Physical and mathematical sight see the abyss of the Universe
"About what we can not talk, we must be silent!" Wittgenstein says in the Tractatus.
"About what we can not talk, we must be silent!" Wittgenstein says in the Tractatus.
What is inexplicable "shows itself", it can not be "told", it could not be told with the language, it is the mystic.
Even he says the same thing that Parmenides and Einstein said.
He indicates, whit the silence, the abyss between language and the Universe.
Even he says the same thing that Parmenides and Einstein said.
He indicates, whit the silence, the abyss between language and the Universe.
We must be silent on the "what it is", on the Universe like whole.
But we can not shut up and we wondered, first of all, if the Universe is an indistinguishable or if it is made of parts, small as you want, one distinct from the another.
The Universe is continuous or discrete?
To answer, let's start proceeding doing a survey. We investigate the nature of "what it is".
Our physical investigation, our experience, show us Poincaré, leads to the antinomy A = B, B = C, A<C, which is repugnant to our logic, we do not feel just accept that reasoning does not end with A = C.
In fact, if A weighs 10, B weighs 11 and C weighs 12 , and if we have an analysis tool that reads only the differences greater than 1, for our examination A = B and B = C, but A<C, because the difference between A and C is visible, while they are not visible the differences between A and B, or between B and C.
But we can not shut up and we wondered, first of all, if the Universe is an indistinguishable or if it is made of parts, small as you want, one distinct from the another.
The Universe is continuous or discrete?
To answer, let's start proceeding doing a survey. We investigate the nature of "what it is".
Our physical investigation, our experience, show us Poincaré, leads to the antinomy A = B, B = C, A<C, which is repugnant to our logic, we do not feel just accept that reasoning does not end with A = C.
In fact, if A weighs 10, B weighs 11 and C weighs 12 , and if we have an analysis tool that reads only the differences greater than 1, for our examination A = B and B = C, but A<C, because the difference between A and C is visible, while they are not visible the differences between A and B, or between B and C.
This situation is not remedied, because we will always have differences not detectable, however powerful is our tool of observation or measurement.
The concept of physical continuous, Poincaré concludes, is a creation of our intellect, fielded their own to overcome the blatant violation of a elementary logical principle.
And also the continuous mathematical and geometric contain aporias.
It 'just remember that Euclid creates the geometric point as a non-size, to avoid the absurd and establish a system.
Aristotle, in the book on Physics, observes that the continuous can not be composed of indivisible elements, otherwise its nature would be discrete, not continuous. That is, Aristotle tells us that the elements of the continuum are divisible to Infinity.
Zeno docet.
And again here the Socrates of the Theaetetus, where the first elements have only names, not attributes, not even that of being.
The concept of physical continuous, Poincaré concludes, is a creation of our intellect, fielded their own to overcome the blatant violation of a elementary logical principle.
And also the continuous mathematical and geometric contain aporias.
It 'just remember that Euclid creates the geometric point as a non-size, to avoid the absurd and establish a system.
Aristotle, in the book on Physics, observes that the continuous can not be composed of indivisible elements, otherwise its nature would be discrete, not continuous. That is, Aristotle tells us that the elements of the continuum are divisible to Infinity.
Zeno docet.
And again here the Socrates of the Theaetetus, where the first elements have only names, not attributes, not even that of being.
The thesis of Antisthenes, a disciple of Gorgias.
In fact, at this point of the investigation, there are some doubt on the name of "elements" and "components" of the continuum. Hard to imagine how they, as hypothesized existing can be identified. Elude us in a fog evanescent.
In fact, at this point of the investigation, there are some doubt on the name of "elements" and "components" of the continuum. Hard to imagine how they, as hypothesized existing can be identified. Elude us in a fog evanescent.
Perhaps indeed the continuous and the discrete symbolic constructions are in our thoughts, not attributes of the space-time unity.
A different way, groped to unravel the tangle, consists of the infinitesimal calculus.
Perhaps, in the infinite sets, we can untie the knot of the discrete-continuous.
The first step in the infinitesimal calculus does Galileo wrote in his Discourses and Mathematical Demonstrations Relating to Two New Sciences, when he was under house arrest, after recantation.
Galileo compare the ordered series of natural numbers with the ordered series of their respective square and, by relating strictly and exclusively each element of a series with each element of the other, the two-way link, shows that the former are as many as the seconds.
Yes, they are equal in number, but that number is? How big is an Infinite?
Cantor called the cardinality, the measure of an infinite set.
