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 »

Marvin_Edwards wrote: December 10th, 2020, 11:11 pm
philosopher19 wrote: December 10th, 2020, 9:13 pm


Is space not an existing thing?
Space is a reference to an area of emptiness. We can measure the empty area by measuring the distance between the things that surround it. That gives it size and shape, so it might appear like a thing, but it is not a thing, it is nothing.
I don't understand how something can have size and shape, yet be nothing or not a thing at the same time. More specifically, I don't see how two things can be separated by nothing, for us to be able to measure the distance between them. To me, if they are separated by nothing, then nothing is separating them. If nothing is separating them, then nothing is separating them (which implies they are one or stuck together). Thus, no measurement can be taken in relation to their separation as there is nothing to measure between them, because there is nothing separating them.
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Re: The true solution to Russell's paradox

Post by Marvin_Edwards »

philosopher19 wrote: December 11th, 2020, 5:49 am
Marvin_Edwards wrote: December 10th, 2020, 11:11 pm

Space is a reference to an area of emptiness. We can measure the empty area by measuring the distance between the things that surround it. That gives it size and shape, so it might appear like a thing, but it is not a thing, it is nothing.
I don't understand how something can have size and shape, yet be nothing or not a thing at the same time. More specifically, I don't see how two things can be separated by nothing, for us to be able to measure the distance between them. To me, if they are separated by nothing, then nothing is separating them. If nothing is separating them, then nothing is separating them (which implies they are one or stuck together). Thus, no measurement can be taken in relation to their separation as there is nothing to measure between them, because there is nothing separating them.
If they are separated by nothing, then no "thing" is between them, and yet they are separated by distance.
philosopher19
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Re: The true solution to Russell's paradox

Post by philosopher19 »

Marvin_Edwards wrote: December 11th, 2020, 8:16 am
philosopher19 wrote: December 11th, 2020, 5:49 am

I don't understand how something can have size and shape, yet be nothing or not a thing at the same time. More specifically, I don't see how two things can be separated by nothing, for us to be able to measure the distance between them. To me, if they are separated by nothing, then nothing is separating them. If nothing is separating them, then nothing is separating them (which implies they are one or stuck together). Thus, no measurement can be taken in relation to their separation as there is nothing to measure between them, because there is nothing separating them.
If they are separated by nothing, then no "thing" is between them, and yet they are separated by distance.
Is space not a thing?
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Terrapin Station
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Re: The true solution to Russell's paradox

Post by Terrapin Station »

philosopher19 wrote: December 10th, 2020, 5:05 pm
Terrapin Station wrote: December 10th, 2020, 3:56 pm
No, it isn't. Some utterances are noncognitive. They're not true or false. Fiction is one category of such utterances. But fiction can be inconsistent (relative to other things said in the fiction).

If something in fiction is inconsistent, then you know that thins is false.
I write a novel in which I say on page four that Joe Smith is married.

Then on page twenty-four I say that he's a bachelor, and I say this simply because I forgot the characteristics I gave my character.

It's not true or false that Joe Smith is married or a bachelor, because there is no Joe Smith. It's simply something I made up. It's inconsistent--because I'm saying that he's married and then I'm saying that he's not (without intending some change over time in the character, etc.--again, I simply forgot what I said), but it's not true or false. It's noncognitive.
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Re: The true solution to Russell's paradox

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In that situation, if you want to claim that it's either true/false that Joe Smith is/isn't married, what would you say makes it true/false?
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Re: The true solution to Russell's paradox

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Terrapin Station wrote: December 12th, 2020, 9:37 am It's not true or false that Joe Smith is married or a bachelor, because there is no Joe Smith. It's simply something I made up. It's inconsistent--because I'm saying that he's married and then I'm saying that he's not (without intending some change over time in the character, etc.--again, I simply forgot what I said), but it's not true or false. It's noncognitive.
As far as we know, Joe isn't a person that is as real as you and me. But there is a truth in relation to whether your story is consistent (not at odds with reason), or inconsistent/paradoxical (at odds with pure reason). If your story is consistent, then it is at least a hypothetical possibility. As in there may be a parallel universe or world wherein which your story (provided that it has 0 absurdities/paradoxes/inconsistencies in it), is, was, or will be actually made as real as you and me. Where your story is paradoxical, no such thing is possible at all. It is definitively false of all of Existence.

