Let me glance at the tables
(ones not still ‘in progress’).”
fourfolds and sixteenfolds.
As I revised this post over time, it became too long, too strident in some places, and also somewhat repetitive. It became unwieldy, I didn't know what do with it as a piece of writing. And now I've changed my mind about at least a few things in it, too, but I don't feel like doing much rewriting.)
Point at image.
Because there are marked patterns of philosophically relevant fourfolds.
It’s simple logic in some cases, as when two recurrent plain questions mirror each other logically and still stand logically independent of each other, e.g., “is there risk?” and “is there opportunity?” To them beckon four combinations, of course, of simplest answers:
|Three Parameters |
I'm unsure which (if any) shuffling of the above cells best correlates with other fourfolds. A "good" fourfold has not two but three seemingly meaningful two-value parameters though any two render the third one technically redundant. One will usually seem a bit more abstract than the other two, but maybe this depends on the labeling of the parameters ("addressor [Y/N]," "addressee [Y/N]," and, along the diagonals, "dividing participants [Y/N]").
Yet, some philosophically relevant fourfolds echo each other in ways for which I have not yet managed, at least to my satisfaction, to uncover the reasons, even when the fourfolds separately from each other have seemed clear enough. Turn a sign this way, then that, align it with others, the world seems to crack open, and the chase may be on. The chase after a recurrent logical pattern in philosophical issues has led through Aristotle’s Four Causes, Thomistic beauty, categories, logical quantities, semiotics, elementary aspects of information theory, the special-relativistic light cone, philosophical classification of research areas, philosophical classification of human & social activities, etc., as reflected in tables below. I’m less interested in “ultimate” philosophical questions than in tracing out this pattern of fourfold structures. Since anybody still reading at this point will probably be wondering, I may as well say now, that four was indeed my favorite number — when I was four years old; five my favorite when I was five; and thereafter I ceased having a favorite number. I started attempting categorization a few decades later, trying first with three, then four, then six. By the time I learned of and started reading the trichotomist C.S. Peirce, I was already an inveterate “fourist.”
|I (rs)↔A (rs) |
There's R, all or
none of it S.
There's R but no RS.
I (rs) ↓ A (rs)
I (rs) &F& A (rs)
There's no RS or there's
no R that's not S.
I (rs)←A (rs)
|A (rs) |
There isn’t R that isn’t S.
All R is S.
|E (rs) |
There isn’t R that’s S.
No R is S.
There isn’t R.
I (rs)' & A (rs)
I (rs)→A (rs)
|I (rs) |
There’s R that’s S.
Some R is S.
|O (rs) |
There’s R that isn’t S.
Not all R is S.
There's RS & there's
R that's not S.
I (rs) v E (rs)
I (rs) v Tv A (rs)
I (rs)↔O (rs)
If there's R, then: there's RS &
there's R that's not S.
I (rs) A (rs)
If there's R, some of it is S.
If there's R, some of it isn't S.
I (rs) | A (rs)
A F F I R M O
N E G O
|...(maybe unnamed) |
"exclusive" or "eclectic"
It’s philosophically helpful that one cultivate an intuition for common transparent logical fourfolds, since philosophy is a science or study of reason (among other things, including reason’s crackups). As a study of inference processes, philosophy is specially allied, on the concrete side, with the human and social studies, and, on the abstract side, with deductive study of logic and, beyond it, on inference’s ‘pure’-mathematical side, with the study of ordered structures. Yet, philosophy neither draws its conclusions deductively nor seeks (like the human and social studies) to establish or explain special phenomena by surmise, special experiment, and inductive syllogism, drawing conclusions which would be, formally, neither truth-preservative nor falsity-preservative. Almost by process of elimination it seems that, if one wishes to see philosophy in terms of how it could be distinctly yet still securely and capaciously anchored and related to research in general, then one needs to see philosophy as drawing inductive generalizations (falsity-preservative, not truth-preservative) as conclusions, somewhat as in statistics, yet having for its allied inverse not probability theory but instead deductive logic, and drawing conclusions about reason and experience in general. In that case, it should be philosophically helpful that one cultivate an intuition or instinct for common transparent logical fourfolds present or echoed in intriguing and somewhat opaque structures of alternatives, alternatives involved at a general level in complex sign- & evidence-supported processes of character, competence, sensibility, and intelligence including philosophy itself and all research, to say the least. And it is also then helpful that one seek to abstract pairs of mutually relevant logically two-valued parameters and to systematically explore all their combinations of values, not just some.
I know of no major philosopher who’s been a thoroughgoing — or, more reasonably, a thoroughseeking — tetrast.
 I learned of a philosopher E.J. Lowe who is something of a tetrachotomist and, thanks to Steven Ravett Brown at Ask A Philosopher, I felt it worth looking further into Lowe, found his paper “Recent Advances in Metaphysics” online, but confirmed an earlier disappointment. Lowe’s ontology tops off with two logical quantities, the universal and the particular, corresponding likely to what I call the general and the singular, not that it matters, the point being that the elementary logical quantities characterizing terms are logically not two but four (and involve four conjunctive compounds), while Lowe, with his structure reflecting an undertaken but arbitrarily incomplete account of the logical quantities, veers off in another direction, to double his logical-quantity-defined categories prematurely with categorization according to other considerations.
