No. 55
Author Admin / 2017-11-17
Climate Change Humanities, 6th Week, on Language

6. Metaphor with climate change (언어에 대하여)


Number, Language of Science

Abstracted from the book, "Number, the language of science (1930)" by Tobias Dantzig:


Wasps are known to feed female and male eggs exactly with 10 and 5 victims, respectively, without any confusion. Crow is also known to count number, up to four; a crow built its nest on a watch top, thus, the squire (owner of the building) tried to frighten the crow. Whenever the squire climbed the tower, the crow left the nest and sat on a tree far from the tower to watch the nest, and after the man left, it returned. When two men climbed and one man hided, but the crow was not conceived. Two, three, and four men were cheated, the crow was not either. Finally, above five, the crow lost counting. Interestingly, for mammal, there is no such number counting faculty has been found. Even with many primitive peoples, if they can, they are able to discern up to only 4.

   Counting is often believed base to which human owe for progress in expressing our universe. Once we made numbers from the Nature and/or universe, we have forgotten connectivity between the numbers and corresponding originated objects in nature; for example, number two from butterfly, number three from clover, number four from animal's legs, number five from our fingers, etc. Thus, we call these as forgotten-number images (i.e., cardinal numbers). Then, we acquired the ordinal numbers systems, including binary, quinary, and decimal systems.

   We may have a question which preceded the other between arithmetic and theory of number. We generally believe arithmetic does, but, Tobias Dantzig gave three evidences that support theory of number preceded arithmetic: 1) there was the Hebrew Bible Gematria that used numbers to present meanings, along with words (letters), i.e., double meaning numbers. 2) according to Pythagoreans, even numbers are regarded as soluble, ephemeral, feminine, and earth, while, odd numbers are regarded as indissoluble, masculine, and celestial nature; for example, 1 = reason, 2 = opinion, 3 = first masculine number, 4 = justice, 5 = marriage (as 2 (first feminine number) +3 (first masculine number) = 5). 3) there are Pythagoras amicable numbers which are defined as two numbers of which divisors's sums are equal to the other number; for example, 220 and 284 are amicable numbers each other as divisors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110, thus, summation of those is 284, and divisors of 284 are 1, 2, 4, 71, 142, thus, summation of those is 220. And, there are perfect numbers as well of which divisors' summation is itself; for example, divisors of 6 are 1, 2, 3, thus, the summation is 6, similarly, 28, 496, 8128, ... Here, we can find some magics of these numbers. 6 is number of days of creation, 28 is number of lunar cycle.


The most powerful function of numbers is to make reality in science that has not been existing in the world. One of these is infinity number and its resulting realities in mathematics and science. Infinity concept was intuited and understood in old Greek ages. As we know, Pythagoras found his theory with rectangular triangle. When he found this, he was so happy that he sacrificed an ox even he was vegetarian. However, when he and his pupils calculated x value from equation of 1^2 + 1^2 = x^2, they found a difficulty to get rational number for x from the equation. Even though they might understand a solution from infinite steps of rooting of 2, but, they could not solve this problem. Thus, we know the starting first number, but, we can not know the last number, which is dilemma of infinity. It is 1687 that we finally got the solution to the infinity concept by Newton who published the famous book, Prinpicia of Math, which we already discussed. It is often told that philosopher make concept of new reality, then, mathematician formulates it for utilization and application. After year of 1687, we started to have a new reality in number and methodologies in mathematics and science, for application.


Verbal Behavior


From the Skinner's:

Language has the character of a thing, something a person acquires. The words and sentences of which a language is composed are said to be tools used to express meanings, thoughts, ideas, propositions, emotions, needs, desires, and many other things in or on the speaker's mind. However, verbal behavior is behavior, and has a special character only because it is reinforced by its effects on people, but eventually the speaker himself. If the opening of a door will be reinforcing, a person may grasp the knob, turn it, and push or pull in a given way, but if, instead, he says, "please open the door," and a listener responds appropriately, the same reinforcing consequence follows. The contingencies are different, and they generate many important differences in the behavior which have long been obscured by mentalistic explanations. How a person speaks depends upon the practices of the verbal community of which he is a member. A verbal repertoire may be rudimentary or it may display and elaborate topography under many subtle kinds of stimulus control.


Meaning and Reference

Structuralism, differently from behaviorism, ignores meaning. What is important is not what a person is doing but what his behavior means to him; his behavior has a deeper property relating to purpose, intention, or expectation. But the meaning of a response is not in its topography or form, but is to be found in its antecedent history. Meaning is not properly regarded as a property either of a response or a situation but rather of the contingencies responsible for both the topography of behavior and the control exerted by stimuli. For example, if one rat presses a lever to obtain food when hungry while another does so to obtain water when thirsty, the topographies of their behaviors may be indistinguishable, but they may be said to differ in meaning; to one rat pressing the lever "means' food; to the other it "means" water. Similarly, if a rat is reinforced with food when it presses the lever in the presence of a flashing light but with water when the light is steady, then it could be said that the flashing light means food and the steady light means water, but again these are reference not to some property of the light but to the contingencies of which the lights have been parts.

