Re: Is Russell's paradox in fact fraud?

On Wednesday, September 20, 2017 at 12:56:33 AM UTC+2, vldm10 wrote:
> 1.
> Nicolas Fillion in his publication:
> „Les Enjeux de la Controverse Frege-Hilbert sur les Fondements de la
> Geometrie“
> on page 19, in the section "Zermelo-Russell Paradox", you can find the
> following statements about this paradox:
>
> „According to Russell, he discovered this paradox in 1901 (van Heijenoort,
> 1967a, p. 124). However, the first note about the existence of his discovery
> is in the famous letter to Frege that he sent on 16 June 1902. „
>
> The first published discussion of this paradox is to be found in 1903
> (Russell, 1903).
> This well-known paradox goes as follows: “
>
> „Zermelo himself claimed in a note that he discovered the paradox before
> Russell published it: “I had, however, discovered this antinomy myself,
> independently of Russell, and had communicated it prior to 1903 to professor
> Hilbert among others.”. “
>
> „ (The decisive proof that Zermelo actually discovered the paradox
> independently can be find in (Rang and Thomas, 1981) where it is shown that
> he communicated it to Husserl, thanks to a note dated 16 April 1902 (2
> months before Russell’s letter to Frege). “
>
> 2.
> Jaan van Heijenoort (Jean Louis Maxime van Heijenoort), american
> mathematician, was a pioneer historian of mathematical logic. Many of the
> original papers are contained in his book: From Frege to Gödel. „Bertrand
> Russell sow and approved the translation of of his 1902 letter to Frege. „
> (look at the preface in this book).
> In the letter to Frege, Russell communicates the paradox to Frege.
>
> This book also contains Frege's response to the mentioned Rusell's letter.
> Russell wrote this letter to Frege on June 16, 1902. Frege replied to
> Russell on June 22, 1902.
> In Frege's letter to Russell, there is the following part of the text:
> „Incidentally, it seems to me that expression „a predicate is predicated of
> itself“ is not exact. A predicate is as a rule a first-level function, and
> this function requires an object as argument and cannot have itself as
> argument (subject). „
>
> From this text, it is clear that B. Russell did not understand the
> fundamental elements of Frege's theory - that is, predicates, objects and
> concepts. Russell also did not understand the relationship between objects,
> concepts, and predicates.
> We can notice that these same things did not understand Codd and his
> followers Date and Darwen. Even more, I have not noticed that they have ever
> mentioned concepts and objects, and relationships between concepts,
> predicates, and objects.
>
> 3.
> Barber paradox
>
> (a)
> Barber paradox was used by Bertrand Russell as an illustration of paradox.
> The barber paradox is the folowing: "Barber shaves all those, who do not
> shave themselves."
> The question is, does the barber shave himself?
>
> Since the barber is the only barber in town, then the upper sentence leads
> to paradox.
> But over time, somebody found a solution to this Russell's „illustration“ of
> Barber paradox. This solution is Mary. We can notice that Mary is a woman
> and she has no beard.
>
> We can notice that the barber paradox today is presented differently from
> the one presented by B. Russell - see the above definition of the barber
> paradox labeled with (a).
>
> Today's version of the barber paradox is properly presented, as follows:
>
> (b)
> The barber is a man in town who shaves all those, and only those, men in
> town who do not shave themselves.
> Who shaves the barber?
>
> Still there are people who version of Barber Paradox labeled with (b)
> represent as Russell's version. Of course, version (b) is a paradox, while
> Russell's version (a) of the Barber paradox makes no sense.
>
> 4.
> Gödel's „first incompleteness theorem“ first appeared 1931 in paper „Uber
> formal unentscheidbare satze der Principia Mathematica“ (On formally
> undecidable propositions of Principia Mathematica).
>
> First Incompleteness Theorem: "Any consistent formal system F within which a certain amount of elementary arithmetic can be carried out is incomplete; i.e., there are statements of the language of F which can neither be proved
> nor disproved in F." (Raatikainen 2015).
>
> Related to Godel's first incompleteness theorem we can notice the following:
>
> (a)
> In this theorem, Godel put Russell's theory, which is presented in Russell's
> book Principia Mathematica, in the title of this Godel's work. In this way,
> in fact, Godel has "thrown into a dust" this Russell's theory.
>
> (b)
> Godel's "first incompleteness theorem" did not mention Frege's theory. Frege
> completely constructed the axiomatic system for propositional logic. This
> axiomatic system is complete. Today, this axiomatic system is known as
> "Frege-Lukasiewicz System". Frege has fully established Predicate Logic.
> Kurt Godel also proved that the first order predicate logic is complete
> theory.
> ---------------------------------------------------------------------------
> Now, I can present my conclusion, which is based on presented facts. Ernst
> Zermelo is the first scientist who has defined this paradox. Ernst Zermelo
> is also the first who has solved this paradox. Therefore, this paradox
> should has name Zermelo paradox instead of name Russell paradox.
>
> It is shown that Russell did not understand some basic things that are
> related to Zermelo paradox.
>
> It has been shown that Godel proved that Principia Mathematica is incomplete
> theoty. While Frege's theories - propositional logic and predicate logic are
> complete theories.
> ----------------------------------------------------------------------------
> Does Zermelo's Paradox have some relevance to database theory. The answer is
> - yes, because concept, that is, the predicate, determines the plurality of
> objects that satisfy that concept (predicate). We understand this plurality
> as one object, which we call - set.
> When we talk about Zermelo's solution to this paradox then we need to point
> out two things:
> (i) He solved this paradox at the level of set theory.
> (ii) He solved this paradox by adding a new axiom to the axiomatic system
> of set theory.
>
> Zermelo uses this axiom as some kind of constraint for sets. Therefore, we
> can set the following question: Are the axioms some kind of constrains. The
> answer is - yes. Axioms are some kind of constrains for the corresponding
> theory.
>
> Vladimir Odrljin
Received on Sun Oct 01 2017 - 01:36:29 CEST