À la monist, dualist or dyast, triast — tetrast. I’ve found that the word “tetrastic” already exists, though mostly as a variant, as Gary Richmond pointed out to me, of “tetrastich,” a four-line poem, stanza, or epigram.
“Tetrastic” here means fourfold as either tetradic (four-element) relation or tetrachotomic (four-way dividing). I don’t mean that the world is four elements, e.g., land, wave, wind, sun, or that the mind-matter dualism should be recast as a tetrasm of mind, life, matter, forces in the sense of four mutually alien elements enigmatically combined. (“Tetrasm” sounds bawdy, ergo this Website has at least one thing that maybe, just maybe, would have been undispleasing unto Quine.)
Some items in these fourfolds have mattered amply in philosophy, so it seems significant that they fall not uncomfortably into a common and sometimes intriguing pattern.
|Starts (at t) |
(isn’t till t,
is since t).
|Stops (at t) |
(is till t,
isn’t since t).
|Continues (at t)
(is till t,
is since t).
|Continues-Not-To (at t) |
(isn’t till t,
isn’t since t).
I wonder why philosophers don’t trace out such full sets — for another instance the full set of elementary term-quantities such as the singular and the general. This, given the importance which the “question of universals” has had in philosophy, seems as curious a case of philosophical neglect as I have encountered in my narrow pursuit. Some philosophers will improvise responses mentioning Occam’s Razor, as one can well imagine, but here it cuts against them. Application of half or three quarters of a logical square is less simple and less consistent than application of all of a logical square. Strange would be the museum that, with little or no explanation, displayed many a quadruped running on only three or two of four apparently good legs. It is philosophically needful to satisfactorily explain the applicability or inapplicability of every option in a broad philosophically relevant alternative (in the case under discussion here, a logical square of options) that was initially invoked for some not all of its options. The refusal to attempt such a completion renders suspect the seeming success of the given square’s partial application.
|Will, Conation||Ability, Handling||Affectivity||Cognition|
|Almostward||Trying (out)/(for)||Testing, devising||Desire||Fancy, immed. impression|
|Laterward||Seeking||Preparing, approach.||Hope, Confid.||Expectation, anticip., etc.|
|Barelyward||Taking, picking||Achieving||Pleasure, Satisf.||Noticing, discernment|
|Earlierward||Adhering, habit||Maintaining, skill||Attachment||Memory|
Also, too seldom (or so it seems) has a philosopher (Peirce is an exception) done, and kept in view, inventory of the items to which a structure of logical alternatives will be applied, inventory toward which one shouldn’t scorn Roget’s thesaurus.
Mendeleev in his cabin labored over various arrangements of pieces of a chart, in search of the structure which became his periodic table. Yet, in philosophy, incompletely explored logical structures are applied to incompletely inventoried items, and Occam’s Razor is invoked to call the job finished. Rules of thumb about logical structure might help to avoid some of the omissions, conflations, and foreshortenings involved in this. More or less off the top of my head, for instance:
1. The smallest sets of multiple deductive logical options (notwithstanding the eight implicitly provided by the Aristotelian Square of Opposition) are usually 2, 4, and 16. (I regard philosophy as tending to draw ampliative inductions as conclusions, but also regard it as a setting for the development of domain-independent deductive formalisms based on “contingent” or phenomenologically based assumptions, albeit such that the proceeding as a whole is utimately an ampliative induction guided by standards of cogency and illuminativeness regarding phenomena in general.)
2. Check that one has defined one’s parameters in a consistent manner. (E.g., if one defines logical term quantities such as the universal, the general, and the special such that the terms may be either monadic or polyadic, then one should likewise define the singular, even if it means giving the singular another name, so as to keep the parameter of monadicity/polyadicity consistently independent of the parameter of logical term quantity; if one is proceeding exploratorily, then one’s logic should not prejudge which philosophical views one should adopt in such matters as whether there’s any point to defining a monadically-or-polyadically-singular quantity. Such an anti-pre-judicial consistency, in the logical exploration of logical quantities, matters especially when one is interested in grasping logical quantities in a general way (general like statisticality and information) as mental perspectives characteristically emerging even without formal articulate ado as scopes in research and intelligent decision-making, performance, affectivity, cognition, etc., of whatever kind. The singular is a case in point (and, by now, obviously a case on my mind), understood, as it usually is, as being in two oppositions, one versus the general, and the other versus the polyadic.)
3. Do not jump to conclusions about seemingly trivial or seemingly near-empty combinations of parametric options. That’s an occasion rather to review and check one’s parameters for consistency of independence, and to review and check one’s inventory of the items to which one hopes to apply the logical or categorial structure. Listen and scout around for what the logic is “trying to tell you.”
Now, I usually think of a fourfold in the square 2x2 arrangement, not unlike the simplest typology in morphological analysis. Obviously sometimes it’s easier just to lay it out 1,2,3,4, especially when it supplies column or row headings.
