miércoles, 16 de marzo de 2011

Human egoism and overpopulation, big economics and political problems

“The pride of man makes him love to domineer, and nothing mortifies him so much as to be obliged to condescend to persuade his inferiors. Wherever the law allows it, and the nature of the work can afford it, therefore, he will generally prefer the service of slaves to that of freemen.”
Adam Smith. An Inquiry into the Nature and Causes of the Wealth of Nations (1776), Book III, Chapter II

1. Overview
1.1. The system of private property
1.2 The postulates of the economy are only intellectual exercises
1.3 Base of the political systems
2. Original Accumulation, vision of Adam Smith and Karl Marx
3. Comparison between the two points of views
4. The population growth, appreciation of Adam Smith and Thomas Robert Malthus
5. Unsustainable
6. Conclusions
1. Overview
Why does exists poor’s and rich’s?
Why one’s does governs and others obey?
For understanding the scope and answer those questions, first of all it is necessary consider two essential aspects: a) how was created the first wealth in the world? and, b) how did evolve the societies toward the different forms of government?
In the first stages of the human development, man lived in small groups of peasants and in a communitarian economic system, where shared the means of life with other members of the group; but that Honey Moon did not last too much. The human egoism dominated man hearts and appeared the first signs of struggle for the Earth resources and the dominium of one’s men over other men.
At the beginning of the times, land was communitarian property and nobody had individual rights over her.
1.1. The system of private property
The first big jump toward the new political and economic system of private property was the appropriation (robbery) of land by the strongest and rich men; this led to the establishment of the private property on land. The second step was the accumulation of stock. The first forms of capitalism appeared at the end of feudalism; however, the previous appropriation of land was the first expression of the wealth concentration.
But what did determine that deep change ---robbery of land and private property--- in the social behavior of man?
The answer is: a) the fear and b) the sexual instinct. The fear to the lack or scarcity of material means of life and the uncontrolled desire of sex. But pure love, fraternal love also exists and it is the other big might that inspire human beings life. The fear provokes the wealth accumulation wish because man wants to assure the goods that need. But for obtaining those goods he requires, in turn, to dominate the other people; therefore he searches the politics power.
Man made war to appropriate land and women of the conquered lands. In the Holy Scriptures and in the world history there are numerous examples of this. The fear and the sexual desire ---pleasure--- are the two forces that determine man behavior.
As a consequence of the uncontrolled sexual appetite ---and fertility--- the population grew; the effect of that growth was the multiplication of the social needs. The material means of life began to be scarce and this fact developed the human instincts of survival and the human egoism. Each one began to fight against other for the possession of the limited resources.
Land is the primary resource. And land encompasses the other essential resources. Land is wealth, the true wealth. Therefore, the first action of man was to appropriate land. But land and their physical expressions ---in material goods--- was not enough. Hence man created other symbol of wealth: the money.
Everyday the population grew more and more. But the resources do not augmented in balanced proportion and, moreover, they were not distributed fairly. This has been the essential cause of poverty and richness of one’s and others. The rich and strongest men ---since the physical and intellectual point of view--- have taken the best part of the earth resources and the capital factor; the poor’s and weak has received nothing.
In its first stage, the process of expropriation of the weak peasants was made through blood and fire. In parallel to the robbery of land to the peasants and the accumulation of stock, the rich and strongest men developed the political institutions ---states, governments, laws--- to guarantee their property and privileges and the dominium of the poor’s and weak . The maintenance of that process along the centuries has been based in the same principle: the violence. But ---in the modern times--- employing a romantic and false justification: the prevalence of law. The juridical system of the countries is the base where is supported the privileges of the owners of the power and wealth. It is too its moral justification. You must obey the law. It does not matter if the law is fair or unfair, moral or immoral. If you do not obey, the system has the legal force to punish you. The financial crisis of the year 2008 in the United States and other Industrial countries is an excellent example of the unfair laws. The bankers ruined their banks --- but kept their personal fortunes--- and the governments had to give them millions of money in bailout. That is the law.
