## Tuesday, April 29, 2008

### Zero

For a proper understanding of the evolution and the need for the concept of zero we need to understand how our current number system has evolved from its ancestors. The very need for the concept of zero did not arise till the number systems themselves were well developed. The advancement in the number system necessitated the need for the concept of zero as we now know it. We can identify two distinct manifestations of zero; one is zero as a placeholder and the other is zero as a number, the former has  much earlier origin than the later.

Humans probably before having the concept of numbers or counting then, would have begun with enumeration. By enumeration it is meant that we simply keep a track of objects in a collection or a set by matching the objects with other objects used as counters. A shepherd can keep the track of sheeps in the flock, by keeping pebbles which are equal in number to the number of sheep s in the flock or equivalently [if possible] by counting body parts. Then just by matching each sheep with each pebble the record of number of sheep s can be maintained. When the number of sheep s is increased or decreased the same number of pebbles or other counters can be increased or decreased correspondingly. The other counters that one can have for this type of counting can include the human body itself. In fact many primitive societies do indeed have a counting system based on the body parts. This is the most basic system of counting that we can have. No language is needed for such one-to-one counting.

When the languages developed, particular words were created for various body parts, so these words were used instead of the body parts themselves. This is a transition from enumeration to numeration. Thus one has to remember only the word names in order for counting. But this does not imply the idea of cardinality of number being present in this numeration. For the notion of cardinality of a number to be used in the idea of numeration it required some time. When the questions were asked in the form How many...? in the ancient texts, the answers to these type of questions are given best in terms of the cardinal number. From this further growth would be, the concept of ordinality i.e. the order of things is not important when counting objects. It relates to the fact that the last number enounced in a set not only assigns a certain name to the last object in the set to be matched but also tells us how many objects are there in that set altogether.

The further development of this numeration is the formation of numeration systems. The need for the number systems typically arose from the following question:

What is to be done when the finite ordered sequence of counters is exhausted, yet more objects remain to be matched?

This particular question was answered in different ways only one of which led us to the current number system we have. One of the most simple solutions to this is to extend the ordered sequence of counters. So that we invent new symbols or names to accommodate the excess objects that are to be matched. But this approach makes no sense when we have large number of objects that are to be matched.

A simpler way which lends itself well to the written representation, was extension by repetition. The extension by repetition implies a number system which is based on the additive principle. Most of the primitive number systems are based on the additive principle. Here the figures are entirely free. Their juxtaposition entails adding together their values. In a number system based on the additive principle it makes no difference where you place the symbols corresponding to the numbers. Some of the numbers systems based on the additive principle are; Egyptian, Cretan, Hittite, Greek, Aztec, Roman, Sumerian etc. As an example of the additive principle we consider the Egyptian system. In this system if we want to represent the number 5247 it can be represented in following ways:

When we break down the representation based on the additive principle we get the following:

Thus we see that in the representation of a number in the number systems based on the additive principle. Since addition is both commutative and associative, irrespective of where we place the base numbers the final number that is represented by the various combinations of these numbers remains the same.

This system though seems simple puts a lot of cognitive load on the user. First of all there are different symbols for different numbers and in many of these number systems the symbols have some intuitive association [at least in the lower range] to the number that they represent. So to represent large numbers a large number of different symbols were to be used. In our example of representing the number 5247 in the Egyptian hieroglyphic notation  we have used a total of 18 symbols. Many times for representing large numbers new symbols had to be introduced. The arithmetic operations with these systems presented another difficulty. The number systems based on the additive principle are not well suited for arithmetic operations. For example consider the following sum in the Roman notation:

The above sum gives us no clue to what is supposed to be done. Though there are methods to perform this operations, but the procedures involved are very complicated. The above sum in the current notation would be:

In the number systems based on the additive principle the number signs are static in nature, which have no operational significance. The number signs in this case are more like abbreviations which can be used to write down the results of the calculations performed by some other means. To do arithmetical calculations, the ancients generally used auxiliary aids such as abacus or a table with counters.

The enumeration, numeration as we have seen do not have any requirement for the concept of zero as a number or a placeholder. The same is true with the number systems based on the principle of addition, in these systems there is no requirement of the concept of zero.

The next step in the evolution of the number systems was the hybrid system, called so because it involves use of both addition and multiplication. In the hybrid system when the symbols for lets say symbols for 1000 and 5 are presented together, they meant 5 x 1000 = 5000, whereas in the additive system they will mean 1000+5=1005. In the hybrid system there were basic symbols for the numbers, and symbols for various powers of the base, for example in a base 10, system the symbols for 100, 1000 etc. These number systems used the additive principle for representing numbers below 100.

In case of complete hybrid systems there were special symbols for the numbers 1 - 9, and all numbers including the tens were represented as a product of these base numbers and the powers of 10. This increased the range of numbers that can be represented. The notable hybrid systems are Assyro-Babylonian, Phoenician, Singhalese, Mari, Chinese, Ethiopian, Tamil, Malayalam, and the Mayan. We consider an example from the complete hybrid systems to represent the number 5247 from \cite{uni1}.

When we break down the representation based on the multiplicative principle we get the following:

The hybrid systems thus need a specification of the powers of the base which, determine the value of the number in a given position. This brings us a step closer to the positional number systems based on the multiplicative principle. The hybrid system are not all forgotten and are still in use today. When we verbally read a number it is more of a hybrid number system that we use that a positional number system. That is to say when we read the number 5247, we spell it out as five-thousand two-hundred and forty-seven. Here when we verbally read a number we also explicitly give its corresponding powers just like in case of the hybrid number system. Even in this case the need for zero is not there, the hybrid systems can work without the use of the concept of zero.

So to conclude the hybrid systems are  "Systems based [at least after a certain order] on a mixed principle [both additive and multiplicative] that invokes multiplication rule to represent consecutive order of units.''

We now move to the positional systems or multiplication based systems. These systems have a more abstract representation. The value of a figure in these positional systems varies according to the position in which it occurs in the representation of the number. Due to this the coefficients of the power of the base, into which the number has been decomposed appear. For example in a particular representation the actual value of a number, lets say 5 will depend on which position 5 is present in. If 5 is present in the units place then it represents 5, when it is present in the tens place it represents 50, and so on. If in the hybrid system if we remove the symbols used and just have the numbers only we have a positional number system. In this case the powers of the base for our case take base as 10, are implicitly figured out from the position of the numerals in the representation of the number. We know that in the positional representation of the number 5247, 5 is in the thousands place, 2 is in the hundreds place etc. Once this order is fixed then can we represent a number without any ambiguity? If we just consider the coefficients of the number 5247, the the answer to this probably seems to be true. But is it always so? For answer to this consider another example. Suppose we want to represent a number 1043 in the positional number system. In case of hybrid number system the representation would be like this:

so if we now drop the powers of the base, and just take the coefficients we are left with:

