Peirce on learning and teaching

1 Learning and teaching: Peirce and the categorial foundations

In many of his writings, Charles Sanders Peirce (1839–1914) addresses pedagogical issues, as readers of Chinese Semiotic Studies know from Cary Campbell’s paper “Toward a pedagogy of Firstness” (2018). In three chapters of Semiotic theory of learning (Stables et al. 2018), the author of this paper has given a comprehensive survey of Peirce’s semiotic pedagogy. This article aims at presenting a precis of its main topics.

Peirce was not only a theoretician of pedagogy; he was also a gifted academic teacher, as reports of his students Christine Ladd-Franklin (1916) and Joseph Jastrow (1916) show. “Not argument, but discovery,” made Peirce such a great teacher, wrote Jastrow on May 6, 1914, in an obituary in The Nation. Peirce described his method of teaching as making his students think for themselves: “Neither reading books nor working exercises, — whether they be trivial or serious, will suffice to develop the reasoning powers” (MS 444; Eisele 1964: 52).

The foundations of Peirce’s philosophy of learning and teaching are in his phenomenology. A phenomenon is “whatever is present at any time to the mind in any way” (CP 2.186, 1903). Since Aristotle, philosophers have classified all phenomena in a short table of some 10–12 fundamental categories. Peirce reduced his own list to no more than three categories, first defined as Quality, Relation, and Representation, later simply as Firstness, Secondness, and Thirdness.

Firstness is the category of phenomena considered in themselves, still unrelated to anything else, for example, the taste of a peach or the color yellow, but also the chaos of happenings not yet determined by any law. Secondness describes phenomena in the dyadic relation of a First with a Second. Action immediately followed by reaction, cause by effect, experience of unreflected reality, contingent facts with still unknown causes are examples. Thirdness is the category of a Third mediating between a First and a Second, the category of mediation, signs, semiosis, reasoning, interpretation, generality, growth, time, continuity, and habits.

The phenomena in triadic interactions may be most diverse, for example, moments in time (in relation to the past and the future), loci in space (in their three-dimensional determination), thoughts and feelings (in relation to those that precede and follow): “The beginning is first, the end second, the middle third. […] A fork in a road is a third; it supposes three ways […] Sympathy, flesh and blood, that by which I feel my neighbor’s feelings, is third” (CP 1.337, c.1875).

The prototype of Thirdness is semiosis. A sign may be a word, a picture, a gesture, a thought, an idea. It acts as a mediator between the object it represents and the interpretant, i.e. the effect it produces in an interpreting mind. Take the skull-and-crossbones label ☠ to a bottle: First, there is that label, which is the sign. Second, there is the sign’s object, the poisonous liquid. Third, there is the so-called interpretant, the effect on the sign’s interpreters, presumably, the habit not to drink it.

2 Why learning is a phenomenon of Thirdness

First and foremost, learning pertains to Thirdness since it is a process of semiosis, a sign process. We learn that (1) a phenomenon, a sign, represents (2) something else, its object, and (3) we then acquire the habit of interpreting the sign as representing that object. Since no cognition is “not determined by a previous cognition” (CP 5.213–259, 1868), we can only learn through and from signs, but the learners are not only human beings, but also the signs themselves. They learn from their users while they grow in meaning (Nöth 2016a). Thus, “men and words reciprocally educate each other; each increase of a man’s information involves and is involved by, a corresponding increase of a word’s information” (CP 5.313, 1868). With the knowledge they accumulate in time, signs also act as educators from whom we can learn, at the same time as the signs learn from their users, as they attribute new meanings to them (Nöth 2014a, 2014b).

We acquire knowledge of objects of signs by our immediate experience of them or from meanings attributed to them in discourse. These two modes of learning pertain to the denotation and the signification of signs. Adopting the terms introduced by the Scottish philosopher William Hamilton (1730–1803), breadth (denotation) and depth (signification), Peirce distinguishes between wide and deep learning: “‘Wide’ learning is, in ordinary parlance, learning of many things; ‘deep’ learning, much knowledge of some things” (CP 2.394, 1867).

Learning is reasoning insofar as “every reasoning connects something that has just been learned with knowledge already acquired” (CP 7.536, 1899), but while reasoning is highly conscious, learning is less so. “All learning is virtually reasoning; that is to say, if not reasoning, it only differs therefrom in being too low in consciousness to be controllable and in consequently not being subject to criticism as good or bad” (CP 7.536, 1899).

