engineer says to the Humanists
In the early seventies, as a young engineer, I enrolled in the course of Applied Mathematics, organized by the Institute of Mathematics Sciences. Not satisfied me enough working knowledge of the car manufacturer. Was preparing a subconscious to another profession, who is now doing, for the past 30 years.
lecturers were eminent mathematicians from all over Polish Polish. Numerical methods taught young then (now retired), Dr. Janina Jankowska University Warsaw. Her husband, Michael, was, in turn, a little later, my professor for doctoral study. Their books of numerical methods are still classics. Andrew studied Computer Science and Christopher Targowski Rey. Functional analysis, in turn, taught Wroclaw Professor Stanislaw Hartman.
We were normal exams, I was in college. I wish I had kept the index from the signature of Professor Hartman, a student and collaborator of legendary, world-renowned professor at the University of Lviv Hugo Steinhaus. I got five. And even if a professor gave her a little "for the good intentions" (For us "volunteers" were very mild), nevertheless, happy. His book "Introduction to functional analysis" included with the motto "The Shoemakers'. Once, in some of his, sadly fragmentary publication of engineering, I used the same motto.
now learned to bestow great awe books starting with "Introduction to ...". You could quickly lose the thread, because it usually has already been allowed to ... the end. I understood then that the venerable professor, looks similar the handsomest of the brothers Marx was not joking when we cordially advised buying the book.
These additional classes highly expanded my horizons. Functional analysis gave me a new intuition of space. I saw that if there are other "worlds", the other as to the nature, but capable of being derived from the world, which is obvious, because I exist in it from birth-world three-dimensional space.
But the ordinary world began to be perceived differently. I look at it from a distance, as a special case of "worlds" invented by Banach and Steinhaus in Lviv and the Scottish Coffee wyrysowanych kopiowym pencil on marble countertop table, napkins and a thick notebook as a gift from Mrs. Banachowej. strange characters, incomprehensible to Mr JOHNNY whether Tońcia, a favorite "Mr. Elder," the two friends, donoszącego coffee and cognac.
I was fascinated. Each new section of the manual analysis of the functional (but not starting with the word 'Introduction ... ") Includes a description of a new kind of space, the new land on the other side of the mirror.
Some I liked the less others more.
Banach space was like for a very Polish, homely, almost trivial. I remember I was a little disappointed that such a "poor" space is called Polish name, while the Hilbert space, another math genius, but the Anglo-Saxon, it was more predestynujące properties for comparison with the land of Carroll, moreover, also a mathematician.
English Queen was very surprised when after reading "Alice in Wonderland" and demanded all the works of this promising fabulist, and brought her some "introductions to ..."
I started on my own to study different issues in math and "read and understand the book of American mathematicians Nagel and Newman, Kurt Gödel's theorem of . Austrian mathematician at the age of 25 years (!) Eagerly also benefited from the achievements of two Polish friends, and was the greatest mathematician of the twentieth century, and ... Platonist.
Its main achieve as soon as we get, but I want to finish this Platonic topic.
Well, Gödel believed in the spirit of Platonic realism, that "mathematical entities" exist and are not by mathematicians - invented or constructed, but discovered, in the sense
in which Columbus discovered America. That was already too much for me, I felt dizzy and long antagonized the philosophy. Today is that I was not shocked.
But Gödel's theorem has had an electrifying impression on me, especially that with talent pisarskiemu American authors probably all understand.
In short, it comes in it is that the system of axioms and inference rules formulated for natural numbers we are dealing with the "devil's alternative: either we get a contradiction or incompleteness of the system.
So either we have a "complete" system of axioms, and then we can prove all the allegations, including two mutually contradictory, or incomplete, we have a system, although consistent, but it is true there are claims that this system can not be proved.
You have to go outside the system and then such a claim impossible to prove as true.
new head spin!
Then Gödel and successors discovered how gradually extend the system so that it progressively more complicated and still have control over the problem of completeness and consistency.
deductive systems can build a much more complicated than the arithmetic of natural numbers.
In a sense, nothing it does not make. Once and for all hope is buried on the final formalization of systems, based on a set of axioms.
You could say that Gödel's theorem leans behind us and the good Lord lets us face: And I bratku you, you want me to formalize? It's on!
A computer today is the very mundane problem. Nothing is certain! Programs work or not. Mostly not. Hence, the most popular word in IT to upgrade:)
What conclusions?
In short, there are two:
1) A person who wants everything to take "the logic", recalls a boy who one day told his mother that he decided to add to infinity.
2) Even a simple logical reasoning is not fun for schoolchildren and requires care, competence and continuous use of the verification results - another method.
Kurt Gödel felt in this problem, like a fish in water. He could.
known is the story of when as a candidate for a U.S. citizen, he seemed to test the knowledge of the Constitution of the judge. Despite the friend's advice proved to him that the land can immediately build an authoritarian regime like a fascist. Only by a great sense of Judge of humor and the fact that he waited in the corridor that adept friend, the great Albert Einstein, which greatly impressed the judge, the greatest mathematician of the twentieth century passed this exam.
And the sky on systems more complex than the system of natural numbers, on the grounds that his memorable Godel formulated such an allegation is really fun when it will be anti-boggling.
For instance, in theology. After all, we have a number of additional problems, which are a source of new errors. For example, the problems of conceptual meaning. Then the ratio of the implication or apparent contradiction may be not because of the assumptions and rules of inference, but a normal fault within the meaning of the word.
But I do not want to enter into a foreign territory for me. I hope that the REAL philosophers and theologians know it.
I'm not sure if some "humanist logicians" who, after his discovery that the "slant lift it, announce it as revealed truth, they realize the muddy ground like tread.
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