But this is not correct, since 143 is another number and not 1043.Similarly if we take just the coefficients of the number 10403, they are again 143. In case of the non-positional system this was not a problem, since every power and the corresponding coefficient was made explicit. But here if we just consider the coefficients of the number in a particular base, we cannot be sure that the number that we are representing is correct, unless we know for sure that a particular coefficient corresponding to a particular power is not present. In case of 1043 we have the coefficient of 100 absent. Some of the earliest positional systems that were developed suffered from the same problem. In case of the Babylonian system, we are not sure of how to read a particular number in many clay tablets, and the number has to be guessed from the context of the problem. Since the Babylonians used a base of 60, so a number [lets take 5247] was represented as:

In this case there was no ambiguity in base 60 number would be written as [1;27;27]. But even in this case there was no guarantee that the number represented is the number that we want. Suppose if we want to represent 3627 in this notation, then it would be represented as:

which is very easy to confuse with

Thus we see that in case of the positional number system we required a notion that tell us whether a particular coefficient is absent. This requirement initiated the need for the concept of zero. So the discovery of zero was therefore a necessity for the strict and regular use of the rule of the position, and it was therefore a decisive stage in the development of mathematics. So how do we make sure that something is not present in a particular position in a given positional representation of a number. It becomes essential then to have a special sign whose purpose is to indicate the absence of anything in particular position. This thing which signifies nothing, or the empty space, is in fact the \textsl{zero}. As \cite{uni1} pg. 668 puts it: "To arrive at the realisation that empty space may and must be replaced by a sign whose purpose is precisely to indicate that it is empty space: this is the ultimate abstraction, which required much time, much imagination, and beyond doubt great maturity of mind.''

The concept of zero has been discovered three times in the history independently. It was discovered first by the Babylonians, the Mayans and the Indians. All these three civilizations used the positional number system for which the concept of zero is needed. The Babylonians tried to get away with this difficulty by leaving empty space where the missing  coefficients of particular order were to be found. Hence they would write a number such as [1; 6] for lets say 3606. But this did not solve the problem completely. In copy or reading these spaces could be overlooked, and particularly when two or more space were to be given it could be confused with one space. But since the Babylonians has the base as 6o the need for writing numbers with zero in between arises on a very few occasions than it does in the number system with base 10. In case of the sexagesimal numeration only in 59 integers below 3600 this arises; as compared to 917 cease in the base 10 system \cite{boyer}. The Babylonian zero is the first zero to arrive on the scene. To denote absence of a coefficient of a particular order in their representation of the number, the Babylonians used a special sign [after fourth century BCE], which is the a cuneiform sign looking like a double oblique chevron. The Mayans developed their positional system with base 20, but they were not consistent with the use of the powers of the base after the third position \cite{uni2} pg 670. The Mayans understood the concept of zero sign, but they did not have its operational usability due to their inconsistent positional system. In case of the Babylonians it was never understood as a number synonymous with empty and never corresponded to the meaning of null quantity. So we see that in spite of having the notion of zero the Mayans and teh Babylonians did not get much further in this. The Mayan and the Babylonian zeros are as given in the figure.

If we work out the number represented in these notation the numbers are:

In the Babylonian notation.

In the Mayan notation.

The credit of having a well conceived positional system, which is operationally useful goes to the Indians. This step was taken by simplifying the hybrid notation, by suppressing the signs indicating the powers of the base. This required a much higher level of abstraction: the zero. This can be regarded as "... the supreme discovery of mathematicians who soon would come to extent it, form its first role of representing empty space, to embrace truly numeric meaning of a null quantity.'' The Indian civilization was the only one to achieve this great feat. This system came up as a result of conjunction of three great ideas :

1.The idea of attaching each basic figure with signs removed from intuitive associations.
2. The idea of a positional number system, in which the value of a number depends on its position in the representation.
3. The idea of a full operational zero, filling the empty spaces of missing units and at the same time having the meaning of a null number.

In the system thus developed it does not matter what signs or base we use for the system, if it rests strictly and rigorously of the principle of position and incorporates the full concept of the symbol for zero. The discovery of zero in India and the place value were inventions unique to the Indian civilization. The roots of the development of the positional number system in India can be traced to the use of spoken sanskrit [संस्कुत] numeral system [Treatment of the development of Indian positional system follows from \cite{uni1}, \cite{uni2}]. The sanskrit spoken language has for each power of ten an individual name, ``... so that to express a given number, one only had to place the name indicating the order of units between the name of the order of units that was immediately below it and immediately above it.'' In fact there are names to the powers of 10 till 10^140 \cite{uni2} pg. 134. This is what is required in a positional number system. From the sanskrit spoken numeral system the Indian system of numerical symbols was formed. As soon as place value system was rigorously applied to the nine simple units, the use of a special terminology was indispensable to indicate the absence of units of a particular order. The sanskrit language already possessed the word shunya [शुन्य] to express void or absence, which also an element of mystical and religious philosophy. So to express the new mathematical notion of zero the term shunya could be used. This is how the word came to perform the function of zero as a part of the counting system.

Indian mathematicians before discovering the place value system, used their fingers or concrete mathematical devices. The most common was the abacus; from left to right, the columns representing the various powers of ten. The first nine numerals were traced in sand or dust, inside the column of a particular decimal order. Thus the number 5247 would have been represented in the following manner :

If a particular order of units was missing, one only needed to leave that particular column empty. Thus for representing 5047 we would write:

So with all this the necessary 'ingredients' for the creation of the written place value system had been amassed by the Indians:

• Distinct representation of one to nine numbers, which had forms unrelated to the number they represented.
• Discovery of the place value system.
• Invention of the concept of zero.

Still some things were still absent for the perfection of the number system:
• The nine numerals were only used in accordance to addition principle for analytical combinations using numerals higher than or equal to ten, the notation was very basic and limited to numbers below 100,000.
•  Place value system was only used with sanskrit names for numbers.
• Zero was only used orally.

The only thing that remained was to combine these ideas. By using the nine bramhi [ब्राम्ही] numerals on the dust abacus this stage already had been reached.

The two methods of expressing the numbers bramhi numerals and sanskrit names of numbers were known to the Indian mathematicians. In the dust abacus the numbers were drawn in contemporary style. The numbers in sanskrit were expressed in orders of ascending powers of ten; from the smallest to the highest. So that 4769 is written as:

And it is read in sanskrit as:

नव शष्टि सप्तशत् च चतुरसहस्त्र
Meaning: nine sixty seven hundred and four thousand.

In the written numerals however the opposite order was used. The evidence for these methods goes back to third century BCE. IF we look at these two opposite ways of representing the number, indicates an inconsistency. This is what the Indian mathematicians expressed as :

अंकानाम वामतो गति:

Meaning: principle of the movement of numerals from the right to the left.

