13·     Meaning Spaces

1. Semiotic systems
2. Codetermination
3. Dynamics and state spaces
4. Denoting and signifying
5. Conceptual spaces
6. Minds and signs
7. Logical spaces
8. Cultural spaces
9. Continua

Meaning is an event, generated in semiosis and merging with other events in the continuous flow of signs.

— Raposa 2020, 7

Thus, all knowledge comes to us by observation, part of it forced upon us from without from Nature's mind and part coming from the depths of that inward aspect of mind, which we egotistically call ours; though in truth it is we who float upon its surface and belong to it more than it belongs to us. Nor can we affirm that the inwardly seen mind is altogether independent of the outward mind which is its Creator.

— Peirce, CP 7.558 (1895)

For the real world is the world of sensible experience, and it is a part of the process of sensible experience to locate its facts in the world of ideas.

— Peirce, CP 3.527 (1897)

Par l'espace, l'univers me comprend et m'engloutit comme un point. Par la pensée, je le comprends.

— Pascal (Pensées, i. 6)

Semiotic systems

The phenomenon that distinguishes life forms from inanimate objects is semiosis. This can be defined simply as the instinctive capacity of all living organisms to produce and understand signs.

— Thomas Sebeok (2001a, 3)

Consider a very simple life form, a single living cell, say an amœba. Does it understand anything? Does it read any signs? Does it even feel anything? Since human feeling is clearly a function of the human nervous system, it seems most unlikely that an organism with no nervous system at all could feel (let alone understand) in the way that humans do. But, since each of us began life as a single cell, we can be equally sure that the human way of understanding has developed and evolved from a process taking place in even the simplest forms of life – a protosemiotic process.

Every living cell ‘knows’ how to stay alive, how to maintain its own integrity. This ‘homeostatic’ self-maintenance or self-regulation involves responding to changes in its internal milieu – changes which are often contiguous, or causally related, to changes in its external milieu. The cell doesn't need to include a separate set of instructions for doing all this; its knowing is not separate from its being. It doesn't need to know anything about the ‘rules’ that determine what it does in response to changes in its environment. Certain physical/chemical changes trigger other physical changes without recourse to any conscious decision-making.

But suppose one change leads to another which leads to another in a regular (non-random) pattern: c1 > c2 > c3. Then c2 mediates between c1 and c3. For example, something bumps into our amœba and it reacts to that contact by drawing back from it, or by trying to consume it. This is a different situation from one billiard ball bumping into another: the amœba's reaction was provoked by a clash with its external world, but it was powered by an internal energy source, its own metabolism, and guided by the nature of its internal dynamics. Some reaction at the molecular level must have mediated between the perturbation and the response. An actual transformation of energy (such as a chemical reaction), when caused by the collision to determine the organism's response, could be considered as a sign: its dynamic object is the actual “bumping” event, and its interpretant is the amœba's observable movement.

The sign itself, the chemical reaction, is what Peirce called an Actisign (EP2:483), or a Sinsign, ‘an actual existent thing or event which is a sign’ (EP2:291; here ‘the syllable sin is taken as meaning “being only once,” as in single, simple, …’). But if its interpretant is the regular response of the organism to that type of change in its situation, then the regulation is itself a sign, namely a legisign, ‘a law that is a Sign’ (EP2:291). This ‘law’ or ‘rule’ governing the response is not a one-time event or existing thing but a habit, in Peirce's broad sense of that word, a general tendency to respond in that way whenever that kind of situation recurs. ‘That way’ is the general kind of actual occurrence (c2) that will work as the means of getting from c1 to c3.

Any being capable of learning from experience inhabits an outer world by sustaining an inner world of habits, which in turn sustain both one's autonomy and one's fitness to occupy an ecological niche. In that sense the guidance system comprehends the universe that physically contains it. As Pascal said (above), thought (semiosis) and space mutually “contain” one another to create a universe in meaning space. One learns by engaging in semiosis, by reading signs which inform one's guidance system. Signs capable of doing this are called ‘informational signs, quasi-propositions, or Dicisigns’ by Peirce (EP2:275) in his 1903 classification of sign types. We will take a closer look at these below.

This learning process, pervading the biosphere, is the evolution of semiosis. As organisms and their relations with their situations grow more complex, habits grow from automatic responses to autonomic functions of nervous systems to the ‘self-control’ of intentional guidance systems.

The Dynamical Object of a genuinely informational sign, being ‘an object of actual Experience’ (SS 197), is always “outside” of the interpreting system in the sense of being beyond its control – and therefore able to make a real difference to its self-control, its habit-system, its ‘inner law.’ As the flow of energy depends on the difference between source and sink, the flow of semiotic ‘energy’ depends on the Secondness of object to sign. But as Gregory Bateson (1979, 113) observed, animals respond to stimuli ‘with energy got from metabolism’ and not from the stimulus. This is how semiotic causality or ‘determination’ differs from efficient causality.

‘In the “control” of action by information, the energy is already available in the respondent, in advance of the impact of events’ (Bateson 1979, 113); he calls this collateral energy. Likewise the collateral experience which locates the dynamic object of a sign in some common reference space must be the interpreter's experience, as neither the utterer nor the sign can provide it. The same goes for the event of meaning: a sign lives by determining an endless series of interpretants, and although each is mediately determined by the object, ‘the function of the dynamic object is not to generate but to constrain a series of interpretants’ (Colapietro 1988, 19). Only a living semiotic system with its own intentions can direct its own attention to the object of a sign, which it must do if the interpretant sign is to be informed by the sign which determines it.