1.2 The postulates of the economy are only intellectual exercises
In all the political and economical systems, the politics and the private economy advance together. The private economy cannot work without the institutional political support. The private economy is not independent and do not dominate the market. The private economy depends of the politics because the most important economics decisions ---the economic policies--- are taken by the politicians and the governments and not by the economists neither the entrepreneurs. For the mentioned reason, the postulates of the economic theory, the laws and the mathematical base of the economy ---like science--- are only intellectual exercises over situations that can occur or not in the true reality. In all the political and economical regimes are the governments ---through their policies--- who determine in last instance the conduct of the market. However, it is necessary underline that the politics and the politicians need the cooperation of the business and the entrepreneurs to reach the goals of the economic and social development. The public economy and the private economy, though have different objectives, need achieve basic agreements to benefit the society.
1.3 Base of the political systems
Since their creation, the political systems were established over a basic principle: the use of force or the threat of use of force. All the political systems are sustained in that principle. Man obey only for fear or own interest. The rulers and the rich know it perfectly. They employ both.
But man searches power and wealth for a basic reason: to satisfy his sexual desire. That is the true truth but nobody is able of to recognize it openly. The society has two faces: a) the apparent, institutional, legal and moral and b) the real, the true and not recognized. The Adam Smith’s concept that heads this work is a good example of the true human beings feelings. Fear, hedonism and egoism govern its life.
The world problems have two kinds of causes: a) intangibles and b) the materials.
The human egoism ---that is equivalent to the uncontrolled desire of pleasure--- is the foremost intangible cause of the big problems of the world. That uncontrolled wish of pleasure provokes the uncontrolled desire of sex, of wealth and politics power possession.
But the big desire of sex is, in turn, the cause of the overpopulation and this, the source of the big material problems of humanity: a) the overexploitation of the natural resources, b) the damage to nature and environment, c) unemployment, d) poverty and e) illnesses. In the table may be appreciated the hierarchy of the diverse situations.

2. Original Accumulation, vision of Adam Smith and Karl Marx
The study of the Original Accumulation is essential for the comprehension of the evolution of wealth along history.
Adam Smith employed the term “Previous Accumulation”, Karl Marx used the words “Primitive Accumulation” but I prefer “Original Accumulation.”
Adam Smith (1753-1790) is the father of the Economic Liberalism. His vision regarding the Original Accumulation is a concept that cannot be ignored in the study of richness. The opposite thesis of the Economic Liberalism is the Scientific Socialism. Karl Marx (1818-1883) is considered the father of this conception and for that reason his opinion about the Original Accumulation must be taken in account.
In the book An Inquiry into the Nature and Causes of the Wealth of Nations (1776), Book I, Chapter VIII, Adam Smith wrote:
“Of the Wages of Labour
The produce of labour constitutes the natural recompense or wages of labour.
In that original state of things, which precedes both the appropriation of land and the accumulation of stock, the whole produce of labour belongs to the labourer. He has neither landlord nor master to share with him. But this original state of things, in which the labourer enjoyed the whole produce of his own labour, could not last beyond the first introduction of the appropriation of land and the accumulation of stock. It was at an end, therefore, long before the most considerable improvements were made in the productive powers of labour, and it would be to no purpose to trace farther what might have been its effects upon the recompence or wages of labour.
As soon as land becomes private property, the landlord demands a share of almost all the produce which the labourer can either raise, or collect from it. His rent makes the first deduction from the produce of the labour which is employed upon land.”
