MS 447-454 (1903) - Lowell Lecture I

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new principles of expression will be used.

Before going any further, I must show you how the third and fourth principles work when they are taken together. For there are some quite puzzling forms.

But first of all I must make you acquainted with a few words that are convenient in talking about these expressions.

In the figure last drawn, "It shall lighten" is singly enclosed; that is, one line, and one only, completely encircles it. "It shall thunder" is doubly enclosed, since two portions of the line, and only two completely encircle it. Suppose I make this assertion

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both true; first that if a house is struck by lightening property will be destroyed; and second, that it shall lighten, then it will bw true that insurance will be high.

Here parts of the expression are three and four times enclosed. Now I say of any part of an expression which is encircled any odd number of times that it is oddly enclosed and of any part that is encircled any even number of times, reckoning zero as an even number, that it is evenly enclosed. Therefore I say of a part that is not enclosed at all that it is evenly enlosed. This will be found convenient.

I call this whole system of expression the System of Existential Graphs. By an existential graph, or as I shall commonly call it a graph, I mean anything which taken by itself would, acending to the principles of thia system, represent