Codetermination

Semiosis is the processual engine which propels organisms to capture ‘external reality’ and thereby come to terms with the cosmos in the shape of species-specific internal modeling systems. This index-anchored model of the Umwelt operates as a circuit to suit the evolutionary purposes of each species and every individual.

— Sebeok (2001b, 15)

The internal space in which this ‘model of the Umwelt operates’ constitutes the primal meaning space for any organism capable of meaning, or of experiencing qualia. For instance, as observed in Chapter 12, the quality of sense experience is determined by the form of the relation between dynamic (external) object and (internal) nervous system. Thus, while the form of a sign's object determines the sign to determine an interpretant sign of the same object, the form of the interpretant is co-determined by the current ‘state of information’ of the bodymind. This semiotic relationship means that meaning can occur only to a complex system with variable habits coupled to the complexities of an external world. We can think of the semiotic ‘determination’ process as selecting specific habits for activation, so that they propagate and translate the form communicated by the sign. The development of one's habit-system, including sign-reading habits, is constrained by the form of one's embodiment. In order to mean something, a sign has to make a real connection between a dynamic object and the form of a feeling.

Every mode of understanding corresponds to the mode of being of the interpreter.

— Henry Corbin (1971, 145)

Ray Jackendoff (2002, 268) offers this ‘uncontroversial postulate’: ‘People find sentences (and other entities) meaningful because of something going on in their brains.’ Even less controversial, though, is the observation that we are not conscious of meaning, when it happens, as something our brains do. We usually experience meaning as something that signs do, or that we do as utterers and interpreters of signs.

For a symbolic species, a language is the first thing that comes to mind when we think of a semiotic system. Meaning is something we expect language to do, and likewise we expect other people to mean something when they say something intentionally. But things and events can be meaningful to anybody with a nervous system, whether it uses language or not, and whether the significant thing was an intentional utterance or not. One example given by Jakob von Uexküll: a whiff of butyric acid is very meaningful for a tick, as a signal that causes her to let go of whatever she is clinging to, so that she falls toward her prey. The meaningfulness of this sign has evolved along with the tick: butyric acid marks the presence of a mammal, and responding to it has enabled the tick species to find its food, survive and reproduce. This kind of “natural sign” is pervasive in the biosphere; semiosis is more than human.

The meaning of a natural sign depends on the kind of system which has evolved to read it, and the interpretant depends on the intentionality of the organism engaged in the meaning cycle. Walter Freeman explains how this engagement is embodied in brain dynamics:

I propose that meanings arise as a brain creates intentional behaviours and then changes itself in accordance with the sensory consequences of those behaviours. Aquinas and Jean Piaget both called this process ‘assimilation.’ It is the process by which the self comes to understand the world by adapting itself to the world. The contents of meaning derive from the impact of the world, principally the social impact of actions of other humans upon ourselves, and they include the entire context of history and experience we have already acquired. Although the contents of meaning are largely social in origin, the mechanisms of meaning are biological and have to be understood in terms of brain dynamics.

— Freeman (1999a, 11)

In speaking of ‘the contents of meaning,’ Freeman uses the container metaphor in a way that implies the inside-outness of the world; for here the ‘contents’ of meaning (whatever is included within it) are derived from dialogue with the external world, yet ‘contained’ internally, within the ‘intentional structures’ embodied in the brain.

This intentional mechanism has its price, which is the isolation of each brain. With respect to energy and information each brain is an open system with continual throughput, but with respect to meaning it is a closed system. This is because meaning is constructed afresh by each brain in the context of its individual genetic, experiential, and cultural history. Geometrically, intentionality can be conceived as a structure, and the meaning of an event is a place in that structure. Because the patterns of neural activity are self-organized by chaotic dynamics, so also are the frames of reference of each intentional structure. Hence there is no way by which to cross reference meanings between these individual structures.

— Freeman (1995)

Dynamics and state spaces

In order to understand the internal dynamics of any system, we can diagram events as occurring in its state space, which is

a map of all the possible states a system can assume, with paths or trajectories indicating its tendencies over time. Such a map is often shown as a topographical surface pocked by wells or valleys that stand for attractors and hills that stand for repellors. Attractors are defined as stable, recurrent, or resilient states in which systems tend to settle or get stuck. Attractors are surrounded in the state space by basins – regions of states that gravitate to the attractor. Repellors are states the system tends to move away from or avoid.

— Lewis and Granic (2000, 8-9)

A system capable of meaning, or of any kind of sign-reading, is a living bodymind incorporating a nervous system “moving” from “state” to “state” in its own state space. A ‘state’ is an abstraction from this constant self-changing; the ‘state space’ is a diagram of possible states which we draw from observation of the more or less regular patterns of change. Again, the example most obvious to a human being is a human being.

The biology of meaning includes the entire brain and body, with the history built by experience into bones, muscles, endocrine glands and neural connections. A meaningful state is an activity pattern of the nervous system and body that has a particular focus in the state space of the organism, not in the physical space of the brain.