To learn means to advance from what “we already know to the knowledge of novel truth” (CP 4.476, c.1903). A learning process is a process of mediation between two states of mind, ignorance and knowledge. Doubt, questioning, and criticism are powerful mediators in this process. One who has no doubts is one who believes to know everything and therefore cannot learn anything new:

The first condition of learning is to know that we are ignorant. A man begins to inquire and to reason with himself as soon as he really questions anything, and when he is convinced, he reasons no more. […] It is easy to see what truth would be for a mind which could not doubt. That mind could not regard anything as possible except what it believed in. (CP 7.322–23, c.1873)

Learning creates belief-habits because it “guides us in our judgments” (CP 4.531, 1906). Like inferring, learning, is “the conscious and controlled adoption of a belief as a consequence of other knowledge” (CP 2.442, c.1893). When children learn that fire is dangerous, they have only learned something when they really believe that this is so and have faith in reasoning. This belief must become a habit that guides future action, for “when you say that you have faith in reasoning, what you mean is that the belief-habit formed in the imagination will determine your actions in the real case” (CP 2.148, c.1902). Acquired beliefs are always modifications of previous beliefs (EP 2:463, 1913). “What makes men learn? Not merely the sight of what they are accustomed to, but perpetual new experiences which throws them into a habit of tossing aside old ideas and forming new ones” (NEM 4: 142, 1897–1898).

Habits are Thirdnesses in time, mediating between past and future thoughts and actions. At the same time, learning is a habit of habit change since it requires unlearning. It is a “habit of taking and laying aside habits” (CP 6.101, 1901). “Perfect readiness to assimilate new associations implies perfect readiness to drop old ones” (Peirce 1898: 192). The flexibility of the child’s mind, “the plasticity of childhood” (p. 192) is the paradigm of a mind capable of habit-taking and habit change in learning. Peirce distinguishes between the acquisition of habits of thought, which are embodied in beliefs that guide our judgments (Thirdness), habits of conduct and action (Secondness), and habits of feeling and imagining (Firstness), which are embodied in expectations (cf. Nöth 2016b). Habits and beliefs create expectations in the same way in which signs create expectations about future situations in which we may use them. In their orientation toward the future, beliefs presuppose imagination, since expecting something to happen means imagining how it will happen:

An imagination is an affection of consciousness which can be directly compared with a percept in some special feature, and be pronounced to accord or disaccord with it. Suppose for example that I slip a cent into a slot, and expect on pulling a knob to see a little cake of chocolate appear. My expectation consists in, or at least involves, such a habit that when I think of pulling the knob, I imagine I see a chocolate coming into view. When the perceptual chocolate comes into view, my imagination of it is a feeling of such a nature that the percept can be compared with it as to size, shape, the nature of the wrapper, the color, taste, flavor, hardness and grain of what is within. (CP 2.148, c.1902).

Hence, learning is not only acquiring habits of believing and acting, but also habits of feeling and imagining. The habits we acquire must be sufficiently flexible to allow for habit change. This begins with the capacity of cells to adapt to patterns of stimulation. “Were the tendency to take habits replaced by an absolute requirement that the cell should discharge itself always in the same way, or according to any rigidly fixed condition whatever, all possibility of habit developing into intelligence would be cut off at the outset; the virtue of Thirdness would be absent” (CP 1.390, 1887).

The insight that learning is necessarily a continuous process comes from Peirce’s principle of fallibilism, which states that “our knowledge is never absolute but always swims, as it were, in a continuum of uncertainty and of indeterminacy” (CP 1.171, c.1897). Since whatever we learn “can never be absolutely and certainly completed or finished,” learning has no foreseeable end. Learning cannot be immediate. It takes time to learn, “not merely because it continues through every instant of that time, but because it cannot be contracted into an instant” (CP 1.381, c. 1885).

Another reason why learning has no end unless it is interrupted by external circumstances is the incompleteness of representation. No sign represents its object in all of its details. The ideal teacher is therefore not the one who knows or pretends to know everything, but the one who knows that lifelong learning is necessary. “It is not the man, who thinks he knows it all, that can bring other men to feel their need of learning, and it is only a deep sense that one is miserably ignorant that can spur one on in the toilsome path of learning” (CP 5.583, 1898).

