The Second Trichotomy. Thought of the Day 120.0


The second trichotomy (here is the first) is probably the most well-known piece of Peirce’s semiotics: it distinguishes three possible relations between the sign and its (dynamical) object. This relation may be motivated by similarity, by actual connection, or by general habit – giving rise to the sign classes icon, index, and symbol, respectively.

According to the second trichotomy, a Sign may be termed an Icon, an Index, or a Symbol.

An Icon is a sign which refers to the Object that it denotes merely by virtue of characters of its own, and which it possesses, just the same, whether any such Object actually exists or not. It is true that unless there really is such an Object, the Icon does not act as a sign; but this has nothing to do with its character as a sign. Anything whatever, be it quality, existent individual, or law, is an Icon of anything, in so far as it is like that thing and used as a sign of it.

An Index is a sign which refers to the Object that it denotes by virtue of being really affected by that Object. It cannot, therefore, be a Qualisign, because qualities are whatever they are independently of anything else. In so far as the Index is affected by the Object, it necessarily has some Quality in common with the Object, and it is in respect to these that it refers to the Object. It does, therefore, involve a sort of Icon, although an Icon of a peculiar kind; and it is not the mere resemblance of its Object, even in these respects which makes it a sign, but it is the actual modification of it by the Object. 

A Symbol is a sign which refers to the Object that it denotes by virtue of a law, usually an association of general ideas, which operates to cause the Symbol to be interpreted as referring to that Object. It is thus itself a general type or law, that is, a Legisign. As such it acts through a Replica. Not only is it general in itself, but the Object to which it refers is of general nature. Now that which is general has its being in the instances it will determine. There must, therefore, be existent instances of what the Symbol denotes, although we must here understand by ‘existent’, existent in the possibly imaginary universe to which the Symbol refers. The Symbol will indirectly, through the association or other law, be affected by those instances; and thus the Symbol will involve a sort of Index, although an Index of a peculiar kind. It will not, however, be by any means true that the slight effect upon the Symbol of those instances accounts for the significant character of the Symbol.

The icon refers to its object solely by means of its own properties. This implies that an icon potentially refers to an indefinite class of objects, namely all those objects which have, in some respect, a relation of similarity to it. In recent semiotics, it has often been remarked by someone like Nelson Goodman that any phenomenon can be said to be like any other phenomenon in some respect, if the criterion of similarity is chosen sufficiently general, just like the establishment of any convention immediately implies a similarity relation. If Nelson Goodman picks out two otherwise very different objects, then they are immediately similar to the extent that they now have the same relation to Nelson Goodman. Goodman and others have for this reason deemed the similarity relation insignificant – and consequently put the whole burden of semiotics on the shoulders of conventional signs only. But the counterargument against this rejection of the relevance of the icon lies close at hand. Given a tertium comparationis, a measuring stick, it is no longer possible to make anything be like anything else. This lies in Peirce’s observation that ‘It is true that unless there really is such an Object, the Icon does not act as a sign ’ The icon only functions as a sign to the extent that it is, in fact, used to refer to some object – and when it does that, some criterion for similarity, a measuring stick (or, at least, a delimited bundle of possible measuring sticks) are given in and with the comparison. In the quote just given, it is of course the immediate object Peirce refers to – it is no claim that there should in fact exist such an object as the icon refers to. Goodman and others are of course right in claiming that as ‘Anything whatever ( ) is an Icon of anything ’, then the universe is pervaded by a continuum of possible similarity relations back and forth, but as soon as some phenomenon is in fact used as an icon for an object, then a specific bundle of similarity relations are picked out: ‘ in so far as it is like that thing.’

