Selections from C.S. Peirce, “A Guess at the Riddle”, CP 1.354–416
359. First and Second, Agent and Patient, Yes and No, are categories which enable us roughly to describe the facts of experience, and they satisfy the mind for a very long time. But at last they are found inadequate, and the Third is the conception which is then called for. The Third is that which bridges over the chasm between the absolute first and last, and brings them into relationship.
We are told that every science has its Qualitative and its Quantitative stage; now its qualitative stage is when dual distinctions,—whether a given subject has a given predicate or not,—suffice; the quantitative stage comes when, no longer content with such rough distinctions, we require to insert a possible half-way between every two possible conditions of the subject in regard to its possession of the quality indicated by the predicate.
Ancient mechanics recognized forces as causes which produced motions as their immediate effects, looking no further than the essentially dual relation of cause and effect. That is why it could make no progress with dynamics. The work of Galileo and his successors lay in showing that forces are accelerations by which a state of velocity is gradually brought about. The words cause and effect still linger, but the old conceptions have been dropped from mechanical philosophy; for the fact now known is that in certain relative positions bodies undergo certain accelerations.
Now an acceleration, instead of being like a velocity a relation between two successive positions, is a relation between three; so that the new doctrine has consisted in the suitable introduction of the conception of Threeness. On this idea, the whole of modern physics is built.
The superiority of modern geometry, too, has certainly been due to nothing so much as to the bridging over of the innumerable distinct cases with which the ancient science was encumbered; and we may go so far as to say that all the great steps in the method of science in every department have consisted in bringing into relation cases previously discrete.
— Charles S. Peirce, “A Guess at the Riddle”, MS 909 (1887–88).
First published in CP 1.354–416. Reprinted in EP1, 245–279.