## The Absolute Russell Set Exists

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### Re: The Absolute Russell Set Exists

browser32 wrote:
I should not have to define in this thread everything that has already been defined elsewhere.

Nonsense. The phrase "absolute Russell set" does not appear on the Internet except as a reference to the standard Russell set.

I truly doubt your text defines such a thing the way you're using it. Feel free to post a screen shot though, maybe I'll learn something.

browser32 wrote:That decreases the value of this thread

It would not be possible for anyone to do that.

browser32 wrote: and increases its unattractiveness to people looking for original thought.

LOL.
wtf

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### Re: The Absolute Russell Set Exists

wtf wrote:The phrase "absolute Russell set" does not appear on the Internet except as a reference to the standard Russell set.

I am referring to the standard Russell set. However, the Russell set, according to page 432 of the aforementioned Barwise and Etchemendy (1999, 2000, 2002, 2003, 2007, 2008), is the set of all things that are not elements of themselves, not the set of all sets that are not elements of themselves. The set of all things that are not elements of themselves is a more natural and better set to be called the Russell set than the other set. It's more comprehensive. I concede I did coin the term the absolute Russell set myself. But my term was readily derived from page 432 of Barwise and Etchemendy (1999, 2000, 2002, 2003, 2007, 2008), where they put the word absolute in parenthesis.

wtf wrote:I truly doubt your text defines such a thing the way you're using it.

Barwise and Etchemendy (1999, 2000, 2002, 2003, 2007, 2008) do not seem to formally define the absolute Russell set; they only describe and discuss it.

wtf wrote:Feel free to post a screen shot though, maybe I'll learn something.

This is where copyright law comes into play. I'm hesitant to copy a copyrighted formal definition or symbolic expression, especially when it may not be common knowledge. I actually, in my past post at viewtopic.php?p=2699066#p2699066, which I previously cited in this thread twice already, did not use the same letter to represent the absolute Russell set as Barwise and Etchemendy (1999, 2000, 2002, 2003, 2007, 2008) do. I was afraid it might be a copyright violation or plagiarism.

wtf wrote:It would not be possible for anyone to do that.

I disagree. It could be worse. It could get worse.

wtf wrote:LOL.

I wish to be enlightened and to advance.
Paul E. Mokrzecki
browser32

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### Re: The Absolute Russell Set Exists

browser32 wrote:I concede I did coin the term the absolute Russell set myself.

Thanks, that only took me a week to drag out of you, after you claimed several times that you found it in a math book.
wtf

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### Re: The Absolute Russell Set Exists

So what you are calling the "absolute Russell set," everyone else calls the proper class of all sets (or things, really doesn't matter) that are not members of themselves. That's really all there is to all this.
wtf

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### Re: The Absolute Russell Set Exists

wtf:

I'm not as familiar with class theory as I am with set theory. If you are correct, then my claim is that the absolute Russell proper class exists.

I'd rather keep the discussion focused on sets rather than classes. There's no need to speak in terms of classes when it's evident I'm speaking in terms of sets.
Paul E. Mokrzecki
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### Re: The Absolute Russell Set Exists

browser32 wrote:
I'm not as familiar with class theory as I am with set theory. If you are correct, then my claim is that the absolute Russell proper class exists.

Yes. It does. As I've noted a couple of times, $$R = \{x : x \notin x\}$$ defines the Russell class. It's the class of all things that are not members of themselves. It "exists" in the sense that its definition does not lead to contradiction. Of course here we are talking about formal logical existence, not anything in the real world. I hope we agree on that.

browser32 wrote:I'd rather keep the discussion focused on sets rather than classes. There's no need to speak in terms of classes when it's evident I'm speaking in terms of sets.

That's fine. But the claim that $$R$$ is a set leads to a contradiction.

Of course you could say it exists in an inconsistent version of set theory. Nothing wrong with that. As you've already pointed out, in an inconsistent system everything is true.
wtf

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### Re: The Absolute Russell Set Exists

But even here it is not settled, since contradiction and non contradiction are in an Absolute Russell set , self inclusive sets?

The feeling I have is, that redefinition does nothing but reassert the primacy of naive logic. Can that allowance withstand other succeeding arguments? Or, is it other systems of classes , when weighed in, Change the balance ?
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### Re: The Absolute Russell Set Exists

Meno_ wrote:But even here it is not settled, since contradiction and non contradiction are in an Absolute Russell set , self inclusive sets?

The feeling I have is, that redefinition does nothing but reassert the primacy of naive logic. Can that allowance withstand other succeeding arguments? Or, is it other systems of classes , when weighed in, Change the balance ?

