The Tetrast
Sketcher of various interrelated fourfolds.

Semiotic triad versus tetrad.

August 24, 2006.
(Recentest significant change: April 5, 2007 except for a long-overdue correction on October 28, 2013: I had said "recipient" when I should have said "destination").

Collateral experience

Quote C.S. Peirce, Transcribed by Joseph Ransdell from Letter to Lady Welby December 23, 1908 (and also appearing in Semiotics and Significs: Correspondence Between Charles S. Peirce and Victoria Lady Welby, Charles Hardwick, editor, Indiana U. Press, 1977, page 83):
"Its Interpretant is all that the Sign conveys: acquaintance with its Object must be gained by collateral experience."
End quote.

Quote C.S. Peirce: Collected Papers of Charles Sanders Peirce volume 8, paragraph 179 (1909) (also in The Essential Peirce volume 2, pages 493-4):
"All that part of the understanding of the Sign which the Interpreting Mind has needed collateral observation for is outside the Interpretant. .... It is...the prerequisite for getting any idea signified by the sign."
End quote.

Quote C.S. Peirce, Collected Papers of Charles Sanders Peirce volume 8, paragraph 314 (March 14, 1909):
"We must distinguish between the Immediate Object, -- i.e. the Object as represented in the sign, -- and the Real (no, because perhaps the Object is altogether fictive, I must choose a different term, therefore), say rather the Dynamical Object, which, from the nature of things, the Sign cannot express, which it can only indicate and leave the interpreter to find out by collateral experience. For instance, I point my finger to what I mean, but I can't make my companion know what I mean, if he can't see it, or if seeing it, it does not, to his mind, separate itself from the surrounding objects in the field of vision."
End Quote.

Semiosis: Object, Sign, & Interpretant

Semiosis = inference process.
An object (a.k.a. a semiotic object) = a subject matter of a sign and an interpretation.
A sign = not necessarily a linguistic symbol, but anyway something interpretable as saying something about something.
An interpretant (a.k.a. an interpretant sign) = an interpretation in the sense of product or content (rather than act or activity) of interpretation.

Peirce's basic semiotic structure is, when stated in the order of logical determination, object-sign-interpretant. (That's determination in Peirce's sense of specialization, bestimmung.) The semiotic object determines. The sign determines and is determined; likewise the interpretant (the interpretant is also a sign). The determination is triadic. The object determines the sign to determine the interpretant to be related to the object as the sign is related to the object. This determines the interpretant as a sign to determine a still further interpretant. Semiotic triadism claims that semiotic object, sign, and interpretant are the three basic semiotic elements and thereby entails the claim that everything logically determined or logically determining, is logically determined or logically determining as a semiotic object or a sign or an interpretant.

A sign is "almost" its (the sign's) object and conveys information about the object, but is not the object (except in the limit case where they are one, determined and determining as one), so a mind's experience of the sign is not that mind's experience of that sign's object. So, the mind needs experience of the object collaterally to the sign or sign system representing the object to the mind. I add that if experience of the sign were automatically experience of the object, there would be no need and no possibility for anything to serve distinctly as a sign. And of course there would be no way, under Peirce's Pragmatic Maxim, to distinguish sign from object.

The interpretant is the sign's meaning or ramification clarified, such that the interpretant itself is a sign (a) of the object and also (b) of interpretant's "predecessor" as a sign of the object, a sign which the interpretant construes regarding the object.

