The true solution to Russell's paradox

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philosopher19
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Re: The true solution to Russell's paradox

Post by philosopher19 »

RJG wrote: March 9th, 2021, 7:45 am
philosopher19 wrote:..."is a member of itself" (...and "members of themselves").
Phil, this phrase (above) is scattered throughout much of what you write, which raises a red flag to me. Maybe set theory allows this, but from a purely logical or mathematical perspective this is an impossibility. X can never be outside/inside itself, or before/after itself, or anything but itself, for X<X is a logical and mathematical impossibility. But since I am not familiar with set theory I can't really disagree with what you say here.
I understand and I don't want you to engage in something that you are not comfortable with. But simply put, is the set of all existing things anything other than Existence (that which exists everywhere by definition or that which is Omnipresent) Is It Itself not an existing thing? So isn't It Itself a member of Itself?

Do you not think Existence to be Self-Sufficient and Self-Sustaining and Self-Contingent?

I would describe Existence as the true Self, or the true member of Itself. What do you make of the following:

I am in Existence and Existence Is in me

There's no end to the Existence in me when one focuses on the Infinitesimal. There's also no end to the Existence that is outside of me when one focuses on the Infinite. Since I am in Existence and Existence Is in me (as opposed to non-Existence being in me), does it not follow, that from my point of view, Existence Is In Existence?

Consider a list of all lists. Note that our focus has shifted here from existents, to lists. Is it not the case that a list of all lists actually lists itself? Existence Itself exists, only because It exists. All other existents exist because Existence Exists.

Consider the meaning of 'meaning'. The meaning of 'meaning' is just one meaning. All triangle are shapes. All triangles are members of the semantic of shape. Is it not the case that all meanings are meanings? Is it not the case that all meanings are members of the meaning of 'meaning'? As existents, all meanings are members of the existent Existence. As meanings, all meanings are members of the meaning of 'meaning'.

I don't want to force you into a discussion. I just want to offer you what may be of interest or benefit to you. If this is not a discussion you're comfortable with (because you say you are not familiar with set theory) or would like to have, then I understand. But you are aware of the semantic of 'set'. You are also aware of all other semantics. That is all you need. What Frege proposed was a theory that was true to the semantic of 'set'. He just couldn't explain it properly (as evidenced by his inability to respond to Russell's question) and then he thought his understanding of the semantic of 'set' was actually absurd (when it fact it wasn't).
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RJG
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Re: The true solution to Russell's paradox

Post by RJG »

philosopher19 wrote:But simply put, is the set of all existing things anything other than Existence (that which exists everywhere by definition or that which is Omnipresent) Is It Itself not an existing thing? So isn't It Itself a member of Itself?
This is how I see it (wrongly or rightly) - "Existence" or "the set of all existing things" is not an actual "thing" and therefore does not contradict itself (i.e. "a member of itself" contradicts logic; X<X is impossible).

"Existence" is a mental construct; an abstraction that represents all existing things, but is not a thing itself. In other words, "Existence" is just a bodily experience; a mental thought; which itself is a composition of sensory experiences formed by the rules of our language residing in memory, and therefore not a "thing" (noun), but more an action; "experience" (verb).

Again, this is just my best (wholly biased) stab at it. I am in no position to question or invalidate your view or understanding. That's about all I have left to contribute to this discussion. You have certainly given much more thought to this than I have.

Thanks for the good mental exercise, I've enjoyed it, but now must move on, ...until we meet again!
Steve3007
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Re: The true solution to Russell's paradox

Post by Steve3007 »

RJG wrote:"Existence" is a mental construct; an abstraction that represents all existing things, but is not a thing itself.
Given that Phil idiosyncratically uses the word "Existence" to denote "the set of all existing things", I agree with you here. Sets are abstract concepts, not real things in themselves.