3 Education in the domain of Secondness

Learning occurs in processes of mediation between the known and the unknown. Mediation means Thirdness, but this does not exclude Secondness and Firstness, because any Third presupposes a Second. Learning always involves Secondness, too. Secondness “meets us in such facts as Another, Relation, Compulsion, Effect, […] Occurrence, Reality, Result” (CP 1.358, 1887). We are faced with Secondness in phenomena for which we have no explanation for explanation is Thirdness. Such phenomena may take us by surprise; we resist. They are “brute […], regardless of law or of any third subject” (CP 5.469, 1907).

Education in the domain of Secondness means learning from experience, experiments, practical life, or indexical signs. John Dewey’s famous principle of learning by doing exemplifies its role in education (cf. Liszka 2013). Through doing (Secondness), we acquire new knowledge (Thirdness). It means developing practical skills through experience, to learn from nature, from experience, from actions and reactions. We learn from “the rough and tumble of life,” while we “are continually bumping up against hard facts. We expected one thing, or passively took it for granted, and had the image of it in our minds, but experience forces that idea into the background, and compels us to think quite differently” (CP 1.324, 1903).

Peirce distinguishes between genuine Secondness and Secondness as degenerated Thirdness. The genuinely second “consists in our knocking up against it. A hard fact is of the same sort; […] I cannot think [it] away, but am forced to acknowledge [it] as an object or second beside myself” (CP 1.358, c.1890). As degenerated Thirdness, Secondness is a “weakened modification” of Thirdness (1903: 167; CP 5.68–69). An example is a plan implemented in some action, insofar as the plan (Thirdness) “brings about a Secondness but does not regard that Secondness as anything more than a fact” (CP 1.538, 1903).

Secondness in Thirdness can also be observed in Peirce’s typology of signs (CP 2.243–53, 1903). The genuine sign of pure Thirdness is the symbolic legisign, a sign based exclusively on laws or rules, unrelated to its object. Degenerated to Secondness, the symbol turns into an index and the legisign into a sinsign. Genuine symbolic legisigns are Thirdnesses, hard to learn because they are abstract, invisible and give no evidence of what they mean. Take the example of the word dog. It does not tell us what it means; in its spelling, it is, ironically, the reverse of g-o-d. Already the pure sound image, i.e. the law how to represent the symbol, is hard to acquire. Learners need to hear it repeatedly or see it in writing before they can memorize it. However, singular instances of pronouncing or writing are only sinsigns, ephemeral singular signs. What needs to be learned is the rule, the symbolic legisign.

To learn new words, indexical signs are requisite (Campbell 2016). Only they can connect the sign with the reality it represents. Teachers need to show, to indicate a dog before the learners can learn the symbol that represents it. Without indices, symbols cannot mediate experience for “all knowledge comes to us by observation, part of it forced upon us from without from Nature’s mind” (CP 7.558, c.1893). Indices are the signs that connect us with reality as a positive fact (CP 4.448, c.1903). Hence, learning from indexical signs is also a method of taking doubt off the learner’s mind, the “uneasy and dissatisfied state from which we struggle to free ourselves and pass into the state of belief” (CP 5.372, 1877). Learning from mistakes, error, and doubt is learning from Secondness insofar as the learner encounters resistance. Knowing leaves thinking and learning “at rest.” The mind seems to have reached a “stopping place” (CP 5.397–98, 1878). Doubt and error, by contrast, leave the mind in a state of unrest, spurring the “will to learn.” It results from the clash between a habit of believing and evidence that incompatible with these beliefs and causes an “irritation” of the learner’s belief (CP 5.397–98, 1878).

In experience, the Thirdness of learning is degenerated to Secondness because experience involves the reality of the external environment, which is not only “eminently hard and tangible,” “very familiar,” but also “forced upon us daily,” and hence “the main lesson of life” (CP 1.358, c.1890). Experience teaches lessons of “limitation, conflict, constraint” (CP 1.358, c.1890), hence Secondness, whereas a human teacher is a mediator in Thirdness. The experience that brings Secondness into the predominance of the Thirdness in the learning process is the “common experience which nobody doubts or can doubt, and which nobody ever even pretended to doubt” (CP 1.358, c.1890). It is not experience in the sense of a daily routine. This would be a habit or a habit of expectation, hence Thirdness. Peirce illustrates his theory of learning through experience by the proverb, “Experience is our only teacher” (Peirce 1903, 159; CP 5.50). Even students of philosophy must not be restricted to book reading only. Without practical exercises, learning is doomed to fail. Book reading cannot substitute experience.