Not only does a sign require and address itself to interpretation, but the interpretant itself is a sign, a night's womb to a further interpretant dawn, just as a translation is into something itself further translatable, a ramification has ramifications, and meaning means, means ceaselessly and sometimes to our chagrin (Merleau-Ponty said "we are condemned to meaning") — and so the interpretant is a sign, promoting and provoking further interpretation. But the interpretant, though it's a sign, is not an object's "mere" sign which one would never guess is also a sign about a previous thing-as-sign about the same object. Instead the interpretant is a sign referring to the interpreted sign as well as to the object, and in fact practically all signs are like this in the interpreter's perspective, links in chains stretching both fore and aft, just not always with clarity (so usually it's a relative question, a role question — "is it the sign or the interpretant?" — just like the question of which codings are encodings and which are decodings). Perpetual interpretation is sometimes to our chagrin and sometimes otherwise, all because it helps us see around the bends of anything and everything -- equations, planets, hearts. Signs and interpretants lead beyond experience to places to which experience could conceivably reach.
There is one passage, Collected Papers of Charles Sanders Peirce volume 6, paragraph 338, dated circa 1909 and (also as 1908), from "Some Amazing Mazes, fourth curiousity," where Peirce says that collateral observations are indices, but that is inconsistent with the other passages, including the 1909 passage above. Mats Bergman has said that the passage sounds "anomolous" and also "very 1860s" in its characterization of index and icon as "thought-signs," and said "Peirce distinguishes three kinds of indicatively effective signs, and mostly holds all of these separate from the relation s that form collateral experience" (in "Re: Mats Bergman's paper" Tuesday, 1 June 2004 at peirce-l; I've reproduced it here). Ten Peirce quotes on collateral experience, collateral observation, etc., supplied by Joseph Ransdell, can be found at "Collateral observation (quotes)" at Peirce Matters.

Verification & the recognizant

I use the term "verification" as a "forest" term for the various "trees" of confirmation, corroboration, proof, and even disverification, disconfirmation, etc. I cover with this also the idea of verification be it strong or weak, certainly not necessarily some infallible kind of verification. Also, by "verification" I do not mean only a conscious deliberate act, or some sort of counterpart thereto at a neuronal level.Representation per se is not verification, but still a sign can be evidence; however, its evidentiary/verificational status is not its meaning or interpretant. As a sign's meaning or ramification is formed into its interpretant, so a sign's legitimacy and verificational status is formed into its recognizant.

Peircean triad,
augmented to a tetrad
by incorporating
a semiotically determined,
object-observant subject.

Object. Sign. Interpretant. Recognizant. Peircean triad, augmented to a tetrad by incorporating a semiotically determined, object-observant subject.
I use the term "recognizant" to mean verification as a stage in semiosis. A term formed from the word "establish" might be better in some respects.

Why collateral experience?

Peirce employed the conception of collateral experience to explain how the mind knows of the things to which a sign refers. That was his purpose, but it amounts also to checking the referents of an interpretant, and so forth. There in fact would be no other way to confirm an interpretant, an interpretation, but by collateral experience, and it is natural in the consideration of semiosis to suppose that that is just what happens. There would be no way to know the quality connoted by a symbol of a quality, but by collateral experience. And so forth. Conditions change, so one has to keep observing and at least spot-checking. And, either the mind resorts to memory in order to form a recognition out of collateral experience, or the mind seeks to acquire the needed collateral experience; or the mind doesn't reasonably recognize the interpretant except as saliently uncertain in its truth or its validity. Peirce held that there are only three basic elements of semiosis: object, sign, and interpretant. Yet, if all semiosis is in logically determinational relationships with recognition based on experience collateral to sign and interpretant in respect of the object, then one will have a lot of trouble justifying the notion that such recognition is not a universal element of semiosis and semiotic determination. One can consider recognition as being mediated by semiosis; but that semiosis also includes a recognitive aspect, even when the semiosis is unconscious. One can test and learn, unconsciously. A system which can't test its own character can't learn, and if it can't learn, then it can't evolve in the semiotic sense, and is not semiosic. If that unconscious semiosis doesn't involve unconscious learning, then it isn't semiosis. Yet semioticians go on saying things like "every decoding is another encoding," playing on the analogy {decoding : interpretant} = {encoding : sign} = {source : semiotic object}, as if it didn't raise some sort of problem that they have no analogue for the information-theoretic recipient destination, the one to whom falls any task of finding inconsistencies and redundancies between the message or message set, and the real world; the recipient's destination's viewpoint underlies reinforcement or redesign (evolution) of the whole given communication system. Well, I can't scold them into intellectual curiosity on the issue.

