Toward Universal Literacy: from Computer Science Upward

This is a plea for universal literacy—the ability to comprehend the world through schemata: to mentally collect, design and redesign, and to generate instances from schemata. Today, the pair of concepts "schema–instance" is a domain of computer science, thereby establishing a significant contribution to the foundation of universal literacy.

What is literacy? The meaning of the notion has been expanded considerably in the past few decades. In an edition of Webster’s Dictionary circa 1960, the definition of literacy is restricted to "the ability to read and write." A 1995 edition of Webster’s includes "a person’s knowledge and culture and the ability in a particular subject or field, such as computer literacy." Clearly, literacy has something to do with language, and only in a fundamental sense with ordinary spoken and written language. Within the Anglo-American pragmatism the ordinary language was explored under the leadership of John Austin, who coined the famous phrase, "How to do things with words." If we ask for a person’s ability to do things with words, then literacy is immediately addressed.

Today, literacy is being tested widely: The PISA test¹ of the OECD member states² is considered an outstanding example (see www.pisa.oecd.org). In 2000, the literacy of 15-year-old students was tested in an international experiment. Some nations were shocked at the outcome (for example, the U.S. was ranked 15th, Germany 21st, among the 31 countries comprising the OECD). The scientific value of PISA contributes to a more precise definition of literacy in the sense of an ability to do things with words. An abstraction hierarchy is the very core of PISA; the structure of PISA is quite simple: From test problems at a very concrete level (find information in texts) to an intermediate level (interpretation of texts) up to the highest level of abstraction (reflection and assessment of texts). Not particularities of individual countries, but general problem solving and the understanding of the world were the topics to achieve an international comparability. The test was basically cultural-invariant, but was transformed into a cultural-dependent test in some countries. Because literacy is a paramount issue in modern life, a tremendous effort was invested.

The aforementioned Anglo-American pragmatism made it very clear to all involved in the exploration of literacy that the terms knowledge and ability are intimately connected to each other. Wittgenstein, the academic teacher of Austin, stated in a famous aphorism in his Philosophical Investigations: "The grammar of the word ‘to know’ is evidently closely related to that of ‘can’, ‘to be able to’. But also closely related to that of ‘to understand’ (‘Mastery’ of a technique)." Wittgenstein contributed a lot to pragmatism: "…the meaning of a word is its use in the language…".

Back to Top

Schema and Instances

The pair of concepts "schema–instance" has taken a predominant role in computer science (CS). Programs are schemata of a process. At runtime, instances are produced and are sometimes called threads of control. In database systems, conceptual schemata are designed, for example, relational schemata, under which tuples are subsumed as instances. Consider, for example, an employee relation as a schema and particular employee records as instances of that relation. Abstract data types, like all types, are schemata. Imagine an abstract data type of a square, realized by a class with its drawing methods (operations). A particular square called object is an instance of that class. A movement of a robot’s arm is an instance, the underlying program is a schema. All simple data types of programming languages are schemata. Integer, for example, is a schema and 1, 2, 3, … are its instances. All these examples show that schemata and their instantiations belong to the very core of CS. The Greek word "schema" means shape or form. Therefore, some people suggest referring to our subject as in.schema.tics instead of in.forma.tics, a renaming that seems to be appropriate.

There is a tradition that paramount concepts have their history in the development of sciences. The American linguist N. Chomsky called this famous pair "competence–performance." With a schema, competence is available to perform an instantiation, sometimes called actualization. Further back in history we see the Swiss linguist F. de Saussure with his term "langue–parole." An entire language is considered as a schema, whereas actual talking (parole) is an instantiation of that language. Finally, we must mention the initiator of modern discussion, the American logician C.S. Peirce, who coined the term "type–token," in particular with respect to symbols. The schematic aspect of a symbol reflects its type, the actually written sign is a token (instance). Since the times of Peirce, and not since the advent of modern programming languages, integer is a type and 1, 2, 3, … are its tokens or instances.

The point we emphasize here is the insight that the pair "schema–instance" is not only indispensable when acquiring computer literacy, but the history of these concepts indicates the pair is of similar importance to the foundation of a universal literacy. Since CS is the only modern science utilizing our pair of concepts as a central theme, it has an establishing position and responsibility in the definition of modern universal literacy in the sense of Anita Borg [1]. Thus our subtitle "From CS upward" seems to be justified. Universal literacy is an infinite subject matter: it is a never-ending tower, where just some anthropological foundations of that tower can be outlined.

What is a schema and what are its instances? A very general and popular definition is given by Lorenz [2]. A schema represents a universal, an instance a singular aspect of an object. This definition can best be explained by referring to the anthropological notion of a dialogue between a listener (B) and a speaker (A). A speaker, the active person, generates an instance in a (speech-) action. A listener, the passive person, recognizes the instance as an instantiation of a schema. A speaker is a generator of an instance, a listener is a recognizer of an available schema. In other words: The recognizer B understands the generator A in the sense that A and B are communicating with one another. "Communication" is derived from the Latin word "communis" (to have in common). What A and B have in common, what they share is a schema according to which A generates (produces) an instance and B recognizes that instance. A reading-writing situation is similar. Using the example of a non-understanding: If A writes for B an unreadable symbol (say, the letter z on the blackboard), then his traces of chalk are not an instance of the schema (type) z, because z is unreadable, that is, z is incomprehensible or incommunicable. Instances of Chinese pictograms are unreadable for most Western people—they cannot read them, because they have no schema knowledge. Western people in general are illiterate as far as Chinese characters are concerned.

