THEORY OF TYPES
| Collection | International Encyclopedia of Systems and Cybernetics |
|---|---|
| Year | 2004 |
| Vol. (num.) | 2(2) |
| ID | ◀ 3531 ▶ |
| Object type | Epistemology, ontology or semantics |
A logical theory that prohibes self-membership in sets (i.e. no class can contain itself as a member), or more generally logical self-reference in meaning systems, in order to avoid paradoxes.
The Theory of Types was elaborated by B. RUSSELL and A.N. WHITEHEAD in their “Principia Mathematica” (1925).
It introduced within the classical dichotomy “true — false” the meaninglessness escape, saving formerly unsolvable logical tangles.
K. KRIPPENDORFF however observes: “… by exorcising self-reference, the theory of logical types has retarded the development of theory, largely cognitive theory, in areas where self-reference is prevalent. With its focus on circularity, cybernetics has transcended the theory and essentially solved the problems self-reference originally posed” (1986, p.75).
This seems right only for the specific viewpoint of second-order cybernetics, as proposed by H.von FOERSTER.
From this angle, R. HOWE and H.von FOERSTER thus state the fundamental point of theory of types: “The properties of the observer shall not enter into the description of his observations” (1975). With this proviso, Epiminedes, who is a Cretan, has no logical right to make any statement on the Cretans that may include himself, as a source of internal contradiction. (as for example, saying that all Cretans are liars).
However, from the viewpoint of autopoiesis, no observer finds him/herself in a position to totally separate him/herself of the observed reality, because any external stimulus entering him/her is perceived in accordance with his/her internal organization.
This is not to deny the theory of types, but, on the contrary, shows the absolute necessity to learn to relativize the conclusions that we obtain from our observations of reality.
Theory of types is clearly related to GÖDEL 's Incompleteness Theorem, as well as to BATESON's double bind.
See also
Logical types (Theory of)