Meno_, I read some of your other posts on the forum and I realize that you are only communicating in your own particular style; and not at all trying to annoy me personally. Thus it was wrong for me to attack you personally. I apologize.

I still do not understand most of what you write. But some of your references are interesting as I look them up. I think there is a kernel of interestingness in your exposition, if only I could discern it.

I hope you'll accept my apology and perhaps try to explain yourself better to a humble math guy like me.
wtf

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### Re: The Absolute Russell Set Exists

Removed .
Meno_
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### Re: The Absolute Russell Set Exists

Meno_ wrote:Removed .

In the spirit of the discussion ... an empty message means everything.
wtf

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### Re: The Absolute Russell Set Exists

wtf wrote:
Meno_ wrote:Removed .
o

In the spirit of the discussion ... an empty message means everything.

You're right , and upon reassessing my obvious lack of preparation , and need to properly respond. don't take my erasure as anything else but a preparation for a reasonably written format.

I must admit, I have a lot to do until then.
I am confident of that in general terms.
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### Re: The Absolute Russell Set Exists

Meno_ wrote:But even here it is not settled, since contradiction and non contradiction are in an Absolute Russell set , self inclusive sets?

You raise two interesting points.

First, there is nothing wrong with self-inclusive sets.

Why can't we have a set $$x$$ such that $$x \in x$$? There is no reason we can't, and in fact this is perfectly consistent with the other axioms of set theory. But for intuitive reasons -- namely, $$x \in x$$ violates our intuitions about sets -- we don't want to allow that. So we simply declare an axiom that says we can't have $$x \in x$$.

Of course then we might still have $$x \in y$$ and $$y \in x$$, or even longer chains such as $$x \in y$$, $$y \in z$$, and $$z \in x$$. So there is a clever axiom that outlaws all of these circular chains of inclusion. It's called the axiom of foundation or sometimes the axiom of regularity.

What happens if we don't include foundation in our axioms? Then we get the study of non well-founded set theory. It's obscure but it's studied and even applied in some disciplines.

So first point, there is nothing inherently wrong with self-membership. It's only outlawed in standard set theory because it doesn't fit our intuition about what sets should be.

The second point is that browser has a misunderstanding about contradictions. Just because you have some proof that ends in a contradiction, it doesn't mean math is broken or that everything is true. It just means that you have to throw out the assumption that led to the contradiction.

For example in Euclid's famous proof of the infinitude of primes, we start by assuming that we have a finite list of all the primes, then we show that this leads to a contradiction. We haven't broken math or proved everything is true. All we've done is shown that the assumption that there are finitely many primes is false. Nothing else.

Browser keeps saying that because we have some proof that leads to a contradiction we can use that contradiction to show that math is inconsistent. But that's wrong. All we're showing in the Russell proof is that the class, or collection, of things that are not members of themselves can not possibly be a set. That's all we've shown. There are no implications beyond that fact.

Meno_ wrote:The feeling I have is, that redefinition does nothing but reassert the primacy of naive logic.

Interesting word choice. Naive set theory is the essentially Frege's failed set theory in which sets can be formed out of unrestricted predicates, such as the "set of all things that are not members of themselves." Russell showed that this idea leads to a contradiction. So naive set theory fails. Sets can't be thought of as simply collections of things satisfying some predicate. Rather, a set is something that conforms to our axioms, which are chosen carefully to avoid contradictions.

Note: "Naive Set Theory" is also the name of a standard undergrad set theory text by Paul Halmos. It's NOT actually about naive set theory; it's about axiomatic set theory. No idea why Halmos chose that inaccurate title but it's a great book, highly recommended for people interested in set theory. Very readable.

https://en.wikipedia.org/wiki/Naive_Set_Theory_(book)

Meno_ wrote: Can that allowance withstand other succeeding arguments? Or, is it other systems of classes , when weighed in, Change the balance ?

Russell's paradox shows that the collection of all things that are not members of themselves can not possibly be a set. In ZFC (the standard axiom system for math) there is no such thing as a proper class, so in ZFC we simply say the Russell set doesn't exist. But there are other systems of set theory that formalize proper classes, and then the Russell class has official standing as a proper class: a well-defined collection that's "too big" to be a set.
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### Re: The Absolute Russell Set Exists

wtf wrote:The second point is that browser has a misunderstanding about contradictions. Just because you have some proof that ends in a contradiction, it doesn't mean math is broken or that everything is true. It just means that you have to throw out the assumption that led to the contradiction.