(We have some common ground! :D )
philosopher19
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Re: The true solution to Russell's paradox

Post by philosopher19 »

RJG wrote: March 10th, 2021, 9:09 am
philosopher19 wrote:But simply put, is the set of all existing things anything other than Existence (that which exists everywhere by definition or that which is Omnipresent) Is It Itself not an existing thing? So isn't It Itself a member of Itself?
This is how I see it (wrongly or rightly) - "Existence" or "the set of all existing things" is not an actual "thing" and therefore does not contradict itself (i.e. "a member of itself" contradicts logic; X<X is impossible).

"Existence" is a mental construct; an abstraction that represents all existing things, but is not a thing itself. In other words, "Existence" is just a bodily experience; a mental thought; which itself is a composition of sensory experiences formed by the rules of our language residing in memory, and therefore not a "thing" (noun), but more an action; "experience" (verb).

Again, this is just my best (wholly biased) stab at it. I am in no position to question or invalidate your view or understanding. That's about all I have left to contribute to this discussion. You have certainly given much more thought to this than I have.

Thanks for the good mental exercise, I've enjoyed it, but now must move on, ...until we meet again!
Ok, but if you fancy more mental exercises, then here you go:

So you don't think Existence is an actual existing thing. What about the Omnipresent? Is the Omnipresent an actual exiting thing? Can we say that it exists everywhere? And with that being the case, can we say Existence (where Existence = that which is Omnipresent) exists everywhere?
Steve3007
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Re: The true solution to Russell's paradox

Post by Steve3007 »

philosopher19 wrote:What about the Omnipresent? Is the Omnipresent an actual exiting thing? Can we say that it exists everywhere? And with that being the case, can we say Existence (where Existence = that which is Omnipresent) exists everywhere?
You seem to have a longstanding fondness for fallacies of ambiguity/equivocation - either giving something a different name in the hope that that will somehow change something (as in the above case) or using the same word for two different concepts but using the fact that it's the same word to obfuscate this. You do this with the word "Existence" (variously with an upper or lower case 'E', depending on how much you want to try to make the identity between It and God) to mean two different things, but then claiming things about it based on the fact that those two different usages have the same letters in the same order.

This has been pointed out to you quite a few times. You've ignored it. I guess you'll just keep ignoring and repeating?
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RJG
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Re: The true solution to Russell's paradox

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philosopher19" wrote:So you don't think Existence is an actual existing thing. What about the Omnipresent?
philosopher19, I think we (you and I) are using these words in different contexts or meanings, and is the reason for my confusion in understanding what you are really saying.

For example, from my perspective, "existence" is just a property of some object. Existence is not the object itself. An object has existence or it doesn't. It is real or it is imaginary.

And similarly, "omnipresent" is again just a property of some object. Omnipresent is not the object itself. An object that "exists everywhere" is an "omnipresent" object. For example, "God is omnipresent" means God is the object that exists everywhere.

philosopher19 wrote:Can we say that it exists everywhere?
What is "it"? …does "it" = "objects", ...or "objects that exist everywhere"?

philosopher19 wrote:And with that being the case, can we say Existence (where Existence = that which is Omnipresent) exists everywhere?
I think you are trying to say -- "stuff (that exists) exists everywhere", or "there is nowhere where stuff does not exist". Is this what you are saying?
philosopher19
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Re: The true solution to Russell's paradox

Post by philosopher19 »

RJG wrote: March 15th, 2021, 9:49 pm And similarly, "omnipresent" is again just a property of some object. Omnipresent is not the object itself. An object that "exists everywhere" is an "omnipresent" object. For example, "God is omnipresent" means God is the object that exists everywhere.
Take x to be the object that exists everywhere (the omnipresent). Is it not the case that x necessarily exists? Can you have two worlds or universes separated by non-existence? No, therefore one x is omnipresent, and it encompasses all worlds, realities, beings, and so on.