Your story can only be a story if it consists of semantics. The same is true for any given theory proposed. If I propose to you a theory about triangles, then I am proposing something in relation to the semantic of triangles. If the theory I propose contradicts this semantic (for example, I say something like triangles can have four sides under special conditions that we make up), then my theory is definitely wrong in relation to the semantic of triangle. So it's not a triangle theory. Triangle theory (or a theory on triangles) must be in line with the semantic of triangle.

Set theory is the same. Any set theory must be in line with the semantic of set. If the theory is inconsistent/paradoxical with regards to the semantic of set, it must be rejected as being a theory of sets. There is only one theory of sets that is not contradictory. The one that Frege proposed. He just couldn't deal with Russell's confusion with regards to semantics and labels, which ended up confusing him as well. So he gave up, and so did all famous philosophers and mathematicians who followed him.
In that situation, if you want to claim that it's either true/false that Joe Smith is/isn't married, what would you say makes it true/false?
If something is inconsistent/paradoxical/irrational, it is definitely false. As in there is no way it is true of Existence. If your story about John was consistent, then it is at least a hypothetical possibility. As in it may be the case that John as you describe him, comes to be as real as you and me. Another Big Bang or another world as real as ours, is not hypothetically impossible. A married bachelor is hypothetically impossible. To deny that Existence is the set of all existing things, or to deny the set of all sets as being semantically consistent with regards to the semantic of set, is hypothetically impossible/paradoxical (which is what the rejection of Frege's set theory amounts to). I don't know if the following will be of interest to you. One is about the infallible and indubitable nature of semantics, the other is about how Existence must be actually Infinite:

https://philosophyneedsgod.wordpress.co ... semantics/

https://philosophyneedsgod.wordpress.co ... at-exists/
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Re: The true solution to Russell's paradox

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philosopher19 wrote: December 13th, 2020, 7:45 am
Terrapin Station wrote: December 12th, 2020, 9:37 am It's not true or false that Joe Smith is married or a bachelor, because there is no Joe Smith. It's simply something I made up. It's inconsistent--because I'm saying that he's married and then I'm saying that he's not (without intending some change over time in the character, etc.--again, I simply forgot what I said), but it's not true or false. It's noncognitive.
As far as we know, Joe isn't a person that is as real as you and me. But there is a truth in relation to whether your story is consistent (not at odds with reason), or inconsistent/paradoxical (at odds with pure reason). If your story is consistent, then it is at least a hypothetical possibility. As in there may be a parallel universe or world wherein which your story (provided that it has 0 absurdities/paradoxes/inconsistencies in it), is, was, or will be actually made as real as you and me. Where your story is paradoxical, no such thing is possible at all. It is definitively false of all of Existence.
Which is all irrelevant to whether it's true that Joe Smith is married or not. Before we go on, do you understand now why it's not true or false that Joe Smith is married?
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Re: The true solution to Russell's paradox

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Terrapin Station wrote: December 13th, 2020, 9:01 am Which is all irrelevant to whether it's true that Joe Smith is married or not. Before we go on, do you understand now why it's not true or false that Joe Smith is married?
In your story, if Joe is married, then it is true that the Joe in your story is married. If he is a bachelor, then that is the truth. What cannot be true, is that Joe is both married and a bachelor at the same time. If your story, or any theory that you propose, or anything that you say is not paradoxical/inconsistent or meaningless gibberish, then what you say is definitely true. Try saying something that is non-paradoxical, yet not true at the same time. I will demonstrate to you that this is impossible.

Should we not make a distinction between that which is definitely false (hypothetical impossibilities/absurdities/paradoxes...things that don't and can't ever exist or be true), and that which is coherent and meaningful (that which is consistent and at least a hypothetical possibility?