And in the Introduction of the Book II about Of the Nature, Accumulation, and Employment of Stock, Smith wrote:
“In that rude state of society in which there is no division of labour, in which exchanges are seldom made, and in which every man provides everything for himself, it is not necessary that any stock should be accumulated or stored up beforehand in order to carry on the business of the society. Every man endeavours to supply by his own industry his own occasional wants as they occur. When he is hungry, he goes to the forest to hunt; when his coat is worn out, he clothes himself with the skin of the first large animal he kills: and when his hut begins to go to ruin, he repairs it, as well as he can, with the trees and the turf that are nearest it.
But when the division of labour has once been thoroughly introduced, the produce of a man's own labour can supply but a very small part of his occasional wants. The far greater part of them are supplied by the produce of other men's labour, which he purchases with the produce, or, what is the same thing, with the price of the produce of his own. But this purchase cannot be made till such time as the produce of his own labour has not only been completed, but sold. A stock of goods of different kinds, therefore, must be stored up somewhere sufficient to maintain him, and to supply him with the materials and tools of his work till such time, at least, as both these events can be brought about. A weaver cannot apply himself entirely to his peculiar business, unless there is beforehand stored up somewhere, either in his own possession or in that of some other person, a stock sufficient to maintain him, and to supply him with the materials and tools of his work, till he has not only completed, but sold his web. This accumulation must, evidently, be previous to his applying his industry for so long a time to such a peculiar business.
As the accumulation of stock must, in the nature of things, be previous to the division of labour, so labour can be more and more subdivided.” End of the quotes.
In his book, Capital, A Critique of Political Economy, 1867, Part VIII, Primitive Accumulation, Karl Marx wrote:
“We have seen how money is changed into capital; how through capital surplus-value is made, and from surplus-value more capital. But the accumulation of capital presupposes surplus-value; surplus-value presupposes capitalistic production; capitalistic production presupposes the pre-existence of considerable masses of capital and of labour power in the hands of producers of commodities. The whole movement, therefore, seems to turn in a vicious circle, out of which we can only get by supposing a primitive accumulation (previous accumulation of Adam Smith) preceding capitalistic accumulation; an accumulation not the result of the capitalistic mode of production, but its starting point.
This primitive accumulation plays in Political Economy about the same part as original sin in theology. Adam bit the apple, and thereupon sin fell on the human race. Its origin is supposed to be explained when it is told as an anecdote of the past. In times long gone by there were two sorts of people; one, the diligent, intelligent, and, above all, frugal elite; the other, lazy rascals, spending their substance, and more, in riotous living. The legend of theological original sin tells us certainly how man came to be condemned to eat his bread in the sweat of his brow; but the history of economic original sin reveals to us that there are people to whom this is by no means essential. Never mind! Thus it came to pass that the former sort accumulated wealth, and the latter sort had at last nothing to sell except their own skins. And from this original sin dates the poverty of the great majority that, despite all its labour, has up to now nothing to sell but itself, and the wealth of the few that increases constantly although they have long ceased to work. In actual history it is notorious that conquest, enslavement, robbery, murder, briefly force, plays the great part. In the tender annals of Political Economy, the idyllic reigns from time immemorial. Right and “labour” were from all time the sole means of enrichment, the present year of course always excepted. As a matter of fact, the methods of primitive accumulation are anything but idyllic.
In themselves money and commodities are no more capital than are the means of production and of subsistence. They want transforming into capital.
The capitalist system presupposes the complete separation of the labourers from all property in the means by which they can realize their labour. As soon as capitalist production is once on its own legs, it not only maintains this separation, but reproduces it on a continually extending scale. The process, therefore, that clears the way for the capitalist system, can be none other than the process which takes away from the labourer the possession of his means of production; a process that transforms, on the one hand, the social means of subsistence and of production into capital, on the other, the immediate producers into wage labourers. The so-called primitive accumulation, therefore, is nothing else than the historical process of divorcing the producer from the means of production. It appears as primitive, because it forms the prehistoric stage of capital and of the mode of production corresponding with it.
The economic structure of capitalist society has grown out of the economic structure of feudal society. The dissolution of the latter set free the elements of the former.