It is common to look at a schema and its instances from pragmatic, semantic, and syntactic perspectives. The methodological question behind this semiotic classification is what comes first. CS prefers to start with syntax, following its mathematical roots. However, the tradition of Anglo-American pragmatics changed the order: First comes the pragmatic aspect (for example, speech acts in a dialogue), then the semantic issue follows, and finally syntactic questions are discussed. Paraphrasing Wittgenstein: "…the meaning (semantics) of a word is its use (pragmatics) in the language." Asking for a universal literacy, pragmatics comes first and syntax last. In CS, pragmatics is deferred to what is called application; CS follows primarily a design strategy without considering aspects of literacy.

In systems design, a binary relation "instance_of" is formally introduced. The assignment of instances to its schema is unique, that is, if x1 instance_of S1 ^ x1 instance_of S2, then S1 = S2.

Back to Top

Teaching and Learning

The very point we want to make here is the idea that learning may be interpreted as schema acquisition. Literacy in this approach is the availability of acquired schemata plus the capability of self-acquisition (self-learning). Without the component of self-acquisition we are reduced to education. Beyond the capability of self-acquisition, literate people have the ability to memorize acquired schemata for a very long time. To reach the state of literacy, institutions like schools, high schools, and universities are needed. Organized teaching-learning situations are typical for these institutions. Teachers are focused on teaching schemata—not instances—because schemata enable the understanding of instances. The converse does not hold. A host of pedagogical sciences was established to describe teaching-learning situations in some detail and at various levels of schema acquisition. Teaching-learning situations may be outlined here by referring to a trivial example drawn from the physical world of human bodies.

Examples in the literate word of mind are more complex. Let’s have a look at the situation "teaching-learning swimming" [2] with a teaching person X and a learning person Y. The action schema "swimming" is taught. X may demonstrate the schema "swimming" in the dry by showing to Y the particular movements of arms and legs. Y tries to imitate until both are convinced that a real test in the water with real instantiations of a swim schema may take place. Examples in the world of mind are more complicated, because the control aspect is much more subtle. It is important to mention that people spend a lot of time in teaching-learning situations. Think of people in an unfamiliar city asking pedestrians for directions to a particular location. The pedestrians are outlining the schema of the route to take and the nonresidents try to generate an instance. The success is always an open issue.

More complicated are teaching-learning situations, for example, when an audit trail in an accounting system or the tuning of numerically controlled machines are subject to teaching. In any case, teaching-learning situations are distinct from other activities occurring in daily life.

Back to Top

Illiteracy and Justice

In Roman law, from which Western cultures inherited many aspects, judges had to consider the following principle: "Ultra posse, nemo obligatur," which translates into English as "Beyond one’s capability, nobody is obliged." In simple words: If you can not, you should not. Logically speaking: "Can not implies should not" or formally: ¬A –> ¬B. However, A (can) and B (should) are not absolutely, but relatively understood with respect to a goal g and by means of m. We write: ¬A_m g –> ¬B_m g.

The Roman principle of justice still holds in Western countries. It is entirely inappropriate to ask someone to do something if he or she is unable to do it. Western constitutions and the Charter of the United Nations introduced the concept of dignity of human beings—requesting an unable person to do what seems to be unattainable is not compatible with that person’s dignity. Social laws in all Western countries have taken the Roman principle of justice into account.

The means m is frequently not a physical tool, but a schematic description of plans requiring teaching: a teaching-learning situation. An illiterate person is unable to understand and to instantiate plans. It is now fundamental in applying justice to decide with whom the burden of proof lies. Let’s think of a dialogue between someone proposing the Roman principle (the state in general) and a person claiming to be unable to attain a goal g by means of m. In dialogical logic, the one who proposes is called proponent. The presumptive unable person is called opponent. He has the right to single out the condition ¬A_m g for discussion. The logical situation now prescribes that the opponent—the unable person—has to prove his inability: ¬A_m g. In case he succeeds, the proponent is obliged to grant ¬B_m g and the proven unable is out of obligation. However, if the proof fails, the proponent is free and not bound by the Roman principle. Clearly, the burden of proof lies with the unable person. It is an open question how to prove inability in the form of illiteracy. In the case of disabled persons it seems to be easy and may be obvious; in other cases, it depends on circumstances not to be discussed here.

In his ethics, the famous German philosopher Immanuel Kant took the Roman principle and applied to it the classical logical law of conversion called contraposition. If ¬A_m g –> ¬B_m g holds, Kant concluded classically, then B_m g –> A_m g must hold as well. Expressed in words: If a person should reach the goal g by means of m, the person can do it. In brief: If you should, you can. This is difficult and Kant was quite often blamed for his rigidity. However, Kant’s conclusion could be a motto appearing in the emblem of any university. Kant is addressing, in particular, young people who are able to accomplish and achieve—these people should strive for a universal literacy and, therefore, with Kant in their minds, they can do it.

Back to Top

Back to Top

Back to Top