Is a theory of sets that is definitely contradictory/paradoxical, not definitely false?
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Re: The true solution to Russell's paradox

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philosopher19 wrote: December 13th, 2020, 12:49 pm
Terrapin Station wrote: December 13th, 2020, 9:01 am Which is all irrelevant to whether it's true that Joe Smith is married or not. Before we go on, do you understand now why it's not true or false that Joe Smith is married?
In your story, if Joe is married, then it is true that the Joe in your story is married.
That's not the question I'm asking you though. I'm asking you if you understand why it's not true or false that Joe Smith is married (not "in the story") if I write a novel about Joe Smith (and give his marital status).
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Re: The true solution to Russell's paradox

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Terrapin Station wrote: December 13th, 2020, 1:50 pm
philosopher19 wrote: December 13th, 2020, 12:49 pm

In your story, if Joe is married, then it is true that the Joe in your story is married.
That's not the question I'm asking you though. I'm asking you if you understand why it's not true or false that Joe Smith is married (not "in the story") if I write a novel about Joe Smith (and give his marital status).
Yes, I understand your point. But I think you are confusing true/false of our reality, to true/false of all of Existence. Joe is in your story. This is true. Whether there is your Joe in our reality, is unknown to us (unless you have defined him in such a way as to make it hypothetically impossible for him to be in our reality. Then we can say with certainty, that Joe does not exist in our reality). Where you define Joe as a married bachelor, then Joe certainly does not exist in our reality, nor does he or will he exist in any reality in any way, shape, or form.

Do you understand my point that if something is absurd or paradoxical, it is definitely false? I have answered your question, but you have not yet answered this question.

Again, it doesn't matter if someone made x or ZFC up. If x or ZFC is absurd/paradoxical, it's wrong. It cannot be representative of Existence or reality in any way shape or form. If you make a up a theory or story, and in your story Joe is both married and a bachelor, then your story can't even be a hypothetical possibility. If it's not absurd, then it's at least a hypothetical possibility.

Regarding sets, only Frege's set theory is non-paradoxical. Only Frege's set theory is not false. Do you understand my point?
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Re: The true solution to Russell's paradox

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Marvin_Edwards wrote: December 2nd, 2020, 12:08 pm
detail wrote: December 2nd, 2020, 10:40 am

Sorry i interchanged categories with classes in settheory. If you replace the word category with class you will see , that my remark in Zermelo-Fraenkels set/class theory works. See for https://en.wikipedia.org/wiki/Class_(set_theory)
Couple of interesting things in the article. One is that its suggests Russel's paradox is escaped by classes because classes cannot themselves have classes, but the notion of a "proper" class immediately splits classes into proper classes and improper classes. So, we have all classes which include proper classes and improper classes, resulting in the notion of classes that contain classes. Second, the word "conglomerate" was introduced in order to provide something to contain classes.

If set theory wants to formally define a hierarchy of collection terms that's fine. But Russel's paradox is resolved by the rule that a collection cannot be a member of itself.

I think that most people work with terms of collection outside of formal set theory. We have place settings for dinnerware. We have universities that contain colleges that contain classes. And so on.
Well , the problem for proper classes and improper classes , is that both classes are classes but you do not know if they are sets, one is for certain no set , the proper classes . It should be taken for granted that both are no sets , unless the introduction of the word class would be led to absurdity.
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Re: The true solution to Russell's paradox

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philosopher19 wrote: December 13th, 2020, 7:11 pm Yes, I understand your point. But I think you are confusing true/false of our reality, to true/false of all of Existence. Joe is in your story.
What would a "our reality"/"of all existence" distinction be here? Are you talking about a epistemology/ontology distinction?
This is true. Whether there is your Joe in our reality, is unknown to us (unless you have defined him in such a way as to make it hypothetically impossible for him to be in our reality.
You're thinking that we might write a fiction where the fiction somehow turns out to accidentally correspond to real-world entities, etc.?
Do you understand my point that if something is absurd or paradoxical, it is definitely false? I have answered your question, but you have not yet answered this question.
I understand that you're claiming that, but it's mistaken. I'm explaining to you why it's mistaken. You apparently don't buy the category of "noncognitive." You'd have to explain why you think it's an illegitimate category.
Again, it doesn't matter if someone made x or ZFC up. If x or ZFC is absurd/paradoxical, it's wrong. It cannot be representative of Existence or reality in any way shape or form.
And indeed sets are not representative of existence or reality. Sets are something we make up. We invent them just like we invented hobbits, vampires, etc.
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Re: The true solution to Russell's paradox