The reality, as it is experienced in everyday life, is the reality of Secondness, which turns out to be the most prominent of the three categories of learning because “the practical exigencies of life” are ubiquitous (CP 8.266, 1903). In Secondness, the First and the Second meet without mediation. “Experience […] comes out most fully in the shock of reaction between ego and non-ego. It is there the double consciousness of effort and resistance. That is something which cannot properly be conceived. For to conceive it is to generalize it; and to generalize it is to miss altogether the hereness and nowness which is its essence” (CP 8.266, 1903).

The secret of all progress in learning lies in the students’ “Will to Learn” in a spirit of genuine doubt toward and dissatisfaction with the present state of knowledge. This is a powerful engine of learning. Peirce attributes an element of compulsivity to it, which characterizes once more its Secondness. Learning has an element of rational coercion due to two factors of the dynamics of reasoning. One is that we cannot stop learning, since the truths that we discover are never complete. The effect of this impulse is “a dissatisfaction with one’s present state of opinion […], a sense of the unsatisfactoriness of the present condition of knowledge” (Peirce 1898: 171; CP 5.583). The other is that “inquiry of every type, fully carried out, has the vital power of self-correction and of growth,” which imposes restrictions on the inquirer’s mind (Peirce 1898: 170; CP 5.582).

A most significant effect of learning by experiment, according to Peirce, is the one of surprise. “It is by surprise that experience teaches us all she deigns to teach us” (Peirce 1903, 160; CP 5.51, EP 2, 154). Surprise is especially involved in acquiring new knowledge because surprise and new experience can change old beliefs. We “believe until some surprise breaks up the habit. The breaking of a belief can only be due to some novel experience” (c.1905, CP 5.524, 1905).

4 Education in the domain of Firstness

Since the only characteristic of Firstness is being unrelated to any other phenomenon, the phenomena of Firstness are most diverse. Qualities are among them, for example, being “red, bitter, tedious, hard, heartrending, noble” (CP 1.418, c.1896), but also feelings, spontaneity, novelty, chaos, freedom, and unrestrained imagination. None of these phenomena depends on others. Hence, “the idea of First is predominant in the ideas of freshness, life, freedom. The free is that which has not another behind it, determining its actions” (CP 1.302, c.1894).

Mere Firstness cannot be taught, since phenomena of pure Firstness are simply what they are in their “suchness.” “The mere experience of a sense reaction is not learning. That is only something from which something can be learned, by interpreting it. The interpretation is the learning” (CP 7.536, 1899). Such phenomena say nothing about in how far they are like, or different from, other phenomena. Consider feelings as Firstnesses. We only “think different feelings to be alike or different,” but “feelings in themselves cannot be compared and therefore cannot be alike, so that to say they are alike is merely to say that the synthetical consciousness regards them so” (CP 1.383, c.1890).

Nevertheless, learning in the domain of Firstness is of great pedagogical relevance insofar as it is also the category of musement, daydreaming, imagination, and creativity. Peirce’s concept of musement describes a mental state in which a free play of ideas is possible. Without any rules or restrictions, the mind is allowed to produce uncontrolled associations and to imagine other worlds than the one that really exists (CP 6.452–465, 1908). Progress in knowledge acquisition requires creative minds audacious enough to foresee future developments through imaginative foresight:

Now is it not of all things the most wonderful, that the mind should be able to create an idea for which there is no prototype in nature, nor anything in the least resembling it, and that by means of this utter fiction it should manage to predict the results of future experiments and by means of that power should during the nineteenth century have transformed the face of the globe? (CP 7.686, 1903)

Firstness is also relevant to education in its forms of interpretation in which they appear as Firstnesses in Thirdness, as in the three Firstnesses of Peirce’s sign trichotomies, qualisigns, i.e. signs consisting of a mere quality, iconic signs, and abductive arguments. Education in the domain of Firstness thus also means learning from, and teaching by means of, qualisigns, iconic signs, and abductive reasoning.

A qualisign is a “quality in so far as it is a sign”; it is “necessarily an Icon,” but not necessarily a visual representation (CP 2.243–53, 1903). A qualisign may be conveyed by any sensory experience, sight, sound, smell, touch, or taste. Peirce argues that qualisigns should be part of any general curriculum when he postulates the necessity of observation directed toward “the qualities of objects” (1898: 183) and goes on to distinguish three kinds of Firstnesses. The first is “the idea of a simple original quality.” The second is the one of a “quality essentially relative, such as that of being ‘an inch long,’” and the third is “the idea of a quality that consists in the way something is thought or represented, such as the quality of being manifest” (CP 1.534, 1903).

