Self-Reference and Logic

Self-reference is used to denote any situation in which someone or something refers to itself. Object that refer to themselves are called self-referential. Any object that we can think of as referring to something—or that has the ability to refer to something—is potentially self-referential. This covers objects such as sentences, thoughts, computer programs, models, pictures, novels, etc. The perhaps most famous case of self-reference is the one found in the Liar sentence: “This sentence is not true”. The Liar sentence is self-referential because of the occurrence of the indexical “this sentence ” in the sentence. It is also paradoxical. 1 That self-reference can lead to paradoxes is the main reason why so much effort has been put into understanding, modelling, and “taming ” self-reference. If a theory allows for self-reference in one way or another it is likely to be inconsistent because self-reference allows us to construct paradoxes, i.e. contradictions, within the theory. This applies, as we will see, to theories of sets in mathematics, theorie