Charles S. Peirce
Chapter IV: The Conception of Time Essential in Logic
MS 238 (Robin 390): Writings 3, 105-106
July 1, 1873
1873 July 1Investigation, if pushed far enough, will carry all minds to the same belief, independently of what their opinions were at the outset. The process is therefore clearly one which introduces new elements of thought, and these are termed sensations. Every thought not a sensation is determined by something previously in the mind. Such determination of one thought by another must also enter into the process of investigation, or we should be perfectly passive in the business and there would be no distinction of a right and a wrong method of research, which is presupposed in logic.
Every mind which passes from doubt to belief in any way must have ideas which follow after one another in time. But every mind that reasons must have ideas which not only follow after others but are caused by them, and every mind that reasons consciously,that criticises arguments,must be aware of this influence of one idea upon another.
Thus, a succession of time among ideas is obviously presupposed in the conception of a logical mind, but that this time need progress by a continuous flow, as time actually does, rather than by discrete steps, is not at first so clear.
A continuum (such as time and space actually are) is defined as something any part of which however small itself has parts of the same kind. Every part of a surface is a surface, and every part of a line is a line. The point of time or space is nothing but the ideal limit towards which we approach indefinitely close without ever reaching it in dividing time or space. To assert that something is true of a point is only to say that it is true of times and spaces however small or else that it is more and more nearly true the smaller the time or space and as little as we please from being true of a sufficiently small interval. For example, we say that a body can occupy but one position at any instant. Now, in point of fact, bodies exist in time and are always moving. But what is true is that the shorter the time for which the body's position is considered, the more determinate it is, and by taking this time sufficiently short the extreme range of its positions can be made less than any assigned difference. And so nothing is true of a point which is not at least on the limit of what is true for spaces and times. A discrete quantum, on the other hand, unlike a continuum has ultimate single parts, which differ from all larger parts in their absolute separation from one another, no two of them having any similar part in common. Any collection of things is such a quantum. It has parts which are themselves collections, and different collections may have parts in common. But in the process of separating such a quantity you finally come to the single things and these are no longer susceptible of such division.