Since the brahmi had a limited numeral base [highest number expressed was 90,000], so any calculation larger than this was to be expressed in the sanskrit names for the numbers. In the dust abacus extremely large computations could be performed, and the successive columns in the abacus always rigorously corresponded to the consecutive powers of ten. The same mathematical structure was present in the sanskrit counting system. Thus each system was a mirror image of the other. Though the numbers are read from the right to the left from the smallest to the largest. The structure of the abacus is such that the mathematician has no other choice but to follow the principle
अंकानाम वामतो गति: principle of the movement of numerals from the right to the left.

The solution to write a number in this way was to start with the column for the simple units. This led to the abandonment of the old system. By beginning with highest power of ten, one immediately knows the size of number we are dealing with, but this did not facilitate drawing. Hence the opposite system was adopted; no matter how high a number, there could be no mistake as to which column to write it in. This was conserved when the positional notation was invented using numerical symbols.

All this lead to the following notation, "the numbers reading from left to right in descending powers of ten, constituting a faithful reproduction, minus the columns, of its representations on the abacus, as well as reflection of the abridged form of the corresponding sanskrit expression. Thus came the decimal position values which were given to the first nine numerals of the old notation. This was the birth of the modern numerals.

Now to convey the absence of units in a particular decimal order a new symbol was necessary. This was not required in the case of the abacus, but in the new positional system it became a necessity. The  language already had the word symbol that expressed the concept zero, the shunya, it also conveyed the concepts such as sky, space etc. The circle has been considered as the representation of the sky, hence through a simple transposition of ideas it came to represent the concept of zero. Another sanskrit term representing zero was bindu [बिंदु], which literally means "point''. The point is the most insignificant geometrical figure, but for Indians the point represents the universe in non-manifest form. The point is the elementary of all geometrical figures, with potential for creating all the shapes, and hence was associated with zero. Zero is the most negligible quantities, but most fundamental of all abstract mathematics. The point also thus came to represent the zero. The two forms of the Indian zero are as shown in the figure below.The most likely time that the positional value system and zero were discovered is in the middle reign of the Gupta dynasty which ruled the Gangetic plains from about 240 to about 535 CE.

Along with the loaded philosophical connotations that were associated with the word shunya it served to mark the absence of units within a given decimal order in any position; the point or the little circle were used in the same way. This zero was also a mathematical operator; if placed after a number, it meant the number was multiplied by ten. Thus the three significant ideas that we have mentioned earlier were combined to give us the modern positional number system. Soon after this the concept of zero was perfected. Zero was given the status of a number, i.e. to say its cardinality was recognised. After this various arithmetic operations on and with zero were defined, which led to foundation of modern algebra .

The Arabs got this positional number systems from the Indians. The Europeans in turn got this system from the Arabs. The origin of the word zero or cipher can be traced back to this transfer of the positional number system to the Europeans from the Arabs. The Indian word for zero is shunya, from this the Arabic name sifr meaning vacant was given. When this was transferred to the Europeans the sound was kept but not the sense; Fibonacci called it zephirum. This was then passed over as zeuro, ceuero, and zepiro, which finally led to the current day synonyms which are the zero and the cipher.

References

Boyer C. B. :
Zero: The Symbol, the Concept, the Number
National Mathematics Magazine, Vol. 18, No. 8 , May 1944

Irfah G. :
The Universal History of Numbers I
Penguin, 2005

Irfah G. :
The Universal History of Numbers II
Penguin, 2005

Ore O. :
Number Theory and Its History
Dover, 1948

### Kohlberg's Theory of Moral Development

Moral Development

In this article the Kohlberg’s Theory of Moral Development is discussed. Kohlberg’s theory is a direct continuation of the Piaget’s work on the same issues. Kohlberg's methodology, and why he considers structure more important than content are discussed. The key aspects of the typical reasoning in the moral judgments of each level are discussed. The developmental issues and the criticisms of the theory are presented in the later sections. Also the various aspects of morality being context, culture and time dependent are discussed.

Introduction
The very word ‘moral’ colloquially means of or relating to principles of right and wrong in behavior. Moral behavior as understood in a everyday notion, relates to the behavior of an individual which is acceptable in the contemporary society. One thing is for sure that the moral development is not innate, it comes through our own thinking about the moral problems, with inputs from the interactions that we have with the society. There are three major components of morality, viz. the emotional component, cognitive component, behavioral component. The emotional component reﬂects the fact that we can relate to the harm that we cause to other person. The cognitive component emphasizes the fact that
thinking about the social understanding helps us to make more elaborate judgment’s about actions. Finally the behavioral component relates to the fact that exposure to morally relevant thoughts and feelings can only increase the chances that we will act accordingly but does not guarantee the same.

The biological and the psychoanalytic theories focus on emotional aspect of the morality, cognitive developmental theories on the moral thought, whereas the social learning theory has focused on the behavioral aspects. These theories disagree with what is the primary cause, but the trend that is seen
in the moral development is that a person starts from “externally controlled responses” and goes on to “behavior that is based on inner standards.” In the following sections we mainly consider the theories of moral development of Piaget and Kohlberg which elaborate the cognitive developmental aspect of
morality.

Piaget’s Theory of Moral Development

From this perspective the maturity in cognition and social experience lead to the development in the moral understanding of the child as a whole. Piaget’s work on the aspect of the moral development in children is the pioneering work in the cognitive development aspect of morality. For studying the
children’s ideas about morality Piaget depended upon open ended clinical interviews. By clinical interviews it is meant that a child is asked some questions and probed futher in the reasoning behind a particular response given. Piaget in particular asked about the rules in game of marbles. The children were also given stories in which the character’s intentions [ either wrong or right ] and the consequences of such a action were varied. The best kno twn such example is that of John and Henry. In these stories each of the boy breaks diﬀerent number of cups, one with ‘wrong’ intention and other with no intention. The children are asked the question that which one of them is naughtier and why. The two
stories are like this [1]:

Story A: A little boy who is called John is in his room. He is called to dinner. He goes into the dining room. But behind the door there was a chair, and on the chair there was a tray with ﬁfteen cups on it. John couldn’t have known that there was all this behind the door. He goes in, the door knocks against the tray, bang go the ﬁfteen cups and they all get broken!

Story B: Once there was a little boy whose name was Henry. One day when his mother was out he tried to get some jam out of the cupboard. He climbed up on to a chair and stretched out his arm. But the jam was too high up and he couldn’t reach it and have any. But while he was trying to get it he knocked over a cup. The cup fell down and broke.

The responses that Piaget got from children between ages 5 and 13 he could identify two general stages of the moral understanding viz. heteronomous and autonomous morality.

