, but be false. Hence the loose way of talking about *the* sentence ascribing to itself a certain property has to be used with caution. The properties of self-referential sentences can be very sensitive to the way these sentences are constructed.
Några invändningar eller synpunkter?
Hint:
For instance, [the sentence in square brackets is not true] is about itself,
and it says about itself that it is not true.