Just like the qualisign, the icon is a limit category. ‘A possibility alone is an Icon purely by virtue of its quality; and its object can only be a Firstness.’ (Charles S. PeirceThe Essential Peirce_ Selected Philosophical Writings). Strictly speaking, a pure icon may only refer one possible Firstness to another. The pure icon would be an identity relation between possibilities. Consequently, the icon must, as soon as it functions as a sign, be more than iconic. The icon is typically an aspect of a more complicated sign, even if very often a most important aspect, because providing the predicative aspect of that sign. This Peirce records by his notion of ‘hypoicon’: ‘But a sign may be iconic, that is, may represent its object mainly by its similarity, no matter what its mode of being. If a substantive is wanted, an iconic representamen may be termed a hypoicon’. Hypoicons are signs which to a large extent makes use of iconical means as meaning-givers: images, paintings, photos, diagrams, etc. But the iconic meaning realized in hypoicons have an immensely fundamental role in Peirce’s semiotics. As icons are the only signs that look-like, then they are at the same time the only signs realizing meaning. Thus any higher sign, index and symbol alike, must contain, or, by association or inference terminate in, an icon. If a symbol can not give an iconic interpretant as a result, it is empty. In that respect, Peirce’s doctrine parallels that of Husserl where merely signitive acts require fulfillment by intuitive (‘anschauliche’) acts. This is actually Peirce’s continuation of Kant’s famous claim that intuitions without concepts are blind, while concepts without intuitions are empty. When Peirce observes that ‘With the exception of knowledge, in the present instant, of the contents of consciousness in that instant (the existence of which knowledge is open to doubt) all our thought and knowledge is by signs’ (Letters to Lady Welby), then these signs necessarily involve iconic components. Peirce has often been attacked for his tendency towards a pan-semiotism which lets all mental and physical processes take place via signs – in the quote just given, he, analogous to Husserl, claims there must be a basic evidence anterior to the sign – just like Husserl this evidence before the sign must be based on a ‘metaphysics of presence’ – the ‘present instant’ provides what is not yet mediated by signs. But icons provide the connection of signs, logic and science to this foundation for Peirce’s phenomenology: the icon is the only sign providing evidence (Charles S. Peirce The New Elements of Mathematics Vol. 4). The icon is, through its timeless similarity, apt to communicate aspects of an experience ‘in the present instant’. Thus, the typical index contains an icon (more or less elaborated, it is true): any symbol intends an iconic interpretant. Continuity is at stake in relation to the icon to the extent that the icon, while not in itself general, is the bearer of a potential generality. The infinitesimal generality is decisive for the higher sign types’ possibility to give rise to thought: the symbol thus contains a bundle of general icons defining its meaning. A special icon providing the condition of possibility for general and rigorous thought is, of course, the diagram.

The index connects the sign directly with its object via connection in space and time; as an actual sign connected to its object, the index is turned towards the past: the action which has left the index as a mark must be located in time earlier than the sign, so that the index presupposes, at least, the continuity of time and space without which an index might occur spontaneously and without any connection to a preceding action. Maybe surprisingly, in the Peircean doctrine, the index falls in two subtypes: designators vs. reagents. Reagents are the simplest – here the sign is caused by its object in one way or another. Designators, on the other hand, are more complex: the index finger as pointing to an object or the demonstrative pronoun as the subject of a proposition are prototypical examples. Here, the index presupposes an intention – the will to point out the object for some receiver. Designators, it must be argued, presuppose reagents: it is only possible to designate an object if you have already been in reagent contact (simulated or not) with it (this forming the rational kernel of causal reference theories of meaning). The closer determination of the object of an index, however, invariably involves selection on the background of continuities.

On the level of the symbol, continuity and generality play a main role – as always when approaching issues defined by Thirdness. The symbol is, in itself a legisign, that is, it is a general object which exists only due to its actual instantiations. The symbol itself is a real and general recipe for the production of similar instantiations in the future. But apart from thus being a legisign, it is connected to its object thanks to a habit, or regularity. Sometimes, this is taken to mean ‘due to a convention’ – in an attempt to distinguish conventional as opposed to motivated sign types. This, however, rests on a misunderstanding of Peirce’s doctrine in which the trichotomies record aspects of sign, not mutually exclusive, independent classes of signs: symbols and icons do not form opposed, autonomous sign classes; rather, the content of the symbol is constructed from indices and general icons. The habit realized by a symbol connects it, as a legisign, to an object which is also general – an object which just like the symbol itself exists in instantiations, be they real or imagined. The symbol is thus a connection between two general objects, each of them being actualized through replicas, tokens – a connection between two continua, that is:

Definition 1. Any Blank is a symbol which could not be vaguer than it is (although it may be so connected with a definite symbol as to form with it, a part of another partially definite symbol), yet which has a purpose.

