5 Jun 2016

Peirce (CP1.288–1.292) Collected Papers of Charles Sanders Peirce, §2, “Valencies"


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 1: Introduction


§2: Valencies [1.288–1.292]




Brief summary:

Peirce’s phenomenology is a phaneroscopy; it will give a taxonomy of types of phanerons (phenomena). It will do so by distinguishing the phanerons on the basis of the types of their indecomposable parts’ structures. We cannot distinguish one indecomposable part from another by means of their internal structures, as they have none. Instead, we must distinguish them on the basis of an external structure. The only viable candidate for such an external structure is valency, which is the number of relational bonds one part may make with other parts. The indecomposable parts of phanerons can only take one of three possible valency structures: monadic [valency of 1, only self-relatable, to make a singular structure], dyadic [valency of 2, forming only one bond with another, to make a paired structure], and triadic [valency of 3, forming two bonds to make a tripled structure]. It is not really possible for a phaneron’s indecomposable part to have no valency, that is, to be medadic [and as such it would be unable to form even a stable self-relation]. However, were it to be so, it would come into and pass out of our awareness instantaneously, without registering in our memory. 







[Peirce’s taxonomy of types of phanerons will distinguish them on the basis of the differences in their indecomposable parts’ structures.]


[Recall from sections 1.284–1.287 that the phaneron is the sum of all phanerons, which are anything that can come before the mind’s awareness (in other words, they are phenomena in the phenomenological sense). This means that] we should always be able to determine that something is a phaneron so long as it is something that has come to our phenomenal awareness.  We next consider the elements of the phaneron that are logically indecomposable or at least that under our direct inspection we cannot decompose into smaller parts. Peirce will now attempt to produce a taxonomy of types of these indecomposable phenomenal components. There may be many ways to do this, of which Peirce is aware of two: one of them divides the types according the form of the indecomposable parts’ structures and the other divides the types according to the indecomposable parts’ matters. After much work on the second type, Peirce abandoned it, and now favors the method based on structure.

There can be no psychological difficulty in determining whether anything belongs to the phaneron or not; for what- | ever seems to be before the mind ipso facto is so, in my sense of the phrase. I invite you to consider, not everything in the phaneron, but only its indecomposable elements, that is, those that are logically indecomposable, or indecomposable to direct inspection. I wish to make out a classification, or division, of these indecomposable elements; that is, I want to sort them into their different kinds according to their real characters. I have some acquaintance with two different such classifications, both quite true; and there may be others. Of these two I know of, one is a division according to the form or structure of the elements, the other according to their matter. The two most passionately laborious years of my life were exclusively devoted to trying to ascertain something for certain about the latter; but I abandoned the attempt as beyond my powers, or, at any rate, unsuited to my genius. I had not neglected to examine what others had done but could not persuade myself that they had been more successful than I. Fortunately, however, all taxonomists of every department have found classifications according to structure to be the most important.





[Since the indecomposable parts cannot be said to have an internal composition on the basis of which we might distinguish one type from another, we instead will use the external trait of valency, which, like in chemistry, means the number of connecting bonds one type can make with other types.]


[Peirce seems to first make the following point. If we decompose something into its indecomposable parts, that means we cannot distinguish one such part from another on the basis of their internal features. For, to do so would mean that one has a different internal composition than the others. But since they are indecomposable, that means they do not have any internal parts on the basis of which we might distinguish one from the other by means of their internal features. However, we could distinguish them on the basis of how one sort can interact with others, perhaps something like how we note as among the properties of a chemical substance its manners of interaction (or its non-interactability) with other materials. I regret that I do not know anything about chemistry. It seems that the divisions of chemical elements that Peirce gives corresponds roughly with the vertical groupings of elements in the periodic table. So the noble gasses, which tend not to form compounds with other elements, are roughly the elements that Peirce  calls medads, because they have a valency of 0. I suspect then that the next group of elements are those that tend to form a singular bond with other elements, and they are called monads. And so on through the rest of the groupings. Maybe the reason that these groupings do not correspond exactly to the periodic table groups is because the science of chemistry has since learned new things that contradict what was known at Peirce’s time. Let me quote.]