— Freeman (1999a, 157)

Thelen and Smith (1994, 179) describe how ‘knowledge grows out of specific experiences’ and

how specific experiences are interpreted by past experience: the pattern of activity in neural processes depends on the life history of the organism.… the topology of the state space depends on the specific patterns of activity that emerge in real time. From these ideas, we can see how changes over the developmental time scale will emerge. With the continuous experience of perceiving and acting, deep and stable attractors will emerge in the landscape of the state space and stable attractors will affect the paths caused by other experiences. More specifically, some attractors are deep and stable enough that they will cause many experiences to yield the same mental event. They will constitute generalized predictions about the world. In other words, they will perform the functions generally ascribed to conceptual knowledge.

A concept in logical space corresponds to an attractor in biological meaning space, just as a habit does to an attractor in behavior space (Chapter 9). These spaces share some common principles, ‘topological universals’ which govern the way they are shaped. In Freeman's account, each brain has its own ‘frame of reference,’ its own meaning space. Its closure and consequent isolation are normally hidden from us because we map the public resources of language onto these private topologies. This mapping also conceals the polyversity intrinsic to language: as you make sense of these sentences, you have no direct way of knowing whether they play the same role in your meaning space that they played in the author's.

Every species has its Innenwelt as a meaning space; what a nonsymbolic species can't do is experiment with different mappings between Innenwelt and Umwelt, by taking these maps apart in imagination and recombining them to consider unrealized possibilities and guess at their potential for actualization. A symbolic species can do this by mapping a self-organizing system of signs onto their Umwelt so that relations among signs map onto relations among objects and actions within it. From a logical point of view, propositions are the basic elements of this semiotic mapping.

According to Peirce, ‘a proposition is a Dicisign that is a Symbol’ (Peirce, EP2:282). The intended interpretant of such a Dicent Symbol represents it ‘as being, in respect to what it signifies, really affected by its Object, so that the existence or law which it calls to mind must be actually connected with the indicated Object’ (Peirce, EP2:295). To indicate an object is to single it out for attention. ‘All propositions relate to the same ever-reacting singular; namely, to the totality of all real objects’ (EP2:208); but the limitations of our attention force us to focus on only a few of these objects at a time, leaving the rest in the background.

Denoting and signifying

We learn from experience by seeing and saying something about an object. Traditionally, the part of a proposition which denotes its object is called the subject, and the part which informs us about that object is called the predicate. The predicate generally represents the form of the relations involved in some kind of complex object/event, which form is connected to the object by the proposition. A predicate is always general, i.e. is applicable to a range of individual objects, so that it's up to the interpreter (with the help of the subject) of the sign to single out some object of attention and judge whether the predicate applies to it or not. To the extent that the form signified by this predicate does apply to that object, the proposition is true.

As for the ‘meaning,’ logicians have recognized since Abélard's day and earlier that there is one thing which any sign, external or internal, stands for, and another thing which it signifies; its denoted breadth, its “connoted” depth. They have further generally held, in regard to the most important signs, that the depth, or signification, is intrinsic, the breadth extrinsic.

— Peirce, CP 8.119 (1902)

Every legisign signifies through an instance of its application, which may be termed a Replica of it. Thus, the word “the” will usually occur from fifteen to twenty-five times on a page. It is in all these occurrences one and the same word, the same legisign. Each single instance of it is a Replica. The Replica is a Sinsign.

— Peirce, EP2:291

‘The signification of a complex symbol is determined by certain rules of syntax which are part of its meaning’ (EP2:317), and these ‘rules’ are intrinsic to the language or symbol system internalized by the user as a set of habits. To the extent that your Innenwelt is linguistic (or otherwise symbolic), it determines what you can signify by means of symbols, creating an intrinsic meaning space.

The breadth or extension of a sign, on the other hand, is extrinsic to it, being the range of dynamic or ‘Mediate’ objects to which it can refer.

The Mediate Object is the Object outside of the Sign; I call it the Dynamoid Object. The Sign must indicate it by a hint; and this hint, or its substance, is the Immediate Object.

— Peirce, EP2:479

In Chapter 10 we heard from Terrence Deacon that ‘symbols do not directly refer to things in the world, but indirectly refer to them by virtue of referring to other symbols,’ which they can do ‘by virtue of occupying determinate positions in an organized system of other symbols … This system of relationships between symbols determines a definite and distinctive topology that all operations involving those symbols must respect in order to retain referential power’ (Deacon 1997, 99). The subject of a proposition directs attention within that definite topology, while the indexical component of the symbol locates its dynamic object – which may be an individual thing or event, or a nexus of them, or a process, or an imaginary entity inhabiting the commens.

Conceptual spaces

As we saw in Chapter 12, ‘No object can be denoted unless it be put into relation to the object of the commens.’ And we can say nothing about any object unless we can locate its qualities (or relations with other things) in the dialogic or cultural meaning space which is the form of the commens.

But insofar as we can communicate symbolically, we also have an inner world, an Innenwelt, in common; and this is populated by thought-signs which we call concepts. The biological basis of psychological concepts lies undoubtedly in the self-organizing dynamics of the nervous system, which are similar from person to person. Thus ‘it appears reasonable to assume that the psychological conceptual spaces of humans are, at least in their fundamental dimensions, close to identical’ (Gärdenfors 2000, 81). However, each bodymind has to learn its own way of mapping back and forth between linguistic symbols and conceptual space. Hence the polyversity of language.

The contents of conceptual space are not an unstructured heap that simply grows larger as we add more. The growing structure has an organic unity, so a change to any part ripples through it all. This applies to the public domain of science as well as the private domain of experience.