Axiom 1. It is the nature of every symbol to blank in part. [ ]

Definition 2. Any Sheet would be that element of an entire symbol which is the subject of whatever definiteness it may have, and any such element of an entire symbol would be a Sheet. (‘Sketch of Dichotomic Mathematics’ (The New Elements of Mathematics Vol. 4 Mathematical Philosophy)

The symbol’s generality can be described as it having always blanks having the character of being indefinite parts of its continuous sheet. Thus, the continuity of its blank parts is what grants its generality. The symbol determines its object according to some rule, granting the object satisfies that rule – but leaving the object indeterminate in all other respects. It is tempting to take the typical symbol to be a word, but it should rather be taken as the argument – the predicate and the proposition being degenerate versions of arguments with further continuous blanks inserted by erasure, so to speak, forming the third trichotomy of term, proposition, argument.

Richard Wagner: Parsifal

Art which transcends its own time, in addition to mirroring the artist’s quest for truth, is also a source of inspiration for those who contact it. Such art is often extremely complex and its profound meaning difficult to discern. Richard Wagner is one of the most controversial and wholly misunderstood artists of the past 200 years; and his opera Parsifal one of the most complicated works.


Wagner felt the first impulse to write Parsifal at the age of 31. He was in Marienbad working on the opera Lohengrin when he read Wolfram von Eschenbach’s ParzivalThis epic poem brings together various mythical traditions; Wagner later added elements from other legends. Three years later, in 1848, the main features of Parsifal flowed over into the draft of a drama entitled “Jesus of Nazareth,” in which Mary Magdalene takes the place of Kundry. In May 1856 Wagner wrote the draft for a Buddhist drama with the working tide “Der Sieger” (“The Victor”), in which the features of what later became Parsifal are already clear. Wagner spent Good Friday 1858 in his Zurich retreat where he had a vision and decided on the main motifs of the opera.

In the years that followed, individual characters began to take shape. At the same time, however, Wagner experienced the immense difficulties presented by the subject matter. Time and again he postponed committing anything to paper — he was plagued with such doubts that he felt like giving up the whole idea. It was not until August 1865 that he wrote a detailed draft at King Ludwig II’s insistence. But a further twelve years elapsed before the work was completed in April 1877, being published in book form the same year. The composition of the music took five more years, and only on July 26, 1882, did the first performance take place in the “Haus Wahnfried” in Bayreuth. Thirty-seven years had gone by between the first idea for the work and its completion.

Concerning Wagner’s knowledge of occultism, we know he was acquainted with Freemasons, with whom he entered into fierce debate, and with the Rosicrucians. In his library, now situated in Bayreuth and open to the public, there are translations of the Upanishads and the Mahabharata, which were just being published in his time. I suspect that Richard Wagner had exceptional intuitive abilities and could see many extremely subtle realms and interrelations directly; also that he suffered deeply because all too often he simply could not find the words to express what took place so clearly before his spiritual eye. It is therefore understandable that he identified with the figure of Amfortas: Wagner believed in living life to the full; he also saw things but could not grasp them. The basic spiritual tendency running through the opera is compassion or buddhi. Reincarnation and karma are clearly described in several places — without them the whole drama would be inexplicable.

A number of symbols and mythical elements are important for a general understanding of the work. First, the symbol of the Grail combines elements of legends from Persia and Asia Minor with those from Celtic mythology. The Grail, the cup which Jesus Christ used at the Last Supper, was made from the stone which fell from Lucifer’s crown as he plunged to earth. Lucifer (the Light-bringer) brought the mental principle to evolving humanity. The stone from Lucifer’s crown can therefore be regarded as ego-consciousness or “I am I”: without the awakening mind principle humanity would not be able to acquire knowledge, and the first step along this path is “I am I.” That this stone was fashioned into a cup or bowl which was used to catch the blood of Christ elevates its meaning because it then stands for the divine self, atma-buddhi. As Wagner remarked, it becomes “Grail consciousness” — purified, redeemed “I am.” The Grail is entrusted to Titurel. He gathers a brotherhood of knights around him, called the knights of the Grail, who devote themselves to the service of this Grail consciousness through noble deeds.

A second important symbol is the spear, derived from the spear of Longinus who, it is said, thrust it into Christ’s side during the crucifixion, shedding the Savior’s blood. It stands for higher mind, that part of us which must decide whether the mind will aspire to spirit or succumb to material desire.

A third central symbol is the swan, denoting the north. Wagner uses the swan as a symbol of those beings who, though still devoid of individual consciousness, are located in the divine realms, but have their whole development before them; this symbol is identical with that of the angel. In the last scene a dove appears, symbol according to Wagner of “divine spirit, which floats down idealistically onto the human soul.” It is the Holy Ghost or Spirit — atma-buddhi.

