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

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Tags: circular logic, coalgebra, generalised number, generalised numbers, graph theory, logic, logical circular logic, math, mathematics, maths, number, Paul Finsler, philosophy, poset, posets, set theory

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