A few of the fourfolds shown in this post are obvious, at least when laid out. For others I have argued or expect to argue in various posts here. One of the 4x4 tables below involves the philosophical classification of research fields. I don’t know of any philosophical attempts to do this with research fields as currently evolved, but would be interested to hear of any. Birger Hjørland has written: “There is not today (2005), to my knowledge, any organized research program about the classification of the sciences in any discipline or in any country. As Miksa (1998) writes, the interest for this question largely died in the beginning of the 20th century.”
|From post “A periodic table of aspects of humanity which lend themselves to social compartmentalization.”||A periodic table of the maths, sciences, & areas intermediate between them. See post “Logical quantities, categories of research, and categories.”|
...to 1st level
...w.r.t. 1. Decision- makings, power.Appropriation,
...w.r.t. 2. Abilities, means.Production, processing,
...w.r.t. 3. Affectivity, ends.Consumption,
...w.r.t. 4. Cognition, checks.Assimilation,
|≣ ↓ Each row: |
a research ‘family.’
|||| Each column:
a research ‘coterie of friendly cousins.’
|1. Mapping, pathfinding (objectification-like processes):||2. Counting, measure, apportionment (representation-like processes):||3. Calculation, coding, appraisal (interpretation-like processes):||4. Inference, reason (& reason’s crackups) (inferential & |
1. Decision- makings, power...↑
Affairs of power (polit., milit., etc.).
Business, trade, economic affairs.
Show, sports & games, fashion, etc.
Case-building, debate, dialogue, etc.
|1. Pure Mathematics: |
Subject in scope:
universals that aren't universes
|Many-to-many (graph theory, topology, simult. eqs., extremization, etc.).||One-to-many (enumeration, measure, integration, etc.).||Many-to-one (algebra & groups, derivatives, etc.).||One-to-one (math-induction applicability conditions, structures of order, limits, etc.).|
2. Abilities, means...↑
Practices (cooperation, tolerance, etc.):
Management, compliance, etc.
Work, labor, skill-plying, etc.
Recreations, hobbies, entertaining, etc.
Study, communication, etc.
|2. Applied yet mathematically deep mathematics: |
forward-only deduction (except in historical overlaps with pure maths)
Subject in scope:
|Deductive maths of optimization.||Deductive maths of probability.||Deductive maths of information.||Deductive maths of logic.|
3. Affectivity, ends...↑
Valuings (communion, joining, etc.):
Ruling / governing valuings (relig., morals, etc.).
“Care-how,” valuings re: work, production, competence, etc.
Affective and gratificational valuings.
Cognitive valuings, curiosity, love of knowledge, rigorism, etc.
|3. Abstract yet positive- phenomenally deep sciences/studies: |
Subject in scope:
|Inverse optimization problems [Google on them ].||Statistical theory.||Descriptive & inductive information theory.||Philosophy.|
4. Cognition, checks...↑
Disciplines (supports, checks, & balances):
Ruling / governing arts.
Object(ive) in scope:
“Know-how,” practical / productive arts/scis.
Object(ive) in scope:
Affective arts (music, literature, visual, dramatic, etc.).
Object(ive) in scope: totalities, universes
Sciences, maths, & disciplines intermediate between them.
Object(ive) in scope: universals that aren't universes
|4. Concrete empirical (“special”) sciences/studies: |
Subject in scope:
(multi-)singulars among more singulars
|The 4 turns of becoming:||4 rough tags:||The 4 phases of code-bound communic.||4 phases of intelligent communication (code-unbound enough to try out & evolve codes):||The 4 stages of creative process (Helmholtz & Poincaré). |
~ The 4 stages of aesthetic apprehension (revised Joyce).
~~ The 4 aesthetic properties (Aristotle plus
|4 categories:||4 sets of kinetic & associated mechanical conceptions:||The 4 Causes’ revised principles , & the 4 Causes a little revised:||4 kinds of complex systems:||4 levels of concrete phenomena:||The human forms of revised principles of the 4 Causes:|
|Starts (at t) |
(isn’t till t,
is since t).
|Main cause, driving cause.||Source.||Semiotic object |
~~ Due directive magnitude, due force
|System’s external momenta or forces.||Agens, beginning, effector (Aristotle: "initiating source of change or rest").||Sensitive dependence on initial conditions (await inverse-optimizational treatment?).||Forces.||Will, conation, character.|
|Continues (at t) |
(is till t,
is since t).
|Further cause, intermediate cause.||Encoding.||Sign |
~~ Due proportion, due rhythm, harmony, etc.
|Whetherhood (Y/N, probability, informativeness, logical conditioning, etc.).||System’s internal energy or power (down thru the elementary particles) |
(rest energy :: rest mass)
|Sustinens (patiens), middle, means, matter/process ||Fluctuation-smoothing dependence on intermediate-stage conditions (stochastic processes).||Matter.||Ability, competence.|
|Stops (at t) |
(is till t,
isn’t since t).
|Main effect, |
|Decoding.||Interpretant (interpretation) |
~ Takenness, enrapturement.