That's incorrect; I do not have to throw out the assumption. I am permitted to keep the assumption. That permission was discussed in another thread I started, "Anything Can Be Postulated" at viewtopic.php?f=1&t=193975. An assumption and a postulate are in a sense the same; they are both a proposition that is assumed to be true.

wtf wrote:Browser keeps saying that because we have some proof that leads to a contradiction we can use that contradiction to show that math is inconsistent.

That would be an oversimplification. The proof is not just any proof; it is a proof of a very counterintuitive claim.

wtf wrote:Russell showed that this idea leads to a contradiction.

That's what's traditionally said, but it's not true. I'm interested in taking the other road.

wtf wrote:Note: "Naive Set Theory" is also the name of a standard undergrad set theory text by Paul Halmos. It's NOT actually about naive set theory; it's about axiomatic set theory. No idea why Halmos chose that inaccurate title but it's a great book, highly recommended for people interested in set theory. Very readable.

I did previously encounter that book for sale online. I thought it interesting how somebody would work to such an involved level in naive set theory, since the theory's inconsistent. Perhaps I shouldn't judge a book by its cover.
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### Re: The Absolute Russell Set Exists

browser32 wrote:That's incorrect; I do not have to throw out the assumption. I am permitted to keep the assumption. That permission was discussed in another thread I started, "Anything Can Be Postulated" at http://www.ilovephilosophy.com/viewtopi ... 1&t=193975.

I've learned fromexperience that it's not helpful to me to follow your links to your other posts. Please say what you have to say in the thread I'm reading.

Why are you permitted to keep the assumption? If I assume there are finitely many primes and that 11 is the largest one, and then I show that 2 x 3 x 5 x 7 x 11 + 1 must be divisible by some prime larger than 11, how do you figure you can keep the assumption that 11 is the largest prime?

browser32 wrote: An assumption and a postulate are in a sense the same; they are both a proposition that is assumed to be true.

If an assumption leads to a contradiction we throw it out. Of course if you like working with inconsistent systems you may certainly keep assumptions that lead to contradictions, but then you get a useless system.

browser32 wrote:That would be an oversimplification. The proof is not just any proof; it is a proof of a very counterintuitive claim.

Math is full of counterintuitive claims. What does that have to do with keeping assumptions that lead to contradictions?

browser32 wrote:That's what's traditionally said, but it's not true. I'm interested in taking the other road.

It's not just "traditionally said." It's formally proved. If $$R = \{x : x \notin x\}$$ and we assume $$R$$ is a set, we get a contradiction. It's a very well known proof. It's disingenuous to characterize this as "traditionally said." It's like saying it's traditionally said that there is no largest prime. Well yeah, it's traditionally said because Euclid proved it and the proof is understandable to high school students.

browser32 wrote:I did previously encounter that book for sale online. I thought it interesting how somebody would work to such an involved level in naive set theory, since the theory's inconsistent. Perhaps I shouldn't judge a book by its cover.

You should definitely read that book. It's very clear and understandable and you'll learn a lot from it.
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### Re: The Absolute Russell Set Exists

wtf wrote:Why are you permitted to keep the assumption?

I am permitted to keep the assumption because there is no rule that requires me to do otherwise.

wtf wrote:If I assume there are finitely many primes and that 11 is the largest one, and then I show that 2 x 3 x 5 x 7 x 11 + 1 must be divisible by some prime larger than 11, how do you figure you can keep the assumption that 11 is the largest prime?

The assumption can be kept because the assumption implies no contradiction.

wtf wrote:If an assumption leads to a contradiction we throw it out.

In a proof by contradiction, that's what we do. But no assumption ever has to be thrown out. The first proof of ex contradictione quodlibet at https://en.wikipedia.org/wiki/Principle ... sion#Proof actually assumes a contradiction at the very first step, and proceeds therefrom.

wtf wrote:Of course if you like working with inconsistent systems you may certainly keep assumptions that lead to contradictions, but then you get a useless system.

Inconsistent systems aren't necessarily useless. Naive set theory, for example, has brought society much enlightenment. Inconsistent systems themselves can be used to prove trivialism, as I've argued in another thread I started, "Inconsistent Theories Metatheoretically Prove Trivialism" at http://onlinephilosophyclub.com/forums/ ... =2&t=15559. That thread was somewhat inspired by the discussion I have been having with you in this thread.

wtf wrote:What does that have to do with keeping assumptions that lead to contradictions?