Heteronomous Morality [ ∼ 5 - 10 years]

Before the beginning of this stage the children show little understanding that rules govern the social behavior. At about 5 years of age the children enter the period of heteronomous morality and begin to show concern for the rules. The word heteronomous means under the authority of other, the children view the rules as handed down by the authorities. The rules are unvarying and require strict obedience. The factors that limit the child’s understanding according to Piaget are:

1. The unquestioned respect for rules and those enforce them.
2. Egocentrism.

As young children think that view of all the people about the rules are same, their moral understanding is characterized by realism, which means that they regard the rules as “external features of reality, rather than as subjective, internal principles that can be modiﬁed at will.” The presence of realism and egocentrism leads to young children focussing on the objective consequences rather than the intent. In the stories about John and Henry, John is considered more naughty because he broke more cups, even if he did not wrong intent in doing so. Another thing that the children having heteronomous morality believe in is the concept of immanent justice i.e. they believe that wrong doing always leads to punishment. The punishment thus received is inescapable and can be through a variety of events.

Autonomous Morality [ ∼ 10 years and above]

The autonomous morality is the next stage in Piaget’s theory of moral development. Through the interactions with peers children become aware that people have diﬀerent views than their own. They realize that intentions are more important than the objective consequences in moral judgments. Thus
in the two stories mentioned, they do not consider John as naughty, even if he broke more cups because he simply did not intend to do so. On the other hand Henry is considered naughty as he has intent to steal the jam, even in the process he broke less cups. The conﬂicts with peers are settled in mutually beneﬁcial ways. The concept of reciprocity is developed in children. By reciprocity it is meant that, “they express the same concern for the welfare of  others as they do for themselves.” The most familiar expression of reciprocity is the Golden Rule:
Do unto others as you would have them do unto you.

Reciprocity is the main driving force in the understanding of children in autonomous morality. Children realize that, “rules are ﬂexible, socially agreed on principles that can be revised to suit the will of the majority.” The children can question the logic of the rules and just do not blindly follow them, they can realize that at times there may be good reasons to break a rule. Punishment are also seen in the light of principle of reciprocity. The punishment should be meted in an even-handed way to everyone responsible for the oﬀense, thus guaranteeing justice for all.

Evaluation of Piaget’s Theory

Piaget’s two stage theory gives a general account of the development of the moral understanding in children. The essential aspects of the theory relate with Piaget’s view that child’s development in general goes through a stagewise manner dependent on the age. The followup studies indicate the conclusions of Piaget that “moral understanding is supported by cognitive maturity, release from adult authority, and peer interaction. We now consider some aspects of this theory that have been questioned.

Intentions and Moral Judgments

Considering the stories of John and Henry, they present a biased view of child’s reasoning as more damage is coupled with good intentions and vice versa. If the same scenario is presented on the same grounds of damage, even the younger children can judge the ill intentioned person as naughtier. Also by the age of 4 years children are able to recognize the diﬀerence between lying and truthfulness, two morally relevant intentional behaviors. Thus the capacity to consider intentions appears in children much earlier than Piaget believed a deeper understanding does not arise till they reach autonomous morality.

Piaget assumed that heteronomous children assume the authority of adults with unquestioned respect, but studies have revealed the contrary. The preschoolers judge stealing, hitting as wrong regardless of the opinions of authority. Also peers can be regarded as authorities, e.g. a class captain. Thus “young children’s concepts of authority do not focus solely on status and power.” Contrary to
this many factors are responsible at an earlier age than assumed by Piaget, these factors include, “the attributes of the individual, the type of behavior to be controlled, and the context in which it occurs.

Stagewise Progression

Another aspect of Piaget’s theory is that characterstics associated with each stage do not correlate very highly, as would be expected if each stage represented a “general unifying organization of moral
judgments.” Thus child’s moral thought appears as “patchwork of diverse parts.” But to this Piaget recommended that, “the two moralities be viewed as ﬂuid, overlapping ‘phases’ rather than as tightly knit stages.” Also studies indicate that the moral development goes beyond the two stages of Piaget. Kohlberg’s work presented in the later sections is a direct continuation of the Piaget’s work on moral development.

Kohlberg’s Extension of Piaget’s Theory

Lawrence Kohlberg [1927 - 1987] following Piaget’s work on the aspect of moral development in children began on similar lines the search for stages of moral development and study of how moral understanding is intimately tied to the cognitive growth. The methodology that Kohlberg adopted for the study of moral was same of Piaget viz. the clinical interviews, but instead of asking children to
judge the naughtiness of a character of a story Kohlberg presented children with moral dilemmas. A moral dilemma is “a conﬂict situation presented to subjects, who are asked to decide both what the main actor should do and why.” In a moral dilemma two moral values are pitched against each other. The conﬂict in the mind of sub ject with regard to these two moral values, and its subsequent
resolution serves as an index of the moral development. This enables the experimenter to get a better picture of the reasoning behind the moral decisions. The best known moral dilemma is the the ‘Heinz dilemma,’ in which the subject is presented with conﬂict between two moral values viz. obeying the law [not stealing] and value of human life [saving a dying person] [2]:

Heinz Steals The Drug
In Europe, a woman was near death from a special kind of cancer. There was one drug that the doctors thought might save her. It was a form of radium that a druggist in the same town had recently discovered. The drug was expensive to make, but the druggist was charging ten times what the drug cost him to make.
He paid \$200 for the radium and charged \$2,000 for a small dose of the drug. The sick woman’s husband, Heinz, went to everyone he knew to borrow the money, but he could only get together about \$ 1,000 which is half of what it cost. He told the druggist that his wife was dying and asked him to sell it cheaper or let him pay later. But the druggist said: “No, I discovered the drug and I’m going to make money from it.” So Heinz got desperate and broke into the man’s store to steal the drug-for his wife. Should the husband
have done that?
In the response received from the sub jects [72 boys of ages 10, 13 and 16 in the core sample] to the moral dilemma presented above Kohlberg was more interested in the structure than the content of the response. So just a ‘yes’ or ‘no’ response to the question presented above will not provide us with the reasoning behind this moral judgment. In fact for the ﬁrst four stages that Kohlberg identiﬁed, both the responses are found with diﬀerent reasoning at each stage. To ﬁnd out this reasoning the ‘why’ questions are asked and the sub ject is further probed with other related dilemmas. Based on the diﬀerent response he got from the children Kohlberg was able to classify them into various stages.
Kolhberg was able to identify three general levels and six stages in all for the moral development in children.

Kohlberg’s Stages of Moral Development

Level I Preconventional Morality
At this level the morality of the person is externally controlled and can be identiﬁed with the main features of the Piaget’s heteronomous stage. The children accept the rules of the authority and the actions are judged by the consequences and not the intent. The moral understanding is based on
rewards and punishments.

Stage 1 Obedience and Punishment Orientation
This stage is similar to Piaget’s heteronomous stage of moral thought. The child regards the rules as ﬁxed, handed down by adults which must be obeyed at all costs. The child is unable to take two points of view for the moral dilemma.
The typical pro-stealing and anti-stealing responses are as follows [Taken verbatim from [1]]:

Pro-Stealing: “If you let your wife die, you will get in trouble. You’ll be blamed for not spending money to help her, and there’ll be an investigation of you and the druggist for your wife’s death.”

Anti-Stealing: “You shouldn’t steal the drug because you’ll be caught and send to jail if you do. If you do get away, your conscience would bother you thinking how the police will catch up with you any minute.”