The first act of the opera, which takes place in the realm of the Grail, begins with trombones sounding the reveille. Gurnemanz, teacher and guardian of the secret wisdom of the Grail, wakens two squires lying asleep under a tree, saying: “Do you hear the call? Give thanks to God that you are called to hear it!” That the reveille sounds from the realm of the Grail indicates that it is a spiritual call. Buddhi penetrates the consciousness of the awakening men and Gurnemanz feels it to be a blessing. He calls on his pupils to give thanks, for he knows that few are granted the privilege of feeling this call of buddhi.

At this time Amfortas, King of the Grail, lies sick and wounded, the wound being an external symbol for inner events. In his striving towards higher things, Amfortas battled in the realm of the lower mind ruled by the black magician Klingsor and lost the spear (mind). Klingsor wounded him in his side with the spear, a wound which will not heal. This wound is the pivot of all further action. It is the fissure between the higher self and the personal self, caused by the fact that the mental principle was directed into the earthly realm where it is now ruled by Klingsor, or mind linked with desire. Gurnemanz and the squires, impelled by buddhi, now try to alleviate the pain suffered by the King of the Grail. They wish to bathe the wound, though Gurnemanz in his wisdom knows this will be of no avail. The King’s wound, an inner wound, cannot be closed by baths or ointments. Wrapped in thought, he sings: “There is but one thing can help him, only one man.” When a knight asks the man’s name, he avoids answering.

Then Kundry enters the scene, appearing wild one moment, lifeless the next. She presses on Gurnemanz a small crystal vessel containing balsam with which Amfortas might be healed. Kundry personifies the desire nature, messenger and temptress at the same time. On the one hand, desire binds us to earthly things, while on the other it provides the first impulses to understand what is hidden. Thus Kundry serves both the Grail and also, as temptress, Klingsor who seeks to divert people from the quest for the divine through the power of the senses. Wagner remarks that the black magician

beclouds the divine judgment of man through the sense impressions of the material world, and thereby leads him into a world of deception.

A dispute arises between the knights of the Grail and Gurnemanz about Kundry (desire). The squires mistrust her, but Gurnemanz says:

Yes, she may be under a curse. She lives here now — perhaps reincarnated, to expiate some sin from an earlier life not yet forgiven there. Now she makes atonement by such deeds as benefit our knightly order; she has done good, beyond all doubt, serving us and thereby helping herself.

Naturally, Kundry was also involved when Klingsor seized the spear of mind from Amfortas.

In his pain, Amfortas addresses the Grail and asks for a sign of help. In a vision he describes how someone will come to help him: “Enlightened through compassion, the innocent fool; wait for him, the appointed one.” This announcement of the foolish innocent (“Fal parsi,” hence Parsifal) refers to the reincarnating ego, which hastens from life to life. If the reincarnating ego gives full expression to its divine individuality in its personal life, the inner fissure — the wound — will be closed again, for the mind which has been directed to things of matter will be turned back to the divine.

Before divinity can be attained, however, human evolution has to be experienced. At the outset, mankind is completely unself-conscious and lives in a state of divine innocence, untouched by things of matter and without an independent mind, a state symbolized by the swan. It has to leave this state, descend to the physical realm, and experience all the conflicts that evolution entails. Through the associated suffering and the development of the thinking principle, humans learn from their own experience to feel compassion for other beings.

These developments find their corollary in the departure of young people from their parental home, the maternal plane. Such a departure is often very difficult and may be accompanied by a great deal of pain and many reproaches; but this break is absolutely necessary if young people are to go through their own experiences and develop the ability to think for themselves, though this simultaneously causes the maternal principle much grief. The result is often condemnation by one’s fellowmen.

This “descent” or gaining of independence by the monad is represented by Wagner in the slaying of the swan by Parsifal. Gurnemanz sternly reproaches Parsifal for killing the swan with an arrow. Parsifal is at first filled with childlike pride at his accuracy but becomes increasingly disturbed when he looks at the dead bird, and for the first time he feels pity. Gurnemanz inquires of Parsifal his name and origin, but Parsifal cannot remember and replies: “I had many, but I know none of them any more.” The only name he remembers is that of his mother: Herzeleide (Heart’s Sorrow). Kundry is able to provide more information about his origin: his father was killed in battle, and his mother ” reared him up in the desert to folly, a stranger to arms.” Parsifal nevertheless recalls that one day he saw the knights of the Grail riding along the forest’s edge: “I ran after them, but could not overtake them; through deserts I wandered, up hill and down dale.”

