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
Quine may refer to:
* Quine (computing), a program that produces its source code as output
* Quine's paradox, in logic
* Quine (surname), people with the surname
** Willard Van Orman Quine (1908–2000), American philosopher and logician
See al ...
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
Mathematical logic is the study of Logic#Formal logic, formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory (also known as computability theory). Research in mathematical logic com ...
, there is generally no analog of the pronoun.
Indirect self-reference was studied in great depth by
W. V. Quine
Willard Van Orman Quine ( ; known to his friends as "Van"; June 25, 1908 – December 25, 2000) was an American philosopher and logician in the analytic tradition, recognized as "one of the most influential philosophers of the twentieth centur ...
(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
See also
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References
{{DEFAULTSORT:Indirect Self-Reference
Self-reference
Theoretical computer science