MS 466-467 (1903) - Lowell Lecture IV

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being able to scribe the same graph as many times as we please on any vacant places we like. Now each of the areas of any cut corresponds exactly to some one point or place locus of the sheet of assertion where there is mapped, though undeveloped, the real state of things which the graph of that area denies. In fact it is represented by that line of the sheet of assertion which the cut itself marks. By taking time enough I could develope this idea much further, and render it clearer; but it would not be worth while, for I only mention it to prepare you for the idea of quite different kinds of sheets in the gamma

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part of the system. These sheets represent altogether different universes with which our discourse has to do. In the Johns Hopkins Studies in Logic I printed a note of several pages on the universe of qualities,— marks, as I then called them. But I failed to see that I was then wandering quite beyond the bounds of the logic of relations proper. For the relations of which the so-called “logic of relatives” treats are existential relations, which the non existence of either relate or correlate reduces to nullity. Now, qualities are not properly speaking individuals. All the qualities you actually have ever thought of might, no doubt, be counted; since you

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have only been alive for a certain number of hundredths of seconds; and it requires more than a hundredth of a second actually to have any thought. But all the qualities any one of which you readily can think of are certainly innumerable; and all that might be thought of exceed, I am convinced, all multitude whatsoever. For they are mere logical possibilities, and possibilities are general, and no multitude can exhaust the narrowest kind of a general. Nevertheless, within limitations which include most ordinary purposes qualities may be treated as individuals. At any rate, however, they form an entirely different universe

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from the universe of existence. It is a universe of logical possibility. As we have seen, although the universe of existential fact can only be conceived as mapped upon a surface by each point of the surface representing a vast expanse of fact, yet we can conceive the facts are sufficiently separated upon the map for all our purposes; and in the same sense the entire universe of logical possibilities might be conceived to be mapped upon a surface. Nevertheless, in order to represent to our minds the relation between the universe of possibilities and the universe of actual existent facts,

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if we are going to think of the latter as a surface, we must think of the former as three-dimensional space in which any surface would represent all the facts that might exist in one existential universe. In endeavoring to begin the construction of the gamma part of the system of existential graphs, what I had to do was to select, from the enormous mass of ideas thus suggested a small number convenient to work with. It did not seem to be convenient to use more than one actual sheet at one time; but it seemed that various different kinds of cuts would be wanted.