All things that exist, actually exist. x itself exists. All things that exist, exist as a member of x (as opposed to existing as members of non-existence or outside the omnipresent). Do you agree with this so far?
philosopher19
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Re: The true solution to Russell's paradox

Post by philosopher19 »

Steve3007 wrote: March 15th, 2021, 5:50 am
philosopher19 wrote:What about the Omnipresent? Is the Omnipresent an actual exiting thing? Can we say that it exists everywhere? And with that being the case, can we say Existence (where Existence = that which is Omnipresent) exists everywhere?
You seem to have a longstanding fondness for fallacies of ambiguity/equivocation - either giving something a different name in the hope that that will somehow change something (as in the above case) or using the same word for two different concepts but using the fact that it's the same word to obfuscate this. You do this with the word "Existence" (variously with an upper or lower case 'E', depending on how much you want to try to make the identity between It and God) to mean two different things, but then claiming things about it based on the fact that those two different usages have the same letters in the same order.

This has been pointed out to you quite a few times. You've ignored it. I guess you'll just keep ignoring and repeating?

What seems crystal clear to me, does not seem crystal clear to you. I have concluded that we cannot find any meaningful common ground with regards to the topic at hand. This is why I stopped discussing the matter with you. You say things have been pointed out to me, and I have pointed things out. We have not found common ground.
Steve3007
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Re: The true solution to Russell's paradox

Post by Steve3007 »

philosopher19 wrote:...We have not found common ground.
Yes, I can see why if two people disagree on fundamentals that there's no point continuing a discussion. But I still find it puzzling that you can't seem to see where you're committing basic fallacies of ambiguity and using words in hopelessly muddled ways.

Still, it was interesting chatting, albeit briefly. All the best, Steve.
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RJG
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Re: The true solution to Russell's paradox

Post by RJG »

philosopher19 wrote:Take x to be the object that exists everywhere (the omnipresent). Is it not the case that x necessarily exists?
Yes, if X exists everywhere, then it necessarily exists.

philosopher19 wrote:Can you have two worlds or universes separated by non-existence? No, therefore one x is omnipresent, and it encompasses all worlds, realities, beings, and so on.
Okay, if this X is omnipresent, then it exists everywhere, agreed.

philosopher19 wrote:All things that exist, actually exist. X itself exists.
Okay, I don't disagree.

philosopher19 wrote:All things that exist, exist as a member of x (as opposed to existing as members of non-existence or outside the omnipresent).
This is where you lose me (or I lose you). How can something logically be a member of itself? - I think what you have actually proved is that X infinitely exists. In other words, since X cannot logically be a member of itself, therefore if it exists, it must 'infinitely' exist.

philosopher19 wrote:Do you agree with this so far?
I agree that, that which exists, has always, infinitely existed; i.e. has never not-existed.
philosopher19
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Re: The true solution to Russell's paradox

Post by philosopher19 »

Steve3007 wrote: March 16th, 2021, 9:35 am All the best, Steve.
Cheers Steve.
philosopher19
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Re: The true solution to Russell's paradox

Post by philosopher19 »

RJG wrote: March 17th, 2021, 7:36 am This is where you lose me (or I lose you). How can something logically be a member of itself? - I think what you have actually proved is that X infinitely exists. In other words, since X cannot logically be a member of itself, therefore if it exists, it must 'infinitely' exist.
I don't mean a member of itself like a box containing itself and yet being outside of itself at the same time. I mean something like this:

All existents are contingent on the Omnipresent for their existing (including the Omnipresent Itself because It is an existent. So the Omnipresent is self-contingent. Only the Omnipresent is self-contingent with regards to existing. All other things are non-self contingent precisely because they are contingent on the Omnipresent for their existing). If X (the Omnipresent) did not exist, then no existent would exist. Thus, all existents are dependent on X for their existing. In this sense (in the sense of existing), all existents are members of X, including Itself.
Fellowmater
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Re: The true solution to Russell's paradox

Post by Fellowmater »

Though I've understood the logic behind's Russell's paradox for long enough, I have to admit I've never really understood why mathematicians and mathematical historians thought it so important. Most of them mark its formulation as an epochal moment in mathematics, it seems to me. To my uneducated self, Russell's paradox seems almost like a trick question, like a child asking what the largest organism on Earth is, and getting back an answer talking about a giant fungus.
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