In the history of primitive accumulation, all revolutions are epoch-making that act as levers for the capital class in course of formation; but, above all, those moments when great masses of men are suddenly and forcibly torn from their means of subsistence, and hurled as free and “unattached” proletarians on the labour-market. The expropriation of the agricultural producer, of the peasant, from the soil, is the basis of the whole process. The history of this expropriation, in different countries, assumes different aspects, and runs through its various phases in different orders of succession, and at different periods. In England alone, which we take as our example, has it the classic form.” End of the quotes.
3. Comparison between the two points of view
Adam Smith presents an ascetic or perhaps an eclectic appreciation of the Original Accumulation. He does not explain openly how the violence, the murder and the robbery of land to the first commoners, the first peasants, was the base of the process. Smith recognizes the landlord’s rights to explode the peasants and receiving rent.
On the contrary, Karl Marx highlights how the violence was the method employed by the first rich to accumulate its primary wealth before the apparition of the first forms of capitalism.
This appreciation on the origin of wealth would determine the position of each one of them regarding the paper of capitalism in the society.
If you consider that something is right and moral you accept it, but, on the contrary, if you think that something has been not acquired by right and moral methods, perhaps you will reject it. Adam Smith considered the capitalists methods like something right. Karl Marx taught the contrary.
Along the centuries the workers had been simple slaves.
The philosophical position of Marx contributed ---years later--- to change the social and economic situation of the workers, because it opened the door to new reformists movements, like the syndicates, and new political parties, that fought by their social rights. For example, an Italian friend, remembers me that at the beginning of the 20th century, in Italy, cradle of western culture, the peasants were formally freemen but, in the social and economic reality, they were true slaves. He told me: “it was Benito Mussolini who made the first social reforms to improve the quality of life of the Italian peasants. At the beginning of his politics career, Mussolini was socialist. Mussolini, for first time, gave to the Italians peasants a participation in the benefits of production. In an official decision, he imposed that 55 per cent of the benefits of production had to be given to the peasants; the other 45 per cent was for the capitalists owners of land”, assured my friend.
The Marxist communism was a result of the unfair economical and social conditions that existed in Russia, the Eastern Europe and China. But the Marxist Communism did not change those unfair conditions. On the contrary, the communism created new dictatorships that devastated those countries during the past 20th century.
The nations that had reached the most standards of economic and social progress are those countries that had adopted an intermediate model between capitalism and socialism, like the Nordic countries. For example, I read recently, that Norway is the country with the major level of happiness.
4. The population growth, appreciation of Adam Smith and Thomas Malthus
The high rate of population growth is the principal cause of the economic and social problems of the world. In the last two hundred years, the world population grew as never before.
But the most paradoxical is that the maximum growth has been registered in the poorest and underdeveloped countries.
So far, the world, as a whole, has not focused its attention in this problem. Only the principal countries directly affected by the phenomenon, like China, have taken in account the issue.
If there is not a global consensus on the need of demographic control, the situation will be every day worse and in too few years will be unbearable. To ascertain this, it is enough to see how the poverty augments in sustained form in the underdeveloped nations. The poverty has many causes but one of the first is the overpopulation. It is not the same a family with two children than a family with six or eight children.
In the time of Adam Smith, 18th century, the situation was different. As a matter of fact he assured that:
“The most decisive mark of the prosperity of any country is the increase of the number of its inhabitants”. End of the quote. An Inquiry into the Nature and Causes of the Wealth of Nations (1776), Book One, Chapter 8, Of the Wages of Labour.
But Thomas Robert Malthus (1766-1834) thought something different; in his book An Essay on the Principle of Populations, Book One, Chapter One, Malthus assured that:
“It may safely be pronounced, therefore, that population, when unchecked, goes on doubling itself every twenty-five years, or increases in a geometrical ratio.