A reader may very intelligently ask, How is it possible for an indecomposable element to have any differences of structure? Of internal logical structure it would be clearly impossible. But of external structure, that is to say, structure of its possible compounds, limited differences of structure are possible; witness the chemical elements, of which the "groups," or vertical columns of Mendeléeff's table, are universally and justly recognized as ever so much more important than the "series," or horizontal ranks in the same table. Those columns are characterized by their several valencies, thus:

He, Ne, A, Kr, X are medads (μηδέν [méden] none + the patronymic = ιδης [idés]).

H, L [Li], Na, K, Cu, Rb, Ag, Cs,-,-, Au, are monads;

G [Gl], Mg, Ca, Zn, Sr, Cd, Ba, -,-, Hg, Rd [Ra], are dyads;

B, Al, Sc, Ga, Y, In, La, -, Yb, Tc [Tl], Ac are triads;

C, Si, Ti, Ge, Zr, Sn, Co [Ce], -, -, Pc [Pb], Th, are tetrads;

N, P, V, As, Cb, Sb, Pr [Nd], -, Ta, Bi, Po [Pa], are properly pentads (as PCL[5], though owing to the junction of two pegs they often appear as triads. Their pentad character is particularly required to explain certain phenomena of albumins);

O, S, Cr, Se, Mo, Te, Nd [Sm], -, W, -, U, are properly | hexads (though by junction of bonds they usually appear as dyads);

F, Cl, Mn, Br, -, I, are properly heptads (usually appearing as monads);

Fe, Co, Ni, Ru, Rh, Pd, -, -, -, Os, Tr [Ir], Pt, are octads; (Sm, Eu, Gd, Er, Tb, Bz [?], Cl [Ct], are not yet placed in the table.)





[First Peirce will need to deal with the problem of him importing other notions into his phaneroscopy.]


In a similar manner to how chemical substances are grouped by valency, Peirce will distinguish types of phanerons on the basis of the valencies of their indecomposable parts. [But recall from section 1.287 that Peirce said his methodology will only involve an examination of the phenomenal givens and that it will not import other theories into the study of phanerons. Yet, here he seems to be doing just that with this notion of valency that we find in chemistry.] But this means that before moving on to the actual analysis of phanerons, Peirce will first need to deal with the problem of him importing preconceived notions into his phenomenological study.

So, then, since elements may have structure through valency, I invite the reader to join me in a direct inspection of the valency of elements of the phaneron. Why do I seem to see my reader draw back? Does he fear to be compromised by my bias, due to preconceived views? Oh, very well; yes, I do bring some convictions to the inquiry. But let us begin by subjecting these to criticism, postponing actual observation until all preconceptions are disposed of, one way or the other.





[Given the unviability of the one other possible method, it is necessary that we use valency to differentiate types of indecomposable phaneron parts.]


[(I do not follow this section, so you can skip to the quotation below.) For one reason or another, Peirce will now ask whether or not valency is the sole formal way that phanerons can possibly differ from one another. I am not sure what this has to do with preconceptions, as mentioned in the prior section. Perhaps the idea is that if he can show that it is necessary for us to use valency, then it does not matter if it is preconceived, because it is the only means and so it is necessary and thus furthermore we might have arrived upon it naturally anyway. (For, we would not have arrived upon any other means.) Putting aside the motivations for the question, the answer Peirce gives, and he admits this, is very puzzling, and I will not be able to give a good interpretation. To understand it, we need to know what he means by “relations between bonds”. Relations between parts I would think are bonds. But what are relations between bonds? Is it a numerical relation, as in one bond has for example two more valency values than another one? Or can one bond (holding between parts) create a relation of some sort with the others, like a bond between bonds themselves? The only sense I can give “relations between bonds” are the numerical valency relations. But then it gets even more confusing. We need next to distinguish (a) divisions by variations of such relations between bonds from (b) divisions according to valency. But according to the only sense I can give to (a), I am unable to distinguish it from (b). So without understanding the meanings here, I cannot give any interpretation for the first part of 1.291. I quote it below for your own interpretation. The next part I also cannot interpret. It seems we need to know about his notion of the ten trichotomies of signs. He shows then that the total number of classes for them is 59049. I am not sure what this has to do with phanerons. My best guess regarding the overall points is the following, but I caution that it is almost certainly wrong. The main idea seems to me to be that there is a pragmatic reason why we need to use valency as the determining trait. For, it will keep the number of classes down to a very small number. Were the number too large, it would no longer serve a taxonomic purpose, because we want to make the types comprehensible rather than incomprehensible. And they would become incomprehensible if there too many of them. Now, were we not to use valency, we would be using another means (I do not know what) which happens to make way to many classes. (That other means might for example be to classify the types on the basis of every possible combination of parts rather than on the number of other things each one sort tends to combine with. But I just guess.) So since this other way does not suit the purpose of the examination, we have just valency as the only viable means.]