If one claim is less intuitive than a second claim is, then it may be that the first claim is more difficult to keep as an assumption than the second claim is. People have limited strength. They have limited abilities. People may be uncomfortable acting on a belief that is difficult to attain or maintain. They may be unable to act on such a belief.

wtf wrote:It's disingenuous to characterize this as "traditionally said."

That's what it is at this point in time; Russell's paradox is disingenuous. It's hackneyed. It's more ingenious to talk about the existence of the absolute Russell set than it is to talk about its nonexistence.

wtf wrote:It's like saying it's traditionally said that there is no largest prime. Well yeah, it's traditionally said because Euclid proved it and the proof is understandable to high school students.

As I said at viewtopic.php?p=2699066#p2699066, which I have now cited for the fourth time in this thread, and as I said at https://twitter.com/paulemok/status/988543393432293377, the existence of the absolute Russell set implies trivialism. The two proofs I provided of the existence of the absolute Russell set earlier in this thread, at viewtopic.php?p=2699904#p2699904 and viewtopic.php?p=2699659#p2699659, make evident that the existence of the absolute Russell set implies some contradiction. Since those proofs prove the existence of the absolute Russell set, the set exists. Since the set exists, some contradiction exists. Thus, by ex contradictione quodlibet, trivialism is true. Since trivialism is true, there is the largest prime.
Paul E. Mokrzecki
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### Re: The Absolute Russell Set Exists

browser32 wrote:I am permitted to keep the assumption because there is no rule that requires me to do otherwise.

There is a principle that we are seeking a consistent framework for mathematics. You are entitled to desire an inconsistent framework, but that seems pointless.

browser32 wrote:The assumption can be kept because the assumption implies no contradiction.

If you think 11 is the largest prime, we're done. Actually we are done. You haven't said anything new in quite a while.

browser32 wrote:In a proof by contradiction, that's what we do. But no assumption ever has to be thrown out. The first proof of ex contradictione quodlibet at https://en.wikipedia.org/wiki/Principle ... sion#Proof actually assumes a contradiction at the very first step, and proceeds therefrom.

You greatly misunderstand proof by contradiction. But if you enjoy typing Latin phrases, by all means enjoy yourself.

browser32 wrote:Inconsistent systems aren't necessarily useless.

I would agree. But "not necessarily useless" is not the same as "We should adopt inconsistent mathematics." The latter would be counterproductive.

browser32 wrote:Naive set theory, for example, has brought society much enlightenment. Inconsistent systems themselves can be used to prove trivialism, as I've argued in another thread I started, "Inconsistent Theories Metatheoretically Prove Trivialism" at http://onlinephilosophyclub.com/forums/ ... =2&t=15559. That thread was somewhat inspired by the discussion I have been having with you in this thread.

You should not assume I have not looked at your other online work. I've seen the nudes, I've seen the restraining order filed against you. What of it? If you have something to say, say it here.

browser32 wrote:If one claim is less intuitive than a second claim is, then it may be that the first claim is more difficult to keep as an assumption than the second claim is. People have limited strength. They have limited abilities. People may be uncomfortable acting on a belief that is difficult to attain or maintain. They may be unable to act on such a belief.

Whatever that word salad means.

browser32 wrote:That's what it is at this point in time; Russell's paradox is disingenuous. It's hackneyed. It's more ingenious to talk about the existence of the absolute Russell set than it is to talk about its nonexistence.

If you reject the concept of mathematical proof, we're done. Which we are.

browser32 wrote:As I said at http://www.ilovephilosophy.com/viewtopi ... 6#p2699066, which I have now cited for the fourth time in this thread, and as I said at https://twitter.com/paulemok/status/988543393432293377, the existence of the absolute Russell set implies trivialism. The two proofs I provided of the existence of the absolute Russell set earlier in this thread, at http://www.ilovephilosophy.com/viewtopi ... 4#p2699904 and http://www.ilovephilosophy.com/viewtopi ... 9#p2699659, make evident that the existence of the absolute Russell set implies some contradiction. Since those proofs prove the existence of the absolute Russell set, the set exists. Since the set exists, some contradiction exists. Thus, by ex contradictione quodlibet, trivialism is true. Since trivialism is true, there is the largest prime.

All the best.
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### Re: The Absolute Russell Set Exists

wtf wrote:There is a principle that we are seeking a consistent framework for mathematics. You are entitled to desire an inconsistent framework, but that seems pointless.

Through ex contradictione quodlibet, every inconsistent framework for mathematics is consistent.