Willard Quine, in his essay ‘Two Dogmas of Empiricism,’ described empirical science in such organic terms: ‘our statements about the external world face the tribunal of sense experience not individually but only as a corporate body …. The unit of empirical significance is the whole of science’ (Quine 1961, 41, 42). Our model of the world, whether formal/scientific or informal/preconscious, is a web or network woven together in such a way that changing any part of it may determine further changes. At the same time, the need for simplicity urges us to minimize those changes, either by ignoring new experience that threatens to disrupt the habitual model, or by incorporating its implications into the model in whatever way best suits the current structure of the web.

The ‘network’ shape of the model, then, is not like the shape of the meaning cycle, which represents time as a one-way flow around the circle. This new model is a meaning space inhabited by concepts: meanings ‘take place’ within it. ‘Science’ as a public model (rather than a method/process of modeling/knowing) is embodied in an organic form which changes over time. Quine's picture of that form or body of knowledge has a core/periphery structure: messages come into the model (science) from its periphery, and the closer to the ‘core’ a conceptual structure is, the less it is affected by input from the world.

For habitual language users, the form of conceptual space is intimately related to the forms of the language. But those forms also reflect the forms of systemic embodiment. Leonard Talmy (2000) compares the structure inherent in grammatical forms with those involved in visual perception, and generalizes to an ‘overlapping systems model’: ‘the possibility is that each major cognitive system has some conceptual structuring properties that are uniquely its own, some properties that it shares with some cognitive systems but not with others, and some properties that run in common through all the systems’ (Talmy 2000, I.93).

If we picture conceptual space as a network, we picture a concept as a node in the network: the meaning of a word is the node it names, and the meaning of a node consists of its relationships with other nodes. Conceptual meaning space is analogous to an ecosystem, in which each species occupies a multidimensional niche defined by its potential interactions with the various entities which compose the ecosystem. Similarly, the meaning of a concept is the role it plays in the conceptual system as a whole.

In the lexicon of evolutionary biology, a niche is the space occupied by a species, i.e. the part of an ecosystem which is most directly involved with the continuing life of the species. You could say it is a third-person view of the Umwelt of that species. ‘Purely descriptively, a niche is the outward projection of the needs of an organism, or, in G. E. Hutchinson's definition, it is a multidimensional resource space’ (Mayr 1988, 135). There are certain concepts that you personally need in order for your internal dialog to maintain the integrity of your Innenwelt and thus make sense of your Umwelt. When you use language for that purpose, the niches in your meaning space get filled by words as the dialectical need arises. (‘Word’ here is being used rather loosely; to be more precise, we should speak here of lexemes, linguistic units which may actually be phrases, or roots, or other units larger or smaller than words.) Words are selected for current purposes from the repertoire offered by the language.

All this talk of niches is necessarily vague and hard to verify. Since there is no way to ‘cross reference meanings,’ as Freeman put it (above), how could we find out whether it even makes sense to speak of a niche in your meaning space being ‘the same’ as a niche in mine? But the beauty of this model is that it explains this vagueness even while exemplifying it. It does not pretend to transcend its own limitations. Since any investigation into the relations between word and meaning must employ as tools some of the very phenomena under investigation, this construction project is at least as fallible as any other cognitive project.

What makes any internal model useful to its host is that it is ‘index-anchored.’ An indexical sign anchors the model in external reality ‘because it is in dynamical (including spatial) connection both with the individual object, on the one hand, and with the senses or memory of the person for whom it serves as a sign, on the other hand’ (Peirce, BD ‘Index’). For example, the impact of light causes a physical change in a retina, film or photographic sensor. This produces an image which, in the case of a photograph, is an index of whatever the camera was pointed at when the shutter was open. But the form of the resulting image can only be represented iconically: in order to convey any information, the index must involve an icon. Moreover, the reader of that index, in order to be informed by it, must already know how to read it, must be in the habit of reading photographs.

Likewise a pointing ‘index’ finger acts as an index by directing attention to something in the environment of both the pointer and the reader of the index – but this only happens if the reader is in the habit of interpreting a pointing finger as an act of directing attention elsewhere. Such a habit is practically universal among humans and rare among other species. In other words, a pointing finger acts an an index only because it is involved in a symbol system, a habit-system in which signs are used intentionally to denote individual things or events, signify general forms or patterns of relationship, and identify those things as specific instances of these general forms. Logically, a relationship is ‘the conception of a fact about a set of things abstracted from the representation of the things themselves or, in other words, a predicate which requires more than one subject to complete a proposition, or conception of a fact’ (Peirce, CP 6.318, 1909). The subjects of a proposition, taken together, denote the object which it ‘signifies, or indirectly images, in the predicate’ (BD ‘Subject’).

Minds and signs

Among humans, symbols and other legisigns live in consensual meaning spaces. ‘Every conventional sign is a legisign. It is not a single object, but a general type which, it has been agreed, shall be significant’ (Peirce, EP2:291). However this ‘agreement’ need not be deliberate or conscious; most of the many words in your vocabulary have never been “legislated” to mean what they do – rather those meanings have evolved through generations of use. As Zhuangzi observed, ‘a path is made by people walking on it.’ The people (and their walks) are individual, but the path is for general use. All symbols are legisigns, inhabiting niches in a meaning space familiar to their users; thus an alternate name for a legisign is Famisign (EP2:483).

Terrence Deacon (2012, 398) gives an example to show how interpretation of a sinsign can lead to the development of legisigns, as a ‘consequence of necessary stages of constructing an interpretation.’

