MS 466-467 (1903) - Lowell Lecture IV

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when that time does come, our logical forms will become very much more metamorphosed by introducing that consideration than they are in modal logic, where we take account of the possibility of ignorance as compared with the simple logic of propositions de inesse, as non-modal propositions in which the ideas of possibility and necessity are not introduced are called.

I will here take leave of this department of the gamma graphs in order to consider another. Instead of saying that opium puts people to sleep we may say that opium has a dormitive virtue. In that particular case

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little or nothing is gained by the more complicated expression. But in some cases there is a great gain. When, for example, instead of saying that a particle moves we say that the particle describes a line we introduce an abstraction in the same manner as when we talk of a dormitive virtue. But the advantages here are manifest, since we may imagine a filament to occupy the whole line at once, and we may further imagine that that filament moves in such a manner that at each moment it altogether quits the line which it is momentarily occupying. Here again we may introduce an abstraction and say that the filament generates a surface. Then we may imagine a material film to occupy the whole surface at once, and may

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imagine that the film moves in such a way that at each moment it is quitting the surface at which it is just arriving; and if it is not restricted to the space of our ordinary intuition we may say that the character of its motion describes defines determines a particular solid space, tridimensional at each point of it. This space, probably much more peculiar than the simple space we know, might, for aught we can see, be occupied all at once by a body. And we cannot see why this body should not move so that at every instant every part of it with possible exceptions should it should altogether quit the space that it at that instant occupies; and so on.

Here we see that the introduction of abstractions has led us to conceptions some of which, at any rate, are of the highest value. The others teach us still more if it can in any way be shown that

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they are impossible, and how they are so.

Hegel, I suppose, would regard a point as far more abstract that three dimensional space. This is, according to my principles of terminology, an abusive, or at any rate, an unadvisable use of the word abstraction. But what Hegel means is that it is nearest to experience in its totality. In the case of space we pass backward in this way. Here is a glass object. Everything isn't glass. There is besides air. No air is glass. There is however something no part of which is altogether glass and no part altogether air. It is glass-air. This is the surface between the glass and the air.

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Now we place a little water against a part of that surface. There are now three surfaces, one of glass-air, a second of glass water, a third of air-water. There is some thing that is, in the same sense, between the glass-air surface and the glass-water surface; and this must necessarily also be between either of those and the water-air surface. It is the line where glass air and water meet. Now let us put a piece of putty over a portion of that line. There are now three additional surfaces, the putty-glass surface, the putty-air surface, and the putty-water surface, and there are three additional lines, the