MS 466-467 (1903) - Lowell Lecture IV

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[diagram] mean that U is a graph precisely expressing V. It is necessary to place V in the saw-rim as I call the line about it, because in thus speaking of a sign materialiter, as they said in the middle ages, we require that it should have a hook that it has not got. For example, [diagram] asserts, of course, that if it hails, it is cold de inesse. Now a graph asserting that this graph is scribed on the sheet of assertion, will be [diagram] This graph only asserts what the other does assert. It does not say what the other does not assert. But there would be no difficulty in expressing that

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We have only to place instead of [diagram] wherever it occurs [diagram].

We come now to the graphical expressions of beta graphs. Here we require the following symbols,

Gamma Expressions of Beta Graphs

[symbol] means Y is a ligature whose outermost part is on X. [symbol] means g is expressed by a monad spot on X whose hook is joined to the ligature Y on X. [symbol] means g is expressed by a monad spot on X whose hook is joined to the ligature Y on X. [symbol] means g is expressed by a dyad graph on X whose first and second hooks respectively are joined on X to the ligatures Y and Z. [symbol] means g is expressed by a triad graph on X whose first, second, and third hooks are joined on X to the ligatures Y, Z, W, respectively.

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[symbol] means g is expressed by a tetradic spot on X whose first to fourth hooks are joined on X to Y, Z, U, V, respectively.