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A statement can be said to be self referential when it is its own subject. This sort of statement can cause a lot of confusion. Self referencing statements are not things like "I am the most wonderful person in the world" sentences like these refer to the author of the sentence not the sentence itself. Most of the time self referencing statements are perfectly acceptable as in "This statement is true" which is perfectly acceptable but not all such statements are. Propositions like "this statement is false" are where the real fun begin. Less clearly demonstrative of the self referencing sentence paradoxes but more amusing are statements like "when you are not looking this sentence is in spanish." If the first statement is true then it is false and since it IS false it is therefore true continuing ad nauseum. On the other hand the sentence about spanish does not lead us into any causal loops but is simply unprovable to be true or false much like the famous koan "if a tree falls in the forest and no one is around to hear it does it make a sound?" These statements are accompanied by more mathematically formal statements like the famous russels paradox. Discovered by bertrand russel it is a problem in set theory. Let the set M be defined as the set that contains all sets that are not members of themselves. So a set A is a member of M if and only if A is not an element in itself. Let us now ask ourselves if M is contained in itself. If it is a set in itself then by the definition of M it is not a member of M. But since it cannot be a member of M then it fits the definition and is. The set M is a well defined set that finds uses within cantor set theory and this paradox has caused some trouble for that field of logic.

The solution of many logicians to these paradoxes is that statements simply should not talk about themselves. Logicians have classified self referencing statements into types depending on exactly what the nature of the reference is a type 0 statement is one that makes something else its subject. A type one statement is one whose subject is itself. Type two statements are ones whose subject is statements about itself. type three have sujects about statements about the statement and so on and so forth. Many logicians simply ban statements of order higher than 0. So in the case of russels paradox when disregarding higher order statements M does not contain itself because that would require applying M to itself making a type 1 statement that is meaningless.

The story of self reference does not stop there however but only gets more interesting. Take the law of the excluded middle which states that for any proposition p The statement P or not P is true. So take for instance the statement The earth is a banana. Applying the law of the excluded middle we know that the statement "The earth is a banana or the earth is not a banana." is true regardless of the earths state of fruitiness. The law of the excluded middle is essentially the same as the principle of bivalence. Bivalence is the proposition that all statements are either true or false. If we hold all logical statements of higher order than 0 to be meaningless then we needn't challenge the validity of the principle of bivalence. However allowing self referential statements to keep some sort of significance we are necessarily brought to the conclusion that not all statements need be true or false. Since Since the proposition "this statement is false" is valid we must admit that it can neither be proved true or false. These sorts of statements take up the space of that so called "excluded middle". Godel echoed this sort of statement when he proved that in any set of axioms if they are consistient they are not complete. Meaning that if every statement in the system can be proved true or false according to the axioms that in fact every statment can be proved both true and false.