Consider the interpretation of the chevron insignia on a military jacket. Initially, it appears just a coloured shape, an iconic sinsign. As similar shapes are seen on other shoulders, it develops from an iconic sinsign to an iconic legisign (shapes of the same type). As it is understood to distinguish the individual wearing it, it becomes interpreted as an indexical legisign (pointing to something about this person). When its particular configuration is understood to designate that person’s military rank it becomes interpreted as a symbolic legisign. The same sign vehicle thus is the locus for a sequence of interpretive phases in which both the relationship of the sign vehicle to other sign vehicles and the relationship of the sign vehicle to its reference are progressively developed.

Just as interpretants develop through ‘interpretive phases,’ meanings evolve over historical time through the recurrence and growth of symbols.

Symbols grow. They come into being by development out of other signs, particularly from icons, or from mixed signs partaking of the nature of icons and symbols. We think only in signs. These mental signs are of mixed nature; the symbol-parts of them are called concepts. If a man makes a new symbol, it is by thoughts involving concepts. So it is only out of symbols that a new symbol can grow. Omne symbolum de symbolo. A symbol, once in being, spreads among the peoples. In use and in experience, its meaning grows. Such words as force, law, wealth, marriage, bear for us very different meanings from those they bore to our barbarous ancestors. The symbol may, with Emerson's sphynx, say to man,

Of thine eye I am eyebeam.

— Peirce, EP2:9-10

Growth in this sense is an organic process of development or evolution. How did legisigns, symbols and language evolve from the kind of protosemiotic process outlined above? Here's one guess: as organisms grew more complex, so did self-regulation, including the processes mediating between perturbing events and bodily responses. These processes became more semiotic, in the sense that the interpretant of each sign was more likely to be itself a sign (which determined yet another internal interpretant) rather than an overt movement. Internal signs developed into whole systems (complete with inner loops) mediating between percepts and precepts, between body-maps and habits. As Hurford (2007) argues, they began to function like concepts and propositions long before the advent of language as we know it. The Innenwelt of a complex organism had to economize by self-simplifying, by representing its relations with its Umwelt as an internal model, an iconic sign of those relations, indexed to the current moment of its bodily dynamics (including sensations). These signs increasingly informed the habits, which in turn guided the performance of the organism, thus becoming legisigns.

For any member of a symbolic species, the form of the guidance system is intimately related to the form of the symbol system or language which is its main medium of communication. Human thoughts, concepts, words, propositions, arguments and texts are all symbols and/or parts of symbols. Anthroposemiosis (the human use of signs) is characterized by far more complex symbol systems than any other semiotic domain of which we know, and these bestow a distinctive shape (or rather topology) on the human ‘signification sphere’ (Brier 2008, 32). But there is a deeper, more-than-human logic underlying all systems capable of evolving or learning by experience.

The growth of symbols – their increase in breadth, depth or information – leads to the growth of symbol systems. Once again, ‘if any signs are connected, no matter how, the resulting system constitutes one sign.’ Moreover, ‘every sign,— or, at any rate, nearly every one,— is a determination of something of the general nature of a mind, which we may call the “quasi-mind”’ (Peirce, EP2:389). Quasi-minds are ‘things capable of varied determination as to forms of the kind communicated’ (EP2:544). In a 1906 manuscript (MS 283), Peirce gave a remarkable sketch of a ‘quasi-mind’ as itself a ‘perfect sign’ – ‘perfect’ in its restless, dynamic activity:

Consider then the aggregate formed by a sign and all the signs which its occurrence carries with it. This aggregate will itself be a sign; and we may call it a perfect sign, in the sense that it involves the present existence of no other sign except such as are ingredients of itself. Now no perfect sign is in a statical condition: you might as well suppose a portion of matter to remain at rest during a thousandth of a second, or any other long interval of time. The only signs which are tolerably fixed are non-existent abstractions. We cannot deny that such a sign is real; only its mode of reality is not that active kind which we call existence. The existent acts, and whatsoever acts changes.… It is abstractly conceivable that a particle should remain at rest; but in fact, it never does so.

Every real ingredient of the perfect sign is aging, its energy of action upon the interpretant is running low, its sharp edges are wearing down, its outlines becoming more indefinite.

On the other hand, the perfect sign is perpetually being acted upon by its object, from which it is perpetually receiving the accretions of new signs, which bring it fresh energy, and also kindle energy that it already had, but which had lain dormant.

In addition, the perfect sign never ceases to undergo changes of the kind we rather drolly call spontaneous, that is, they happen sua sponte but not by its will. They are phenomena of growth.

Such perfect sign is a quasi-mind. It is the sheet of assertion of Existential Graphs.…

This quasi-mind is an object which from whatever standpoint it be examined, must evidently have, like anything else, its special qualities of susceptibility to determination. Moreover, the determinations come as events each one once for all and never again. Furthermore, it must have its rules or laws, the more special ones variable, others invariable.

— Peirce, MS 283:279–83 (1906); EP2:545

Logical spaces

Since the reality of the ‘perfect sign’ is ‘of that active kind we call existence,’ Peirce's ‘Existential Graphs’ are aptly named as a way of visualizing the continuous activity of the ‘quasi-mind’ – or more specifically, of the mind engaged in learning by experience. Peirce's intention was to ‘construct a diagram to illustrate the general course of thought’ (CP 4.530, 1906), but actually this requires a sequence of diagrams, so that EGs give us ‘moving pictures of thought’ (CP 4.8, 1906). Each graph in the sequence is like a single frame of a motion picture. Since the mind is itself ‘a sign developing according to the laws of inference’ (Chapter 12), the EG system analyzes the development process as a series of transformations of graphs. Each graph in the sequence represents a step in the process as if it were a “state of mind.” The ‘laws of inference’ are represented by a set of rules (‘permissions’) governing the transformations from one “state” to the next.