The monad yearns for more than a solitary, peaceful life. Kundry confirms this, and informs him of his mother’s death. Parsifal springs furiously at her, but Gurnemanz restrains him. Thus although the monad is endowed with a feeling of right and wrong, mind is not yet fully developed. It therefore turns, in conjunction with desire, to anger and rage. Gurnemanz, the initiate, restrains him.

The rest of the opera describes what takes place during this descent of the human monad. Gurnemanz has already recognized that Parsifal is someone who can restore the divine harmony. He offers to lead him to the feast of the Grail. Both move into their inner, spiritual realms, represented by the temple of the Grail. This realm lies beyond the differentiation of space and time. Hence Parsifal remarks: “I scarcely tread, yet seem already to have come far.”

Gurnemanz answers: “You see, my son, time here becomes space.” This is because the inner vision appears to the physical person as space. Gurnemanz warns Parsifal to pay close attention to everything he encounters and later to take it back into the realm of his personal consciousness. Before them both a scene opens with a pillared hall where the knights of the Grail carry in Amfortas. The covered shrine of the Grail is carried before them. In the background can be heard the voice of Titurel, the former guardian of the Grail, who received the Cup from the angel’s hands and learned the occult mysteries in an inner vision. He says, “Amfortas, my son, are you in your place? Shall I again today look on the Grail and live?” This indicates that the life forces of spiritual traditions steadily weaken if they are not renewed by intuitive, creative individuals. Time and again attempts are made to establish a spiritual, compassionate brotherhood. If, however, the innovators fail, the effort comes to a standstill; the teachings ossify, and what used to be the content becomes a veil, until nothing is left of the original impulse. Titurel must therefore die.

So Titurel calls upon Amfortas to view the Grail. But Amfortas is incapable of doing so — he has lost the mental principle to Klingsor, the lower mind. Titurel now calls for the uncovering of the Grail, the revelation of occult wisdom. When, at his insistence, this takes place, Amfortas is racked with pain: for those imprisoned in the lower mind, the sight of divine wisdom is unbearable. The tragedy of such a situation is clear. On the one hand, such people are impelled by divine, buddhic impulses; on the other, they are completely entangled in the world of deception and sensuality. When the full, idealistic nature of the Grail appears to Amfortas, so great becomes his despair that he begs to die. But the Chorus sings again: “Enlightened through compassion, the innocent fool: wait for him, the appointed one.”

Gurnemanz, who led Parsifal to this inner vision, stands beside Parsifal throughout the scene. At the end he asks Parsifal: “Do you know what you have seen?” But Parsifal cannot answer, as he is overcome by the suffering he has seen. Gurnemanz angrily dismisses him. Parsifal is not yet able to help, as this requires more than just a vision of things occult. He must first acquire occult knowledge on the physical plane. This alone will enable him to internalize what he has seen and make it part of his consciousness. Only in this way can the divine be carried over into all realms.

The Occultic

The whole essence of truth cannot be transmitted from mouth to ear. Nor can any pen describe it, not even that of the recording Angel, unless man finds the answer in the sanctuary of his own heart, in the innermost depths of his divine intuitions. — The Secret Doctrine


How are those “innermost depths” to be sounded, so that knowledge of reality may be won? Through training, discipline, and self-born wisdom. Such training and soul-discipline is the distinguishing mark of the Mystery colleges, which since their inauguration have been divided into two parts: the exoteric form commonly known as the Lesser Mysteries, open to all sincere and honorable candidates for deeper learning; and the esoteric form, or the Greater Mysteries, whose doors open but to the few and whose initiation into adeptship is the reward of those whose interior nobility enables them to undergo the solar rite.

Universal testimony of stone and papyrus, symbol and allegory, cave and crypt, tells of the twofold trial of neophytes. Jesus the Avatara spoke to the multitudes in parable, but “when they were alone, he expounded all things to his disciples” (Mark 4:34). The Essenes had their greater and minor Mysteries, in the former of which Jesus of Nazareth is believed to have been initiated.