~~ Radiance, vibrance.
|Attribute||System’s external energy or power.||Actum, |
|Corrective (feedback) dependence on output conditions (cybernetic processes).||Life.||Affectivity, sensibility.|
(isn’t till t,
isn’t since t).
|Further effect, ||Destination.||Recognizant (recognition, verification, etc.).||Verification. |
~~ Wholeness, (structural) integrity.
|Substance (this man, this horse) (or hypostatization).||System’s internal momenta or forces (including down thru the elementary particles) (statically or otherwise balanced relative to an observer at rest).||Sustentum, check, form, structure, evidence, etc.||Fortificative dependence on sign-&-evidence conditions ||Intelligent life.||Cognition, intelligence, knowledge.|
Tetrastic structures seem to have been neglected by philosophy, at least in comparison to dyads and dichotomies and even to triads and trichotomies. Yet they seem to work rather well to bring a little more system to some traditional philosophical structures, and it’s useful to cultivate an intuition for them. In deductive logic, there are the logical connectives, the quantificational forms, etc., and a logician gets to know those structures inside and out. I would argue that philosophy is the field which deals with the inverse problem to that of deductive theory of logic (or as it’s sometimes called nowadays, just plain “logic”), rises to concerns of a general kind with complex processes of the intelligent mind and heart, and of society, and tends to draw ampliatively inductive conclusions.
 Of course, if philosophers do not so conceive of it, then in an important sense philosophy is not the field which deals with the inverse problem to that of (deductive theory of) logic, rises to concerns of a general kind with complex processes of the intelligent mind and heart, and of society, and tends to draw ampliatively inductive conclusions. But what other secure place will persist for philosophy as primarily a research discipline, and a major one at that? Philosophy — cast by some in philosophy’s linguistic analysis school as the analysis of arguments, in contradistinction to logic as the theory of arguments (by which I take them to mean deductive theory of arguments themselves deductive, inductive,
Meanwhile, the “children” — really, the sibs and cousins — have grown up and the mansion has become a city where philosophy retains a place for the time being. Amateur and professional alike in philosophy delight in complex reasoning processes, and philosophy’s reflexivity ever tempts them to go at it with might and main. But, again, no real place, no secure and capacious place, remains for philosophy in modern research, except in the family of fields drawing inductive generalizations as conclusions, researching phenomena in general (e.g., statistical theory), where philosophy would fit reasonably well as the ampliatively-inductive inverse of deductive theory of logic, likewise as statistical theory is the inverse of probability theory. Recognition of this as philosophy’s locus means attributing to philosophy a distinctive and affirmative core which broadly, deeply, brightly, and firmly anchors and relates philosophy to research in general. (In that place, philosophy remains capable of producing essentially domain-independent deductive formalisms based on “contingent” or phenomenologically developed assumptions.)
It might be a good idea to work out a reasonable elementary level of philosophy, just as there are elementary levels of communication theory, cybernetics, statistical theory, etc. E.g., in a sense, philosophy studies reason : philosophers treat, as subject matter, things (or stuff or whatever), and signs and evidences of them, and interpretations thereof, and recognitions / (dis)confirmations thereof. And, in a sense, philosophy studies experience and phenomena in general : Philosophers do not, qua philosophers, make cogent surmises to entities and laws subject to special tests; nor qua philosophers do they draw deductive and mathematical conclusions, tried though some have so to base philosophy. So, if philosophical conclusions are by ampliative induction (as distinguished from surmise and from any kind of deduction), then — philosophy’s sibs are its fellow areas of research into phenomena in general, and the family consists of: (1) the young field of inverse optimization problems; (2) statistical theory; (3) the descriptive and ampliatively-inductive areas of information theory; and (4) philosophy itself — and philosophy’s inter-family band of friendly cousins includes its fellow areas of research into reason and reason’s crackups, and consists of: (1) order and mathematical-induction applicability conditions; (2) deductive mathematics of logic; (3) philosophy itself; and (4) areas much pitied and envied — for their conclusions, as cogent as they can make them, are by that power of surmise which is a wonder at their subject matter’s heart as well
This is to say that philosophy stands to formal and mathematical logics, as statistical theory stands to probability theory. (A nice thing about tetrastics is that they lead one to trace out patterns of so-called inverse relationships.) Tetrastic structures do recurrently peek out or emerge in philosophy but go undiscussed as a theme, appear recurrently with sometimes less transparency than has been brought to those in deductive logic. So, it’s good for the philosophically minded person to become familiar with some of the more obviously structured ones (not to mention with at least some elementary deductive-logical structures!).
The semiotic tetrads which I have pursued echo the tetrachotomies. Also, no element of such a tetrad can be reduced to any of its fellows; nor can such a tetrad discard one of its four elements without losing its integral semiotic or, if you prefer, integral semiotic-cum -observationalistic, character. I do not aspire to frame a Peirce-style reduction thesis about an irreducibility and sufficiency of tetrads generally. But the semiotic tetrads do align with the tetrachotomies, and more than one such tetrachotomy is conceived in terms of a given pair of closely related independent two-value parameters generating exactly four possible options of the given kind. That sort of sufficiency and irreducibility may prove extendible to the semiotic tetrads themselves. So tetrastics are not entirely the potential mere uncontroversial workaday philosophical tool that I was starting to make them seem, and they’ve led me into some arguments (usually amicable!) with Peirceans.