The rate according to which the productions of the earth may be supposed to increase, it will not be so easy to determine. Of this, however, we may be perfectly certain, that the ratio of their increase in a limited territory must be of a totally different nature from the ratio of the increase of population. A thousand millions are just as easily doubled every twenty-five years by the power of population as a thousand. But the food to support the increase from the greater number will by no means be obtained with the same facility. Man is necessarily confined in room. When acre has been added to acre till all the fertile land is occupied, the yearly increase of food must depend upon the melioration of the land already in possession. This is a fund; which, from the nature of all soils, instead of increasing, must be gradually diminishing. But population, could it be supplied with food, would go on with unexhausted vigour; and the increase of one period would furnish the power of a greater increase the next, and this without any limit.” End of the quotes.
5. Unsustainable
Nevertheless all the advances achieved by science and technology and the development of the democratic institutions, hundreds of millions of people suffer hunger. Already it is not only a problem of distribution but a problem of production. Man has devastated the environment and the natural resources. The scarcity of water is every day something real in too many places of the world. The deforestation and pollution of seas, rivers and lakes is the other evident reality.
“Until recently economic theory has not seriously considered that a global shortage of natural resources could occur, and even less a global shortage of water and petroleum.” Pablo Rafael Gonzalez, A Statistical Yearbook 2008. Running Out How Global Shortages Change the Economic Paradigm, page 11, Algora Publishing, New York. 2008.
But the global shortages of natural resources have begun and are visible in countries and regions where there was abundance in the past recent. The stress or scarcity of water exists already in several regions of the United States and Mexico, in the Caribbean and in South America in unthinkable countries like Brazil and in other countries as Bolivia, Peru and Chile. The same happen in some countries of Europe, like Spain and Italy, in the Middle East, Africa and Asia.
The stress or scarcity of water is and will be the gravest problem that humanity will face at mid term; their consequences will be disastrous for the wellbeing of the world population.
The global scarcity of natural resources is, and will be, a consequence of two phenomenons: a) the overpopulation and b) the overexploitation of the resources.
6. Conclusions
- For the comprehension of the current economic and social disparities it is necessary to know the evolution of wealth since the first times.
- The Original Accumulation is the previous period to the Capitalist Accumulation.
- The Original Accumulation of wealth was a consequence of two facts: a) the robbery of land by the strongest and rich men and b) the violence and crime against the first peasants.
- In its first stage, capitalism used analogue methods but substituted crime by the overexploitation of the workers, especially women and children.
-The economy depends of the politics, because in all the countries, the most important economic decisions are taken by the politicians and the governments and not by the economists neither the entrepreneurs.
- The human egoism is the foremost intangible cause of the world problems and the overpopulation the first material cause.
- If there is not a global consensus on the need of demographic control, the situation will be every day worse and in too few years will be unbearable.
- So far, the world society has not given the due importance to the problem of stress or scarcity of water that is the most important challenge for the population survival.
- The overpopulation and the overexploitation of the resources are destroying the planet and, if that trend continues, in too few years the Earth might be inhabitable.
- It is something essential, vital for mankind, to detain the destruction of the forests and to begin a global campaign of reforestation. This might be a way to combat the poverty, create millions of ecological employments and preserve the water and the environment.

martes, 15 de marzo de 2011

Relativity of the mathematical exactitude, philosophy of science

“The geometric analysis of the ancients and the algebra of the moderns, besides that they embrace only matters highly abstract, and, to appearance, of no use, the former is so exclusively restricted to the consideration of figures, that it can exercise the understanding only on condition of greatly fatiguing the imagination; and, in the latter, there is so complete a subjection to certain rules and formulas, that there results an art full of confusion and obscurity calculated to embarrass, instead of a science fitted to cultivate the mind. By these considerations I was induced to seek some other method which would comprise the advantages of the three and be exempt from their defects.”
