How rationalist ideas based in the mathematical logic affect the life of millions of people, the European crisis

Index

1. Extract
2. Relativity of the economic concepts, a reflection on the mathematical logic applied to the economy
3. Usefulness of the mathematical abstractions, the infinitesimal calculus
4. Conclusions

1.      Extract

The mathematical logic is employed to justify some behaviors in the real life; for example, the mathematical logic is used in economy to demonstrate why it is necessary a balance between income and spending of the states. That mathematical premise is employed currently by the European Central Bank and the International Monetary Fund to maintain its economic policy in Europe.

In the first part of this work it is demonstrated that the mathematical logic is not always the right way. In the second part it is developed a concrete example which prove how the mathematical abstractions sometimes neither can be used effectively in the real world.

2.      Relativity of the economic concepts, a reflection on the mathematical logic applied to the economy

European countries like Spain, Italy, Portugal, Ireland and Greece suffer severe economic restrictions that are affecting the life of millions of people. The cause of those restrictions is the wrong belief that austerity is the right way that the economies must follow. The desideratum of that belief is that balanced budgets are the ideal objective for the construction of healthy economies. But that rational and logic concept is not truth in all the cases. The fiscal and financial deficit is not always something bad. For a people or for a private enterprise the lack of financial resources is a sign of weakness or peril of insolvency but for the governments no. The fiscal and financial deficit of the states reveals that the economy as a whole is growing and therefore the resources are insufficient.  It demonstrate also that the private investment is not enough and that it is necessary the help of the state for assuring the normal economic development of the countries. The states, the governments, moreover, have an advantage that does not have the personas neither the private enterprises: the governments have the sovereign capacity to print money; therefore they can solve their internal financial necessities printing more money. What the governments cannot do is to print the money of other countries, in this case, international means of payment, like the U.S. dollar or the euro. The unique institutions that can issue U.S. dollars and euro are the U.S. government and the European Central Bank, respectively.   All this is a proof of the economic concepts relativity: the scarcity of financial resources is not ever something bad, it depends on who is the actor; if the actor is the public sector the financial deficit is different than if the actor is a person or a private enterprise.

The European economic crisis has its origin in the fact that the states members of the European Union resigned to its sovereign capacity to issue its own national currencies to create a new common currency, the euro. But now they are trapped in the hands of the European Central Bank and the International Monetary Fund, which impose their criteria of austerity. How much time more will resist those countries the impositions?

The problem is that some economists have employed mathematics for intending to give a character of exact science to the economy, but in some cases that pretension of the economists has generated more damages than benefits, like demonstrate the application of rigid and logic mathematical concepts of austerity in Europe.

3.      Usefulness of the mathematical abstractions, the infinitesimal calculus

In this part of the work it is developed a reflection on one of the most important mathematical issues, the infinitesimal calculus. So I want to ratify that the mathematical exactitude not always is exact; it is relative. Therefore, the application of mathematical concepts in the economy is not always a warranty of success.

Begin:

Is it possible the infinite division of the numbers?

Isaac Newton and Gottfried Leibniz taught that it is possible the infinite division of the numbers through the infinitesimal calculus.

But what is the infinitesimal numbers?

The infinitesimal numbers are considered the most reduced amount that the human mind can conceive; it means the numbers nearest to cero. This answer reveals the abstraction of some mathematical concepts.  The infinitesimal numbers should be the most reduced amount that can be measured in the real world and not an abstract conception on the infinite division of the numbers. Numbers are representation of the amounts of matter; numbers do not exist like entities with own life. What exists is the unit. The essence of one thing is different to the essence of other thing and this is the cause of the diversity of things in nature. Therefore the unique number that exists is the number one, which represents the essence and diversity of the things; the other numbers that we know are only additions or fractions of one. For example, two is two times one; nine is nine times one. One half or a quarter is too in essence one unit.

Matter is also one unity. Matter has the same properties of the numbers; this means that matter can be added, subtracted, multiplied and divided. The atomic fission is the proof of this assertion. If numbers are a representation of matter then we can to make the following question:

What is the most reduced amount of matter?

According to the concepts accepted by science molecule is the lesser amount of matter; in turn, molecule is integrated by atoms and these are composed by subatomic particles, neutrons, protons and electrons; each one of them is a different unit.

If this is truth, then the infinite division of matter in the real world has a limit; the limit of the division of matter is the atom and their components; if the former idea is truth then the infinitesimal calculus is an abstraction that can be only partially verified in the reality.

The most reduced infinitesimal particle is always one unit and, on the contrary, the biggest amount of matter is always one unit integrated by an addition of unities. But, in the real world, we arrive ever to a point when we cannot to reduce or to divide more the matter. So far, that point is when we arrive to the molecule, the atom and their components.

Nanotechnology is a new discipline that intends to manipulate the molecular and atomic composition of matter.

Is it possible for nanotechnology to create new unites of measures different to molecule and atoms?

In other words, would be possible to divide more the components of atom?

That is an important question because if new unit of measure different to molecule and atoms are created then the limit of measures of the matter would also change.

The speed of light is the other limited measure that exists in nature hitherto.

Would be possible for science to discover that the speed of light is other and not the measure that has been reveled until now?

If this is so, then a new door toward the infinitude of the numbers division might be opened.

But while the molecule and atom remain like the most reduced amount of matter and the speed of light remain like the maximum speed that man knows, the possibility of infinite division of the numbers will be restricted. Atoms are the limits of the division of matter and the speed of light the limit of the speed in nature; in consequence, that is the lesser amount of matter that exists in the real world and the maximum amount of speed by man known. If this is so, then the philosophic concept of the infinitesimal calculus like infinite division of the numbers would be only one abstraction. The division of the numbers in the real world has a limit and that limit is the lesser amount of matter and the speed of light; in any case that number is one; the lesser amount of matter, the lesser infinitesimal fraction is itself one unit.

The ideas expressed in this epigraph reveals that not always the mathematical abstractions are absolute truths and that, in consequence, not ever may be considered indisputable truths.

The infinite does not end; only God, space and time are infinite and eternal; but the material things always can be measured. The numbers, which are a representation of the material things, also have a limit.

4.      Conclusions

-          The application of rationalist mathematical conceptions has caused a big damage to millions of people in the entire world. In Latin America, during the decade of the ninety years of the 20^th century was applied the same economic program that is being developed now in Europe. The philosophical inspiration of that program is the austerity which main base is the logical assumption of the balance between income and spending. In Latin America the results of that policy was the instauration of leftists and/or nationalists governments in 12 countries, including the big economies like Argentina and Brazil and in nations like Venezuela, Ecuador, Uruguay, Bolivia, Nicaragua, Honduras, El Salvador, Jamaica, Peru and the strengthening of the leftist movement in Mexico. 

-          Mathematics is relative, it is not an exact science; it is a result of the imagination, of the capacity of abstraction of man; therefore in many cases do not have true base in the real world.

-          Mathematics is a hermetic discipline, incomprehensible for the most people. The mathematicians maintain its discipline closed, inaccessible to the majorities. The day that mathematics is simplified and the most people understand their fundaments, that day mathematics will not be more a knowledge exclusive for erudite.

-          The application of the mathematical logic is not a warranty of success in the economic practice.