   In order to extend meanings of the above examples to example of verbal behavior, let's take one speaker and one listener who use verbal behavior for an objective; mother of a son informs the time, with a watch, for the son (without a watch) to leave for his school in time. The meaning of a response for the speaker (i.e., the mother) is the stimulus which controls it (the setting of the watch to inform her son), and the meaning for the listener is the contingencies involving going to school in time. The topographies of the two behaviors themselves do not have any meaning, but, the corresponding contingencies do.


Metaphor: A stimulus present when a response is reinforced acquires some control over the probability that that response will occur, and that this effect generalizes: stimuli sharing some of its properties also acquire some control. In verbal behavior, one kind of response evoked by a merely similar stimulus is called a metaphor. The response is not transferred from one situation to another, it simply occurs because of a similarity in stimuli.


Abstraction: It is the listener, not the speaker, who takes practical action with respect to the stimuli controlling a verbal response, and as a result the behavior of the speaker may come under the control of properties of a stimulus to which no practical response is appropriate. If we show a person a red pencil and say, "what is that?" and he says, "red", we cannot tell what property evoked his response, but if we show him many red objects and he always says, "red", we can do so. The speaker is always responding to a physical object, not to redness as an abstract entity, and he responds "red" not because he possesses a concept of redness but because special contingencies have brought that response under the control of that property of stimuli. Contingencies explain the behavior, and we need not be disturbed because it is impossible to discover the referent in any single instance. We need not deny that abstract entities exist and insist that such responses are merely words. What exist are the contingencies which bring behavior under the control of properties or of classes of objects defined by properties.


Concepts: When a class is defined by more than one property, the referent is usually called a concept rather than an abstract entity. A concept is simply a feature of a set of contingencies which exist in the world, and it is discovered simply in the sense that the contingencies bring behavior under its control. The statement "scientific concepts enable certain aspects of the enormous complexity of the world to be handled by men's minds" is vastly improved by substituting "human beings" for "men's minds".


Sentences and Propositions

The traditional notion of meaning and referent runs into trouble when we begin to analyze larger verbal responses under the control of more complex environmental circumstances. What are the referents of sentences? A sentence surely means more than its separate words meant. Sentences do more than refer to things; they say things. But what are the things they say? A traditional answer is "propositions" which are common elements in sentences. The linguist assigns these elements to syntax or grammar.

   The concept of stimulus control replaces the notion of referent with respect not only to responses which occur in isolation and are called words but also to those complex responses called sentences. The child responds in sentences to events in his environment (events involving more than one property or thing, or relations among things, or relations of actor and acted upon, and so on), and his responses contain elements which he never has any occasion to emit alone. He does so as part of an analysis of the practices of a given verbal community, from which he extracts rues which may be used in the construction of new sentences.


The Manipulation of Words and Sentences

Structuralism has been strongly encouraged in linguistics because verbal behavior often seems to have an independent status. We are inclined to give special attention to its form because we can report it easily, and rather accurately, simply by modeling it, as in a direct quotation. In teaching a child to talk, or an adult to pronounce a difficult word, we produce a model-that is, we say the word and arrange contingencies under which a response having similar properties will be reinforced. Verbal behavior has this kind of independent status when it is in transmission between speaker and listener, for example, when it is the information passing over a telephone wire or between writer and reader in the form of a text. 

   The availability of verbal behavior in this apparently objective form has caused a great deal of trouble. By dividing such records into words and sentences without regard to the conditions under which the behavior was emitted, we neglect the meaning for the speaker or writer, and almost half the field of verbal behavior therefore escapes attention. Worse still, bits of recorded speech are moved about to compose new "sentences", which are then analyzed for their truth or falsity, although they were never generated by a speaker. Both logician and linguist tend to create new sentences in this way, which they then treat as if they were the records of emitted verbal behavior.

   The transformational rules which generate sentences acceptable to a listener may be of interest, but even so it is a mistake to suppose that verbal behavior is generated by them. We may analyze the behavior of small children and discover that part of their speech consists of a small class of "modifiers" and a larger class of "nouns". It does not follow that the child forms a noun phrase of a given type by selecting first one word from the small class of modifiers and selecting second one word from the large class of nouns. This is a linguist's reconstruction after the fact.


The growth of language in a child is easily compared with the growth of an embryo, and grammar can then be attributed to rules possessed by the child at birth. A program in the form of a genetic code is said to "initiate and guide early learning... as a child acquires language". But, the human species did not evolve because of an inbuilt design; it evolved through selection under contingencies of survival, as the child's verbal behavior evolves under the selective action of contingencies of reinforcement. A record of topography needs to be supplemented by an equally detailed record of the conditions under which it was acquired. What speech has the child heard? Under what circumstances has he heard it? What effects has he achieved when he has uttered similar responses? Until we have this kind of information, the success or failure of any analysis of verbal behavior cannot be judged.


Creative Verbal Behavior

In verbal behavior, as in all operant behavior, original forms of response are evoked by situations to which a person has not previously been exposed. The origin of behavior is not unlike the origin of species. New combinations of stimuli appear in new settings, and responses which describe them may never have been made by the speaker before, or heard or read by him in the speech of others. There are many behavioral processes generating "mutations", which are then subject to the selective action of contingencies of reinforcement.