The Chinese Buddhists hold to a well-loved tradition that Buddha Gautama had two doctrines: one for the people and his lay-disciples; the other for his arhats. His invariable principle was to refuse no one admission into the ranks of candidates for Arhatship, but never to divulge the final mysteries except to those who had proved themselves, during long years of probation, to be worthy of Initiation.

Intensity of purpose marks the Hebrew initiates in their shrouding of inner teaching. To the multitude they taught the Torah, the “Law,” but to the few they taught its unwritten interpretation, the “Secret Wisdom” — hokhmah nistorah — “in ‘darkness, in a deserted place, and after many and terrific trials.’ . . . Delivered only as a mystery, it was communicated to the candidate orally, `face to face and mouth to ear.’ ” The Persian and Chaldean Magi also were of two castes: “the initiated and those who were allowed to officiate in the popular rites only” (Isis Unveiled).

Eleusis and Samothrace are limned in exquisite silhouette against the blue-black sky of history. Classical scholars tell us that the Lesser Mysteries were conducted in the springtime at Agrai near Athens, while the Greater Mysteries were celebrated in the autumn at Eleusis. In the Lesser Mysteries the candidates who experienced the first rites were called mystai (the closed of eye and mouth). In the Greater Mysteries the mystai became epoptai (the clear-seeing), who participated in the mysteries of the Divine Elysion — i.e., communion with the divine.

Similarly, the Hindu arhat, the Scandinavian skald, and the Welsh bard guarded the soul of esotericism with the sanctity of their lives and the discipline of their sacred tradition:

Belonging to every temple there were attached the “hierophants” of the inner sanctuary, and the secular clergy who were not even instructed in the Mysteries. — Isis Unveiled.

Further, in all ancient countries “every great temple had its private or secret Mystery-School which was unknown to the multitude or partially known,” and which was attached to it as a secret body. A Mystery school is not necessarily a school of people situated at some specific place, with definite and fixed locality throughout time, and with physical conditions of environment always alike. Wherever the need is great, work must be done; and the “mistake of all scholars and mystics is to put too much emphasis upon places as Mystery-Schools” (Studies in Occult Philosophy).

A Mystery school is not dependent on location; rather it is an association or brotherhood of spiritually disciplined individuals bound by one common purpose, service to humanity, a service intelligently and compassionately rendered because born of love and wisdom. It is a fact, nevertheless, that certain centers appear to be more favorable to success in spiritual things than others. Why, for instance, were the ancient seats of the Mysteries almost invariably in rock-temple or subterranean cave, in forest or mountain pass, in pyramid chamber or temple crypt? Because the currents of the astral light become quieter, more peaceful, cleaner, the farther removed from the madding crowd. Rarely will one find a seat of esoteric training near a large metropolis, for such are “swirling whirlpools . . . ganglia, nerve-centers, in the lower regions of the Astral Light” (Esoteric Tradition).

Hence the locations of the Greater Mysteries were usually carefully chosen and their schools were those which paid no attention to buildings of any kind, mainly for the reason that buildings would at once attract attention and draw public notice, which is the very thing that these more secret, more esoteric Schools tried to avoid. Thus sometimes, when the temples were mere seats of exoteric ritual, the Mystery-Schools were held apart in secret, conducting their gatherings, meetings, initiations, initiatory rites, usually in caves carefully prepared and hid from common knowledge, occasionally even under the open sky as the Druids did among the oaks in their semi-primeval forests in Britain and in Brittany; and even in a few cases having no permanent or set location; but the Initiates receiving word where to meet from time to time, and to carry on their initiatory functions. — Studies in Occult Philosophy

It is the places of quiet, of peace, of strong silence, where the Adepts find themselves drawn, and where the secret or Greater Mysteries can most effectively function. There in the recesses of their initiation chambers the forces and currents are those of the higher astral light, the akasa, the tenuous substance which responds to the higher currents of spirit and intellect. In this way does the Brotherhood transmit its potent spiritual vitality to the initiation halls, and the candidate whose seven-rayed soul is attuned may receive the divine imprint.