Stage 2 Individualism and Exchange
At this stage the children become aware that diﬀerent people have diﬀerent perspectives in a moral dilemma, but this awareness is very concrete. The right action is considered that satisﬁes ones personal needs. Reciprocity is considered as equal exchange of favors. The typical pro-stealing and anti-stealing responses are as follows:

Pro-Stealing: “The druggist can do what he wants and Heinz can do what he wants to do . . . But if Heinz decides to risk jail to save his wife, it’s his life he’s risking; he can do what he wants with it. And the same goes for the druggist; it’s up to him to decide what he want to do.”

Anti-Stealing: “[Heinz] is running more risk than it’s worth unless he’s so crazy about her he can’t live without her. Neither of them will enjoy life if she’s an invalid.”

Both the stages in the ﬁrst level talk about punishment, but the perception in each stage is diﬀerent. Whereas in the ﬁrst stage punishment is linked with [proves] wrongness of disobedience, in the second stage on the other hand punishment is regarded as “simply a risk that one naturally wants to avoids.”
The stage 2 children are considered to reason at the preconventional level as they think “as isolated individuals rather than as members of society.” Also “they see individuals exchanging favors, but there is still no identiﬁcation with the values of the family or community.”

Level II Conventional Morality

In this level as the name suggests the individuals continue to regard the conformity to social rules as important, but the reason not being self-interest but rather maintaining the “positive human relationships and the societal order.”

Stage 3 Good Interpersonal Relationships
The desire to obey rules in stage 3 is in the context of close inter-personal feelings such as love, trust and concern for others. The main belief is that “people should live up to the expectations of the family and community and behave in ‘good’ ways.” The stage 3 person has a capacity“ to view
a two-person relationship from the vantage point of an impartial, outside observer,” which supports this new approach to morality. The motives are considered to be important than the consequences. As in Piaget’s two stages similarly in Kohlberg’s stages, “there is a shift from unquestioning obedience
to a relativistic outlook and to a concern for good motives. For Kohlberg, however, these shifts occur in three stages rather than two.”
The typical pro-stealing and anti-stealing responses are as follows:

Pro-Stealing: “No one will think you’re bad if you steal the drug, but your family will think you’re an inhuman husband if you don’t. If you let you wife die, you’ll be never be able to look anyone in the face again.”

Anti-Stealing: “It isn’t just the druggist who will think you’re a criminal, everyone else will too. After you steal it, you’ll feel bad thinking how you brought dishonor on your family and yourself; you won’t be able to face anyone again.”

Stage 4 Maintaining the Social Order

In stage 4 person has a intent for the beneﬁt of the society as a whole. The moral judgment and behavior is in the context of maintaining social order and no longer depend on the close ties to others. As the stage 4, “subjects take the moral decisions from the perspective of society as a whole, they think from a full-ﬂedged member-of-society perspective.” The typical pro-stealing and anti-stealing responses are as follows:

Pro-Stealing: “He should steal it. Heinz has a duty to protect his wife’s life; it’s a vow he took in marriage. But it’s wrong to steal, so he would have to take the drug with the idea of paying the druggist for it and accept the penalty for breaking the law later.”

Anti-Stealing: “It’s a natural thing for Heinz to want to save his wife, but it’s still always wrong to steal. You have to follow the rules regardless of how you feel or regardless of the special circumstances. Even if his wife is dying, it’s still his duty as a citizen to obey the law. No one else is allowed to steal, why should he be? If everyone starts breaking the law in a jam, there’d be no civilization, just crime and violence.”

It might at the ﬁrst glance seem that stage 1 and stage 4 sub jects are giving the similar responses, but the reasoning that the stage 4 is quite elaborative. Stage 1 children cannot elaborate the reasons, except that stealing will lead to jail, stage 4 respondents, on the other hand have a broader conception of the function of societal laws as a whole, which exceeds the capacity of the stage 1 child.

Level III Postconventional Morality

Individuals in this level move beyond the unquestioning support for the rules and the laws of their own society, hence the name. The morality for such individuals is “in terms of abstract principles and values that apply to all situations and societies.” The individuals in this level of moral reasoning with
a pro-stealing answer to the Heinz dilemma, the reasoning being of course diﬀerent from the previous levels.

Stage 5 Social Contract and Individual Rights

The stage 5 individuals consider the rules as “ﬂexible instruments for furthering human purposes.” They can argue for a change in the societal laws [considered to be unchangeable by the previous stages] when a good enough reason is pressent. At stage 5, people begin to ask, “What makes for a good society?” They begin to think about “rights and values that a society ought to uphold,” and
then see the society from these perspectives.
The typical pro-stealing response is as follows:

Pro-Stealing: “Although there is a law against stealing, the law wasn’t meant to violate a person’s right to life. Taking the drug does violate the law, but Heinz is justiﬁed in stealing in this instance. If Heinz is prosecuted in stealing, the law needs to be reinterpreted to take into account situations in which it goes against people’s natural right to keep on living.”
The stage 5 people regard society is “best conceived as a social contract into which people freely enter to work toward the beneﬁt of all.” Even with some diﬀerences in the society the stage 5 people believe that rational people in the society would agree on some basic points. “First they would all want certain basic rights, such as liberty and life, to be protected, and second they would want some democratic procedures for changing unfair law and for improving society.

Stage 6 Universal Principles

The stage 5 respondents are strong believers in the democratic process. But during a democratic process he outcomes are not always just for the minority group. Hence Kohlberg believed “that there must be a higher stage–stage 6–which deﬁnes the principles by which we achieve justice.” At this highest stage the right action is deﬁned by the self-chosen ethical principles which are valid for the humanity as a whole regardless of societal laws. Most of the social reformers and the moral leaders will fall in the stage 6. The claims of all individuals need to be looked at in an impartial manner respecting basic dignity of all people.

The typical pro-stealing response is as follows:

Pro-Stealing: “If Heinz does not do everything he can to save his wife, then he is putting some value higher that the value of life. It doesn’t make sense to put respect for property above the respect for life itself. [People] could live together without private property at all. Respect for human life and personality is absolute and accordingly [people] have a mutual duty to save one another from dying.”

The stage 6 is called as a theoretical stage as not many individuals are consistently able to respond at this stage. The fact that the moral dilemma presented is not very convincingly able to distinguish between stage 5 and 6 makes this more clear. One issue that can tell the diﬀerence between stage 5
from stage 6 is of civil disobedience. Stage 5 believe more in the democratic process so will be less willing to go in for a civil disobedience. The violation of the law is justiﬁed only when a right is at stake. In stage 6, in contrast, “a commitment to justice makes the rationale for civil disobedience

Theoretical Issues

In this section we brieﬂy consider the main theoretical issues regarding the theory. They include the developmental aspects of the theory, the Piagetian stage concept in the context of Kohlberg’s theory.