Rene Descartes. Discourse on the Method of Rightly Conducting the Reason and Seeking Truth in the Science, 1637, Chapter 2
1. Scope of the thesis
2. Essence of the thesis
3. Importance of Rene Descartes
4. Opening new doors
5. Conclusions
1. Scope of the thesis
The objective of the thesis is to demonstrate that mathematics is relative and not an exact science. This fact opens the door to new point of views, new approaches in the philosophy of science. If mathematics is not an exact science, but relative, their results and the results of the other sciences based in the mathematics must be also relatives.
2. Essence of the thesis
What things are the numbers?
Do they exist in absolute and tangible form?
What things are the geometric figures?
Do they exist?
If they exist, then how, where, why and when can be appreciated by our senses?
A number is an abstract entity, a geometric figure too; they are creations of our minds that do not exist in material form.
The exactitude of mathematics is relative.
A number is a mental representation of one unit. Starting from that representation of the unit has been created all the numbers, which are additional mental representations of one.
One is the unique and primary amount. God is one; the point from which begins all the things that exists in the universe. One represents the same in mathematics. One is the point from where begin all the other measures.
All the numbers that you know come from one. 2, 3, 4, 5, 6, 7, 8, 9, are simple derivations, additions, to one. They do not have own entity. This idea denies the infinitude of the natural numbers. The unique real unit of measure is one. One adopts all the forms that exist in the objective world, as the water takes the form of the container that keeps her. Cero, alone, is nothing. Cero is the contrary expression of one, which is all. 1,000 is one one thousands times. Cero, when is associated to a number, is only a mental representation of the number of times that one has been repeated in that amount.
The primary amount is one; the other amounts are only the result of the increase of that primary amount. Observe that I have employed only the word increase. You can sum, rest, multiply or divide an amount but the result, ever, will be an amount that represents one. All the numbers are simple derivations of one, because of a rational, logic and simple reason: all the mathematical expressions are units, this mean one. The fractions are, per se, units. If you cut a bread by its middle, ½, this new middle is a new unit, a new one itself. ½ is regarding the original bread that already does not exist when you cut the bread; then, ½ is relative; what exist are two new unities integrated by two half, and each one of them is one unity, this mean one. This reveals that the numbers different to one are only names, appearance. One electron is one unit that integrates a major unit, the atom, but the electron, per se, is an independent unit, since the mathematical point of view. The electron is one itself.
One represents the force of God, the primary creation. In that primary creation are the germs of life, the essential elements of all the existent things. One is the atom, which contains the primary source, the primary energy of the universe. The atom encompasses one force ---not two, three, four, etc--- that, when is associated to other one, can develop millions of new ones; that is the principle of the chain reaction. I think that Galileo Galilei understood in a broad sense all this issues and for that reason he said that mathematics is the language of the universe.
The Holy Scriptures says that God created man ---one man--- and from that man God created later woman. From this first one was created a new life. That is the first mathematical expression of the numbers. It means that from one was created other one and was formed the number two that is the sum of one plus one. Man is, therefore, one at the image and similarity of God. Man was one; woman was two, the addition of one to the first one.
The geometric figures are also derivations of one. A triangle is one three times in a mental creation in the space. A circle is the prolongation of one since one point and its return to the same point. A straight line is one mental creation of one dimension between to extremes. Triangles, circle, straight line are simple names that our mind associate to determined figures created also by our own minds. But none of those figures exists per se, with own corporeity, in the objective world. The reason is able of create logic explanations. The problem is that sometimes the logic explanations are not true.
I remember the concept of my first professor of philosophy regarding mathematics. He taught: mathematics is the study of the exact dimensions in the time and the space: in the time is the arithmetic and in the space is the geometry. Some time later of studding that concept I asked myself: exact dimensions regarding what?
There are matters about which the people do not give its opinion because consider that they are truths that can not be set in doubt. And, on the contrary, there are subjects about which the people express their opinions because are not proven truths, or not enough proven truth.
