If the universe is thus progressing from a state of all but pure chance to a state of all but complete determination by law, we must suppose that there is an original, elemental, tendency of things to acquire determinate properties, to take habits. This is the Third or mediating element between chance, which brings forth First and original events, and law which produces sequences or Seconds.
The First is that whose being is simply in itself, not referring to anything nor lying behind anything. The Second is that which is what it is by force of something to which it is second. The Third is that which is what it is owing to things between which it mediates and which it brings into relation to each other.
We have seen that it is the immediate consciousness that is preeminently first, the external dead thing that is preeminently second. In like manner, it is evidently the representation mediating between these two that is preëminently third. Other examples, however, should not be neglected. The first is agent, the second patient, the third is the action by which the former influences the latter. Between the beginning as first, and the end as last, comes the process which leads from first to last.
Among thirds, there are two degrees of degeneracy. The first is where there is in the fact itself no thirdness or mediation, but where there is true duality; the second degree is where there is not even true secondness in the fact itself.
[—] Nature herself often supplies the place of the intention of a rational agent in making a thirdness genuine and not merely accidental; as when a spark, as third, falling into a barrel of gunpowder, as first, causes an explosion, as second. But how does nature do this? By virtue of an intelligible law according to which she acts. If two forces are combined according to the parallelogram of forces, their resultant is a real third. Yet any force may, by the parallelogram of forces, be mathematically resolved into the sum of two others, in an infinity of different ways. Such components, however, are mere creations of the mind. What is the difference? As far as one isolated event goes, there is none; the real forces are no more present in the resultant than any components that the mathematician may imagine. But what makes the real forces really there is the general law of nature which calls for them, and not for any other components of the resultant. Thus, intelligibility, or reason objectified, is what makes Thirdness genuine.
Had there been any process intervening between the causal act and the effect, this would have been a medial, or third, element. Thirdness, in the sense of the category, is the same as mediation.
In the contents of consciousness we recognize three sorts of elements, Firstness, Secondness, Thirdness. [—] What a Third is depends on two other things between which it mediates. Firstness is feeling-quality; secondness is brute reaction; thirdness is mediation.
Let us now take up being in futuro. As in the other cases, this is merely an avenue leading to a purer apprehension of the element it contains. An absolutely pure conception of a Category is out of the question. Being in futuro appears in mental forms, intentions and expectations. Memory supplies us a knowledge of the past by a sort of brute force, a quite binary action, without any reasoning. But all our knowledge of the future is obtained through the medium of something else. [—] Intellectual triplicity, or Mediation, is my third category. […]
Transuasion (suggesting translation, transaction, transfusion, transcendental, etc.) is mediation, or the modification of firstness and secondness by thirdness, taken apart from the secondness and firstness; or, is being in creating Obsistence.
Category the Third is the Idea of that which is such as it is as being a Third, or Medium, between a Second and its First. That is to say, it is Representation as an element of the Phenomenon.
Category the Third exhibits two different ways of Degeneracy, where the irreducible idea of Plurality, as distinguished from Duality, is present indeed but in maimed conditions. The First degree of Degeneracy is found in an Irrational Plurality which, as it exists, in contradistinction [to] the form of its representation, is a mere complication of duality. We have just had an example of this in the idea of Subdivision. In pure Secondness, the reacting correlates are Singulars, and as such are Individuals, not capable of further division. Consequently, the conception of Subdivision, say by repeated dichotomy, certainly involves a sort of Thirdness, but it is a thirdness that is conceived to consist in a second secondness.
The most degenerate Thirdness is where we conceive a mere Quality of Feeling, or Firstness, to represent itself to itself as Representation. Such, for example, would be Pure Self-Consciousness, which might be roughly described as a mere feeling that has a dark instinct of being a germ of thought. This sounds nonsensical, I grant. Yet something can be done toward rendering it comprehensible.
