Cenopythagorean Categories


Digital Companion to C. S. Peirce
Cenopythagorean Categories
1867 | On a New List of Categories | W 2:54-55; CP 1.555

The five conceptions thus obtained, for reasons which will be sufficiently obvious, may be termed categories. That is,
      Quality (Reference to a Ground),
      Relation (Reference to a Correlate),
      Representation (Reference to an Interpretant),

The three intermediate conceptions may be termed accidents.

1867 | On a New List of Categories | W 2:49; CP 1.545-6

§1. This paper is based upon the theory already established, that the function of conceptions is to reduce the manifold of sensuous impressions to unity, and that the validity of a conception consists in the impossibility of reducing the content of consciousness to unity without the introduction of it.

§2. This theory gives rise to a conception of gradation among those conceptions which are universal. For one such conception may unite the manifold of sense and yet another may be required to unite the conception and the manifold to which it is applied; and so on.

1868 | What is Meant by 'Determined'? | W 2:156; CP 6.626

Hegel teaches that the whole series of categories or universal conceptions can be evolved from one – that is, from Seyn – by a certain process, the effect of which is to make actually thought that which was virtually latent in the thought. So that this reflection which constitutes Daseyn lies implicitly even in Seyn, and it is by explicitly evolving it from Seyn that Daseyn is evolved from Seyn. (Hegel’s Werke, Bd. 3, S. 107.) The term “What is” has reference to pure Seyn only; the term “What is somehow” has reference to Daseyn.

1885 | One, Two, Three: Fundamental Categories of Thought and of Nature | CP 1.377

It seems, then, that the true categories of consciousness are: first, feeling, the consciousness which can be included with an instant of time, passive consciousness of quality, without recognition or analysis; second, consciousness of an interruption into the field of consciousness, sense of resistance, of an external fact, of another something; third, synthetic consciousness, binding time together, sense of learning, thought.

1885 | One, Two, Three: Fundamental Categories of Thought and of Nature | CP 1.371

Thus, the three essential elements of a network of roads are road about a terminus, roadway-connection, and branching; and in like manner, the three fundamental categories of fact are, fact about an object, fact about two objects (relation), fact about several objects (synthetic fact).

1885 | Notes on the Categories [R] | CP 1.353

Perhaps it is not right to call these categories conceptions; they are so intangible that they are rather tones or tints upon conceptions. In my first attempt to deal with them, I made use of three grades of separability of one idea from another. In the first place, two ideas may be so little allied that one of them may be present to the consciousness in an image which does not contain the other at all; in this way we can imagine red without imagining blue, and vice versa; we can also imagine sound without melody, but not melody without sound. I call this kind of separation dissociation. In the second place, even in cases where two conceptions cannot be separated in the imagination, we can often suppose one without the other, that is we can imagine data from which we should be led to believe in a state of things where one was separated from the other. Thus, we can suppose uncolored space, though we cannot dissociate space from color. I call this mode of separation prescission. In the third place, even when one element cannot even be supposed without another, they may ofttimes be distinguished from one another. Thus we can neither imagine nor suppose a taller without a shorter, yet we can distinguish the taller from the shorter. I call this mode of separation distinction. Now, the categories cannot be dissociated in imagination from each other, nor from other ideas. The category of first can be prescinded from second and third, and second can be prescinded from third. But second cannot be prescinded from first, nor third from second. The categories may, I believe, be prescinded from any other one conception, but they cannot be prescinded from some one and indeed many elements. You cannot suppose a first unless that first be something definite and more or less definitely supposed. Finally, though it is easy to distinguish the three categories from one another, it is extremely difficult accurately and sharply to distinguish each from other conceptions so as to hold it in its purity and yet in its full meaning.

1892 | The Critic of Arguments. II. The Reader is Introduced to Relatives | CP 3.422

Such, at least, is the doctrine I have been teaching for twenty-five years, and which, if deeply pondered, will be found to enwrap an entire philosophy. Kant taught that our fundamental conceptions are merely the ineluctable ideas of a system of logical forms; nor is any occult transcendentalism requisite to show that this is so, and must be so. Nature only appears intelligible so far as it appears rational, that is, so far as its processes are seen to be like processes of thought. I must take this for granted, for I have no space here to argue it. It follows that if we find three distinct and irreducible forms of rhemata, the ideas of these should be the three elementary conceptions of metaphysics. That there are three elementary forms of categories is the conclusion of Kant, to which Hegel subscribes; and Kant seeks to establish this from the analysis of formal logic. Unfortunately, his study of that subject was so excessively superficial that his argument is destitute of the slightest value. Nevertheless, his conclusion is correct; for the three elements permeate not only the truths of logic, but even to a great extent the very errors of the profounder logicians. I shall return to them next week. I will only mention here that the ideas which belong to the three forms of rhemata are firstness, secondness, thirdness; firstness, or spontaneity; secondness, or dependence; thirdness, or mediation.

