25 Jul 2016

Peirce (CP1.326-1.329) Collected Papers of Charles Sanders Peirce, Vol1/Bk3/Ch2/B/§4, "The Dyad", summary


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.]



Summary of


Charles Sanders Peirce


Collected Papers of Charles Sanders Peirce


Volume 1: Principles of Philosophy


Book 3: Phenomenology


Chapter 2: The Categories in Detail


B: Secondness


§4: The Dyad [1.326-1.329]



Brief summary:

In a dyad, there are two parts that have entered into a union such that they maintain their individuality while also taking on the property of being in a united partnership. Corresponding to each member is a perspective of the whole that takes as its point of origin one member looking out toward the other, and this perspective is also called a “side” of the dyad. An illustration is when in Genesis God said “Let there be light” and there was light. Here there is the dyad of members, God and the created light. There is no third member, not even the act. For, this act is the bond inherent to the dyad and not somehow external or additional to it. And the two sides can be understood in the following way. One side is God commanding, and thereby causing, light to come into existence, and the other side is light’s appearing, which makes God become its creator through its own arising into existence. The first perspective captures the active, primary, fundamental, side of the dyad, while the other perspective captures the  passive, derivative, secondary side of this dyad. We also notice in this example that there was no delay between God’s fiat and the light coming to be. Were there such a mediation, that would have been a third and thus not a dyad. Such a mediating third could also be a reason or a law that makes one thing follow from another. So there is no such reason or law in dyads. We can also conclude that existence is solely a matter of dyads. We know that existence is not in monads, as they are pure potentialities or “may-bes”. And triads are matters of generalities rather than particular existences. (We also know from section 1.298 that there are no higher forms than triads).  Therefore, existence belongs exclusively to dyads. And to exist also means that there are forces causing something to sustain itself despite opposing forces acting against its existence. We say that monads have Being (in that they, as possibilities, are real and they are what they are), but only dyads can exist.






[A dyad is a union of two subjects that are brought into a state of oneness. Somehow the parts maintain their individuality while also taking on the property of partnership. Corresponding to the two parts are two internal perspectives of the dyad. ]


[Frege says that a dyad consists of two subjects that have been brought into oneness. They somehow maintain both their individuality while also constituting a unified structure. The dyad somehow retains both the traits of its monads while also having those of the dyad. Furthermore, each monad making up the dyad gains something from the dyad, that is to say, the dyad “imparts a character to each of them,” and this in some sense is like imparting to the monads the character of twoness. On way the dyad can be understood is by taking one member as primarily as or as the origin of our point of view on the whole. This is one “side” of the dyad. the other way to understand the dyad is by taking the perspective of the other member to realize this other “side” of the dyad. So on the one hand there is a pair of subjects in a dyad, which are the two members themselves. But on the other hand there is this pairing as the two “sides” or internal perspectives of the dyad. Peirce says these sides have their mode of union. I am not sure what he means. Perhaps he means either that they have as their mode that of union, or perhaps he is saying they have their own sort of union, distinct from that of the members understood as constituents rather than as sides. Furthermore, each side has a special character resulting from its being a subject of the dyad. (Recall from section 1.303 that a monad cannot be conceived complexly. Its constitution is singular, as it is not made of parts or aspects.) A dyad, then, unlike a monad, has a variety of features that express dyadic relations.]

A dyad consists of two subjects brought into oneness. These subjects have their modes of being in themselves, and they also have their modes of being, as first and second, etc., in connection with each other. They are two, if not really, at least in aspect. There is also some sort of union of them. The dyad is not the subjects; it has the subjects as one element of it. It has, besides, a suchness of monoidal character; and it has suchness, or suchnesses, peculiar to it as a dyad. The dyad brings the subjects together, and in doing so imparts a char- | acter to each of them. Those characters are, in some sense, two. The dyad has also two sides according to which subject is considered as first. These two sides of the dyad form a second pair of subjects attached to the dyad; and they have their mode of union. Each of them also has a special character as a subject of the dyad.


This description shows that the dyad, in contrast to the monad, has a variety of features; and all these features present dyadic relations.





[Peirce gives as an example of a dyad, God, who is creating light. Here we can only think of these two members with the act of creation being the unifying factor. One aspect is God doing the creating with light being created. The other aspect is light being created and causing God to become the creator.]


[Peirce will give an example of a dyad, although it is a bit odd. He notes how God said, let there be light, and then there was light. In order to understand this as a dyad, we must only think of there being God who is creating light by declaring it to be. We must only think of there being the two subjects, God and the light. We cannot include third elements like this being a verse from the book of Genesis (for here the third member is the book of Genesis), nor should we think of it as a proposition that we can either believe or not (for here the third member is we ourselves). We also should not think of there being two parts to the event, namely, the fiat (which would be like a cause) and the coming to be of the light (which would be like the effect). Rather, the fiat and the coming to be of the light are in “one indivisible fact”. Furthermore, although we have the two subjects, God and the light, and although we also have the act of creation relating the two, we should not think of that act of creation a third member. But how Peirce has us conceive it is a little vague. He says that we should think of it “merely as the suchness of connection of God and light”. I am not sure exactly what that means, but perhaps the idea is that the members are united into a dyad and that unity has a certain quality in this case, namely the quality of creation. I am guessing. Peirce then says that the dyad is the fact, and this fact determines the existence of the light and the creatorship of God. Here perhaps he is thinking of the two sides of the dyad, but I am not sure. In that case, the one singular fact of the unity can be seen as having two sides, that of creating and being created. Specifically, one side is God compelling light to come into existence, and the other side is light making God become its creator by it coming into existence through his power. But still we see that one aspect captures the active, primary, fundamental sides while the other aspect captures the, passive, derivative, secondary side of this particular dyadic relation. Peirce might be saying that all dyadic relations have two sides that can be characterized this way, (as having active/passive sides), but I am not entirely sure.]