Inconsistency, by its very nature, coexists with consistency.

wtf wrote:If you think 11 is the largest prime, we're done. Actually we are done.

I am telling you the objective truth. 11 is the largest prime.

wtf wrote:You greatly misunderstand proof by contradiction.

I'm afraid you may have misinterpreted my paragraph there. I intended its first sentence only to be exclusively about proof by contradiction. The rest of that paragraph, including its last sentence about a proof of ex contradictione quodlibet, is about general proof. The last sentence of that paragraph provides evidence for my claim of the second sentence of that paragraph.

I strongly disagree with your claim that I "greatly misunderstand proof by contradiction." I assure you I understand proof by contradiction. It's clear I use proof by contradiction myself. In my post at viewtopic.php?p=2699066#p2699066, which I have now cited for the fifth time in this thread, I invoked two proofs by contradiction.

Notwithstanding, by ex contradictione quodlibet, a contradiction implies its own nonexistence. Also, by the law of noncontradiction, there is no contradiction. With no contradiction, there is no proof by contradiction.

wtf wrote:If you reject the concept of mathematical proof, we're done. Which we are.

It's clear from the proofs I've given in this thread alone that I have not rejected the concept of mathematical proof.
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### Re: The Absolute Russell Set Exists

I do not agree that were done. Mathematical proof is contingent, not necessary to demonstrate the law of inconsistency.

Simply, the presumption fails, rather the holding the principle ,form the simple reason of the failure of self evident truths.

Nowhere is this more evident then in the proof of God argument where , the quality of perfection of god, is part of his existence. Without the quality of perfection God would not be god.

And lack of existence would detract from his perfection, therefore his non existence would lead to contradiction.

Therefore the presumption of his existence is necessary to avoid contradiction. This was all Russel was saying , as anyone who declared certain inalienable rights.

No rights are inalienable , to found a perfect union, this is what is at the base of the great Trump debate.

Trump is using this contradiction to bring back certain expired assumptions.

Logic through language leads to contradiction, where, the pseudo consistency presents false meanings .

The search for meaning is tainted from the get go.thisnisnwjubtjen genesis of meaning has become such an important part of philosophical study, which could not separate reason from meaning.

By saying thus I hope I don't end up in the trash in of intentions where its sometimes falsely claimed that the man in the middle between antithetical claims , both hold ing. a union of antagonistic attitudes.
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### Re: The Absolute Russell Set Exists

Meno_ wrote:I do not agree that were done.

Of course I did not unilaterally declare the thread to be finished. I couldn't do that if I wanted to. Rather, I said I'm done responding to the OP, having nothing more to say.

Meno_ wrote:Mathematical proof is contingent, not necessary to demonstrate the law of inconsistency.

Meaning unclear.

Meno_ wrote:Simply, the presumption fails, rather the holding the principle ,form the simple reason of the failure of self evident truths.

Self-evident truths from the Declaration of Independence?

Meno_ wrote:Nowhere is this more evident then in the proof of God argument where , the quality of perfection of god, is part of his existence. Without the quality of perfection God would not be god.

And lack of existence would detract from his perfection, therefore his non existence would lead to contradiction.

This is Saint Anselm's famous proof of the existence of God. It leads to the interesting question of whether or not existence is a predicate.

Meno_ wrote:Therefore the presumption of his existence is necessary to avoid contradiction. This was all Russel was saying ,

Russell was saying nothing of the sort. Russell pointed out that Frege's unrestricted set formation leads to a contradiction. Anselm's proof of God has absolutely nothing to do with this.

Meno_ wrote: as anyone who declared certain inalienable rights.

Back to the Declaration.

Meno_ wrote:No rights are inalienable , to found a perfect union,

The phrase "perfect union" of course famously appears in the preamble to the US Constitution.

Meno_ wrote:this is what is at the base of the great Trump debate.

Has nothing to do with anything.

Meno_ wrote:Trump is using this contradiction to bring back certain expired assumptions.

Perhaps you can give an example.

Meno_ wrote:Logic through language leads to contradiction, where, the pseudo consistency presents false meanings .

Meno_ wrote:The search for meaning is tainted from the get go.

I can agree with that. Just as the writing of history often says more about the present than it does about the past. Nevertheless we make the effort.

Meno_ wrote:thisnisnwjubtjen

If you say so. What does that word mean please?

Meno_ wrote: genesis of meaning has become such an important part of philosophical study, which could not separate reason from meaning.

Earlier I said I would make a good faith effort to take you seriously even if not literally, but this latest post of your makes that difficult. You're either trolling or running a poorly-executed chatbot.

