Re: Sensible and NonsenSQL Aspects of the NoSQL Hoopla

On Tuesday, October 8, 2013 6:11:36 PM UTC+2, vldm10 wrote:

> Note that Frege introduced FOL because of his project. He devised “Set Theory"
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> that is based on his definition of the concept. This huge Frege's project was
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> stopped with Russell's paradox, which Russell presented with an example from Set
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> Theory. G. Frege introduced the so called law V, which is actually an axiom.
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> Russell's paradox refers to the law V.
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>
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> In my work from 2008, I showed that Russell's paradox does not make sense and
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> that its conception is wrong. See my thread on this user group: Does the
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> phrase " Russell's paradox " should be replaced with another phrase? , posted on
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> December 11, 2012.
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> In my solution, Frege's law V is accepted as good. So, my work does not improve
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> the law V, because it's good. I've added a theory that is missing in Frege's
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> theory. It was presented on this user group. So, my work is public; it means
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> that my work is subject to criticism. Maybe someone can prove that I am wrong.
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> I'm pretty sure that my work is a good solution.
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>
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> Recently (in 2013) it was shown that it is possible to prove Frege's Theorem,
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> without the use of Frege's law V. It was shown that it is enough to use the
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> "Hume's Principle". In this regard see work from the 2013 : “Frege's Theorem
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> and Foundations for Arithmetic”
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> at http://plato.stanford.edu/entries/frege-theorem/
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>
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> On the other hand, if we accept the law V, then we change the "Set Theory" from
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> the ground up. For example, the "primitives" must be changed in this change.
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> Some axioms of set theory can be derived from Frege's definition of a concept.
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>
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> Thus, with the use FOL, Frege's definition of Concept and with the addition of
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> my work, it is possible to form the new set theory and to derive directly,
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> certain axioms from the existing set theory.
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> Note that my solution has two procedures. One procedure determines whether an
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> object satisfies a certain concept. The second procedure performs the
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> identification of the object that we put in the first procedure. So in my work
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> is the emphasis on semantic procedures. Both of these procedures makes link
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> between mind and the real world (external world).
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>
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> I write about this in order to show that Frege's work not only introduces FOL in
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> set theory, but it also changes the foundations of Set Theory. I also want to
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> point out that after 120 years, mathematicians starting to realize the work of
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> G.Frege in its entirety.
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In the text above, we need some clarification. The term "FOL" I used imprecisely in the first part of the text, to emphasize that Frege introduced FOL. However, it is also known that Frege introduced a second-order logics and generally speaking, he introduced high-order logics. Law V uses second order logic, it uses quantifiers to predicates. In a situation where Russell's paradox is dismissed as irrelevant, there is a problem for the construction of Frege-inspired set theories. In that sense I have left open the question of the use of FOL.

In this user group I showed that with the addition of appropriate theory, Frege's law V is good. This means that Russell's Paradox does not make sense. It also means that the law V is more general than "Hume's Principle". Frege used "Hume's Principle" and he cited Hume. However, many feel that this Frege's citation ought to have been a citation of Cantor.

Vladimir Odrljin Received on Mon Oct 21 2013 - 19:25:17 CEST