In the philosophy of language the naive theory of truth has been
challenged by the Liar Paradox. The Liar Paradox is the contradiction that
emerges from trying to determine whether the sentence
"This sentence is false"
is true or false. The sentence is obviously self-referential in that
it claims itself to be false.
Similarly, in mathematics the naive concept of set has been challenged
by Russell's paradox. Russell's paradox is the contradiction that
emerges from trying to determine whether the sentence
"Is the set of all sets that are not members of themselves an
element of itself?"
is true or false. This sentence, as well, involves self-reference,
though maybe not in an as obvious way as the Liar sentence.
In computer science one of the important problems is the question
of how to implement introspection (self-reflection) in artificial intelligence
agents. Through introspection an agent is able to refer to itself. On the
naive account of agent introspection this again leads to a paradox of self-reference,
e.g. in the form of the Knower's Paradox:
"I know that what I say now is not true."
In the light of these paradoxes the naive theories have to be abandoned and several new, consistent theories are introduced instead. In these theories the paradoxes are avoided either by blocking self-reference altogether or by finding consistent ways to treat self-reference. The blocking strategy will most often result in theories that are limited in important ways. Thus, to construct powerful, consistent theories one has to get to a deeper theoretical understanding of self-reference and of how to live consistently with it.
It turns out that all three paradoxes above are structurally similar. This implies that coming to an understanding of the basic structure involved in self-reference and theoretically investigate how to tame it has promising perspectives for all three fields of research.
Self-reference is not in any way restricted to occur only in the theories considered above. Actually, any theory that could be considered to be part of its own subject matter has some degree of self-referentiality. This applies to many theories of language, economy, sociology, psychology, etc. With respect to these theories an understanding of self-reference is essential to avoid performing unsound self-referential reasoning as in the paradoxes above.
The aim of the conference is to bring together researchers in the fields of philosophy, mathematics, and computer science to present theories of and related to self-reference - especially pertaining to theories that explain and resolve the above paradoxes and thereby advance new theories for the involved fields.