1894 [c.] | The List of Categories: A Second Essay | CP 1.300

The list of categories, or as Harris, the author of Hermes, called them, the “philosophical arrangements,” is a table of conceptions drawn from the logical analysis of thought and regarded as applicable to being. This description applies not merely to the list published by me in 1867, and which I here endeavor to amplify, but also to the categories of Aristotle and to those of Kant. The latter have been more or less modified by different critics, as Renouvier, and still more profoundly by Hegel. My own list grew originally out of the study of the table of Kant.

1896 [c.] | Logic of Mathematics: An attempt to develop my categories from within | CP 1.423

We have already seen clearly that the elements of phenomena are of three categories, quality, fact, and thought.

1898 | Cambridge Lectures on Reasoning and the Logic of Things: Detached Ideas on Vitally Important Topics. Lecture II | CP 4.3

But though there was more unity than in Kant’s system, still, as the subject stood, there was not as much as might be desired. Why should there be three principles of reasoning, and what have they to do with one another? This question, which was connected with other parts of my schedule of philosophical inquiry that need not be detailed, now came to the front. Even without Kant’s categories, the recurrence of triads in logic was quite marked, and must be the croppings out of some fundamental conceptions. I now undertook to ascertain what the conceptions were. This search resulted in what I call my categories. I then named them Quality, Relation, and Representation. But I was not then aware that undecomposable relations may necessarily require more subjects than two; for this reason Reaction is a better term. Moreover, I did not then know enough about language to see that to attempt to make the word representation serve for an idea so much more general than any it habitually carried, was injudicious. The word mediation would be better. Quality, reaction, and mediation will do. But for scientific terms, Firstness, Secondness, and Thirdness, are to be preferred as being entirely new words without any false associations whatever. How the conceptions are named makes, however, little difference. I will endeavor to convey to you some idea of the conceptions themselves. It is to be remembered that they are excessively general ideas, so very uncommonly general that it is far from easy to get any but a vague apprehension of their meaning… .

1898 [c.] | Comments on 'On a New List of Categories' | CP 1.563

As early as 1860, when I knew nothing of any German philosopher except Kant, who had been my revered master for three or four years, I was much struck with a certain indication that Kant’s list of categories might be a part of a larger system of conceptions. For instance, the categories of relation – reaction, causality, and subsistence – are so many different modes of necessity, which is a category of modality; and in like manner, the categories of quality – negation, qualification, degree, and intrinsic attribution – are so many relations of inherence, which is a category of relation. Thus, as the categories of the third group are to those of the fourth, so are those of the second to those of the third; and I fancied, at least, that the categories of quantity, unity, plurality, totality, were, in like manner, different intrinsic attributions of quality. Moreover, if I asked myself what was the difference between the three categories of quality, the answer I gave was that negation was a merely possible inherence, quality in degree a contingent inherence, and intrinsic attribution a necessary inherence; so that the categories of the second group are distinguished by means of those of the fourth; and in like manner, it seemed to me that to the question how the categories of quantity – unity, plurality, totality – differ, the answer should be that totality, or system, is the intrinsic attribution which results from reactions, plurality that which results from causality, and unity that which results from inherence. This led me to ask, what are the conceptions which are distinguished by negative unity, qualitative unity, and intrinsic unity? I also asked, what are the different kinds of necessity by which reaction, causality, and inherence are distinguished? I will not trouble the reader with my answers to these and similar questions. Suffice it to say that I seemed to myself to be blindly groping among a deranged system of conceptions; and after trying to solve the puzzle in a direct speculative, a physical, a historical, and a psychological manner, I finally concluded the only way was to attack it as Kant had done from the side of formal logic.

1902 | Minute Logic: Chapter I. Intended Characters of this Treatise | CP 2.84

I essay an analysis of what appears in the world. It is not metaphysics that we are dealing with: only logic. Therefore, we do not ask what really is, but only what appears to everyone of us in every minute of our lives. I analyze experience, which is the cognitive resultant of our past lives, and find in it three elements. I call them Categories.

1902 | Minute Logic: Chapter I. Intended Characters of this Treatise | CP 2.87

There is no fourth, as will be proved. This list of categories may be distinguished from other lists as the Ceno-Pythagorean Categories, on account of their connection with numbers. They agree substantially with Hegel’s three moments. Could they be attributed to any thinker in well-known history, that would be almost enough to refute their claims to primitivity. It has occurred to me that perhaps Pythagoras brought them from Media or Aria; but careful examination has convinced me that there was not among the Pythagoreans the smallest approach to anything resembling the categories.

1903 | Letters to William James | CP 8.264-5

It rather annoys me to be told that there is anything novel in my three categories; for if they have not, however confusedly, been recognized by men since men began to think, that condemns them at once. To make them as distinct as it is in their nature to be is, however, no small task. I do not suppose they are so in my own mind; and evidently, it is not in their nature to be sharp as ordinary concepts. But I am going to try to make here a brief statement that, I think, will do something for them.