First, then, let us ask whether or not valency is the sole formal respect in which elements of the phaneron can possibly vary. But seeing that the possibility of such a ground of division is dependent upon the possibility of multivalence, while the possibility of a division according to valency can in nowise be regarded as a result of relations between bonds, it follows that any division by variations of such relations must be taken as secondary to the division according to valency, if such division there be. Now (my logic here may be puzzling, but it is correct), since my ten trichotomies of signs, should they prove to be independent of one another (which is to be sure, highly improbable), would suffice to furnish us classes of signs to the number of

310 = (32)5 = (10-1)5 = 105 - 5.104
+ 10.103 - 10.102
+ 5.10 - 1
= 50000
+ 9000
+ 49
= 59049

(Voilà a lesson in vulgar arithmetic thrown in to boot!), which | calculation threatens a multitude of classes too great to be conveniently carried in one’s head, rather than a group inconveniently small, we shall, I think, do well to postpone preparations for further divisions until there be prospect of such a thing being wanted.





[Phaneron elements can only be monads, dyads, and tetrads.]


So since we are using valency to divide phaneron elements, we will be finding them to be medads, monads, dyads, and the like. [We will for some reason think of the different ‘-ads’ as being ideas. Medads are indecomposable ideas that are logically severed from all other indecomposable ideas. Monads are indecomposable elements that are completely characterizable without reference to other elements. Dyads’ traits are ones that are based on relations to another thing, but without referring to some third thing. A triad’s traits involve two different relations with two other things. A medadic indecomposable phaneron part is impossible for some reason, perhaps because it would have no conceptual content whatsoever, even though it could in some sense come before our minds in an absolutely fleeting way. From Peirce description of the possible phenomenal medadic part, I wonder if it would be anything like a hyletic datum in Husserl’s phenomenology or a Deleuzian phenomenal pure differential relation. Peirce then claims that signs require triads. I am not sure why, but perhaps we learn later. He then says that it is evident that a triad cannot be reduced to monads or dyads. However, I did not follow his reasoning for this. Furthermore he says it can be proven that there is no higher valency than three, but I cannot begin to guess how this could be proven.]

If, then, there be any formal division of elements of the phaneron, there must be a division according to valency; and we may expect medads, monads, dyads, triads, tetrads, etc. Some of these, however, can be antecedently excluded, as impossible; although it is important to remember that these divisions are not exactly like the corresponding divisions of Existential Graphs, which have relation only to explicit indefinites. In the present application, a medad must mean an indecomposable idea altogether severed logically from every other; a monad will mean an element which, except that it is thought as applying to some subject, has no other characters than those which are complete in it without any reference to anything else; a dyad will be an elementary idea of something that would possess such characters as it does possess relatively to something else but regardless of any third object of any category; a triad would be an elementary idea of something which should be such as it were relatively to two others in different ways, but regardless of any fourth; and so on. Some of these, I repeat, are plainly impossible. A medad would be a flash of mental “heat-lightning” absolutely instantaneous, thunderless, unremembered, and altogether without effect. It can further be said in advance, not, indeed, purely a priori but with the degree of apriority that is proper to logic, namely, as a necessary deduction from the fact that there are signs, that there must be an elementary triad. For were every element of the phaneron a monad or a dyad, without the relative of teridentity (which is, of course, a triad), it is evident that no triad could ever be built up. Now the relation of every sign to its object and interpretant is plainly a triad. A triad might be built up of pentads or of any higher perissad elements in many ways. But it can be proved – and really with extreme simplicity, though the statement of the general proof is confusing – that no element can have a higher valency than three.






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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