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Terrapin Station wrote: December 14th, 2020, 8:12 am What would a "our reality"/"of all existence" distinction be here? Are you talking about a epistemology/ontology distinction?
You're thinking that we might write a fiction where the fiction somehow turns out to accidentally correspond to real-world entities, etc.?
Provided that the fiction is not paradoxical/absurd, then absolutely, yes. Can you say no to this?
I understand that you're claiming that, but it's mistaken. I'm explaining to you why it's mistaken. You apparently don't buy the category of "noncognitive." You'd have to explain why you think it's an illegitimate category.
What do you mean by noncognitive?

To me, that which is non-cognitive, is that which is meaningless. Unknowns to me such as a 20th sense are meaningless. Absurdities/paradoxes such as a married bachelor or a set that contains all sets that are not members of themselves that is itself not a member of itself, are also non-cognitive/ meaningless.
And indeed sets are not representative of existence or reality. Sets are something we make up. We invent them just like we invented hobbits, vampires, etc.
We can't just throw letters, or words, or concepts together randomly and hope they instantiate meaning. Dajilf is a a type of round square that can sit and stand at the same time. I just made up Dajilf. Despite this, somehow, Dafjil is paradoxical, whilst hobbits and vampires (which someone else came to the semantic of by probably combining other semantics/concepts in a coherent/rational manner) are not absurd/paradoxical. Do you not see the distinction between:

That which is definitively false (married bachelors, a set that contains all sets that are not members of themselves that is itself not a member of itself)
And that which is not definitively false (vampires, hobbits, pink trees, humans, sets, lists, etc.) They are not definitely false because they are either as real as you and me, or they can come to be as real as you and me, or less real like in dreams or video games. You cannot have a round square or married bachelor in a dream or a video game. You can have vampires or hobbits. For all we know, vampires or hobbits may be on our planet, or somewhere in Andromeda (but that's pointless speculation). Importantly, they are not definitely false of Existence.

Are absurdities/paradoxes definitely false of Existence or not?
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Re: The true solution to Russell's paradox

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An interesting earlier exchange about the category "noncognitive", meaning propositions that are neither true nor false:
philosopher19 wrote:Do you understand my point that if something is absurd or paradoxical, it is definitely false?
Terrapin Station wrote:I understand that you're claiming that, but it's mistaken. I'm explaining to you why it's mistaken. You apparently don't buy the category of "noncognitive." You'd have to explain why you think it's an illegitimate category.
philosopher19 wrote:What do you mean by noncognitive?

To me, that which is non-cognitive, is that which is meaningless. Unknowns to me such as a 20th sense are meaningless. Absurdities/paradoxes such as a married bachelor or a set that contains all sets that are not members of themselves that is itself not a member of itself, are also non-cognitive/ meaningless....

...Are absurdities/paradoxes definitely false of Existence or not?
Philosopher19's apparent inability to get his head around the idea that the answers to some questions can be neither true nor false (as shown by his confusion in the last post as to whether he regards the examples being discussed as meaningless or false, and his apparent view that they can somehow be both) sheds some light on more recent discussions in the "Pure reason dictates Existence/God is Perfect" topic.
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Re: The true solution to Russell's paradox

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Another interesting error that shares a lot with the errors made in the other topic:
philosopher19 wrote:All existing things exist. They cannot exist in non-existence. They all exist in something. Call this thing Existence. Call the set of all existing things, Existence. Existence is the set of all existing things (including Itself because it Itself exists).
Using the abstract concept of a set to collectively refer to all existing real things (a set sometimes labelled "universe" or similar), that abstract construct is above referred to by the word "Existence" and is then reified and thereby falsely claimed to itself be a thing and therefore be a member of itself. These are very similar to the errors made by RJG in topics in which he defended the notion that the universe can be known by logical necessity to be infinitely large and old. I remember lots of fruitless discussions there about sets.
Terrapin Station wrote:You seem to be conflating set theory with ontology. :?: :?: :?:
Quite.
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