By the phenomenon I mean whatever is before our minds in any sense. The three categories are supposed to be the three kinds of elements that attentive perception can make out in the phenomenon.

1903 | Harvard Lectures on Pragmatism: Lecture I | CP 5.38

Hegel was quite right in holding that it was the business of this science to bring out and make clear the Categories or fundamental modes. He was also right in holding that these Categories are of two kinds; the Universal Categories all of which apply to everything, and the series of categories consisting of phases of evolution.

1903 | Harvard Lectures on Pragmatism: Lecture II | CP 5.43

A very moderate exercise of this third faculty suffices to show us that the word Category bears substantially the same meaning with all philosophers. For Aristotle, for Kant, and for Hegel, a category is an element of phenomena of the first rank of generality. It naturally follows that the categories are few in number, just as the chemical elements are. The business of phenomenology is to draw up a catalogue of categories and prove its sufficiency and freedom from redundancies, to make out the characteristics of each category, and to show the relations of each to the others. I find that there are at least two distinct orders of categories, which I call the particular and the universal. The particular categories form a series, or set of series, only one of each series being present, or at least predominant, in any one phenomenon. The universal categories, on the other hand, belong to every phenomenon, one being perhaps more prominent in one aspect of that phenomenon than another but all of them belonging to every phenomenon. I am not very well satisfied with this description of the two orders of categories, but I am pretty well satisfied that there are two orders.

1903 | CSP's Lowell Lectures of 1903. 2nd Part of 3rd Draught of Lecture III | CP 1.525

I will, however, make a few remarks on these categories. By way of preface, I must explain that in saying that the three, Firstness, Secondness, and Thirdness, complete the list, I by no means deny that there are other categories. On the contrary, at every step of every analysis, conceptions are met with which presumably do not belong to this series of ideas.

1903 | Syllabus: Syllabus of a course of Lectures at the Lowell Institute beginning 1903, Nov. 23. On Some Topics of Logic | EP 2:272

In the ideas of Firstness, Secondness, and Thirdness, the three elements, or Universal Categories, appear under their forms of Firstness. They appear under their forms of Secondness in the ideas of Facts or Firstness, or Qualia, Facts of Secondness, or Relations, and Facts of Thirdness, or Signs; and under their forms of Thirdness in the ideas of Signs of Firstness, or Feeling, i.e., things of beauty; Signs of Secondness, or Action, i.e., modes of conduct; and Signs of Thirdness, or Thought, i.e., forms of thought.

1904 | Letters to Lady Welby | CP 8.329

The cenopythagorean categories are doubtless another attempt to characterize what Hegel sought to characterize as his three stages of thought. They also correspond to the three categories of each of the four triads of Kant’s table. But the fact that these different attempts were independent of one another (the resemblance of these Categories to Hegel’s stages was not remarked for many years after the list had been under study, owing to my antipathy to Hegel) only goes to show that there really are three such elements.

1904 | A Brief Intellectual Autobiography by Charles Sanders Peirce | Peirce, 1983, p. 77; MS [R] L107(s):7

As to phenomenology, [Peirce] is of opinion that there are at least two sets of categories. After devoting two years to the study of one of these, which corresponds with Hegel’s categories, he became discouraged by the difficulty of attaining any satisfactory approach to certainty, and abandoned the subject. On the other hand, he has found another set, corresponding to Hegel’s three stages, more easy to investigate and extremely useful. He calls these the cenopythagorean categories. They are three in number, Firstness, Secondness, and Thirdness.

1904 | A Brief Intellectual Autobiography by Charles Sanders Peirce | Peirce, 1983, p. 72; MS [R] L107:22

In phenomenology, [Peirce] is of opinion that there are two sets of categories, a long list and a short one; and he admits that there may possibly be still others. Though he devoted two years to the study of the long list, he attained no satisfactory results. The shorter list is called by [the] easily remembered designation of the cenopythagorean categories. These are Firstness, Secondness, and Thirdness.

1905 [c.] | Letters to Mario Calderoni | CP 8.213

I use the word phaneron to mean all that is present to the mind in any sense or in any way whatsoever, regardless of whether it be fact or figment. I examine the phaneron and I endeavor to sort out its elements according to the complexity of their structure. I thus reach my three categories.

1907 | Pragmatism | CP 1.560

In my studies of Kant’s great Critic, which I almost knew by heart, I was very much struck by the fact that, although, according to his own account of the matter, his whole philosophy rests upon his “functions of judgment,” or logical divisions of propositions, and upon the relation of his “categories” to them, yet his examination of them is most hasty, superficial, trivial, and even trifling, while throughout his works, replete as they are with evidences of logical genius, there is manifest a most astounding ignorance of the traditional logic, even of the very Summulæ Logicales, the elementary schoolbook of the Plantagenet era. [—] I was thus stimulated to independent inquiry into the logical support of the fundamental concepts called categories.