Verification, learning, evolution

Any time that you enter a situation with some conjectures, expectations, understandings, memories, etc., you are testing those orientations and even testing your ways of "generating" them, whether that's your purpose or not. And you're always entering a situation with such orientations. And you see what happens, and are surprised, unsurprised, etc. As an intelligent system, you learn from the result and accordingly revise, even if only slightly in particular cases, the system which you are, the system in its structure, design, habits, etc. That is evolution (as opposed, say, to pre-programmed development or a pre-programmed menu of feedback-based adjustments of behavior). A biological mutation might be considered a design test, but the organism does not do the design test, deliberately or otherwise. I.e., it is not in the organism's nature to learn from it as a test. An individual vegetable organism does not evolve even biologically, much less "learn and evolve." But an intelligent mind does learn and evolve. Its semiosis, its inference process, is not just a feedback-based adjustment of behavior, but a consequences-&-signs-based reinforcement, undermining, augmentation, diminishment, renovation, redesign, etc., of the semiotic system itself, in its structure, design, habits, etc. We are sufficiently code-unbound, to be able to test our signs, interpretants, "codes" and systems of signs, etc. and even our verifications. Questions of consistency, truth, validity, soundness, legitimacy, arise in even the minutest relationships among object, sign, and interpretant. Such questions are a universal dimension of semiosis. Consistency, truth, validity, soundness, legitimacy, etc., are formed into the recognizant, just as meaning and implication are formed into the interpretant.

The interpretant is addressed to potentially (dis-)verificatory experience; therefore so are object and sign.

The interpretant, in being conceived of as formed as addressed to experience with practical bearing (conceivable experience with conceivable practical bearing in the case of interpretation or clarification of a conception), depends, thanks to the Pragmatic Maxim,

C.S. Peirce's Pragmatic Maxim

is that one best clarifies a conception by representing it in terms of conceivable experience on which the conception's truth would have some conceivable practical bearing.
for its essential characterization on the conception of an experience tending to support it or to be at odds with it, whether or not verification is a mind's main purpose in a given case. Thus the sign and the sign's object (that which the sign is about, i.e., the sign's "subject matter"), in being essentially characterized in terms of the interpretant relation, are essentially characterized in terms of being addressed ultimately to experiences. Now, an interpretation that there is a horse on the hill determines a verification to be conducted by looking for a horse on the hill. The verification does not merely repeat with more assurance the interpretation's content. Whatever the interpretant's logical quantity in other respects, it has a generality across the various experiences and recognitions to which it appeals, and which, as experiences, are singular (and aren't necessarily crucial tests, either). This includes the experience and observation of that which Peirce called diagrams, as in mathematics.

Representation & interpretation are not verification

To have a sign or interpretant of an object (also, to have an experience of a sign or of an interpretant of an object) is not to have experience of that object, except in the limit case wherein sign or interpretant are their object. Basically, this is because (generally) the sign is not its own object. ("A Sign is a Cognizable that, on the one hand, is so determined (i.e., specialized, bestimmt) by something other than itself, called its Object..." [emphases in original]-- C.S. Peirce, from A Letter to William James, EP 2:492, 1909) The sign almost is the object, enough so as to convey information about the object, but not enough to convey acquaintance with the object (except in the limit case of their being the same thing). Yet to have a recognizant is to have experience of object, sign, and interpretant, respectively as object, sign, and interpretant in respect of one another, and, since this is a matter of definition, it can be rejected if and only if it is reasonably denied that one can have such an experience. Such reasonable denial would have a lot of work to do in showing itself to be reasonable.

Therefore, if something X, logically determined (determined in Peirce' sense, "specialized, bestimmt") through complex logical relationships leading from a triad, amounts to a recognizant, then it doesn't amount to a sign or an interpretant. If it were shown that those logical relationships, for their own part, consisted of nothing but relationships among object, sign, & interpretant, then such showing would amount either
(A) to a showing that triadism fails, for it would have shown that something was logically determined but not logically determined as sign or interpretant, or
(B) to a contradiction, since a relationship of being interpreted would have led to something which can't be an interpretant, and this would be to say that either the analysis was flawed or that the idea of a recognizant had been reduced to absurdity; yet if the idea of experience of object, sign, and interpretant in respect of one another is granted as non-absurd, then what has been shown is that a diagramming of logical relations in terms solely of object, sign, and interpretant is inadequate and can seem to be accomplished only by concealing a contradiction. Basically, either there is experience of object, sign, and interpretant in respect of one another, or there isn't. The rest depends on that.