Charles Sanders Peirce’s triads and trichotomies seem to me to be better when reworked as tetrasms, either by addition of a fourth element or by “dis-conflation” of one element into two, or by deeper reworking. But Peirce’s “triastic” structures are not generally such that I would say that there is in every case some same element missing which you could just pop back into place. Still, insofar as his categorial conceptions of reaction, quality, and representation are involved, and insofar as the category of representation is the category of meaning (in a broad sense), I hold that what’s missing as a separate category is that of legitimacy and of one thing’s counting as another legitimately — particularly for evidentiary and interactional purposes. However, I see this extra category as the logical or semiotic category; so what do I do with Peirce’s Thirdness as Representation? Insofar as it characterizes a “communication” system but not a verificatory system, I think of it as value or importance, perhaps in a kind of information-theoretic sense. Now, to emphasize ideas like those of value or importance is, I think, to emphasize the third communication stage, decoding (1st, source; 2nd, encoding; 3rd, decoding; 4th, destination), or the third semiotic stage, the interpretant (I see a fourth stage in semiosis: collaterally based recognition). Such is the kind of threeness or thirdlike-ness that I find there.
Now, Peirce’s own writing shows a constant awareness that knowledge and reasonable belief are reached through adequately explored experience and indeed research. This awareness is the outer essence of his Pragmaticism (the inner essence being his recommendation that, in clarifying one’s conceptions, one best does so in terms of conceivable experience that would conceivably have practical relevance).
But I think that Peirce’s Pragmaticist view is not adequately built into Peirce’s basic semiotic structure which is object-sign-interpretant (sign = not necessarily a linguistic symbol, but anyway something interpretable as saying something about something; interpretant = interpretation in the sense of product, rather than activity, of interpreting; there’s an old word “interpretament ” from Medieval Latin interpretamentum (see Charles Short’s definition via Perseus Tufts) which means an interpretation as a product; Peirce probably knew the word well but perhaps thought it too lengthy).
Absent, from the object-sign-interpretant triad, is the semiotically determined relationship whereby the sign and its interpretant (which is a mere construal) are brought to the experiential test against the object which they merely represent. Pragmaticism itself agrees that there is no way but the passing of such a test for sign and interpretant to merit recognition as legitimate and truthful. A sign is “almost” its (the sign’s) object and conveys information about the object, but is not the object, so familiarity with the sign is not familiarity with the object. The interpretant is the sign’s meaning 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. Peirce, unlike so many before and since, saw that there’s much more to signs as a general phenomenon (general like statisticality and information) than “signifier” and “signified.” 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 having reference to an 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), and Peirce unswervingly conceived the interpretive chain as operative all the way down to the level of the infinitesimal and the truly continuous which he ultimately regarded as beyond all multitudes or Cantor’s alephs. Actually so continuous or not, perpetual interpretation is sometimes to our chagrin, yet it also, for instance, lets us see around the bends of planets and hearts. But the caveat, the string attached, is this, that, the mere fact that you interpret, understand, take some appearances, some events, some words, as signs about some object, doesn’t mean that you really know or really reasonably believe or learn anything about that object, i.e., and, as Peirce states, sign and interpretant contain none of the needed familiarity-dependent understanding of the object, and such familiarity and experience must be had collaterally. Therefore, (a) the collateral experience is no mere sign or interpretant in the sense and in those relations in which it is the collateral experience, and (b) only through changes of semiotic frame of reference can such experience be analyzed into signs and interpretants. Likewise (and only likewise) can interpretants be analyzed into pre-interpretant signs, and signs into objects — every supposed reduction of such experience to signs and interpretants marches onward all too powerfully, to reduce away the classic semiotic triad itself. To say that we can shift frames and regard the recognition as a sign or interpretant of some other object (as it likely is) is to say that we can simply bar our eyes from the question of what is the semiotic status or role of the collaterally object-observant recognition of the interpretant and sign as corresponding to the object already in question. We could likewise ignore, as some do, the questions of what is the interpretant, even what is the sign. The sign’s object is not per se the recognition, for then signs and interpretants would never be needed. Nor is the verificative recognition some representational, qualitative, or reactive aspect or relation of interpretant or sign or sign’s object; if that were so, then one or more, among object, sign, and interpretant, could somehow, or in some combination or relation, contain conveyable familiarity with the sign’s object. In sum, it is completely ruled out, that the recognition is interpretant or sign or object or any representational, qualitative, or reactive aspect of any of them or relation among them. Could the recognition still be some kind of relationship among object, sign, and interpretant? Yes, if and only if that relationship contains familiarity with the object. Object-observation-based recognition of the sign and interpretant as corresponding to the object ipso facto contains familarity with the object and conveys such familiarity across the memory and experience of whatever mind (or “commind” or “quasimind”) which it inhabits. There are chains not only of interpretation but also of recognition and verification which are not mere interpretation, mere construal.
Left to its “own devices,” semiosis could not learn the difference between sense and nonsense; it could still, as it does, lead to hopeful monsters, like they say of biological evolution, but hopeful monsters which go untested, unchecked.
Instead there is to philosophically acknowledge as a semiotic phase or element the observational / experiential recognition formed as collateral to sign and interpretant in respect of the object and to explore it as a further complex of semiotically determined relationships. It might be a recognition of a hat being worn as one expected, or a recognition of one’s hopes as unexpectedly fulfilled; or a recognition of a given interpretant as resting soundly enough upon recalled experience. Beyond the category of value, import, meaning, etc., is the category of consistency, truth, validity, soundness, and not just in the sense of the shallow or trivial but even and especially in the sense of the challenging deep. Beyond the end or culmination or actum as actualization, comes the check or checking, the sustentum, alitum, or altum as borneness, sustention, a system’s agencies’ balancement and stabilization. “Beyond” in some logical sense. The check doesn’t shed the end or leave it behind. Edward Dahlberg pounded it into him as a poet that “every perception leads DIRECTLY and IMMEDIATELY to another perception.”