Simulations of Representations: Rational Calculus versus Empirical Weights

While modeling a complex system, it should never be taken for granted that these models somehow simplify the systems, for that would only strip the models of the capability to account for encoding, decoding, and retaining information that are sine qua non for the environment they plan to model, and the environment that these models find themselves embedded in. Now, that the traditional problems of representation are fraught with loopholes, there needs to be a way to jump out of this quandary, if modeling complex systems are not to be impacted by the traces of these very traditional notions of representation. The employment of post-structuralist theories are sure indicative of getting rid of the symptoms, since they score over the analytical tradition, where, representation is only an analogue of the thing represented, whereas, simulation with its affinity to French theory is conducive to a distributed and a holistic analogy. Any argument against representation is not to be taken as meaning anti-scientific, since it is merely an argument against a particular scientific methodology and/or strategy that assumes complexity to be reducible, and therefore implementable or representable in a machine. The argument takes force only as an appreciation for the nature of complexity, something that could perhaps be repeated in a machine, should the machine itself be complex enough to cope with the distributed character of complexity. Representation is a state that stands-in for some other state, and hence is nothing short of “essentially” about meaning. The language, thought that is incorporated in understanding the world we are embedded in is efficacious only if representation relates to the world, and therefore “relationship” is another pillar of representation. Unless a relationship relates the two, one gets only an abstracted version of the so-called identities in themselves with no explanatory discourse. In the world of complexity, such identity based abstractions lose their essence, for modeling takes over the onus of explanations, and therefore, it is without doubt, the establishment of these relations that bring together states of representations as taking high priority. Representation holds a central value in both formal systems and in neural networks or connectionism, where the former is characterized by a rational calculus, and the latter by patterns that operate over the network lending it a more empirical weight.


Let logic programming be the starting point for deliberations here. The idea behind this is using mathematical logic to successfully apply to computer programming. When logic is used as such, it is used as a declarative representational language; declarative because, logic of computation is expressed without accounting for the flow of control. In other words, within this language, the question is centered around what-ness, rather than how-ness. Declarative representation has a counterpart in procedural representation, where the onus is on procedures, functions, routines and methods. Procedural representation is more algorithmic in nature, as it depends upon following steps to carry out computation. In other words, the question is centered around how-ness. But logic programming as it is commonly understood cannot do without both of them becoming a part of programming language at the same time. Since both of them are required, propositional logic that deals primarily with declarative representational languages would not suffice all alone, and hence, what is required is a logic that would touch upon predicates as well. This is made possible by first-order predicate logic that distinguishes itself from propositional logic by its use of quantifiers(1). The predicate logic thus finds its applications suited for deductive apparatus of formal systems, where axioms and rules of inferences are instrumental in deriving theorems that guide these systems. This setup is too formal in character and thus calls for a connectionist approach, since the latter is simply not keen to have predicate logic operate over deductive apparatus of a formal system at its party.

If brain and language (natural language and not computer languages, which are more rule-based and hence strict) as complex systems could be shown to have circumvented representationism via modeling techniques, the classical issues inherent in representation would be gotten rid of in the sense of a problematic. Functionalism as the prevalent theory in philosophy of mind that parallels computational model is the target here. In the words of Putnam,

I may have been the first philosopher to advance the thesis that the computer is the right model for mind. I gave my form of this doctrine the name ‘functionalism’, and under this name, it has become the dominant view – some say the orthodoxy – in contemporary philosophy of mind.

The computer metaphor with mind is clearly visible here, with the former having an hardware apparatus that is operated upon by the software programs, while the latter shares the same relation with brain (hardware) and mind (software). So far, so good, but there is a hitch. Like the computer side of metaphor, which can have a software loaded on to different hardwares, provided there is enough computational capability possessed by the hardware, the mind-brain relationship should meet the same criteria as well. If one goes by what Sterelny has hinted for functionalism as a certain physical state of the machine realizing a certain functional state, then a couple of descriptions, mutually exclusive of one another result, viz, a description on the physical level, and a description on the mental level. The consequences of such descriptions are bizarre to the extent that mind as a software can also find its implementation on any other hardware, provided the conditions for hardware’s capability to run the software are met successfully. One could hardly argue against these consequences that follow logically enough from the premisses, but a couple of blocks are not to be ignored at the same time, viz, the adequacy of the physical systems to implement the functional states, and what defines the relationships between these two mutually exclusive descriptions under the context of the same physical system. Sterelny comes up with a couple of criteria for adequate physical systems, designed, and teleological. Rather than provide any support for what he means by the systems as designed, he comes up with evolutionary tendencies, thus vouching for an external designer. The second one gets disturbing, if there is no description made, and this is precisely what Sterelny never offers. His citation of a bucket of water not having a telos in the sense of brain having one, only makes matters slide into metaphysics. Even otherwise, functionalism as a nature of mental states is metaphysical and ontological in import. This claim gets all the more highlighted, if one believes following Brentano that intentionality is the mark of the mental, then any theory of intentionality can be converted into a theory of of the ontological nature of psychological states. Getting back to the second description of Sterelny, functional states attain meaning, if they stand for something else, hence functionalism gets representational. And as Paul Cilliers says it cogently, grammatical structure of the language represents semantical content, and the neurological states of the brain represent certain mental states, thus proving without doubt, the responsibility on representation on establishing a link between the states of the system and conceptual meaning. This is again echoed in Sterelny,