Meno_ wrote:By saying thus I hope I don't end
up in the trash in of intentions where its sometimes falsely claimed that the man in the middle between antithetical claims , both hold ing. a union of antagonistic attitudes.

It's difficult to take your post seriously. Surely it's fair for me to say that. I was going to ask if perhaps you are not a native speaker of English, but even that doesn't account for the strangeness of this post.
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### Re: The Absolute Russell Set Exists

Fair.I'm not even going to try to defend the above,it was very late and try to pull things together,

. albeit unsuccesively.

The merit of my argument , nevertheless, as tenuous, has redeemable featured.

Contradiction on the naive logical level, contrasts with the later, more expanding scientifically based level. Here, ordering of sets , based on types- qualities, expressed through adverbs, rather then verbs, ( where verbs are prone to express the duality of exisyence.

adverbs qualify, through modified, not primary logic, deliniations of meaning, consistently and subtly, shading the extreme inclusive/exclusive logic through language. The grey area has a limited backward look into the inception of such language, and philology. can not trace the origin, in an exclusive set of membership.

Political ambiguity and contradiction then, are present in politics, Trumpism, St. Anselm, and even the Declaration of Independence utilize the progressive languages, whereby the logical nuances are exemplified.

Such declarations of basic rights, do not express the coming ambiguity between the coming inherent contradiction between rights of life, liberty and the enjoyment of life, in light of the non comprehension of factors of Capitalistic accumulation which may (and did) work against such prematurely ideal constructs, and hence when political scientists talk of a Constitutional Crisis, it is not too far a stretch to interpret. these in terms of absolute exclusivity. versus inclusivity between them, and the emergence of modified conceptual grey areas.

Logically, duality has been more based on intuitive levels of understanding, such as Kant brought into recognition .However, it is the correctness of such premature deliberations, that became a sort of foreseeable development, upon which Hegel, Marx, came to create their own developments.

Logic through the evolution of language, which finally reveals the actual contradictory experiences of living these logical. contradictions meaningful. bear them out in realitu5

Yes my English is not primarily of native origin but.acquired secondarily , so it plays into the differential systems between the logical systems.

That Hungarian, my first, is a very unique language type (I've heard it said) thanks for noticing.

Other than this I have nothing to add, and I brought Anselm, into the discussion , fully understanding the significance of his failure. Mixiing what now has been seen as two different kinds of systems of logic, literally exemplifies the two languages I am at times conflating. Incidentally Hungarian being the more literal language,not that this alone makes the difference

Finally, I'm not adverse to be found wrong, with differences of opinion of varying phonetical and grammatical systems of thought.
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### Re: The Absolute Russell Set Exists

Meno_ wrote:Political ambiguity and contradiction then, are present in politics, Trumpism, St. Anselm, and even the Declaration of Independence utilize the progressive languages, whereby the logical nuances are exemplified.

If you're saying that ambiguity exists in society and in language, I completely agree.

That's exactly why we use formal logic and math as realms where ambiguity is eliminated. Logic and math aren't the same as the contradictions of the world. But that doesn't mean that logic and math are somehow tainted by the confusion of language and the world.
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### Re: The Absolute Russell Set Exists

wtf wrote:
Meno_ wrote:Political ambiguity and contradiction then, are present in politics, Trumpism, St. Anselm, and even the Declaration of Independence utilize the progressive languages, whereby the logical nuances are exemplified.

If you're saying that ambiguity exists in society and in language, I completely agree.

That's exactly why we use formal logic and math as realms where ambiguity is eliminated. Logic and math aren't the same as the contradictions of the world. But that doesn't mean that logic and math are somehow tainted by the confusion of language and the world.

Perhaps my brushstrokes were leaving too broad a trace in implying that the very basis of the use of logic that has created the very contradictions through language, as useful as they appear within themselves.

You may laugh, but the most obvious being is Hegel's systemic logical approach in forming reality through the logical adaptation of language as the mirror of reality speaks for itself.The question then becomes not that logic is wrong, but it can misrepresent reality by assuming that it can systematically apply its methodic dual aspect to order , types of dual functions to semantic usage.

Is this a case of finding fault with either language or logic, or, is it based on the assumption that dual , contradictory thinking is due to the construction of the structure of the brain itself, wherein duality is merely a functional processing of the physiology of the brain?

Either assumption is exctrinsically factual, but intrinsically conflated, which leads to paradoxical contradiction.