Cantor then exposes his continuum hypothesis around 1878: Every infinite subset of the continuous has the cardinality of the natural or that of the continuum.
There is a further cardinality between that of the real numbers and the set of natural numbers? No, says Cantor.
This conjecture have never found a demonstration (such as the set theory has not found a satisfactory adjustment of the internal consistency), for nearly 140 years until today, even if the most important and logical mathematicians of the world are committed to it, without interruption.
A different way, groped to unravel the tangle, consists of the infinitesimal calculus.
Perhaps, in the infinite sets, we can untie the knot of the discrete-continuous.
The first step in the infinitesimal calculus does Galileo wrote in his Discourses and Mathematical Demonstrations Relating to Two New Sciences, when he was under house arrest, after recantation.
Galileo compare the ordered series of natural numbers with the ordered series of their respective square and, by relating strictly and exclusively each element of a series with each element of the other, the two-way link, shows that the former are as many as the seconds.
Yes, they are equal in number, but that number is? How big is an Infinite?
Cantor called the cardinality, the measure of an infinite set.
Cantor then exposes his continuum hypothesis around 1878: Every infinite subset of the continuous has the cardinality of the natural or that of the continuum.
There is a further cardinality between that of the real numbers and the set of natural numbers? No, says Cantor.
This conjecture have never found a demonstration (such as the set theory has not found a satisfactory adjustment of the internal consistency), for nearly 140 years until today, even if the most important and logical mathematicians of the world are committed to it, without interruption.
Gödel dedicated decades of reflections and some public conferences. Without outcomes by himself deemed conclusive.
How many are the points of a Euclidean line? This is the question that underlies the hypothesis.
To understand this, it happens that on a straight Euclidean line I put the natural numbers, 1, 2, 3, 4, then add the related numbers , -1, -2, -3, -4, then still the rational numbers 1/2, 1/3, 1/4, and so on.
How many are the points of a Euclidean line? This is the question that underlies the hypothesis.
To understand this, it happens that on a straight Euclidean line I put the natural numbers, 1, 2, 3, 4, then add the related numbers , -1, -2, -3, -4, then still the rational numbers 1/2, 1/3, 1/4, and so on.
For each addition the numbers seem more, the set looks more dense.
But, when I add irrational numbers, like pi greek ones, the straight line becomes saturated, it becomes a continuous, the elements disappear and suddenly I find myself with a totality. The elements are not more numerous, they disappear.
This is a different form of the same conjecture. Tertium non datur.
But, when I add irrational numbers, like pi greek ones, the straight line becomes saturated, it becomes a continuous, the elements disappear and suddenly I find myself with a totality. The elements are not more numerous, they disappear.
This is a different form of the same conjecture. Tertium non datur.
Aleph one indicates the cardinality of the continuum.
Aleph zero indicates the size of a discrete set, it is fully within the dialectic of the rational faculty.
Aleph one indicates the size of the continuum, is out of rationality, outside of logos, is attainable only with the intuitive faculty.Logos and Nòos.
And nothing between them.
Perhaps too may the question: "What is the cardinality of the continuum?" And there is a bizarre response: "what it is."
This risky answer also responds to the question of Gödel on the existence of a "maximum" in the collection of increasing cardinality. There would be a maximum, which is also a minimum.
Even in the case of set theory and infinitesimal analysis, we are exercising a point of view, I do not think that we should never think that it is a "objective" look , "certainly fair", that we are giving the "realistic description of the reality "that we have captured the essence ".
The dogma is always lurking, imbues the language, the thought. And it does rot.
The reality of space-time, however, shows no propositions, and even contradictions or paradoxes. The paradoxes and the antinomies are reserved for our languages.
Aleph zero indicates the size of a discrete set, it is fully within the dialectic of the rational faculty.
Aleph one indicates the size of the continuum, is out of rationality, outside of logos, is attainable only with the intuitive faculty.Logos and Nòos.
And nothing between them.
Perhaps too may the question: "What is the cardinality of the continuum?" And there is a bizarre response: "what it is."
This risky answer also responds to the question of Gödel on the existence of a "maximum" in the collection of increasing cardinality. There would be a maximum, which is also a minimum.
Even in the case of set theory and infinitesimal analysis, we are exercising a point of view, I do not think that we should never think that it is a "objective" look , "certainly fair", that we are giving the "realistic description of the reality "that we have captured the essence ".
The dogma is always lurking, imbues the language, the thought. And it does rot.
The reality of space-time, however, shows no propositions, and even contradictions or paradoxes. The paradoxes and the antinomies are reserved for our languages.
