Re: Sensible and NonsenSQL Aspects of the NoSQL Hoopla

On Thursday, September 26, 2013 3:35:24 AM UTC+2, James K. Lowden wrote:
> On Wed, 25 Sep 2013 15:05:06 -0700 (PDT)
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> Because of your fondness for Frege, and not knowing much about the
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> subject,

I am focused on the work of a scientist rather than some idealized picture about the scientist. I think that work of G. Frege belongs to the group of the most significant results in mathematics. However I also consider important works of others great mathematicians, such as Godel, Tarski, Hibert, Cantor etc. In fact, we do not know these scientists, as people, we don't know them by their personalities, ethic values, human values etc. Therefore I just write about their scientific works.
As for Frege, I think that his work was degraded on one hand, and on the other hand his work was used by some other scientists. Here, first of all I think on B. Russell, and also those who have supported B. Russell

>I spent an hour tonight reading the first hit Google returned
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> for "first order logic history":
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> http://www.mcps.umn.edu/philosophy/11_4moore.pdf
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> From that article, I can only conclude that one can credit many
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> contributors to FOL. Whether or not Frege gets the credit he deserves
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> is a question over which reasonable people can disagree.
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To my knowledge, this article is inaccurate. To me, some important things and events of that period are well known. This article begins with the Skolem in 1923rd However, Frege's first major work in logic was published in 1879 under the title Begriffsschrift. Many important things were happened between 1879 and 1923, for example, set theory was created during this period, including Zermelo’s axioms.

G. Frege's main idea was that the whole of mathematics can be ground on logic. Therefore Frege had a grandiose idea, to do mathematics as an extension of logic. The entire work of Frege, roughly speaking, comes from this idea. Of course, in Frege's work was also included Set Theory. G. Frege had a great written correspondence with G. Cantor.

In 1889, G. Peano published his work, Arithmetics principia, with his axioms of natural numbers. Peano introduced the simple, computable procedure (mathematical induction), which effectively works with infinite set of natural numbers. This is the first compete mathematical theory that is based on logic.

Frege also did the theory of natural numbers based on logic, in that period. Mathematicians today reveal a surprisingly good idea in Frege's work. Note that only Peano and Frege at that time used different symbols for math and logic. Most of today's symbols from logic and set theory come from G. Peano. Often, in the books the reader can find the claim that B. Russell came up with the idea that mathematics can be founded on logic. Note that B. Russell was 17 years old when Giuseppe Peano and Gottlob Frege published their books in which the mathematical theories were built on logic.

In this article, which you mentioned, the author begins to write about the logic from 1923: “In 1923, when a young Norwegian mathematician named Thoralf Skolem argued that set theory should be based on first-order logic, it was a radical and unprecedented proposal”.
Note that Frege introduced FOL because of his project. He devised “Set Theory" that is based on his definition of the concept. This huge Frege's project was stopped with Russell's paradox, which Russell presented with an example from Set Theory. G. Frege introduced the so called law V, which is actually an axiom. Russell's paradox refers to the law V.

In my work from 2008, I showed that Russell's paradox does not make sense and that its conception is wrong. See my thread on this user group: Does the phrase " Russell's paradox " should be replaced with another phrase? , posted on December 11, 2012.
In my solution, Frege's law V is accepted as good. So, my work does not improve the law V, because it's good. I've added a theory that is missing in Frege's theory. It was presented on this user group. So, my work is public; it means that my work is subject to criticism. Maybe someone can prove that I am wrong. I'm pretty sure that my work is a good solution.

Recently (in 2013) it was shown that it is possible to prove Frege's Theorem, without the use of Frege's law V. It was shown that it is enough to use the "Hume's Principle". In this regard see work from the 2013 : “Frege's Theorem and Foundations for Arithmetic”
at http://plato.stanford.edu/entries/frege-theorem/

On the other hand, if we accept the law V, then we change the "Set Theory" from the ground up. For example, the "primitives" must be changed in this change. Some axioms of set theory can be derived from Frege's definition of a concept.

Thus, with the use FOL, Frege's definition of Concept and with the addition of my work, it is possible to form the new set theory and to derive directly, certain axioms from the existing set theory. Note that my solution has two procedures. One procedure determines whether an object satisfies a certain concept. The second procedure performs the identification of the object that we put in the first procedure. So in my work is the emphasis on semantic procedures. Both of these procedures makes link between mind and the real world (external world).

I write about this in order to show that Frege's work not only introduces FOL in set theory, but it also changes the foundations of Set Theory. I also want to point out that after 120 years, mathematicians starting to realize the work of G.Frege in its entirety.

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> I was particularly struck by Hilbert's disagreement with Frege over the
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> truth of axioms,
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I see this debate as a significant contribution to the creation of new mathematical theories that have influenced the history of mathematics. These are primarily the theory of axiomatic theories and Model Theory. As for the axiomatic theories, Frege and Hilbert had opened the door of the room into which entered K. Godel, 30 years later, and surprised the world of science with his work.
So I think that these two great mathematicians, each in their own way made a significant contribution to the development of mathematics in this discussion. Note that this discussion lasted several years, and that some other people also participated in the debate, in addition to Frege and Hilbert.

Vladimir Odrljin Received on Tue Oct 08 2013 - 18:11:36 CEST