Peirce introduced EGs to his audience in a 1903 lecture at the Lowell Institute in Boston. A transcription of the whole lecture is available on this site; details of the following sketch of the EG system are drawn from that source unless otherwise noted.

According to Peirce it is ‘a necessity of Logic’ ‘that every logical evolution of thought should be dialogic’ (CP 4.551). In the EG system, each graph is part of a dialogue about things existing in some universe of discourse. The dialogue begins with the blank sheet or surface on which a graph may be ‘scribed’:

It is agreed that a certain sheet, or blackboard, shall, under the name of the Sheet of Assertion, be considered as representing the universe of discourse, and as asserting whatever is taken for granted between the graphist and the interpreter to be true of that universe. The sheet of assertion is, therefore, a graph.

— CP 4.396, 1903 ‘Syllabus’ (R 478)

Each explicit assertion scribed on the sheet takes the form of a proposition. In order to represent the relations between propositions within a reasoning process, our diagram needs to show spaces separated from the space represented by the whole sheet. But since they are scribed on the sheet of assertion, they are visually included in that space as well as separated from it. One of these separate spaces or areas, as Peirce called them, can be marked off by a boundary drawn around it, or by being differently colored or shaded. Areas may also include other areas marked off from them, so that a graph can become as complex as necessary to represent the thought; but areas cannot overlap (as Venn diagrams do).

According to Peirce, the most ‘immediately useful information is that which is conveyed in conditional propositions,’ which are expressible in this form: “If you find that x is true, then you may know that y is true.” To show this visually, we need an if-space and a then-space. These are represented in EGs by a ‘scroll.’ In the graph replicated here, x represents the if-clause and y the then-clause of the conditional proposition. The same graph could represent a simple argument in which x is the antecedent and y is the consequent. To express this relation verbally, we can say that y follows from x, or that x logically implies y, or that class x includes y, depending on the context. This graph is an icon of the consequence relation, which may thus be named illation, implication or inclusion. Peirce came to prefer EGs over algebraic notations because they represent such logical relations more iconically.

For the sake of simplicity, he began his Lowell explanation of the EG system with analysis of the ‘conditional proposition de inesse,’ a special form which ‘says nothing at all about any real connection between antecedent and consequent’ but merely shows the abstract relation of consequence between them. This was necessary to keep the focus on mathematical or necessary reasoning, which ‘can never answer questions of fact.’

Also for the sake of simplicity, the objects of the propositions represented by EGs are assumed to be individual or existing things, even though the universe in which they exist is imaginary. ‘Individual’ things are defined as fully determinate, which entails that every proposition about them is either true or false, with no third option (the principle of excluded middle). This principle does not apply to propositions about general subjects (EP2:350), which are very common in the real world of human semiosis.

Since Peirce maintained ‘that there is but one primary and fundamental logical relation, that of illation’ (CP 3.440), he realized that ‘the concept of the negation is not primitive and has to be derived from the illative sign of the scroll’ (Pietarinen, LF1, Kindle Location 2139). This is why he takes the trouble in his Lowell lecture to explain why we can read a single ‘cut’ enclosing a graph as saying that the graph is false. Thus if x and y in the scroll graph above are propositions, we can read the graph as follows: “It is not true that x is true and y is not true.” This is a more complicated way of saying that x implies y, or ‘If x then y’; but it greatly simplifies the reading of the deeply nested graphs needed to represent more complex assertions.

In his lecture, Peirce proceeded to explain the rules or ‘permissions’ which allow us to transform graphs without ever converting a true graph into a false one. All of this applies to propositional logic, i.e. relations between propositions in deductive reasoning. To depict relations between subjects and predicates within propositions, Peirce needed to introduce another basic sign called the line of identity. This enhancement, accompanied by a few new rules, generated the ‘beta part’ of the EG system, introduced in the later part of his lecture. In the fourth Lowell lecture he explained the limitations of the beta part:

Its reasonings generally turn upon the properties of the relations of individual objects to one another. But it is able to do nothing at all with many ideas which we are all perfectly familiar with. Generally speaking it is unable to reason about abstractions. It cannot reason for example about qualities nor about relations as subjects to be reasoned about. It cannot reason about ideas. It is to supply that defect that the gamma part of the subject has been invented. But this gamma part is still in its infancy.

Cultural spaces

In a written or printed text, punctuation can mark boundaries between meaning spaces. Parentheses, for instance, can be used to include a parenthetical expression (within a sentence like this one) by marking it off from the main idea. Quotation marks are another example. In this book i generally use ‘single quotation marks’ to enclose the exact words copied from another text, to show that these words were meant by another (specified) writer before being imported into this writer's context. I use “double quotation marks” to indicate that the words enclosed are used by (unspecified) others in a way that may differ from my own usage. (Some people call these “scare-quotes” when they signify a kind of “warning” about the usage they mark.) Many other writers and printers use double quote marks in the way i use single ones, but i've tried to make my own usage consistent in this text.