Now for Thirdness. Five minutes of our waking life will hardly pass without our making some kind of prediction; and in the majority of cases these predictions are fulfilled in the event. Yet a prediction is essentially of a general nature, and cannot ever be completely fulfilled. To say that a prediction has a decided tendency to be fulfilled, is to say that the future events are in a measure really governed by a law. If a pair of dice turns up sixes five times running, that is a mere uniformity. The dice might happen fortuitously to turn up sixes a thousand times running. But that would not afford the slightest security for a prediction that they would turn up sixes the next time. If the prediction has a tendency to be fulfilled, it must be that future events have a tendency to conform to a general rule. “Oh,” but say the nominalists, “this general rule is nothing but a mere word or couple of words!” I reply, “Nobody ever dreamed of denying that what is general is of the nature of a general sign; but the question is whether future events will conform to it or not. If they will, your adjective ‘mere’ seems to be ill-placed.” A rule to which future events have a tendency to conform is ipso facto an important thing, an important element in the happening of those events. This mode of being which consists, mind my word if you please, the mode of being which consists in the fact that future facts of Secondness will take on a determinate general character, I call a Thirdness.
This element of our daily & hourly experience, the element of the conformity of fact to thought, – this element whose being such as it is consists in this that it has such reference to an object independent of it as to bring a third thing (the interpretation) into the same triadic relation to that same object, – this character of a sign, the being an exponent of thought, is what I call the element of Thirdness in the phenomenon.
But we constantly predict what is to be. Now what is to be, according to our conception of it, can never become wholly past. In general, we may say that meanings are inexhaustible. We are too apt to think that what one means to do and the meaning of a word are quite unrelated meanings of the word “meaning,” or that they are only connected by both referring to some actual operation of the mind. Professor Royce especially in his great work The World and the Individual has done much to break up this mistake. In truth the only difference is that when a person means to do anything he is in some state in consequence of which the brute reactions between things will be moulded [in] to conformity to the form to which the man’s mind is itself moulded, while the meaning of a word really lies in the way in which it might, in a proper position in a proposition believed, tend to mould the conduct of a person into conformity to that to which it is itself moulded. Not only will meaning always, more or less, in the long run, mould reactions to itself, but it is only in doing so that its own being consists. For this reason I call this element of the phenomenon or object of thought the element of Thirdness. It is that which is what it is by virtue of imparting a quality to reactions in the future.
We are too apt to think that what one means to do and the meaning of a word are quite unrelated meanings of the word “meaning,” or that they are only connected by both referring to some actual operation of the mind. Professor Royce especially in his great work The World and the Individual has done much to break up this mistake. In truth the only difference is that when a person means to do anything he is in some state in consequence of which the brute reactions between things will be moulded to conformity to the form to which the man’s mind is itself moulded, while the meaning of a word really lies in the way in which it might, in a proper position in a proposition believed, tend to mould the conduct of a person into conformity to that to which it is itself moulded. Not only will meaning always, more or less, in the long run, mould reactions to itself, but it is only in doing so that its own being consists. For this reason I call this element of the phenomenon or object of thought the element of Thirdness. It is that which is what it is by virtue of imparting a quality to reactions in the future.
Let us proceed in the same way with Thirdness. We have here a first, a second, and a third. The first is a positive qualitative possibility, in itself nothing more. The second is an existent thing without any mode of being less than existence, but determined by that first. A third has a mode of being which consists in the Secondnesses that it determines, the mode of being of a law, or concept. Do not confound this with the ideal being of a quality in itself. A quality is something capable of being completely embodied. A law never can be embodied in its character as a law except by determining a habit. A quality is how something may or might have been. A law is how an endless future must continue to be.
Now in genuine Thirdness, the first, the second, and the third are all three of the nature of thirds, or thought, while in respect to one another they are first, second, and third. [—] The third is thought in its role as governing Secondness. It brings the information into the mind, or determines the idea and gives it body. It is informing thought, or cognition. But take away the psychological or accidental human element, and in this genuine Thirdness we see the operation of a sign.
… I was long ago (1867) led, after only three or four years’ study, to throw all ideas into the three classes of Firstness, of Secondness, and of Thirdness. This sort of notion is as distasteful to me as to anybody; and for years, I endeavored to pooh-pooh and refute it; but it long ago conquered me completely. Disagreeable as it is to attribute such meaning to numbers, and to a triad above all, it is as true as it is disagreeable. The ideas of Firstness, Secondness, and Thirdness are simple enough. Giving to being the broadest possible sense, to include ideas as well as things, and ideas that we fancy we have just as much as ideas we do have, I should define Firstness, Secondness, and Thirdness thus:
Firstness is the mode of being of that which is such as it is, positively and without reference to anything else.