Within the semiotic triad of object, sign, and interpretant, there is no way to understand how a sign can verify or (dis-)confirm anything — no way to capture the common idea of evidence as being a kind of sign. Only if a sign has not only purport or meaning clarifiable into an interpretant, but also observational legitimacy or authority solidifiable into a recognition, a “recognizant,” is it possible to understand the evidentiary and verificatory character of a sign — for a “mere” sign can after all, on the basis of experience with the object, count observationally in some regard as the object itself (and do so without being confused with the object). Without all this, signs would require constant collateral observations comprehensively checking them. Signs would fail to expand our horizons and to let us peer, so to speak, around corners near and far. If signs always failed in this way, they would succeed in little else. And, for its part, experience would be impoverished of all that continually leads it beyond itself.
Now, an observation or experience, for its part, is semiotically determined, enriched, informed, fortified — how? How else? than by being formed as collateral to sign and interpretant in respect of the object.
To be able to clearly conceive and express such things — this welcome slackening of a counterproductively over-strict need for direct experience of the object in order for the sign to work at all, and a simple statement of the relationship through which semiosis determines and informs experience — are gains reached through recognizing the collaterally based recognition as a stage and element of semiosis. Now, Peirce classes the mathematical diagram as an icon, defined by resemblance to its
To hold instead, as a last resort, that verification is not a semiotic or logical stage but is part of an “outside” of semiosis, an “outside” into which semiosis merely characteristically joins or bonds, is to deny the verificational heart of logic’s guiding research interest; it is also to deny, that the characteristic verificative joining, bonding, or anchoring of objects, signs, and interpretants to recognitions is characteristic of semiosis. It is to deny the depth and rootedness of the world’s logical or semiotic aspect and to make the wrong kind of distinction between logic and facts. In the idiosyncrasy-shunning spirit which it cultivates, one should just as well exclude surmise from the kinds of inference.
It is also to be noticed that the sign qua pre-interpretant may saliently have arisen in, and as, observation and experience of the particular or general object (object-experience by another mind (or quasimind) or by the same qua other or by the same qua same), and that this is really a distinctive perspective of the pre-interpretant sign — that of a judge or judgment, measurant or measurement, describer or descriptor witness of the object, perhaps being an aspect or part of the object itself, anyway something which (a) may, separately, be interpreted as a sign implying said object when the object is unavailable (at least in the relevant regards) (e.g., “The car is long and orange ? It could well be Jack’s”) and (b) means more than, ramifies beyond, that which it patently is. Furthermore its familiarity, such as it may be, with the general or particular object may be the interpreter’s own but is generally unconveyable (qua familiarity by the sign qua sign) and is at any rate generally less far-reaching than the (further) meaning; anyway the thing, in those regards in which it is a sign about the object, does not “contain” familiarity with the object, i.e., such that the interpreter could imbibe of or absorb the familiarity, though for instance a person familiar with an object may for that very reason be a sign to another person about that object. With the kind of generalization possible through such Peircean conceptions as the quasimind, it is probably possible to legitimately analyze every case of a sign both as such a measurer/describer and as already-an-interpretant now under further interpretation. These two perspectives are distinguishable analogously as are encoding and decoding in information theory. However the distinctively pre-interpretant perspective is that of such a (possibly other) measurer/describer (the “encoding”) and in this sense a complete pre-interpretant sign stands as a judgment which tends to persist beyond its origin. The judgment itself may tend to stand less in question, than its meaning or ramifications do, but whatever to any extent stands in question solicits to that extent interpretation.
|1. Objectification. |
Conception, percept, image, etc.
Correlated with: graph theory & maths of many-to-many relationships, deductive theory of optimization, the (young) field of inverse optimization problems, and sciences of motion & forces.
|3. Interpretation. |
Inference to a conception, percept, image, etc.
Correlated with: algebra & maths of many-to-one relationships, deductive theory of information, ampliatively-inductive information theory & cybernetics, and biological sciences.
|2. Representation. |
Correlated with: enumerative combinatorics & maths of one-to-many relationships (measure & integration, etc.), probability theory, statistical theory, and the material sciences.
|4. Recognition. |
Inference to a judgment.
Correlated with: maths of order and one-to-one relationships, deductive theory of logic, philosophy, and the sciences/studies of intelligent life.
I discuss some of the above semiotic matters at greater length in the post “Semiotics: collaterally based recognition, the proxy, and counting-as.”