So it is not a matter of showing that the recognizant can't be boiled down to an interpretant through appeal to very complex relations; instead it is a matter of showing that a recognizant can be formed at all, formed as logically determined by object, sign, and interpretant, and logically determining (quite powerfully) semiosis going forward. This is to say, it is a matter of showing that a mind can form an experience -- a reasonably direct (not reasonably immediate) experience -- of object, sign, and interpretant, respectively as object, sign, and interpretant in respect of one another, such that the experience is logically determined by the semiosis, and this in turn is just to say that a true representation of the experience's content as experienced, will be also a reasonably firm representation of the semiosis, to the extent that the experience suffices to reasonably settle doubt. Now, to deny the aforesaid formability and logical determination of such recognizant is to deny that one can have a reasonably direct and reasonably doubt-settling experience of semiosis. Therefore the price which Peirceans must pay in order to say that there is no recognizant (as a distinct basic semiotic element) is the embracing of the view that semiosis cannot be so embodied as to be experienced as semiosis, experienced with reasonable directness and so as to reasonably settle a doubt about it. The price is also the refusal to embody Peirce's experimentalist view of inquiry in the structure of basic semiotic elements, even though semiosis is inquiry process since it is inference process and is aimed at the reasonable settling of doubt.

Since the recognition, unlike the interpretant, is formed as that which reasonably settles doubt in some respect and yet it is fallible, it is in the bigger picture just a fallible form of that semiosic final stage which not only is logically determined, but also on which the real depends, and which would be a final recognition. The recognition is fallibly that which is depended-on in some respect by the real. Something X (the object) determines Y (the sign) to determine Z (the interpretant) (1) to stand in the same relation to X in which Y itself stands to X, and (2) to determine W (the recognizant) to stand to Y and Z in the same relationship in which X (the object) stands to Y & Z (though obviously not actually in the same "chronology-of-semiosis" relationship). The relationship "(2)" is the interpretant's formation as an appeal to a recognitive experience, a recognition, of object, sign, and interpretant in respect of one another. As the interpretant is a further sign interpretive of sign & representative of object, so the recognition is a further object formed as a mind's experiential subjection to the object, sign, and interpretant. Well, maybe I'll eventually find myself forced to back down from this radical claim of mine (which I posted on the same day that I first thought of it, 8/24-early25/06) that the recognizant is determined by object, sign, and interpretant, to stand in the same relation as the relation in which the object stands to the sign and interpretant. More modest and scaled-back is the claim which I've already been making in various forms, that the recognizant is determined to stand in the same relation (as the object does) to the further ongoing semiosis proceeding from the recognizant.

Interpretant as further sign -- recognizant as further object

The recognizant is a further object just as the interpretant is a further sign, but it can be embodied only in an intelligent system; otherwise it is quasi-embodied in reality only in the sense that reality is quasi-experience, as when we say that reality tests the biological mutation. The original object (X), if it is not itself an embodied recognition, then is a recognition only in the sense that a sign H in a lifeless material process is an interpretant, -- H is then no embodied interpretant in an embodied semiosis, but is an interpretant only in virtue of some mind's or quasi-mind's semiosis about the situation, e.g., something which the (quasi-)mind interprets some other sign to imply/entail to be an index. In the same sense, one's proof, one's verification is in some cases said to consist in some material thing or event; what is actually embodied is the original object or a sign with adequate evidentiary status. In the case of explanatory interpretation, sometimes signs are interpreted to be signs of something represented in that interpretation as being the object which "explains," by being originative of, a determinational process. Thus the order of explanation comes to be regarded as the order of being rather than ends-based order of interpretation and of what is important, good or bad, what first of all is cared-about, etc.

Why shouldn't there be some fifth element?

