SELF-REFERENCE IN LOGIC
Charles François (2004). SELF-REFERENCE IN LOGIC, International Encyclopedia of Systems and Cybernetics, 2(2): 2980.
| Collection | International Encyclopedia of Systems and Cybernetics |
|---|---|
| Year | 2004 |
| Vol. (num.) | 2(2) |
| ID | ◀ 2980 ▶ |
| Object type | Epistemology, ontology or semantics, Methodology or model |
A.N. WHITHEHEAD and B. RUSSELL definitively established in “Principia Mathematica” the necessity to exclude self-reference in logical statements, in order to avoid paradoxes and contradictions.
This excludes any “… self-referential utterances, statements, propositions, descriptions, etc.”, as stated by R.H. HOWE and H.von FOERSTER (1975, p.1).
A curious result of this discovery is that languages are somehow autopoietic systems, able to produce only a limited — while enormous — number of statements, in accordance with their own combination rules, which by no means guarantee their logical soundness.
The self-reference problem is also related to GÖDEL 's Incompleteness theorem.
See also
Logical types