Tag Archives: logical circular logic

from “On Self-Referential Sentences” by Douglas Hofstadter, originally in Scientific American (January 1981), reprinted in Metamagical Themas (1985) via crystilogic (Source: http://amzn.to/Ka9370)

Image | Posted on by | Tagged , , , , , , , , , , , , , , , | Leave a comment

The theory of universal algebras was well-developed in the twentieth century. [It] provides a basis for model theory, and [provides] an abstract understanding of familiar principles of induction, recursion, and freeness. The theory of coalgebras is considerably [less] developed. Coalgebras … Continue reading

Quote | Posted on by | Tagged , , , , , , , , , , , , | Leave a comment

Paul Finsler believed that sets could be viewed as generalised numbers. Generalised numbers, like numbers, have finitely many predecessors. Numbers having the same predecessors are identical. We can obtain a directed graph for each generalised number by taking the generalised … Continue reading

Quote | Posted on by | Tagged , , , , , , , , , , , , , , , | Leave a comment

The Opposite of Transitivity

rock ≻ scissors ≻ paper ≻ rock “beats” is not a transitive relation. in fact, Rochambot is an example of Logical Circular Logic. Rochambot obeys the non-wellfoundedness axiom (it’s a stream). it’s the cyclic group P₃.

Posted in Uncategorized | Tagged , , , , , , , , , , , , | Leave a comment