Secondness is the mode of being of that which is such as it is, with respect to a second but regardless of any third.
Thirdness is the mode of being of that which is such as it is, in bringing a second and third into relation to each other.
I now come to Thirdness. To me, who have for forty years considered the matter from every point of view that I could discover, the inadequacy of Secondness to cover all that is in our minds is so evident that I scarce know how to begin to persuade any person of it who is not already convinced of it. Yet I see a great many thinkers who are trying to construct a system without putting any thirdness into it. Among them are some of my best friends who acknowledge themselves indebted to me for ideas but have never learned the principal lesson. Very well. It is highly proper that Secondness should be searched to its very bottom. Thus only can the indispensableness and irreducibility of thirdness be made out, although for him who has the mind to grasp it, it is sufficient to say that no branching of a line can result from putting one line on the end of another. My friend Schröder fell in love with my algebra of dyadic relations. The few pages I gave to it in my Note B in the ‘Studies in Logic by Members of the Johns Hopkins University’ were proportionate to its importance. His book is profound, but its profundity only makes it more clear that Secondness cannot compass Thirdness. (He is careful to avoid ever saying that it can, but he does go so far as to say that Secondness is the more important. So it is, considering that Thirdness cannot be understood without Secondness. But as to its application, it is so inferior to Thirdness as to be in that aspect quite in a different world.) Even in the most degenerate form of Thirdness, and thirdness has two grades of degeneracy, something may be detected which is not mere secondness. If you take any ordinary triadic relation, you will always find a mental element in it. Brute action is secondness, any mentality involves thirdness. Analyze for instance the relation involved in ‘A gives B to C.’ Now what is giving? It does not consist [in] A’s putting B away from him and C’s subsequently taking B up. It is not necessary that any material transfer should take place. It consists in A’s making C the possessor according to Law. There must be some kind of law before there can be any kind of giving, – be it but the law of the strongest. But now suppose that giving did consist merely in A’s laying down the B which C subsequently picks up. That would be a degenerate form of Thirdness in which the thirdness is externally appended. In A’s putting away B, there is no thirdness. In C’s taking B, there is no thirdness. But if you say that these two acts constitute a single operation by virtue of the identity of the B, you transcend the mere brute fact, you introduce a mental element [—]
I have not sufficiently applied myself to the study of the degenerate forms of Thirdness, though I think I see that it has two distinct grades of degeneracy. In its genuine form, Thirdness is the triadic relation existing between a sign, its object, and the interpreting thought, itself a sign, considered as constituting the mode of being of a sign.
Thirdness is that mode or element of being whereby a subject is such as it is to a second and for a third; or rather, it is the characteristic ingredient of this definition, which is prominent in the ideas of instrument, organon, method, means, mediation, betweenness, representation, communication, community, composition, generality, regularity, continuity, totality, system, understanding, cognition, abstraction, etc. [—] Thirdness is subject to two grades of degeneracy. All genuine thirdness has a mental character.
This quote has been taken from Kenneth Laine Ketner's 1983 reconstruction of Peirce's 'Autobiography'
…Thirdness, or that which is such as it is in bringing a second into relation to a third. That thirdness cannot be reduced to any combination of secondnesses follows at once from the fact that combination is itself a triadic relation; so that a combination of secondnesses would itself involve an irreducible thirdness.On the other hand, [there] can be no irreducible Fourthness or mode of being defined by a relation between more than three correlates, since it is easily shown that every such relation is definable as a triadic relation among triadic relations.
Tertiality is the Mode of Being of anything insofar as it is such as it is to a Second for a Third.
Peirce has crossed over the word "Thirdness" and replaced it with "Tertiality"
Careful analysis shows that to the three grades of valency of indecomposable concepts correspond three classes of characters or predicates. Firstly come ” firstnesses,” or positive internal characters of the subject in itself; secondly come “secondnesses,” or brute actions of one subject or substance on another, regardless of law or of any third subject; thirdly comes “thirdnesses,” or the mental or quasi-mental influence of one subject on another relatively to a third.