How Development Occurs

Kohlberg’s views are strongly inﬂuenced by the Piagetian framework of child development. The stages of moral development are not seen as a product of maturation i.e. there is no “genetic blueprint” for the stages to occur. The socializing agents do not directly teach new forms of thinking. The stages
that are externally seen are a manifestation of one’s own thinking about moral problems.

Social experiences promote the development of moral thinking, by stimulating our mental processes. When we discuss with others, our view are challenged due to which we are force to think about ‘better’ positions that we can take. The stages of moral development reﬂect these broader viewpoints. Thus our interactions with the society and our own thought process combined gives us the ability to advance from one stage to the next.

The Stage Concept

As already mentioned Kohlberg being a close follower of Piaget, has taken the stage concept of Piagetian framework criteria very seriously. The following aspects of his theory are shown to be related to the Piagetian framework.

Qualitative Diﬀerences

The qualitative diﬀerences in the diﬀerent stages is evident from the diﬀerent response that is given by the individuals in diﬀerent stages. Quantitatively the stages do not seem to have much diﬀerences.

Structured Wholes

The stages are not just isolated responses present given by the individual, but are a more general patterns of response that are found across many domains. Thus the stages are structured wholes in the sense that they truly depict the whole moral development of the individual which is valid across domains.

Invariant Sequence

The stages according to Kohlberg form an invariant sequence. The stages are skipped or moved in a random order. Mostly the cross-sectional data in which children of various age group were interviewed supports this claim of the invariant stage sequence. But the data from the cross-sectional studies are
not conclusive, as a child at higher age could have possibly skipped some previous stage. To resolve this issue longitudinal studies were undertaken. In longitudinal studies the same children are tested regularly after a period of 3 - 4 years. Almost all children in one of the longitudinal study moved through stages without skipping. Another aspect of moral development is that it is very slow and gradual process.

Hierarchic Integration

The knowledge that is learned at the earlier stages is not lost when the individual advances to the next stage, but is very well present in the individual. The higher stage persons are able to understand the arguments of the lower stage but consider it to be naive. When Kohlberg says that his stages are
hierarchically integrated, he means that people do not lose the insights gained at earlier stages, but integrate them into new, broader frameworks. Thia is a very important concept for Kohlberg because it explains the directional nature of the stage sequence. Since the stage sequence does not have a genetic blueprint, the previous stages must form a ‘platform’ for the next stages to emerge. Thus each new stage provides a broader framework for dealing with moral issues and is thus more cognitively adequate than the prior stage.

The stages of moral development also represent increasingly diﬀerentiated structures. The stage 5 people have abstracted the value of life, for example, has become diﬀerentiated from other considerations and say that “we ought to value life for its own sake, regardless of its value to authorities (stage
1), its usefulness to oneself (stage 2), the aﬀection it arouses in us (stage 3), or its value within a particular social order (stage 4). Stage 5 sub jects have abstracted this value from other considerations and now treat it as a purely moral ideal.”

Universal Sequence

The sequence for the stages of moral development should be universal according to Kohlberg. By the term universal it is meant that it should be same across all cultures. Since diﬀerent cultures bring up their children diﬀerently this [the universality of the stage sequence] is not naturally expected. Kohlberg’s response is that “diﬀerent cultures do teach diﬀerent beliefs, but that his stages refer not
to speciﬁc beliefs but to underlying modes of reasoning.”

Cross-cultural research shows that individuals in ‘technologically advanced’ societies move rapidly through the stages of moral development that from the societies which are not. Also in isolated communities nobody goes beyond stage 3. These studies indicate two possibilities, ﬁrst that societal factors
that help the advancement of the stages are prevalent in the ‘technologically advanced’ societies, second that the method of evaluation is not suited for all cultures. This point is more elaborated upon later.

The number of years an individual completes in a school is an important and deterministic parameter in the moral development of individuals. Studies clearly indicate that the children who are educated higher levels show a better trend of moral development. The reasons for this particular ﬁnding could
be the social diversity that is encountered in the college campuses, introduces the people to the issues involving political and cultural groups.

Moral Thought and Moral Behavior

The moral stages of Kohlberg’s theory do indicate the moral thinking of the persons, but whether this thinking actually translates into a moral behavior remains a question. We can actually be quite advanced in our moral thinking, but when it comes to moral behavior we do not actually are on the same level, this maybe due to practical reasons involved. Infact this is one of the criticisms of the theory. Hence a perfect correlation between moral judgment and moral action is not possible. But Kohlberg has given a particular relation regarding the moral thinking and behavior: “The two should come closer together as individuals move towards higher stages of moral understanding.” The
advancement in moral reasoning is related with many aspects of social behavior, particularly being more prosocial, this is consistent with Kohlberg’s prediction.

Moral Thought and Other Forms Of Cognition

Kohlberg states that moral development depends on cognition and perspective taking in a very speciﬁc way. Each moral stage requires certain cognitive and perspective taking abilities but these abilities alone do not guarantee that moral development will occur. Thus these cognitive and perspective taking abilities are deemed to be necessary but not suﬃcient for the moral development of the individual.

Criticisms

In this section we consider some criticisms about the Kohlberg’s theory. The two main criticisms that the theory faces are of gender bias and of cross-cultural diﬀerences. The other include the facts that are already mentioned viz. that moral thought and behavior are diﬀerent. Also people tend to respond diﬀerently in real life and hypothetical situations [this particular aspect was seen during the presentation when asked about the moral dilemma regarding the help in exam]. The theory does not talk about moral development of very young children, where the methodology of moral dilemmas might not work very well. Also many researchers have questioned the very concept of a post conventional morality in Kohlberg’s formulation.

Gender Bias

Females tend to score not very well on the Kohlberg’s scale of moral development, very few females actually went above stage 3 in terms of their scores. The fact that Kohlberg’s stages were obtained from interviews with males, and hence reﬂect a decidedly male orientation was pointed out by Carol
Gilligan a co-author and associate of Kohlberg. According to Gilligan the advance moral thought for males and females has diﬀerent ideals. For males the moral thought revolves around rules, rights and abstract principles, whereas for the females the moral thought revolves around interpersonal relations and the ethics of compassion and care. Thus the ‘scale’ of moral development has been ‘calibrated’ from a male perspective and it is improper to judge the moral development of females by this scale. In fact it has been found that the advanced moral thought revolves around rules, rights, and abstract principles.

The ideal for males the ideal of moral reasoning is impersonal justice, in contrast to female ideal of more aﬃliative ways of living. Women’s morality is more contextualized, it is tied to real, ongoing relationships rather than abstract solutions to hypothetical dilemmas. If these things are taken into account maybe females will score diﬀerently on the moral development. This diﬀerence is most
apparent when real life situations are given instead of hypothetical dilemmas. Although the current evidence “indicates that justice and caring are not gender speciﬁc moralities, Gilligan’s work has had the eﬀect of broadening conceptions of the highly moral person.”

