In Language
A circular reference is not to be confused with the logical fallacy of a circular argument. Although a circular reference will often be unhelpful and reveal no information, such as two entries in a book index referring to each other, it is not necessarily so that a circular reference is of no use. Dictionaries, for instance, must always ultimately be a circular reference since all words in a dictionary are defined in terms of other words, but a dictionary nevertheless remains a useful reference. Sentences containing circular referents can still be meaningful;
- Her brother gave her a kitten; his sister thanked him for it.
is circular but not without meaning. Indeed, it can be argued that self-reference is a necessary consequence of Aristotle's Law of non-contradiction, a fundamental philosophical axiom. In this view, without self-reference, logic and mathematics become impossible, or at least, lack usefulness.
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