It's because the recognizant is that which reasonably settles doubt and suspicion in some respect, and reasonably settles inquiry and semiosis in that respect (reasonably but fallibly). That which began with an object, in its logical instability and determinantness, has been brought to a stable close, so of course there will be no fifth element unless it is interpolated along the path already brought to a stable close. (I should note here, that this stable close is anything but a close of all semiosis -- to the extreme contrary, it is a basis and foundation for further semiosis, the growth of signs, a handhold in the rockface of the world.) I'd like, of course, to be able to say that some matrix of combinatorial possibilities is exhausted by the conceptions of the four basic semiotic elements, but I don't quite see how to do that. However, in any case, the tetrad's members correlate with tetrachotomies of items which are mutually exclusive and co-exhaustive. In the case of a term's or perspective's logical quantity or scope of object reference, the tetrachotomy arises from a pair of logically twinned two-valued parameters.

Tetradic as opposed to 'dyadic' experience

Now, what is really the fourth dimension of semiosis, the fourth element, is not just experience per se, which as a term "experience" is thought of has having only subject-object referents, but instead a recognitive experience, an establishing, which refers to all elements, the object, the experiential subject, and the sign and interpretant reaching from object to experiential subject analogously as encoding and decoding reach from source to recipient destination.

Correlations of the basic semiotic elements with the categories and with logical quantities

1. The semiotic object, at its barest, barer than even the immediate object as usually conceived as a "statistical version" of the object, is a kind of extremal version of the object, it is, appropriately enough in its "barest-ness," a simplest and most parsimonious version, formed from hardly more than a potential transformation leading from objects better known (even if not at all concrete objects), e.g., a mapping or function, or even an anti-derivative or even a many-to-many relationship (the kind expressed as "equations" but not as "equalities"). Object(s)-to-object(s) relationships of this kind are my category I.
2. The sign represents, in its pre-interpretant aspect, a universe, a totality. The conception of a universe or totality, and structures formed in terms of them, is another way of conceiving of "whetherhoods" -- "yes," "no," "if," "[logical] and," "informatively," "probably," "possibly," "feasibly," "optimally," etc. Such are my category II.
3. The interpretant narrows down, from universals and universe, to a general scenario by selection of ramifications in accordance with the standards of value and interest of the interpreting mind. These have the generality of attributes, appearances or positive phenomena in general, which are my category III.
4. The recognizant singularizes in accordance with the singularity, actual situation and historical tapestry, etc., of the recognizing, experiencing mind. This correlates with my category IV, substantia, substance in the sense of this man, this horse.

Substantiae and object(s)-to-object(s) relationships are inverse to each other, are each other "inside out" in that which seems a sufficiently obvious way. Attributes and "whetherhoods" are inverse to each other, are each other "inside out" in a way which becomes more evident when one considers that the attribute, e.g., a diamond's hardness, involves structures of modality, possibility, optimality, probability, etc. Not only are "whetherhoods" the categorial correlate of the attribution of attributes to substantia, so that we can think of attributes as "networked" by whetherhoods, but also there are whetherhoods "networked" within the given attribute. There is more to say about these matters, and about the fact that really it's all four getting "networked" together, but let me move on. I will add that this category system corresponds to families of research -- (I) 'Pure' mathematics, (II) 'applied' yet mathematically deep/nontrivial mathematics (deductive mathematical theories of logic, information, probability, and optimization), (III) abstract yet positive-phenomenally deep studies (of phenomena in general -- philosophy, cybernetic theory, statistical theory, inverse-optimization theory (young field)); and (IV) idioscopy a.k.a. the special sciences, pertaining to substantiae in their histories, geographies, collectivities, tendencies, dependencies, laws, etc., etc.

The semiotic elements also correlate with the categories also in the opposite sequence, as follows:

1. The semiotic object is cognized as (IV) substantia but often by hypostatic abstraction.
2. The sign is cognized as (III) a manifestation, an appearance, an attribute (but often with abstraction involved).
3. The interpretant is cognized as (II) that which ascribes signs to objects, predicates to subjects ("subject" in the "subject & predicate" sense, not in the "experiential subject" sense), attributes to substances, and, in the Peircean picture, qualities to reactions/resistances.
4. The recognizant is cognized as (I) that which puts the objects and their associated signs and interpretants into objects-to-objects relations with the already established things in the already established world as known to the mind. The recognizant, in common parlance, is what "puts them on the map" though in that parlance what is really meant is "recognizes or establishes their place in the territory."

These fourfolds also relate to a fourfold of connection, resemblance, meaning, and legitimacy, embodied in index, icon, symbol, and proxy.
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