Cross-Cultural Diﬀerences

What Kohlberg has essentially done is that he has created a ‘moral yardstick’ with which he intends to measure the morality all the individuals in all cultures. Perhaps it might be the case that the aspects of morality that are rated very highly on Kohlberg’s scale are not considered to be signiﬁcant in some other cultures. And it might be the case that the moral dilemmas presented for evaluation altogether fail to capture the post-conventional morality present in diﬀerent cultures. The Kohlberg’s scale is highly Eurocentric [Western] and might fail to consider the aspects of morality that are alien to the European thought. For studying diﬀerent cultures this ‘moral yardstick’ needs to be ‘re-calibrated’ keeping in mind the particular culture to be studied. Also presenting the same moral dilemma setup in a totally European background might not be a useful idea, the dilemma also needs to be contextualized taking into account the particular culture under study.

Reﬂections

The moral behavior and thinking in a society represent give us an insight into the philosophy and the culture of a society. The major inﬂuences that are responsible for the moral development of the individual according to Kohlberg are the parents, peers, education and the own thought process of the individual. The inﬂuence of religion is not at all considered in the Kohlberg’s developmental theory, whereas religion plays a signiﬁcant role in the development of children at least in the young age. In fact most of the moral judgments that the individuals make are deeply inﬂuenced by the religion they follow. In this regard the position of some religion will be diﬀerent than the other, so a follower of a particular religion will respond to the situation diﬀerently.

Let us take an example of clinical death. If asked with a moral dilemma that involves a person opting for clinical death [hence in a sense committing suicide], the responses that we receive are more likely to vary with respect to the religion of the respondents. Another controversial issue that would raise similar concerns is that of abortion [in a sense considered murder]. Another example on similar lines that could be taken is that of a hunter following a wounded prey, and a response can save or end the prey’s life. The responses in this case will depend on the sort of society the individual has been bought up in [vegetarian vs. meat eating].

The responses that we will get for these real life situations, which also touch upon the religious aspect of the moral judgments will be worth noting. For most of the people religion has the topmost priority in the decisions that are taken in their everyday life. Mostly the religious scriptures and hence religious values guide the moral values and hence moral judgments. A striking example in this regard in the Indian context is that of charity. The religion demands that people do daan [alms], and most people do it not because they feel for the poor, but because the religion demands so. Thus the religious values are conclusive many times in making moral judgments. The religious moral values are passed to the
young children through stories and epics [mostly of Level I Morality according to Kohlberg’s scale ] and also through their social interactions. These interactions form the basis of the moral judgment that a child makes in the future, and removing these inﬂuences can be very hard, as they can be even found in adults. But these age old morality which religion practices might be in many cases totally out of context and in the comtemporary society not of much value. Even then these cannot be overcome even by adults. A very good example of this the ‘moral police’ that are abound in India and elsewhere. ‘What is moral,’ is interpreted from some twisted interpretation of the so called
‘cultural values.’ Most of these ‘moral police’ don’t seem to put any thought of their own to the issues they consider as ‘immoral,’ instead what somebody says is blindly followed without any remorse. On Kohlberg’s scale the so called ‘moral police’ will be at stage 1.

So by asking morally relevant questions that are in direct conﬂicting with one’s outdated religious beliefs can really lead to one’s moral development in this regard.

We cannot really compare the moral values of the contemporary society with that of a society in the past. The rights and the principles that were the ‘guiding lights’ for people in the past might not be even considered in the todays society as relevant. Hence to compare the moral judgments of the people in the past with our own contemporary society does not help. Similarly to compare the moral judgments of two diﬀerent cultures does not provide the index of moral development of a particular culture.

Even in the same culture when the socio-economic diﬀerences are vast the things that are ‘morally right’ for some of the individuals will not be considered as same by everybody. In the Indian context a particular example in this regard can be considered is that of the zamindaari system, the feudal system in India. Whereas the zamindaars considered their ‘moral right’ to own and cultivate large lands, this was not considered as right by the laborers. Or in the larger economic context the ‘moral right’ of the capitalists and the ‘moral right’ of workers do not coincide. In the recent past America’s ‘moral right’ for war was
executed by George Bush to wage a war with Iraq, and ma jority of the American public ‘morally’ supported the war without putting their own thought to it. They would also score for stage 1 in Kohlberg’s stages. So the issues which really matter in one’s perception of the diﬀerent aspect needs to be taken into account when considering the moral stage of the individual. A person in the lower strata of the society might consider stealing from the society as morally justiﬁed [because it is due to society that he poor].

Another aspect that needs to be touched in this regard is that of level 6 of the Kohlberg’s stages of development. The trend that Kolhberg presents for a level 6 behavior is seen in many great spiritual leaders of the past. Infact most of the great leaders did regard their own abstract principles above the
societal laws.

When the world colonization began and the European Empires extended beyond the boundaries of Europe, another example of twisted morality can be seen. Many British authors including Rudyard Kipling regarded the Anglo-Saxon race as a race which was destined to rule, thus ‘morally justifying’ their atrocities against others. Thus it was a ‘moral responsibility’ of the British to rule India. We can hence see that the concept of being ‘morally right’ can be entirely context and time dependent.

The moral dilemmas do come in an individuals life very frequently. According to Kohlberg in the resolution of these dilemmas in the most broader sense result in the moral development in this regard. A very nice example of presenting a moral dilemma and bringing up moral development can be seen in the context of Indian independence. Gandhi’s non-violence principle is an example of moral dilemma that brought about the moral development of an entire Empire. On one hand with the non-violent crowds just marching through the country, the British were not ‘morally justiﬁed’ in attacking them, on the other hand that people can defy their ‘moral right’ to rule was unbearable for them. The British
became so frustrated by this ‘moral dilemma’ that even with all such military might they could not but defeat a non-violent revolt. The resolution of this ‘moral dilemma’ resulted in the ‘moral development’ of the British Empire, which thereafter lost its ‘moral right’ to rule the world.

Summary
As per Kohlberg’s three level, six stage theory, morality changes from concrete towards abstract, principled justiﬁcations for moral choices. Each moral stage en-corporates the previous ones and has certain cognitive prerequisites that are necessary for the development to occur. The moral development does not occur until there is a support present at various levels like family, peers, schooling and society at large. Although justice is given a emphasis more than that of care it does not underestimate the moral maturity of females. As the individuals advance through the stages the moral thinking becomes better related to moral behavior.

The index of moral development that is presented by Kohlberg by presenting the subjects with a moral dilemma needs to be taken with respect to the broader social and cultural context that the particular individual represents so that any bias that is present can be eﬀectively eliminated.

References
[1] Laura Berk: Child Development 3rd Ed. Prentice Hall of India 1999
[2] W. C. Crain: Theories of Development Prentice Hall 1985
[3] Wikipedia

## Monday, April 28, 2008

### What is education?

What do we mean by education?