Investigators of linguistic structure commonly view it as a network, according to Tomasello (2003, 106): ‘the majority view would seem to be that linguistic items and structures are organized in the minds of speakers in a complex, multi-dimensional network – with much variability in how richly particular linguistic units are connected to others.’

A model along these lines, developed by M. Ross Quillian, is described by Eco (1976, §2.12), who refers to it as Model Q (no relation to the hypothetical ‘sayings gospel’ mentioned in Chapter 6). He describes it as ‘a mass of nodes interconnected by various types of associative links’ (2.12.2).

It must appear as a sort of polydimensional network, equipped with topological properties, in which the distances covered are abbreviated or elongated and each term acquires proximity with others by means of short-cuts and immediate contacts, meanwhile remaining linked with all the others, according to continually changing relationships.

For instance, a monotheistically-inclined reader in a genuine encounter with a polytheistic text will discover that a world of many gods is a very different place from a world of only one. Carve divinity up into many divine beings, and none of them will bear the slightest resemblance to a single being who is all of divinity. The myths differ because these different kinds of theism carve up meaning space differently, not because one side sees reality while the other makes up myth. Once you see that God is not a god, and gods are not God, space opens up for a better translation of the respective concepts. One of the more cryptic (or possibly corrupted) sayings in the Gospel of Thomas, 30, may point in this direction:

Jesus said, ‘Where there are three gods, they are gods. Where there are two or one, I am with him.’

— 5G (Meyer has ‘I am with that one’ for final clause. A version of this saying appears in the Greek version of Thomas but the word ‘three’ is a reconstruction of a gap in the text of Papyrus Oxyrynchus. DeConick argues that the original saying was probably ‘When there are three, God [Elohim] is there,’ the first ‘gods’ having been inserted by mistake and the number intended to refer to people. See DeConick 136-7 and cf. Matthew 18: 19-20.)

In a similar way, sciences can render their own meaning spaces more visible by going back to ancient root-sources such as the early Greek cosmologists. The “atoms” of today are fundamentally different from the atoms of the ancient Greek “atomists,” because the original atoms were unsplittable by definition (that being the root meaning of the word ‘atom’). A couple of millennia later, the name was applied to the basic units of the chemical elements, and it “stuck” even after these “atoms” were actually split in the twentieth century; so the current usage of the word atom is a “frozen accident.”

Consider likewise the changing concept of an “element.” Basically it means one of a relatively small but complete set: for instance, the letters of an alphabet are its elements. (In fact the Greeks used the same word, stoicheion, for “letter” and “element.”) In the ancient debates about whether the world was primally made of earth, air, fire or water, none of these four “elements” resemble any of the chemical “elements” recognized today. The reason for the difference between ancient and modern meanings of element is not so much our improved methods of analysis as the difference in the number of ‘elements’: if you carve nature into just four parts, the resulting closed set of parts is incommensurable with a closed set of (say) 92 parts.

When a thinker like Anaximenes says that everything is made of ‘air,’ it would be an obvious misreading to identify this “substance” with what we call “air.” The first and most essential clue to guessing what Anaximenes was referring to is his theory that everything is made of it. It makes no sense now to say that everything is made of any gas or mix of gases, so the air of Anaximenes might better be compared with what Peirce called Firstness, or what William James (in his ‘radical empiricism’) called ‘pure experience.’ In fact, Anaximenes used the word πνεῦμα (as well as aer) for it – the same word usually translated ‘spirit’ (as well as ‘wind’ or ‘breath’) in English versions of the New Testament. Hence Peirce's reference to the universe of Firstness as consisting of ‘airy nothings’.

On the other hand, by the time we can call it ‘experience,’ ‘spirit,’ or ‘firstness,’ or anything else, we have lost immediate touch with it. ‘Stop to think of it, and it has flown!’ (Peirce, EP1:248) – leaving behind only tracks, traces, or tokens which get woven into cosmologies or mythologies. When one of these crosses with a writer's own experience, the result is what we call a work of “literature.”

Literature continues in society the tradition of myth-making, and myth-making has a quality that Lévi-Strauss calls bricolage, a putting together of bits and pieces out of whatever comes to hand.

— Frye (1982, xxi)

Frye's Anatomy of Criticism describes the structure of a literary meaning space analogous to the ‘universal grammar’ of theoretical linguistics (Jackendoff 2002) in that no one language, no single ‘system of thought’ or mythology, exemplifies it perfectly (or even measurably better than other systems). Each system conceals meaning space by revealing it, because each niche must be occupied in order to be functional, but we can only mention the niche by mentioning its occupant, which is variable. We only have names for the values of the variables, and can only call the variables themselves by the names of their values. Becoming conscious of meaning space itself, or of its universality, therefore depends on recognizing the variability and conventionality of names.

The importance of this point for the ongoing creative bricolage is both articulated and exemplified in Frye's introduction to The Great Code (1982, xviii):

Man lives, not directly or nakedly in nature like the animals, but within a mythological universe, a body of assumptions and beliefs developed from his existential concerns. Most of this is held unconsciously, which means that our imaginations may recognize elements of it, when presented in art or literature, without consciously understanding what it is that we recognize. Practically all that we can see of this body of concern is socially conditioned and culturally inherited. Below the cultural inheritance there must be a common psychological inheritance, otherwise forms of culture and imagination outside our own traditions would not be intelligible to us. But I doubt if we can reach this common inheritance directly, by-passing the distinctive qualities in our specific culture. One of the practical functions of criticism, by which I mean the conscious organizing of a cultural tradition, is, I think, to make us more aware of our mythological conditioning.

