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.
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5 comments:

  1. some kantNovember 15, 2011 at 7:09 PM

    A topological ordering would be cool, too.

    ReplyDelete
  2. Alexander R PrussNovember 15, 2011 at 7:29 PM

    What's a topological ordering?

    ReplyDelete
  3. some kantNovember 15, 2011 at 7:42 PM

    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.

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  4. Alexander R PrussNovember 15, 2011 at 8:11 PM

    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.

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  5. Alexander R PrussNovember 16, 2011 at 2:59 PM

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

    ReplyDelete