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. This last is in the present example merely a mere point of view, without any reality corresponding to it. That is one of the special features of the particular example chosen. Of the two aspects of the dyad, then, one is in this instance, fundamental, real, and primary, while the other is merely derivative, formal, and secondary.

(Peirce 164)




[In the example of God creating light, there is an instantaneous act with no mediation and thus no third between God and the coming to be of the light. Dyad’s cannot be governed by reason or law, as this would also be a third (and thirdness should in fact be understood as such a mediation). Existence is not in monads, as they are potentialities. And triads involve generalities rather that existences. So since dyads are immediate, existence is purely dyadic.]


[Peirce explains that he chose this example because there is no intermediating time or process between God’s fiat and the coming to be of the light. The creation is instantaneous. Were there some time or intervening process, then there would be a third member and thus it would not be a dyad. He adds that thirdness can be understood as mediation. This furthermore means that a dyadic event cannot be guided by any reason or law, as this would mediate between the members and serve to connect them. Rather, the event needs to be an act of “arbitrary will or of blind force”. So there is no generality to be understood in a dyad. It is an individual fact and not somehow expressive of a general law. (Recall also from section 1.303 that the monad cannot be understood as an object, because that would require conceiving it in terms of a second thing in relation to which it is an object. And recall also from section 1.304 that the pure quality of feeling, which is monadic, exists as a “may-be” in the sense that it could be said to inhere in some object or be a part of some experience, but if it is not in either of these, it exists no less. In this section I wrote in summary of this idea (the following between ellipsis is copied from that entry). ...

the pure quality of feeling of hearing the train whistle is something that somehow is to be understood as existing apart of our experience of it. So they do not merely exist as being something concretely experienced in the present. Rather, they exist as “may-bes”, because in some way they are distinct from the concrete experiences that may or may not be experiences of these qualities. He seems to demonstrate this distinction with an odd example. He writes, “the word red means something when I say that the precession of the equinoxes is no more red than it is blue, and that it means just what it means when I say that aniline red is red.” But normally we think that qualities are qualities of one thing or another. But qualities of feeling are not to be thought of as inhering in anything. He contrasts qualities of feeling with things like laws. We cannot think of the law of gravity without also thinking that it would have to involve some physical objects with mass. In other words, how can the law of gravity exist if there were not things which could behave in accordance with it? However, we can think of pure qualities of feeling existing without them inhering in some object.

... As such, we might think of the monad in some sense as a potentiality. I am not sure that I follow still, but the idea for Peirce’s next point seems to be that we are not talking about monads in general but rather with monadic qualities, which are potentialities of existence rather than having existence. But a feature of being dyadic is that it exists, perhaps because it is necessarily immediate and given all on its own. Let me quote, as I am not absolutely certain.]

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. For that reason, pure dyadism is an act of arbitrary will or of blind force; for if there is any reason, or law, governing it, that mediates between the two subjects and brings about their connection. The dyad is an individual fact, as it existentially is; and it has no generality in it. The being of a monadic quality is a mere potentiality, without existence. Existence is purely dyadic.





[Being is monadic, as monads are real (even if they are merely potentialities) and thus have being ,but they do not exist, as they cannot be said to be in an oppositional relation with anything else. Existence, as something only dyads can be said to have, is a matter of oppositional forces, as in order for something to existence in some place at some time, it must be able to hold itself together despite other forces acting against it then and there.]


[The next paragraph is very dense and complex, so please refer to the quotation to follow. Let us still try to work through it. We should first try to distinguish Being from existence. Monads (and thus I assume pure qualities) have Being. We do not deny that they are what they are, or that they are real, but we say their are “may-bes” or potentialities. They are what they are and they are real without needing to actually exist in some determinate way. So we can speak of a pure quality, and affirm that it is real, but we do not necessarily say that the quality exists. In order to do so, we would need to place it into an oppositional relation with other actual things, which would mean that it becomes a dyad and thus can no longer be said to be a monad. Now, for things to exist, it is not enough to just be a dyad. The dyadic relations that constitute existence are competitive in some way. For something to exist, there must be some forces which allow it to survive in the face of other forces opposing it and working against its existence. Peirce will use the quote, “The very hyssop that grows on the wall exists in that chink because the whole universe could not prevent it”. We also said that dyads and thus existence do not involve mediating thirds like laws. So Peirce will also say that no law can make something exist. (Something does not exist because some law made it exist but rather it exists because it has been forced to exist or it forces itself to exist despite opposing forces). The next point is not so clear to me. Peirce then says that existence is a presence in some experiential universe. If we are talking about bare physics, and he uses the example of atoms, then it would seem odd to consider such a physical world an experiential one, as if rocks had experiences. I am not sure how we are to interpret this, but we might consider the following things. Peirce we saw previously (in section 1.311 and section 1.313) has a panpsychic perspective of the physical world. So perhaps here he means that things like rocks do have experiences insofar as they are affected by other things. Or perhaps we put aside the idea of panpsychism, and we merely just consider any “dynamical reaction” of one thing and another as constituting an experience of some sort, even if there are no inner states of awareness involved.]

It is to be noted that existence is an affair of blind force. “The very hyssop that grows on the wall exists in that chink because the whole universe could not prevent it.” No law determines any atom to exist. Existence is presence in some experiential universe – whether the universe of material things now existing, or that of laws, or that of phenomena, or that of feelings – and this presence implies that each existing thing is in dynamical reaction with every other in that universe. Existence, therefore, is dyadic; though Being is monadic.




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 [1931].



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