As for semiologists, some of them are no Peirces and seem simply to ignore the critical dimension in the phenomenon under study and to blandly assume that the people are the sheeple manipulated by signs. Whatever one thinks of people generally (I’ve muttered a few times about “the sheeple” myself in a bad mood), this ignoring is simply and uneuphemizably stupid for a student of signs to practice. One may think that the people are sheep deeply asleep, but to discuss them as if they flatly lacked any critical and confirmation-seeking attitudes or approaches is to ignore a basic dimension of the phenomenon, the very dimension from which science itself rises, the dimension which, at bottom, distinguishes intelligent life from vegetable life. Systems and processes such as minds, human users of language, etc., sufficiently
In one of the charts above appears the sequence (1)
Anyway, the conceptions in that sequence constitute my rough inductively generalized take on the issue. My conceptions of the four broadest categories are meant to, among other things, reflect the four broadest categories of things dealt with in all research — the respective subject matters of (1) pure mathematics, (2) applied yet mathematically deep mathematics, (3) abstract but positive-phenomenally deep sciences/studies, and (4) the “special” or concrete empirical sciences/studies. The objects of all such studies — as opposed to the subjects — may tend to the universal wherever possible, but that is a different question. The research families and the categories correlate to four typical logical-quantity-perspectives which are logically based, in such a way as gives them a kind of symmetry and exhaustiveness. They are tetrachotomies, four-way logical divisions of given wholes of logical possibilities.
In other words, I am less interested in a general theory about categorizing, than in pursuing broadest categories. One might say that, notwithstanding the non-idiosyncrasy of logic, I want to get the geography going before I worry too much about the geology and the plate tectonics. To put it another way, there’s set theory, with its infinite hierarchies of infinite sets, and then there are the infinities actually often encountered in mathematics generally — the countable infinity of discrete points on a line, the uncountable infinity of the points in the continuum, and an even more populous infinity, that of curves or functions in the continuum (add discrete finite sets into the mix and you have a foursome). It might be added, that a physical geography may find patterns that an ealier-conceived geology had not thought of. In particular, there seems a pervasive pattern of inverse relationships which I’ve hardly addressed on this Website. I’m starting to need that “plate tectonics”!
Peirce seemed a bit reluctant to use the word “accident” among the categories. Why not an alternative like “property” or “attribute”? Maybe because: “Property” originally meant something like "idiosyncrasy" (not in the sense of “quirk,” but simply of “unique/distinctive but non-essential”); and, through Aquinas and others, “attribute” acquired a sense of “essential attribute.” I long used “accident” in accordance with Peirce. I’m not quite happy with “attribute” which I’ve started using now. I still like it better than “property” it seems less ill-suited to items which we would not often regard as properties, e.g., a thing’s market value or its being within earshot of something loud. I regard the apportionment or “copulation” of attributes to substances as forming still another category, the category which I call “whetherhood,” a kind of variety-enriched version of the olden anitas. Whetherhood’s modes include formal and material truth values, logical dependences, probability, information or informativeness (novelty, distinction or difference that makes a difference), etc.; without them you could not relate attribute to substance and they themselves are not directly affirmable of substances nor are they substances complete with attributes. As apportionments of attributes they are a way of relating attributes to attributes, with regard to relative frequency, overlap, etc. I regard as a further category oneness, otherness, etc., among substances (or among attributes treated as substances, i.e., hypostatized attributes), which I call “object(s)-to-object(s) relators” but which, if I were more daring, I would call “ofhood” or “thanment” (as in “double of..,” “three more than..,” “inverted order of...,” etc., i.e., I’m thinking of operations, functions, antiderivatives, etc.). Whetherhoods apportion explicitly or implicitly in terms of a totality, a universe of discourse, etc., such as to amount to valuations of predicates or propositions or outcomes or states of affairs, etc. Whetherhoods are a way of dealing with attributes simply as divisions of a universe, while object(s)-to-object(s) relators are a way of dealing with substances simply as generic objects endlessly multipliable and rearrangeable. Actual research involving these things necessarily goes far beyond the elementary conceptions outlined here — e.g., apportionment among universes instead of a division of a universe, and of course the development of the imaginative apparatus of set theory. I discuss categories, logical term-quantities, etc., in the post Logical quantities, categories of research, and categories. (There one may learn why the heck I keep saying “polyadic singulars” in my logical-quantity tables.) The following table mostly repeats things from the tables above in this post, but shows some of the alignments more plainly.
|Research family||Typical logical-quantity perspective ||Essential subject matter category||Correlated grammatical form||Correlated kind of abstraction||Typical mode of conclusion drawn|
|1. Pure mathematics.||Universal-cum -general, |
i.e., perspective of the universal that isn’t the universe or totality.
e.g., operation, function, antiderivative, etc., e.g., “inverse sequence of...,” “double of,” “multiplicative product of...,” etc.
|Subject-formative functor.||Info-adding-&-removing abstraction, |
|4. Reversible deduction |
preserves both truth & falsity).
|2. Applied-yet-deep mathematics |
(deductive theories of optimization, probability, information, logic).
|Universal-cum -monadic- or-polyadic -singular, |
i.e., perspective of a universe, collective totality, gamut.
probability, info (qua novelty, newsiness), logical conditioning & compounding, etc., e.g., “not,” “with a probability of 57%,” etc.
|Predicate-formative functor.||Info-increasing abstraction, |
|3. Non-reversible deduction |
(decreases info; preserves truth but not falsity).
|3. Abstract-yet-positive- phenomenally-deep sciences/studies |
(ampliatively-inductive theories of inverse optimization, statistics, information, philosophy).
|Special-cum -general, |
i.e., perspective of the
|Attribute.||Predicate.||Info-decreasing abstraction, |
|2. Ampliative induction |
(increases info; preserves falsity but not truth).
|4. Idioscopy, the special sciences/studies |
(physical, material, biological, human/social).
|Special-cum -monadic- or-polyadic -singular, |
i.e., perspective of singulars that aren’t the only ones.
e.g., you, me, the lamppost, etc.
|Subject.||Concrete (info preserved), |
|1. Abductive inference, surmise |
(adds & removes info; preserves neither truth nor falsity).