Side by side, then, with the well established proposition that all knowledge is based on experience, and that science is only advanced by the experimental verifications of theories, we have to place this other equally important truth, that all human knowledge, up to the highest flights of science, is but the development of our inborn animal instincts.

— Peirce, W4:450

Continua

The principle of continuity is the idea of fallibilism objectified. For fallibilism is the doctrine that our knowledge is never absolute but always swims, as it were, in a continuum of uncertainty and of indeterminacy. Now the doctrine of continuity is that all things so swim in continua.

CP 1.171 (c. 1897)

Meaning spaces are continuous for the same reason that ecosystems and their niches overlap. We can analyze any system into parts, but the parts must be connected or it wouldn't be a system. If the connections are real, then they must occur in the same space, and this space must consist of parts each consisting of parts of the same kind, no matter how small a part of it we select for analysis.

Like any other organic system, meaning space grows more complex by differentiation. When you make a new conceptual distinction that applies to a subject with which you were already familiar, the object of your attention grows more distinct as the depth of the concept increases. When you recognize a new situation in terms of your prior conceptual categories, the breadth of the concept increases. In both cases information increases. When a percept stands out from the phaneron as a newly distinct part of it, it must be related to the other parts in some way, if the new conceptual distinction is going to make a difference to your habits, because the integrity of conceptual meaning space must be maintained as the system develops.

Biologically, perception and cognition begin with a process of articulation. The embryo differentiates itself as it grows, for instance putting forth a bud which becomes an arm, from which a hand develops by further articulating itself into fingers. Perception is likewise a distinction-making process: it does not assemble a world from fragments but articulates the world into parts by focusing attention at a higher resolution. As Christine Skarda puts it, ‘the real problem of perception is that of articulation. The goal of perceptual functioning is to break up the holistic fabric of reality into perceived objects and states of affairs and perceivers of them’ (Núñez and Freeman 1999, 81). Gombrich (2002, 86) takes a similar view: ‘Neither in thought nor in perception do we learn to generalize. We learn to particularize, to articulate, to make distinctions where before there was only an undifferentiated mass.’ Gombrich here is following James J. Gibson, whom he quotes (2002, 23) as follows: ‘The progress of learning is from indefinite to definite, not from sensation to perception. We do not learn to have percepts but to differentiate them.’

Peirce made a similar point about the continuity of logical space in the last of his 1898 Cambridge Lectures:

Now continuity is shown by the logic of relations to be nothing but a higher type of that which we know as generality. It is relational generality.

How then can a continuum have been derived? Has it for example been put together? Have the separated points become welded, or what?

Looking upon the course of logic as a whole we see that it proceeds from the question to the answer – from the vague to the definite. And so likewise all the evolution we know of proceeds from the vague to the definite. The indeterminate future becomes the irrevocable past. In Spencer's phrase the undifferentiated differentiates itself. The homogeneous puts on heterogeneity. However it may be in special cases, then, we must suppose that as a rule the continuum has been derived from a more general continuum, a continuum of higher generality.

CP 6.190-1 (1898)

An increase in breadth of a concept simplifies relations with the external world by gathering more individual objects into that category. An increase in depth increases the number of types, kinds or categories into which the phaneron is carved up, or the number of characteristics which can be predicated of the one subject (the Truth).

Every proposition whatever has the Universe of Discourse for one of its subjects and all propositions have one Subject in common which we call the Truth. It is the aggregate of all realities, what the Hegelians call the Absolute.

— Peirce, EP2:173 (1903)

Scientific inquiry is a communal quest for truth, religion a quest for true community (communal unity). Both move through a medium of Thirdness, but in the one, experience as Secondness is ‘our only teacher’; in the other, feeling as Firstness takes the lead. We find a similar division of labor within the human brain. All animals are anticipatory systems, but humans have evidently taken anticipation further, thanks to our highly developed frontal lobes. According to Walter Freeman (2000, 225),

the frontal lobe refines and elaborates the predictions of future states and possible outcomes toward which intentional action is directed.… Two aspects are noteworthy. The dorsal and lateral areas of the frontal lobe are concerned with cognitive functions such as logic and reasoning in prediction. The medial and ventral areas are concerned with social skills and the capacity for deep interpersonal relationships.

As a way of sensing our collective growth toward completeness, we may imagine ‘the joyful Nirvana’ as a future state, although we may doubt that any individual or collective self will ever be aware of that state (if such awareness is even conceivable). This ‘Nirvana,’ like the ‘Truth’ at which science and philosophy aim, is an ideal limit in a quasi-mathematical sense. However, Truth and Nirvana differ from mathematical objects in that we can only see them from inside the process which generates them; we can't observe them from outside. We have no means of constructing or conceiving a diagram that includes the Absolute Truth, or a state of Universal Continuity; nor could we represent our present state of information as a point (or set of points) on such a diagram in order to measure the distance between that point and the limit we approach. That distance is, we may say, the engine of semiosis, creating the space in which it can happen – a space too vast to measure: ‘though in no possible state of knowledge can any number be great enough to express the relation between the amount of what rests unknown to the amount of the known, yet it is unphilosophical to suppose that, with regard to any given question (which has any clear meaning), investigation would not bring forth a solution of it, if it were carried far enough’ (EP1:139-40). Indeed that is what every member of an investigative community ‘virtually assumes’ (CP 5.430, 1904).

Next chapter: Communicoding →

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