The people consider that mathematics is an exact science; this concept is not enough discussed or not discussed. The exactitude of mathematics is an axiom. The people say yes, mathematics is an exact science and you commit a sin if you express any doubt about it.
But mathematics cannot be an exact science because of a simple reason: mathematics is a creation of man mind and, in consequence, it does not exist in the material reality per se, with own life. You cannot touch, smell, taste or see a number or a geometric figure but like representations of the real objects that exist in the reality.
The numbers and the geometric figures are only mental representations of the things that exist in the objective world.
Mathematics is a set of conventions built by the human being mind. For example, two centuries ago, man established that one meter was a portion of the meridiem that crossed Paris; currently, in the 21st century, man changed that concept and now he says that one meter is a fraction of the speed of light. This new concept was approved recently by the International Agency that controls the measures in the world. This simple example confirms that the exactitude of mathematics is relative. Man changes the concepts and the mathematical measures at his convenience; this demonstrates that mathematics is not an exact science.
When I was a child, a small friend told me: Pablito, (little Pablo), broke the toy to see what does has it inside; I remember that I said to my small friend: I want to play with the toy and to know how it work but I do not desire to destroy it. Now, I would like to know some things but without destroying them.
There is much kind of minds; ones accept the things like they are in appearance while others ask why.
I follow my own way, the dictates of my conscience, hence I write my opinions, it does not matter if they coincide or not with the generalized opinion of the people. There is not a unique truth. I think that the exact sciences are the sciences of nature that can be proven in the reality by mean of the senses. However, there is a hide reality that we cannot perceive with our own senses. We cannot see the atoms but we can experiment their consequences through the experience of their victims (Hiroshima and most recently Chernobyl) for example. One of the objectives of science must be to discover the hide reality of the things, the not apparent.
It is the sensible experience ---direct and indirect--- the main source of the knowledge. The direct experience is our own experience and the indirect the acquired by mean of the experience of other people.
The reason is the other source of knowledge. Our mind has the capacity to create and discover new things. But the creations and discoveries of the mind must be proven in the practice, in the reality of the life. Mathematics is a creation of our mind developed to make the real world more accessible. The mathematics is a form of expression, a language, in the same sense that is the oral and written language. But, while the oral and written language employ words, the mathematics use numbers and geometric figures.
The words, the same as the numbers and geometric figures, are abstract creations of our mind to name the things of the reality.
3. Importance of Rene Descartes
We must mention the work of Rene Descartes (1596-1650), because he is considered the father of the modern Rationalism, philosophical conception that assigns to the intellect the cause of the knowledge. The opposed thesis to the Rationalism, is the Empiricism, which principal exponent was the British philosopher Francis Bacon (1561-1626), creator of the scientific method of research.
Mathematics is a result of the reason; it is, then, a rationalist discipline, different to the empiricist sciences; they are the sciences which results can be proven in a tangible and practice form, following the scientific method of research. You can prove the existence of a tree in any place, but you cannot prove the absolute or corporeal existence of a number or a geometric figure. They belong to the intangible world, to the world of the ideas. The ideas can be transformed in real things or they can represent real things, but the ideas, itself, in its essence, do not have corporeal existence. So that mathematics is an abstraction that does not have corporeal, real existence.
Numbers and figures do not exist; what exist are the material things of the world; we only give name and measures to the things that exist in the objective reality. Man has conceived the figure of a triangle, but the triangles exist only in his imagination. The forms built by our minds sometimes coincide with the objects of the reality and, therefore, the human beings have developed theories and practice about the numbers and figures.
