HUGO Aldave
Plato's account in Book VII of The Republic (Summary interested): Compare, where Socrates tells Glaucon the state of our nature with the following table represents imaginary ... some men locked in a kind of underground dwelling in a cave ... there since childhood, men are chained by the neck and legs, so that they remain immobile and can only see objects in front of them, because the chains are prevent head again ... In this cave, women, and men who are chained, forced to keep staring at the back, behind it is a fire, and between the fire and the prisoners stands a wall on which to walk some men carrying objects of all kinds. The only thing men are captives are, as the images of these beings and these objects, projected on the back of the cave in the firelight. Do not see things as they are, but see only their appearance or simulation. They see nothing but shadows. But not received as such, because their forced captivity has made them accustomed to consider natural family live in a lie and do not realize, his conviction is involuntary complicity with an error ... What a strange scene describe and says foreign prisoners Socrates Glaucon listening to what counts and Socrates replies are equal to us. It could happen, but in the Platonic account, any of the prisoners were freed of their chains and discovered the deception, that he saw things as they are. Then surely feel blinded by the firelight and perplexed by the discovery, and could occur, moreover, the prisoner come out to the surface and had the opportunity to see things not as shown on the inside of the cave but in light of the sun, and the light of day. Released so full of illusions, knowing the true meaning of things, the prisoner would surely cave to try to persuade his former fellow prisoners to fall into serious account the error in which they live. But most likely it will happen, as happened to Socrates and his fellow accustomed to the simulation, tomasen by crazy, make fun of the , and try to eliminate even [1]
nourished frame in "La Republica", we can easily recognize issues ranging. "The genesis and structure the polis and the soul, the cardinal virtues, the distinction between different ontological levels and their correlation with different types of knowledge, the hypothesis of ideas and good, efficient government forms and souls, criticism of the arts, etc, are clearly subordinate to the issue of justice and injustice and their relationship to happiness and unhappiness. [2]
Without wishing perception of cross-cutting, the generative topics can make detailed studies, nevertheless, I am interested in focusing attention simile of the cave and the underlying mathematical
pinpoints is that men can turn into philosophers and therefore the best guardians of the city must undergo a final test apararte evidence of fatigue, fear and pleasure, the new test would in intellectual gymnastics exercised in many areas and many objects of study.
In this line of thought, Socrates Glaucon calls attention to detail line, geometric size had attracted the attention of Surveyors, the line is shown for the first time the incommensurability, one of the most dramatic, but at the same, most exciting and decisive mathematics old. There is also a line either Socrates Glaucon invited to divide into two unequal segments, ie a larger and a smaller one, each of which is then divided into two segments of unequal length as the same proportion.
The line referred Socrates used to distinguish between different ontological levels and their correlation with different types of knowledge, an issue that I reserve for a future article.
Socrates said that the first fault of mathematical activity is undisputed by the hypothesis, but that assumes as self-evident, that is "based theorems demonstrate propositions assumed to be valid, without providing evidence of validity, likewise be identical the need to use images and models linking the sensitive soul of the mathematical to the sensible world and the use of the senses. [3]
How is it possible that the exercise of mathematics is for the soul weary and training to the same extent that they are gymnastics for the body? Socrates, a recognition of remarkable power, but only to some extent. Mathematics or pursue better able to release the soul from the chains, make the shadows turn to the figures, in the light, ie the sensible and becoming, to ideas, even good, accomplished in a word raise the soul of the cave in the sun. However, at this time a failure occurs: can not we turn to animals, plants, and sunlight. . Again, the gaze rests only on ghosts, or images and shadows.
are hints that the power of mathematics lies because they are divine images and shadows of beings, do not match the shadows of the statues, which are visible in the darkness of the cave. Point is emphasized that despite the limitations of the brightness deal intelligible realities. Socrates comes to speak of the divinity of its object.
In any case, within mathematics, even the night light and even clear images and shadows are realities that belong to the intelligible world, which is the world of being and truth, not the future and of opinion.
This leads to what is commonly and justly is identified as the fundamental reason that, for Plato, mathematics has the power to turn the soul from the future, until it is able being achieved and what the self is more luminous, ie good.
mathematics dealing with theoretical purposes that are not sensitive objects, the arithmetic and logistics, for example, do not deal with the tiny operations practical and concrete, of which served the merchants, traders, and whoever serves the math for most of their business, but does great geometry discourses on reconciling, plot, and practiced together completely in order to knowledge, but even if it is knowledge of what is provided rather than what is generated now, now corrupted, and the same is repeated for about astronomy and music theory.
* Text summary recreated and interestingly, based on the work of Dr. Elizabetta Cattannei, Miguel Giusti, and Raul Gutierrez.
( Complementary texts:
"The Spell of Pythagoras. The Discreet Charm of Geometry: Alonso Takahashi
" The rule of number and the Majesty of Concept: Blog: Rumor Hegelian (Hugo Aldave)
[1] [1] [1 ] Rumor Platonic Miguel Giusti. Presentation of the book THE CAVE by Jose Saramago , University of Lima Multiple Use Zone. Lima 2001
[3] Cattanei Elizabetta Mathematics in the central books of the Republic of Plato in the Similes of the Republic VI-VII Plato PUCP Fondo Editorial 2003.
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