The word 'education' can be derived from one of two latin words or from both. These words are educere, which means 'to lead out' or 'to train' and educare which means to 'to train' or 'to nourish'. But this etymology does not give us a understanding behind the term itself.
Colloquially it can mean the sort of training that goes in schools, colleges and universities.

We see some meanings by different people who were related to education and philosophy of it.

Mahatma Gandhi

Education is "an all round drawing out of the best in child and man - body, mind, and spirit."

John Dewey

Education is regarded as the development of "all those capacities in the individual, which will enable him to control his environment and fullfill his possibilities."

We see that the term education refers to two things: they point to education as the process of development of the individual form infancy to maturity a lifelong process.

J. S. Mill explains it thus:

"Not only does it include whatever we do for ourselves, and whatever is done for us by others for the express purpose of bringing us somewhat nearer to the perfection of our nature; it does more; in its last connotation it comprehends even the indirect effects of things of which the direct purposes are quite different, by laws, by forms of government, by the industrial arts, by modes of social life; nay, even by physical fact, not dependent on human will, by climate, soil and local position. Whatever helps to shape human being, to make the individual what he is, or hinder him form what he is not... is a part of his education."

This is the wider meaning of the term 'education', for the narrower meaning Mill says

"the culture which each generation purposely gives to those who are to be its successors, in order to qualify them for at least keeping up, and if possible for raising the level of improvement which has been attained."

Now we look at what are the Indian views on education. The Rig Veda [ऋग वेद] regards education as a force which makes the individual self-reliant as well as selfless. The Upanishads [ऊपनिषद] regard the result of education as being more important than its nature, the end-product of education is salvation [निर्वाण].

Panini [पाणिनी] identified as the training one obtains from nature.

Kanada [कानद] considers to be a mean of self-contentment.

Yajanvalaka [याजनवालक] regarded education as a means to the development of character and usefulness in the individual.

While Vivekanand perceived education as the manifestation of divine perfection already existing in man.

"Education should aim at man-making"
By man making it is meant formation of character, increase in power of mind, and expansion of the intellectual capacities.

While Tagore says that education should help the individual child realize in and through education, the essential unit of man and his relationship with the universe - an education for fullness.

The Indian Education Commission of 1966 says:

"Education, according to Indian tradition is not merely a means to earn a living; nor is it only a nursery of thought or a school for citizenship. It is initiation into the life of spirit, a training of human souls in pursuit of truth and practice of virtue. It is a second birth द्वियाम ज्ञानम - education for liberation."
Past this we now have a look at some Western views on the same.

Plato thought that education should enable one to attain the highest good or God, through pursuit of inherent spiritual values of truth, beauty and goodness.

Aristotle held that education exists exclusively to develop man's intellect in a world of reality which men can know and understand.

St. Thomas Aquinas considered education to be process of discerning the truth about things as they really are, and to extend and integrate such truth as it is known.

More recently behaviorists consider education as a process of conditioning, of providing stimuli, repetition, rewards and reinforcements. '

The social scientists define education as the transmission of cultural heritage - which consists of learned behavior, and includes tangible objects such as tools, clothing, etc. as well as intangible objects such as language, beliefs etc.

"Education is the transmission of knowledge, value and skills of a culture."
The meaning of the term 'education' can be summarily expressed as:
• A set of techniques for imparting knowledge, skills and attitudes.
• A set of theories which purport to explain or justify the use of these techniques.
• A set of values or ideals embodied and expressed in the purposes for which knowledge, skills and attitudes are imparted and so directing the amounts and types of training that is given.
The educational system of any society is a more or less elaborate social mechanism designed to bring about in the persons submitted to it certain skills and attitudes that are judged to be useful and desirable in the society. The gist of all the educational system can be reduced in two questions:
1. What is held valuable as an end?
2. What means will effectively realize these ends?
For ordinary day to day working of the society itself makes it necessary for its members to have certain minimum skills and attitudes in common, and imparting these skills is one of the ends of education. This minimum will be different for different societies.

So we see that in the meaning of what education is, is determined by what are the aims of education. Every educational system must have an aim, for having an aim will provide it with a direction, and make the process more meaningful. One of the objectives of education from what we have seen in the definitions above has a connection to the meaning of life, which in turn is connected to philosophy of the person at that time. Thus the aims of education are dependent on the philosophy which is prevalent in society at that time. The aims of any educational system tell us what it is for. The aims determine the entire character of the educational process: curriculum, pedagogy and assessment. Just because the aims are not explicitly stated it does not mean that they are absent. They can be both implicit and explicit, and can be embodied in the everyday practices of teachers and students, as well as in the government documents. The printing of aims of education in a document is neither necessary nor sufficient for education to have aims, since documents can be ignored.

Education can have more than one aim, so long as the aims are not mutually incompatible. It is not possible for example to aim to produce citizens who will obey the state unquestioningly and at the same time produce people who will question any proposal that they encounter. Many aims are broadly compatible but there exists certain tension. Partly, it is because some aims can be fully achieved at the expense of others. A society has to agree on the priority of the aims, which it wants its future citizens to have.

A listing of general educational aims is as follows:

1. To provide people with a minimum of the skills necessary for them [a] to take their place in the society and [b] to seek further knowledge.
2. To provide them with a vocational training that will enable them to be self-supporting.
3. To awaken an interest in and a taste for knowledge.
4. To make them critical.
5. To put them in touch with and train them to appreciate cultural and moral achievements of mankind.
But are these the normative aims of education or the descriptive ones?

Following Peters [Ethics and Education 1966], the differences between education and other human pursuits are given in three different criterion.

1. 'Education' in its fullest sense, has necessary implication that something valuable or worthwhile is going on. Education is not valuable as a means to a valuable end such as a good job, but rather because it involves those being educated being initiated into activities which are worthwhile themselves, that is, are intrinsically valuable. This is contrasted with training, which carries with it the ideas of limited application and an external goal, that is, one is trained for something for some external purpose, with 'education' which implies neither of these things
2. 'Education' involves the acquisition of a body of knowledge and understanding which surpasses mere skill, know-how or the collection of information. Such knowledge and understanding must involve the principles which underlie skills, procedural knowledge and information, and must transform life of the person being educated both in terms of the general outlook and in becoming committed to the standards inherent in the areas of education. To this body of knowledge and understanding must be added 'cognitive perspective' whereby the development of any specialism, for example in science, is seen in the context of the place of this specialism in a coherent life pattern.
3. The process of education must involve at least some understanding of what is being learnt and what is required in learning, so we could not be 'brain washed' or 'conditioned' in to education.
Well this is really an incoherent attempt to list out things that I have read about education? So far all the philosophers that I have read appear to give a normative meaning of education i.e. to say they tell us "What education ought to be..." Thus they give us what according to their philosophical outlook is the 'normal' version of education. But what I am interested in is the descriptive version; "How actually things are..." The more I look and think about the current educational system the more I think it has deviated from the aims of these great thinkers. Thus the descriptive version will tell us how much this deviation is, and also whether it is for good?