In another form the question manifests not as the etymology of the brain, nor the functional use of the adaptive uses of the brain. It appears convincing to say that the latter has more inclusive features.

The example of the human thought occurring, when in the face of an impending attack by a superior and enhanced attack, most humans will automatically have the thought ,based on a sudden appraisal, that the fight-flight dilemma is not a contest, and this after experiencing countless instances, will result in a logical sequence, by inserting types of characteristics which deter.one whether the action required I'd fight or flight from the threatening situation.

This very primitive almost instinctual act, is not really that, and is more a basis of logical systems then the dual aspect morphology seems to imply.

This is more 'absolutely' true, then the idea that an early sequence can be discovered post ex facto.

This is why the mind , not the brain, sets up very early absolutes, in terms of no exclusive use of thought.

It simply doesn't mean that it has no priority or inclusive function in the process. It took millennia to find out that unraveling this fallacy would take many twists and turns, meanwhile the stage of reality upon which these changes were really utilized , cost unbelievable losses in both lives and material.

The eidectic reduction of logic is demonstrationable exclusive of logic itself, therefore pertinent and necessary to this discussion., in my opinion.
Last edited by Meno_ on Tue May 01, 2018 5:56 pm, edited 2 times in total.
Meno_
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### Re: The Absolute Russell Set Exists

browser32 wrote:The absolute Russell set exists.

Proof.

Lemma. If a statement is false, then it materially implies some contradiction exists.

Proof of Lemma. It is given that a statement is false. So, the hypothesis of the material implication “the statement materially implies some contradiction exists” is false. By the truth table for material implication, any material implication with a false hypothesis is true. So, the statement materially implies some contradiction exists. This concludes the proof of the lemma.

Assume the absolute Russell set exists. As I’ve proved in my post at http://www.ilovephilosophy.com/viewtopic.php?p=2699066#p2699066, the absolute Russell set both is and is not an element of itself. For that reason, some contradiction exists. It follows by ex contradictione quodlibet that no contradiction exists. Discharge the assumption. Thus, by implication introduction, it is materially true that if the absolute Russell set exists, no contradiction exists. So, as a step of the proof that may be questionable, it is not materially true that if the absolute Russell set exists, some contradiction exists. In other words, the absolute Russell set exists does not materially imply some contradiction exists. Using modus tollens with the lemma and previous statement, the statement “the absolute Russell set exists” is not false. Thus, the statement is true. Therefore, the absolute Russell set exists. This concludes the proof.

A possible question with the proof is whether “the absolute Russell set exists materially implies no contradiction exists” strictly implies “the absolute Russell set exists does not materially imply some contradiction exists.” It's fairly intuitive that if a statement implies no contradiction, then it does not imply some contradiction. “The absolute Russell set exists materially implies no contradiction exists” does not tautologically imply “the absolute Russell set exists does not materially imply some contradiction exists;" the four corner entries in the bottommost two rows and the rightmost two columns of the following truth table reveal that in the case where the absolute Russell set does not exist, the former statement is true, but the latter is false.

Truth Table.
p = “The absolute Russell set exists.”
q = “Some contradiction exists.”
p.....q..|..¬q.....pq.....p → ¬q.....¬(pq)
T.....T...|...F.........T............F...............F
T.....F...|...T.........F............T...............T
F.....T...|...F.........T............T...............F
F.....F...|...T.........T............T...............F
This concludes the truth table.

The question of interest, however, regards strict implication, not tautological implication. Both statements describe the epistemically possible case in which the absolute Russell set does exist. So, the question can be reconsidered as whether, in the epistemically possible case in which the absolute Russell set exists, “no contradiction exists” strictly implies “it is not true that some contradiction exists.” The answer is intuitively yes; that strict implication is true in all cases. Therefore, the proof that the absolute Russell set exists is sound.

Paul E. Mokrzecki

I wondered how to read this

browser32 wrote:Any proposition can be a postulate.

Let p be a proposition. It is logically necessary that p is permitted to be a postulate. It is logically necessary that the proposition "p is true in the actual world" is permitted to be a postulate.

If p is a postulate, then: p is true and no contradiction exists.

Proof. It is given that p is a postulate. Then by definition of postulate, p is true.

Assume some contradiction exists. Then there is a contradiction. Discharge the assumption. It is thus proved by contradiction that it is not true that some contradiction exists. So, no contradiction exists.

By conjunction introduction, p is true and no contradiction exists. This concludes the proof.

Since the proposition "p is true and no contradiction exists" is true at all times that p is a postulate, there is never a problem with p being a postulate.

