Tuesday, November 15, 2011

Axiom/definition dependencies in Spinoza's ethics

Using the Tredwell adjacency data, I generated a list of axiom/definition dependencies for all the propositions in Spinoza's ethics. See the Tredwell adjacency data site for a key to what the nodes (e.g., "2P07") are.


some kant said...

A topological ordering would be cool, too.

Alexander R Pruss said...

What's a topological ordering?

some kant said...

It's a linear ordering of the vertices of a directed acyclic graph, based on the dependencies.

For example, consider the DAG:

A -> B
A -> C
B -> D
C -> D
D -> E
D -> F
E -> F
E -> G

Then the sequence A,B,C,D,E,F,G is a valid topological ordering. So is A,C,B,D,F,E,G.

Here are some useful notes and an algorithm.

Alexander R Pruss said...

Ah, so it's a total ordering that agrees with the dependencies. I am pretty sure that Spinoza's original ordering in the Ethics is like that--I have never seen an exception.

Alexander R Pruss said...

I updated this data to count postulates as a kind of axiom.