Charles S. Peirce
[On Time and Thought]
MS 215 (Robin 377): Writings 3, 68-71
March 8. 73
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. Every mind which is capable of logical criticism of its inferences, must be aware of this determination of its ideas by previous ideas. But is it pre-supposed in the conception of a logical mind, that the temporal succession in its ideas is continuous, and not by discrete
steps? A continuum such as we suppose time and space to be, is defined as something any part of which itself has parts of the same kind. So that the point of time or the point of space is nothing but the ideal limit towards which we approach, but which we can never
reach in dividing time or space; and consequently nothing is true of a point which is not true of a space or a time. A discrete quantum, on the other hand, has ultimate parts which differ from any other part of the quantum in their absolute separation from one another. If the succession of images in the mind is by discrete steps, time for that mind will be made up of indivisible instants. Any one idea will be absolutely distinguished from every other idea by its being present only in the passing moment. And the same idea can not exist in two different moments, however similar the ideas felt in the two different moments may, for the sake of argument, be allowed to be.
Now an idea exists only so far as the mind thinks it; and only when it is present to the mind. An idea therefore has no characters or qualities but what the mind thinks of it at the time when it is present to the mind. It follows from this that if the succession of time were by separate steps, no idea could resemble another; for these ideas if they are distinct, are present to the mind at different times. Therefore at no time when one is present to the mind, is the other present. Consequently the mind never compares them nor thinks them to be alike; and consequently they are not alike; since they are only what they are thought to be at the time when they are present. It may be
objected that though the mind does not directly think them to be alike; yet it may think together reproductions of them, and thus think them to be alike. This would be a valid objection were it not necessary, in the first place, in order that one idea should be the representative of another, that it should resemble that idea, which it could only do by means of some representation of if again, and so on to infinity; the link which is to bind the first two together which are to be pronounced alike, never being found. In short the resemblance of ideas implies that some two ideas are to be thought together which are present to the mind at different times. And this never can be, if instants are separated from one another by absolute steps. This conception is therefore to be abandoned, and it must be acknowledged to be already presupposed in the conception of a logical mind that the flow of time should be continuous. Let us consider then how we are to conceive what is present to the mind. We are accustomed to say that nothing is present but a fleeting instant, a point of time. But this is a wrong view of the matter because a point differs in no respect from a space of time, except that it is the ideal limit which, in the division of time, we never reach. It can not therefore be that it differs from an interval of time in this respect that what is present is only in a fleeting instant, and does not occupy a whole interval of time, unless what is present be an ideal something which can never be reached, and not something real. The true conception is, that ideas which succeed one another during an interval of time, become present to the mind through the successive presence of the ideas which occupy the parts of that time. So that the ideas which are present in each of these parts are more immediately present, or rather less mediately present than those of the whole time. And this division may be carried to any extent. But you never reach an idea which is quite immediately present to the mind, and is not made present by the ideas which occupy the parts of the time that it occupies. Accordingly, it takes time for ideas to be present to the mind. They are present during a time. And they are present by means of the presence of the ideas which are in the parts of that time. Nothing is therefore present to the mind in an instant, but only during a time. The events of a day are less mediately present to the mind than the events of a year; the events of a second less mediately present than the events of a day.
It remains to show that, adopting this conception, the possibility of the resemblance of two ideas becomes intelligible; and that therefore it is not inconceivable that one idea should follow after another, according to a general rule. In the first place, then, it is to be observed that under this conception, two ideas may be both present to the mind during a longer interval, while they are separately present in shorter intervals which make up the longer interval. During this longer interval they are present to the mind as different. They are thought as different. And this longer interval embraces still shorter intervals than those hitherto considered, during which there are ideas which agree in the respects which are defined by each of the two ideas, which are seen to be different. During the longer interval therefore, the ideas of these shortest intervals are thought as partly alike and partly different. There is therefore no difficulty in the conception of the resemblance of ideas. Let us now see what is necessary in order that ideas should determine one another, and that the mind should be aware that they determine one another. In order
that there should be any likeness among ideas, it is necessary, that during an interval of time there should be some constant element in thought or feeling. If I imagine something red, it requires a certain time for me to do so. And if the other elements of the image vary during that time, in one part it must be invariable, it must be constantly red. And therefore it is proper to say that the-idea of red is present to the mind at every instant. For we are not now saying that an idea is present to the mind in an instant in the objectionable sense which has been referred to above, according to which an instant would differ from an interval of time; but we are only saying that the idea is present at an instant, in the sense that it is present in every part of a certain interval of time; however short that part may be. The first thing that is requisite to a logical mind, is that there should be elements of thought which are present at instants in this sense. The second thing that is requisite is, that what is present one instant should have an effect upon what is present during the lapse of time which follows that instant. This effect can only be a reproduction of a part of what was present at the instant; because what is present at the instant, is present during an interval of time during the whole of which the effect will be present. And therefore since all that is present during this interval is present at each instant, it follows that the effect of what is present at each instant is present at that instant. So that this effect is a part of the idea which produces it. In other words, it is merely a reproduction of a part of that idea. This effect is memory, in its most elementary form. But something more than this is required in order that the conclusion shall be produced from a premise; namely, an effect produced by the succession of one idea upon another.