There can be no informational sensitivity without representation. There can be no flexible and adaptive response to the world without representation. To learn about the world, and to use what we learn to act in new ways, we must be able to represent the world, our goals and options. Furthermore we must make appropriate inferences from these representations.

As representation is essentially about meaning, two levels are to be related with one another for any meaning to be possible. In the formal systems, or the rule-based approach, these relations are provided by creating a nexus between “symbol” and what it “symbolizes”. This fundamental linkage is offered by Fodor in his 1975 book, The Language of Thought. The main thesis of the book is about cognition and cognitive processes as remotely plausible, when computationally expressed in terms of representational systems. The language in possession of its own syntactic and semantic structures, and also independent of any medium, exhibits a causal effect on mental representations. Such a language is termed by him “mentalese”, which is implemented in the neural structure (a case in point for internal representation(2)), and following permutations allows for complex thoughts getting built up through simpler versions. The underlying hypothesis states that such a language applies to thoughts having propositional content, implying thoughts as having syntaxes. In order for complex thoughts to be generated, simple concepts are attached with the most basic linguistic token that combine following rules of logic (combinatorial rules). The language thus enriched is not only productive, with regard to length of the sentence getting longer (potentially so) without altering the meaning (concatenation), but also structured, in that rules of grammar that allow us to make inferences about linguistic elements previously unrelated. Once this task is accomplished, the representational theory of thought steps in to explicate on the essence of tokens and how they behave and relate. The representational theory of thought validates mental representations, that stand in uniquely for a subject of representation having a specific content to itself, to allow for causally generated complex thought. Sterelny echoes this when he says,

Internal representation helps us visualize our movements in the world and our embeddedness in the world. Internal representation takes it for granted that organisms inherently have such an attribute to have any cognition whatsoever. The plus point as in the work of Fodor is the absence of any other theory that successfully negotiates or challenges the very inherent-ness of internal representation.

For this model, and based on it, require an agent to represent the world as it is and as it might be, and to draw appropriate inferences from that representation. Fodor argues that the agent must have a language-like symbol system, for she can represent indefinitely many and indefinitely complex actual and possible states of her environment. She could not have this capacity without an appropriate means of representation, a language of thought. Mentalese thus is too rationalist in its approach, and hence in opposition to neural networks or connectionism. As there can be no possible cognitive processes without mental representations, the theory has many takers(3). One line of thought that supports this approach is the plausibility of psychological models that represent cognitive processes as representational thereby inviting computational thought to compute.

(1) Quantifier is an operator that binds a variable over a domain of discourse. The domain of discourse in turn specifies the range of these relevant variables.

(2) Internal representation helps us visualize our movements in the world and our embeddedness in the world. Internal representation takes it for granted that organisms inherently have such an attribute to have any cognition whatsoever. The plus point as in the work of Fodor is the absence of any other theory that successfully negotiates or challenges the very inherent-ness of internal representation.

(3) Tim Crane is a notable figure here. Crane explains Fodor’s Mentalese Hypothesis as desiring one thing and something else. Crane returns to the question of why we should believe the vehicle of mental representation is a language. Crane states that while he agrees with Fodor, his method of reaching it is very different. Crane goes on to say that reason: our ability as humans to decide a rational decision from the information giving is his argument for this question. Association of ideas lead to other ideas which only have a connection for the thinker. Fodor agrees that free association goes on but he says that is in a systemic, rational way that can be shown to work with the Language of Thought theory. Fodor states you must look at in a computational manner and that this allows it to be seen in a different light than normally and that free association follows a certain manner that can be broken down and explained with Language of Thought. Language of Thought.