Posts tagged with circular logic

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 numbers as points and directing an edge from a generalised number toward each of its immediate predecessors.

It has been shown that these generalised numbers can be “added” and “multiplied” in a natural way by combining the associated graphs. The sum a+b is obtained by “hanging” the diagram of b onto that of a so the bottom point of a coincides with the top point of b. The product a·b is obtained by replacing each edge of the graph of a with the graph of b where the graphs are similarly oriented.

Paul Finsler, David Booth, Renatus Ziegler in Finsler set theory: platonism and circularity







  • Are the Israelis bellicose because countries are always antagonizing them, or are countries always antagonizing the Israelis because they’re bellicose?
  • Do you think that boy is cute because he likes you, and he likes you more because you like him, and where did this liking start in the first place?
  • If the rich get richer, how do you get rich in the first place? And if poverty leads to violence, lack of education, and ill health, which leads to more poverty, how do you stop the vicious cycle?
  • Do cops mess with people because there are too many criminals around, or do people become uncooperative and untrusting of cops because they’re always messing with people?
  • Nature or nurture?
  • Do Americans commute long distances to work because the country is built around roads, highways, and the assumption that everyone has a car, or is the highway infrastructure good because Americans have so many cars?
  • If child abuse is caused by the parent being abused as a child — if gang violence is usually retaliation for other gang violence — where did it all begin?
  • Does the culture generate the media, or does the media generate the culture?

So many chicken-and-egg questions. Dynamical systems theory comes to the rescue.


the Lorentz attractor

A dynamical system is a time-evolving list of equations that mutually affect each other. In the real world the arrow of causation often runs both ways. By thinking about chicken-and-egg questions as a dynamical system, suddenly circular causation becomes logical, even quantifiable.

fig3

More technicals on linear operators on dynamical systems, some famous examples including ecosystem modeling, mind-body dynamics, Jon Gottman, toy models, and the similarity to (I thought boring) differential equations later.