MS 455-456 (1903) - Lowell Lecture II

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Continuation from p 15.

So much of the system of existential graphs as I have thus far described I term the alpha part of the system. I shall presently describe a beta part, and in another lecture the system will be completed by a gamma part.

There are certain ways in which graphs that are scribed on the sheet of assertion can be modified without any danger of changing a true graph into a false one. Transformations according to any general method that can never change a true graph into a false one I term permissible transformations. In particular, those

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which the principles of the alpha part of the system render permissible shall be termed alpha permissible transformations, and in general I shall use “alpha” freely as a prefix so signify a reference to these principles. Thus, I shall say that the alpha-signs, that is to say the signs of this system heretofore described apart from the graphs themselves[,] are two, and there are besides two peculiar graphs. Namely, the two peculiar graphs are the blank place which asserts only what is already well-understood between us to be true, and the blot which asserts something well understood to be false. The two signs

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which are not graphs are the writing scribing putting of two graph-replicas upon the same area, which if we remember that a blank is a graph, is seen to include the scribing of a single graph as a special case. This idea that scribing a graph is a transformation of a graph already accepted is a very useful one. The other sign is the scroll.

I have just defined a permissible transformation as one which conforms to a general type which in no case can transform a true graph into a false one. But what do we mean by a true graph and a false one? I will not stop at present to analyze fully the meaning,

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because this system of existential graphs is not intended to inquire into the conformity of ideas thoughts to experiences. The universe of our discourse is to be a universe of my imagination, and therefore any graph which I permit to be scribed will be true, unless it is absurd and so amounts to telling you that my universe has no being even in my imagination. Therefore, for our purposes, a true graph is nothing but a graph which will result from a special permission to transform the blank sheet of assertion into the sheet with that graph scribed upon it. As for the general alpha-permissions, they are nothing but the definitions of the

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four general Alpha signs in terms of permissibility.

Let us draw up statements of them. You know that every definition consists of two propositions. Thus if man is defined as a featherless biped, the one proposition Every man is a featherless biped predicates the definition ‘featherless biped’ of the definitum, ‘man’; while the other proposition ‘Every featherless biped is a man’ predicates the definitum of the definition.

Consequently, each sign of the system should furnish us with two rules permissions of transformation.

Beginning then with the sign which consists in mating scribing together, or as we may