by Corry Shores
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[The following is summary. Boldface and bracketed commentary are mine. Proofreading is incomplete, so please forgive my typos.]
Charles Sanders Peirce
Collected Papers of Charles Sanders Peirce
Volume 1: Principles of Philosophy
Book 3: Phenomenology
Chapter 2: The Categories in Detail
§1: Examples of Thirdness [1.337]
A “third” is what weaves intermediary parts between extremities together so to organize the extremities and parts into a more coherent whole. But what is being woven together is not just these parts but as well two structures, namely, the monadic and the dyadic structures. For example, a position is a first (that is, it is monadic). However, velocity (as the dyadic relation between position in correlation with time) or the relation of two successive positions (just their bare coordination) is a second (that is, a dyad). Acceleration (which is the correlation between velocity and time, that is, between a second and a first) or the relation of three successive positions third (that is, a triad). By merely relating two positions, we do not have continuity between them. Rather, we just have a dyadic relation. But when we relate three successive positions, we have a mediation (by means of a third point) that brings the two extremities into a coherent interwoven whole; and thereby we have continuity, which is a perfect example of a third. While action is a second, conduct (which mediates our actions) is a third. Law as a force that effects the world is a second, but legislation and order (which mediate the competing interests of the world) is a third. And sympathy, which mediates between different people emotionally, is a third.
[Thirdness is a mediation between two extremities, with one of the extremities being a first and the other a second, and as well it mediates between a structure with firstness and a structure with secondness. That mediation cannot be a simple immediate direct relation. It needs to be filled-out with parts of some sort (including for example the phases of a process) that are woven together by the third in such a way as to bridge the extremities and combine the structures.]
[Peirce defines the third as “the medium or connection bond between the absolute first and last”. And thus “The beginning is first, the end second, the middle third”. So “The end is second, the means third”. Peirce then gives a series of examples to illustrate thirdness. At this point the idea is not very clear to me, but let us look at the examples. The first is that “the thread of life is a third; the fate that snips it, its second”. I wonder if he means the third is the continuity of life between birth and death which links its extremities into a coherent whole. The next example is that a fork in the road is a third. It supposes three ways, which I suppose are the one road plus the two it branches into. (Perhaps what is important here is that we have a first, namely the single road before it forks, or simply just any of the roads taken by themselves, and we have a second, which is the juncture of any of the two roads, perhaps particularly the ones that are forking. And finally there is the forking intersection itself, which unites the firstness of mere being a road with the secondness of being a divergence between roads, and constituting the third as the mediation between juncture and path. I am just making a wild guess.) It seems his next example is not about a fork in the road, but I am not sure, because it is about roads and the clause is connected by a semi-colon to the sentence about forked roads. The next idea then seems to be that a singular straight road that connects two locations can be understood either as a second or a third. If we only think of it as a connection between two places, it is a second. But if we instead think of it as passing through intermediate places, it is a third. I do not grasp that difference very firmly. Apparently to be a third, you cannot simply be a path between extremities. There needs to be internal parts that are woven together. But I am not sure why. He says that position is first, velocity (which is position correlated to time) or the relation between two successive positions is second, and acceleration (which is velocity correlated to time) or the relation of three successive positions is third. However, velocity understood as something continuous also involves a third. So before we continue with that point, let us try to articulate what thirdness seems to be from these distinctions. When examining secondness and dyads in section 1.327, he said that when the link between the two things in the dyad is immediate, that relation does not constitute a third. With the example of God creating light, the act was like the bond between the two parts, but not as a third thing, but something inherent to them both insofar as they form a coherent dyad.
As an example of a dyad take this: God said, Let there be light, and there was light. We must not think of this as a verse of Genesis, for Genesis would be a third thing. Neither must we think of it as proposed for our acceptance, or as held for true; for we are third parties. We must simply think of God creating light by fiat. Not that the fiat and the coming into being of the light were two facts; but that it is in one indivisible fact. God and light are the subjects. The act of creation is to be regarded, not as any third object, but merely as the suchness of connection of God and light. The dyad is the fact. It determines the existence of the light, and the creatorship of God. The two aspects of the dyad are, first, that of God compelling the existence of the light, and that of the light as, by its coming into existence, making God a creator.
In section 1.327 Peirce further explained that in this example, the causal event is instantaneous. Were it not, then it would have constituted a third, as it would be a mediation.
I chose this instance because it is represented as instantaneous. 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.
I am not certain still how to grasp what makes something a third. But one idea here seems to be that a bare relation or connection is not a third unless it has something (some kind of content) that fills it out somehow. That filling-out might be more parts to it that are woven together. Or it could be a process perhaps with its own distinct phases. At any rate, continuity itself should be considered thirdness “almost to perfection”. This is perhaps because continuity implies a mediation over variation. Peirce further says that moderation is a kind of thirdness, but I am not sure why. Perhaps because it is a mediation between extreme tendencies, and its contents would perhaps be the little from each extreme that it weaves together. His next point is that the positive form of an adjective (e.g. fast) is a first, the superlative (e.g. fastest) is a second, and the comparative (e.g. faster) is a third. But I do not know why a superlative is a second. And also, it is not so clear to me why a comparative is a third, when it would seem to be a bare relation rather than something with some substantial content to it. He then says that action is a second but conduct is a third. That conduct is a third would seem to be on account of one managing their behaviors and mediating their tendencies. But that action would be a second I am not sure why. I suppose it is in the sense of volition, effort, and resistance. He next says that law as an active force is second. Perhaps this would be for example when the police enforce the law or when a change in the law forces people to make changes in certain situations. But, he continues, order and legislation are thirds. I am not sure what this means exactly, but perhaps the idea again is that legislation is a matter of managing legal issues and creating laws that fit within a larger context of other related laws. Order is perhaps a third because it is attained by mediating competing interests by means of law. His final example is that sympathy is a third. If I had to guess why, I would say that sympathy is a means by which different people come into mediating relations with one another.]
By the third, I mean the medium or connecting bond between the absolute first and last. The beginning is first, the end second, the middle third. The end is second, the means third. The thread of life is a third; the fate that snips it, its second. A fork in a road is a third, it supposes three ways; a straight road, considered merely as a connection between two places is second, but so far as it implies passing through intermediate places it is third. Position is first, velocity or the relation of two successive positions second, acceleration or the relation of three successive positions third. But velocity in so far as it is continuous also involves a third. Continuity represents Thirdness almost to perfection. Every process comes under that head. Moderation is a kind of Thirdness. The positive degree of an adjective is first, the superlative second, the comparative third. All exaggerated language, “supreme,” “utter,” “matchless,” “root and branch,” is the furniture of minds which think of seconds and forget thirds. Action is second, but conduct is third. Law as an active force is second, but order and legislation are third. Sympathy, flesh and blood, that by which I feel my neighbor's feelings, is third.
Peirce, C.S. Collected Papers of Charles Sanders Peirce, Vol 1: Principles of Philosophy. In Collected Papers of Charles Sanders Peirce [Two Volumes in One], Vols. 1 and 2. Edited by Charles Hartshorne and Paul Weiss. Cambridge, Massachusetts: 1965 .