Rene Descartes is one of the most influential figures of knowledge; moreover of philosopher of clear expression, was a relevant mathematician and is considerer the father of the analytic geometry. But the clear thought of Descartes led him to see the knowledge and the science from an objective perspective. For example, in the second chapter of the Discourse on the Method of Rightly Conducting the Reason and Seeking Truth in the Science, 1637, he wrote the following:
“The geometric analysis of the ancients and the algebra of the moderns, besides that they embrace only matters highly abstract, and, to appearance, of no use, the former is so exclusively restricted to the consideration of figures, that it can exercise the understanding only on condition of greatly fatiguing the imagination; and, in the latter, there is so complete a subjection to certain rules and formulas, that there results an art full of confusion and obscurity calculated to embarrass, instead of a science fitted to cultivate the mind. By these considerations I was induced to seek some other method which would comprise the advantages of the three and be exempt from their defects.” End of the quote.
The logic question that arises after reading those ideas is: how the father of the analytic geometry could express those opinions about the geometry and the algebra?
The words of Descartes do not require more explanations. Obviously, he had a deep rejection for the algebra and for the forms employed by the ancient geometers; however, he worked in the geometry and developed his own system, named after his death the Cartesian coordinate system.
In his Discourse on the Method, Descartes left for the posterity his four rules to get the truth in the science; the first rule, and most important, is the methodical doubt.
Descartes wrote:
The first rule was never to accept anything for true which I did not clearly know to be such; that is to say, carefully to avoid precipitancy and prejudice, and to comprise nothing more in my judgement than what was presented to my mind so clearly and distinctly as to exclude all ground of doubt.
The second, to divide each of the difficulties under examination into as many parts as possible, and as might be necessary for its adequate solution.
The third, to conduct my thoughts in such order that, by commencing with objects the simplest and easiest to know, I might ascend by little and little, and, as it were, step by step, to the knowledge of the more complex; assigning in thought a certain order even to those objects which in their own nature do not stand in a relation of antecedence and sequence.
And the last, in every case to make enumerations so complete, and reviews so general, that I might be assured that nothing was omitted.
The long chains of simple and easy reasonings by means of which geometers are accustomed to reach the conclusions of their most difficult demonstrations, had led me to imagine that all things, to the knowledge of which man is competent, are mutually connected in the same way, and that there is nothing so far removed from us as to be beyond our reach, or so hidden that we cannot discover it, provided only we abstain from accepting the false for the true, and always preserve in our thoughts the order necessary for the deduction of one truth from another.” End of the quotes.
4. Opening new doors
The acceptance of the first Descartes’ rule opens innumerable questions in many fields of the science. He warned that it not must be accepted like truth something that has not been proven without any doubt. I do not want make explicit mention of doubts, but only remember that the intellectual formulations and speculations are not enough. Something that has not been proven in the practice, in the reality, do not deserve to be considered like a scientific truth, an irrefutable truth; some mathematical assumptions cannot be an exception.
Mathematics is the system of measures employed by the sciences and, in consequence, if some mathematical conceptions can be in doubt, it means that the results in other sciences might be also put in doubt.
There are logic and rational questions linked to the mathematical exactitude, like how, with which level of certainty have been measured the speed of light, the motion of the heavenly bodies, the distance between them? How can be confirmed that those appreciations are right? What is right? What is true? How can be proven that the Einstein’s paradox of the twins is true? How can be assured that some of his appreciations ---that represented a deep change for the sciences of the 20th century--- were not relatives?
5. Conclusions
- Mathematics must be taught with a practice and useful sense and not like a sacred science that do not admit any kind of doubts about their postulates.
- Mathematics should be reduced to the simplest formulas for the general comprehension of everybody.
- The complexity of mathematics comes from the complex minds of men that do not have the clarity to expose their thoughts with clarity; therefore, its ideas ---theorems, formulas, calculus and others--- are incomprehensible.
- Many of those complex mathematical assumptions are good for nothing, like Rene Descartes described the work of the ancient geometers and the algebra.
- An important intellectual task of the sciences must be to review the thesis that has been built in base of mathematical assumptions and, in consequence, ideas not enough proven in the objective reality, but based only in the imagination and the reason. This would be a way to conciliate the two extremes between Rationalism and Empiricism.