Charles S. Peirce
Chapter IV: The Conception of Time Essential in Logic
MS 237 (Robin 391): Writings 3, 102-105
1-2 July 1873Investigation if pushed far enough will inevitably carry any mind to one destined belief, whatever may have been its opinions at the outset. Consequently, there must arise new elements of thought during the process; and these are termed sensations. Every thought not a sensation is determined by something previously in the mind. These also must 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 wrong method of research, which is presupposed in logic.
Every mind which passes from doubt to belief must have ideas which follow after one another in time; every mind which reasons must have ideas which not only follow after others but are caused by them; and every mind which is capable of logical criticism of its inferences must be aware of this influence of one idea upon another.
A succession in time among ideas is thus presupposed in tin-conception of a logical mind; but need this time progress by a continuous flow rather than by discrete steps?
A continuum (like time and space as they actually are) is defined as something any part of which however small itself has parts of the same kind. The point of time or space is nothing but the ideal limit towards which we approach in dividing time or space without ever reaching it, and consequently nothing is true of a point which is not true of a space or time, except that it is the ideal limit. A discrete quantum, on the other hand, unlike a continuum, has ultimate parts, which differ from all larger parts in their absolute separation from one another. That is to say, no two such parts have anything in common.
If the succession of images in any mind were to take place by one being suddenly replaced by another, time for that mind would be made up of indivisible instants. All ideas would be absolutely separated by each being present during one moment and absent at all other times. The ideas of different moments would be cut off from one another and would not be individually the same even if they differed in no other respect than that of being felt at different times. The consequence would be that ideas present at different moments never could be brought together in the mind to be compared, for when either was present the other would be absent. They could therefore never be thought as alike. But an idea has no existence except so far as it is thought, so that it is only what it is thought to be when it is present to the mind. Two ideas present at different limes could therefore have no resemblance. It follows that no idea could determine another, because this implies that one follows after the other according to a general rule, by which every similar idea would be followed by a similar consequent, but where there is no similarity there can be no general rule. Such a mind could certainly not be a logical one. Indeed, if as it seems natural to admit resemblances and differences can only be known through a process of comparison, it could have no consciousness at all.
Abandoning this conception, then, let us contemplate the opposite one, that the flow of time is continuous. In this case we must not say that nothing is present but a fleeting instant, a point of time. For then there would be no present. For a point of time differs in no respect from an interval, except that it is the ideal limit. And if nothing is present for any length of time, nothing is present in an instant. The true conception is that the ideas of a minute are present in the minute and that these are present through the presence of the ideas which occupy the seconds of that minute. These latter are less immediately present than the former; and they in their turn are made present through the ideas of minuter times. But carry the division as far as you may, you will never reach an idea which is quite immediately present. There can be no consciousness in an instant but an idea occupies time. We experience or pass through thoughts as we do the events of a day or a year, without in any moment having one present. [copy A] My idea may be that of an isosceles triangle and the angle opposite the base may while the idea is present gradually increase from 0° to 180°. In this case, during the whole time, I have had the general idea of an isosceles triangle; during the parts of this time more specific ideas. And during the whole time the more specific images are presented as alike in some respects and different in others.
Under this view of the matter two different ideas may have a third idea in common and that not by a figure of speech but literally. Ideas may therefore be similar. They are not similar in themselves but they are so in the wider idea which embraces them both.
A space of time may be too long for any idea to cover. But then the memory of an idea which lasts after it may be compared with it for a while directly and then with itself. Memory may in this way be proved trustworthy and afterwards relied upon. In this way ideas may be similar in an approved memory instead of in a wider idea.
A July 2. 1873
We are familiar with the fact that an idea of any difficulty requires time for its formation. But this is not the fact to which I have reference now. Not only does it take time for an idea to grow but after that process is completed the idea cannot exist in an instant. During the time of its existence it will not be always the same but will undergo changes. Thus, if I think an isosceles triangle the angle opposite the base may vary while the image is present to me. During the whole time every shape of isosceles triangle may have been present; during one part of the time only acute-angled triangles and during the remainder only obtuse-angled triangles. In this way the resemblance of the two kinds of isosceles triangles may be perceived because they both enter into the prolonged consciousness of the isosceles triangle in general. There seems to be no other way in which resemblances and other relations among ideas can be perceived.
It thus appears that as all ideas occupy time so all ideas are more or less general and indeterminate, the wider conceptions occupying longer intervals.
It may perhaps be though that one consciousness extends over more than a limited interval of time. But then the memory of an idea which lasts after it may be compared directly with it so long as there can be an idea which embraces them both. And when that is no longer the case the memory at one time can in the same way be compared with the memory at another time.