In some cases (e.g., the modes of inference) I had arrived at my tetrachotomical version of a Peircean trichotomy before I had read Peirce or learned anything about him beyond his having been a philosopher, though in those cases I tended not to understand my tetrachotomy nearly as deeply as Peirce understood his trichotomy. Peirce has been a boon to me (and I hope he wouldn’t mind my applying to his structures the word “triastic” which he never used). I never even considered tetrads or any kind of polyads until I had read Peirce for a while.
Aristotle’s Four Causes seem a slightly rough tetrachotomy, in some ways a patchwork selection from corresponding terms of a set of closely related tetrachotomies, but certainly much more than a mere list of four items.
I also see four-folds and cosmic quadratures in: the classic info-theoretic source-encoding-decoding-destination setup; the special-relativistic lightcone; special-relativistic kinetics; the classification of research; the classification of areas of human social activity; and sundry. In pursuing these subjects, I’ve found that there’s not exactly a forest of us “fourists,” of the dusty-shelf philosophical variety anyway.
(1) many-to-many — graph theory — optimization — distance, difference (with direction)
(2) one-to-many — enumeration — probability — ratio
(3) many-to-one — group theory — information — logarithm
What is the next step?
(4) one-to-one — order, relations — deductive logic —
Update January 20, 2014: I've cut out a bunch of speculation about the roles of tetration's inverses (hyperlogarithm, hyperroot). I remember years ago speculating via email with Chris Lofting that the "next step" mentioned above would be one of tetration's inverses (hyperlogarithm or hyperroot). At that time I was thinking of arity only in regard to truth values. For a little more discussion, click here. End of update.
Indeed, logical issues grow potentially so complex so rapidly, and sometimes at least seemingly tetratively, that it’s hard to believe that the mind deals with them in anything like the way it deals consciously with logical issues. The conscious mind gets confused and, as a solution, ends up abstracting the logical structure which becomes another chunk or three in the soup. Often many little chunks floating randomly. Same scene, different metaphor, the bicyclist through excess of self-consciousness falls off his bicycle. It’s natural for the mind to shun such crackups. But tetrastic structures are only a little beyond the kind of starting-gate logical complexity (dualistic) with which most people prefer to deal. And if there’s something “more,” something irreducible, in whatever
In one tetrachotomy, a fifth term emerges as the common element of which certain pairs of the first four terms are pairs of complementary forms. It seems no violation of any reasonable tetrastic thesis, instead it seems a natural enough expression of an aspect of a logically fourfold structure, like introducing a quantificational “ T ” (for “quantificational truth”) as the tautologous alternative between opposite corners of the logical Square of Opposition
Quite a few of my tetrastic structures have either emerged as, or taken on the cast of, revisions of Peirce’s triastic structures. Paul Burgess, in a 1988 paper “Why Triadic? ” available at his Website, reviews past attempts to add fourth elements to Peirce’s threes. As far as I can tell, my efforts don’t resemble those.
At the opening of his fragment “Trichotomic” (EP I: 280), Peirce evocatively says:
TRICHOTOMIC is the art of making three-fold divisions. Such division depends on the conceptions of 1st, 2nd, 3rd. First is the beginning, that which is fresh, original, spontaneous, free. Second is that which is determined, terminated, ended, correlative, object, necessitated, reacting. Third is the medium, becoming, developing, bringing about.
If the means-end dichotomy is useful or illuminating, such that any philosophical thought is built on it, then it is both necessary (by the standard of information-theoretic simplicity) and certainly tempting, to at least try to extend it in correlations to all FOUR turns of becoming: starting, continuing, stopping, and abstaining or “continuing not to.”
Here is a down-to-earth example.
In human affairs such that happiness, satisfaction, etc., are the end and the investing of work, preparation, etc., the means, what is the beginning? It might be interesting for the reader to stop for a moment and think of an answer to that before reading on.
Trying, attempting, deliberating, undertaking, trying out, are, I think, the beginning in the same sense that happiness and satisfaction are the end and rational work the means. What is the check (or the checking)?
Knowledge, familiarity, recognition, etc., are the check. One often checks because one knows that nothing is guaranteed, that one is fallible at best, and that success usually involves some luck. One rightly feels at least somewhat lucky in success. Luck, for its part, favors those who try.
Closely coupled yet mutually independent two-value parameters seem quite common. Again, a reason to look for extended or recurrent tetrastic patterns in philosophically interesting structures is that it seems that very few have tried or, at any rate, pursued it far. And related to that is another reason why I like Peirce — he saw his triads and trichotomies in proliferant pattern, pattern whereby he navigated seven seas of metaphysics and indeed all the philosophically journeyable worlds that that astounding polymath could find.