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by my giving my exposition of it no other title than “Note B.” The perusal of Schröder's book convinced me that the algebra was not what was wanted; and in the Monist for January 1897 I produced a system of graphs which I now term Entitative Graphs. I shortly after abandoned that and took up Existential Graphs. The beta part and portions of the gamma part were in running order in a few months; but the work of completely systematizing the beta part was not a job to be hurried up,— or, at any rate, was not so as I conceive such work ought to be done. It was a
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ripening of corn, requiring the heat of hard work, indeed, but above all the ripening effect of time. Meantime, I have been making many and many an attack upon the gamma fortress, and have captured sundry redouts. Of course, I can work with it. But that only supposes such a degree of mastery as one has of a language when one can think in that language. How many people fancy that they know a language very well when they can think in it. If they pursue the study, they will afterward turn back and see that that
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that was merely the time at which their real knowledge of the language was making its first beginning! It is precisely so in graphs. When you have learned to think in them easily without translation then you are ready to begin the real study of them.
The gamma part of graphs, in its present condition, is characterized by a great wealth of new signs; but it has no sign of an essentially different kind from those of the alpha and beta part. The alpha part has three distinct kinds of signs, the graphs, the sheet of assertion, and the cuts. The beta part adds two quite different kinds of signs,
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spots, or lexeis, and ligatures with selectives. It is true that a line of identity is a graph; but the terminal of such a line, especially a terminal on a cut where two lines of identity have a common point, is radically different. So far, all the gamma signs that have presented themselves, are of those same kinds. If anybody in my lifetime shall discover any radically disparate kind of sign, peculiar to the gamma part of the system, I shall hail him as a new Columbus. He must be a mind of vast power. But in the gamma part of the subject all the old kinds of signs take new forms.
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If I were to expound to you fully the theoretically needed new forms of spots, cuts, and ligatures that are required in the gamma part, you would find the complexity of it,— presented in the hurried way that would be necessary,— to be not only tedious but also confusing.
It will be better to give you examples of what I have found most useful, and leave it to you to study out the rest if you care to do so. I shall have a printed syllabus ready for distribution at the next lecture which will be a great help; but even in that I cannot go into the long explanations that would be needed to expound the theory of the gamma part.