Matpic
mathematics, in pictures
Ladder

Class diagrams — the ladder

2 distinct arguments against one idea, from the one that introduces it to the one that assumes the rest.
  1. 4 circles, and the 14 patterns they realise. Closed curves overlapping in the plane, with each region of the arrangement identified by which curves contain it.

    Four circles cannot do it

    Three overlapping circles cut the plane into exactly the eight regions three sets need. Four circles cut it into fourteen, and sixteen are required — so the diagram everyone draws stops working at four, and the reason is a count.

    rung 1 · logic
  2. The 256 syllogistic forms, and the 24 that work. A grid with one cell per syllogistic form, marked according to whether it is valid and what it needs to be valid.

    Twenty-four out of two hundred and fifty-six

    Aristotle's syllogisms are four sentence forms in four arrangements, which makes 256 patterns of argument. Fifteen of them are valid. Nine more become valid if you assume the things being talked about exist, and the gap between those numbers is a two-thousand-year-old disagreement.

    rung 2 · logic

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