In the proposed debate "The Absolute Russell Set Exists," which I recently cited on social media and is located at http://www.debate.org/debates/The-Absol ... -Exists/1/, I, Paul E. Mokrzecki, postulated the existence of the absolute Russell set. The proposition "the absolute Russell set exists" can be postulated without contradiction and thus without trouble.

This leads me to question the sincerity of the OP of this thread.

For behold, all acts of love and pleasure are my rituals

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### Re: The Absolute Russell Set Exists

Jakob wrote:This leads me to question the sincerity of the OP of this thread.

I'm unsure why that would be.
Paul E. Mokrzecki
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### Re: The Absolute Russell Set Exists

Meno_ wrote:
wtf wrote:
Meno_ wrote:Political ambiguity and contradiction then, are present in politics, Trumpism, St. Anselm, and even the Declaration of Independence utilize the progressive languages, whereby the logical nuances are exemplified.

If you're saying that ambiguity exists in society and in language, I completely agree.

That's exactly why we use formal logic and math as realms where ambiguity is eliminated. Logic and math aren't the same as the contradictions of the world. But that doesn't mean that logic and math are somehow tainted by the confusion of language and the world.

Perhaps my brushstrokes were leaving too broad a trace in implying that the very basis of the use of logic that has created the very contradictions through language, as useful as they appear within themselves.

You may laugh, but the most obvious being is Hegel's systemic logical approach in forming reality through the logical adaptation of language as the mirror of reality speaks for itself.The question then becomes not that logic is wrong, but it can misrepresent reality by assuming that it can systematically apply its methodic dual aspect to order , types of dual functions to semantic usage.

Is this a case of finding fault with either language or logic, or, is it based on the assumption that dual , contradictory thinking is due to the construction of the structure of the brain itself, wherein duality is merely a functional processing of the physiology of the brain?

Either assumption is exctrinsically factual, but intrinsically conflated, which leads to paradoxical contradiction.

In another form the question manifests not as the etymology of the brain, nor the functional use of the adaptive uses of the brain. It appears convincing to say that the latter has more inclusive features.

The example of the human thought occurring, when in the face of an impending attack by a superior and enhanced attack, most humans will automatically have the thought ,based on a sudden appraisal, that the fight-flight dilemma is not a contest, and this after experiencing countless instances, will result in a logical sequence, by inserting types of characteristics which deter.one whether the action required I'd fight or flight from the threatening situation.

This very primitive almost instinctual act, is not really that, and is more a basis of logical systems then the dual aspect morphology seems to imply.

This is more 'absolutely' true, then the idea that an early sequence can be discovered post ex facto.

This is why the mind , not the brain, sets up very early absolutes, in terms of no exclusive use of thought.

It simply doesn't mean that it has no priority or inclusive function in the process. It took millennia to find out that unraveling this fallacy would take many twists and turns, meanwhile the stage of reality upon which these changes were really utilized , cost unbelievable losses in both lives and material.

The eidectic reduction of logic is demonstrationable exclusive of logic itself, therefore pertinent and necessary to this discussion., in my opinion.

In fact , to post scripitively answer Jacob's problem with the issue of sincerity with the opus, the impression I get is not consistent with the concept of sincerity, but the phenomenal eidectic reduction to naive realism, which does entail the implausability of retaining a root of meaning, where types having been lost, retaining only formal logical arrangements.

Positivism thus is absolutely concerned with interpreting present meaning with the reduced one, and the absolute set consists as ground to it.

Browser's intention is to show that naive formal , absolute meaning does end in a logical absolute contradiction. at that absolutely reduced logical level, where the existence and the non existence of even of that : vis. of the absolute Russell set exists absolutely.

Browser's demonstration of the absolute Russell set as existentially-phenomenologically reduced, can not delineate between existential/non existential difference on that level, since it belongs to a prior level, a-priori.

It took me a while to understand that logical notation, can not differentiate on an other level which .can encompass
that difference.

Hence the contradiction is supposed to entail the compilation of necessary truths.

So the absolute is really not absolute, except in the logical format of its formal description.

That existence is not a predicate on that level, the contradictory nature of the existence of absolute sets can not be described, , it only can be. demonstrated postscriptively , within the the language used.

I think Browser knows the paradox that the title of the forum implies
Its not insincere, but a showing of the paradoxical nature of the proposition..

The liar''s Paradox literally tries to figure a way out of the paradox, insincerity and lies are the very essence of the argument.
Last edited by Meno_ on Wed May 02, 2018 4:51 am, edited 1 time in total.
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