We cannot learn from pure icons because these are only vague, represent nothing in specific, and convey no information, since they are unconnected to reality: “The idea embodied by an icon […] cannot of itself convey any information, being applicable to everything or to nothing” (CP 3.433, 1896). A diagram may only have a didactic potential when it is an “icon of relations […] aided to be so by conventions,” hence combined with symbols (CP 4.418, 1903). In combination with symbols and indices, the diagram is a sign from which new information can be derived. Maps, for example, are diagrams by the observation of whose details we can discover relations “which before seemed to have no necessary connection” (CP 1.383, 1890).

The semiotic potential of icons is not restricted to creating pictures from existing objects. They can also represent fictional objects never seen before (CP 4.531, 1906). This is why icons have a great potential for creativity. Peirce gives a name to this potential when he calls the icon an “originalian sign” (CP 2.92, c.1902). The icon is “originalian” because it enables the learners to imagine how they “would act under certain circumstances, as showing how another man would be likely to act” (CP 2.92, c.1902).

Peirce distinguishes three subtypes of icons: (1) images, which resemble their object because of “simple qualities” inherent in them; (2) diagrams, which are structurally similar to their object; and (3) metaphors, which evince a similarity mediated by a third sign, both similar and different from the first (CP 2.277, c.1902). Learning from signs that are similar to their object is learning from signs “whose significant virtue is due simply to a Quality” (CP 2.92, 1902). There are icons of possible sensory modalities, visual, auditory, tactile, olfactory, or gustatory. Icons also include mental images, which makes iconic signs apt to represent merely possible realities in multimodal forms.

Auditory icons are particularly relevant to learning how to pronounce a foreign language. When a foreign language teacher sets the focus of learning on the pronunciation of a foreign word, she presents something like a “pure image” of it (CP 8.183, 1903). Without considering the meaning of the word, its phonetic form is nothing but a pure icon, presenting itself to the student’s sense of hearing in its “suchness.”

Diagrams, the second type of iconic signs, are “schematic images” (EP 2:303, 1904). In contrast to a simple image, which resembles its object with respect to “simple qualities,” a diagram represents only the “forms of relation” of its object, whether these refer to real “things,” as in a map, or only to abstract ones, as in the diagram of ideas or merely imaginary objects (NEM 4:315-316, fn1, 1906–1907). Like genuine symbols and indices, pure diagrams are too abstract and therefore too hard to learn. In practice, diagrams are hybrid signs in which the iconic part is combined with indexical and symbolic elements, for example, as in maps or in infographic charts.

The capacity of diagrams to represent relations also explains how and why iconicity can enhance the rhetorical efficiency of rational discourse. A clear argument is one that offers evidence, and “the evident is that which is presented in an image, leaving for the work of the understanding merely the Interpretation of the Image in a Symbol” (MS 339, microfilm 535, Sept 5, 1906). Another reason why and how diagrams are rhetorically efficient in furnishing evidence is that it is possible to derive information from a diagram that the sign itself does not make explicit because diagrams are self-explanatory. By studying a map, for example, we can find out how to get most quickly from one place to another, but the map does not give this information explicitly.

5 Peirce’s pedagogical holism

In the combination of icons with indices and symbols, the didactic value of an icon “consists in its exhibiting the features of a state of things regarded as if it were purely imaginary. The value of an index is that it assures us of positive fact. The value of a symbol is that it serves to make thought and conduct rational and enables us to predict the future” (CP 4.448, c.1903). Peirce concludes that the “most perfect” sign is one “in which the iconic, indicative, and symbolic characters are blended as equally as possible” (CP 4.448, c.1903). This conclusion is perfectly valid for the rhetorical quality of scientific models, even today.

In sum, Peirce’s teaching methodology is based on the advice that those signs teach best and are “the most perfect” ones “in which the iconic, indicative, and symbolic characters are blended as equally as possible” (CP 4.448, 1903). This didactic insight is quite in accordance with the principles of holistic education. Peirce’s didactics is one of teaching with signs that relate not only to the present moment of classroom activity but also to past experience and future expectancies. The reason is that “an icon has such being as belongs to past experience. It exists only as an image in the mind. An index has the being of present experience. The being of a symbol consists in the real fact that something surely will be experienced if certain conditions be satisfied” (CP 4.447, c.1903).