Indirect self-reference

Indirect self-reference describes an object referring to itself indirectly. For example, the "this sentence is false." contains a direct self-reference, in which the phrase "this sentence" refers directly to the sentence as a whole. An indirectly self-referential sentence would replace the phrase "this sentence" with an expression that effectively still referred to the sentence, but did not use the pronoun "this."

If the quine of a phrase is defined to be the quotation of the phrase followed by the phrase itself, then the quine of:

is a sentence fragment

would be:

"is a sentence fragment" is a sentence fragment

which, incidentally, is a true statement.

Now consider the sentence:

"when quined, makes quite a statement" when quined, makes quite a statement

The quotation here, plus the phrase "when quined," indirectly refers to the entire sentence. The importance of this fact is that the remainder of the sentence, the phrase "makes quite a statement," can now make a statement about the sentence as a whole. If a pronoun were used for this, the sentence would be the directly self-referencing "this sentence makes quite a statement." In natural language, pronouns are straightforwardly used and indirect self-references are uncommon, but in systems of mathematical logic, there is generally no analog of the pronoun.

Indirect self-reference was studied in great depth by W. V. Quine (after whom the operation above is named), and occupies a central place in the proof of Gödel's incompleteness theorem. Among the paradoxical statements developed by Quine is the following:

"yields a false statement when preceded by its quotation" yields a false statement when preceded by its quotation

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