Logical deduction (religion, the PoE)

[dybmh]

Please read the whole reply before you respond it's not too long. In case you don't, I'll put the important bits right here at the top.

1. I am not defining a naive set, because a naive set does not have a way to establish hierarchy, inheritance, and relevance. Naive set theory was developed in the 1600s, more modern set theories have these capabilities, at least hierarchy and inheritance along with other axioms to permit the set of all sets.
2. The examples of org charts, family trees, etc, are good examples because the topic is all-inclusive concepts. The periodic table does not need drops of mercury to be all inclusive of the concepts. And. These examples ARE the instances of all the concepts they contain. That is their identity.
3. Literal Infinity does include the concept of "all concepts which do not contain themself." These concepts can be listed, and a copy of that list can be literally stored in Literal Infinity.
4. Literal Infinity does include the concept of itself and all its contents. All of these concepts can be listed, and a copy of that list can be literally stored in Literal Infinity.

That refutes all you arguments.

Now here's a detailed response to what you said:

You specifically brought up religion and the problem of evil. What we are talking about is an abstract concept here, that has no direct connection.

My friend, that's the topic of the thread. That's the purpose. I am attempting to solve the problem of evil. This is step 1. I've mentioned this before, and I think it's at the very beginning of our dialogue.

I've actually explained exactly why it applies to the concept of all concepts. What's more the whole purpose of your LI is to include everything. That means that you cannot have any further logical restrictions, such as those imposed by formal set theories. It is a superset of the archetypal naive set of all sets.

No, all I need is one example of a significant difference between a naive set and the structure I've defined to invalidate the comparison. I gave you that example. I see you didn't quote it. I also brought a link to "Functional Compostion" which is root of the method for producing a set of all sets in more modern set theories.

Naive set theory, which was developed in the 1600s, does not have any sequencing. That means it cannot produce a hierarchy, it cannot produce inheritance. It also has no concept of relevance. It cannot do what any other org chart can do. It cannot do what any other database can do. That means the objection based on "what you're defining is exactly like a set" is a fail.

The concept of all concepts is a concept itself, so must contain itself, otherwise it doesn't include all concepts. That's what leads directly to Russell's paradox.

Not in the structure I have defined. It doesn't need to. But it can. Why? because it's not a naive set, it has tools for establishing a hierarchy, inheritance, and relevance.

None of those have anything like the same problem. Seriously, if you can't see that then no wonder you can't see the problem.

They don't have the same problem because they have a way for establishing a heirarchy, inheritance, and relevance.

None of them are instances of the things they contain. Seriously, if you can't see that distinction, this is pointless.

Yes they are. That is their definition. They ARE the instance of all the concepts they contain.

I was going to go through the rest, but I'm actually going to stop there, because this really, really is literally pointless if you can't see that distinction.

Sounds like you've run out of arguments. What you're missing is WHY each of the examples are all-inclusive.

Hierarchy, Inheritance, Relevance

So, can you really not see that the periodic table isn't an element, a family tree isn't a family member, an organisation chart isn't a position (or a person), a directory structure isn't a directory, and so on,

Let's step back a moment. Respectfully, seriously, if take a look at the very first part of this reply, you'll see the the context had been lost again. And that's OK. It's been a really good deep convo, but it's time to refocus. This is BEFORE creation. None of the things in the structure that I have defined exist yet. We are talking about concepts.

So, no, the periodic table does not need drops of mercury in it, or a lithium tank in it. We're talking about concepts. Not literal "things". OK? There are no things. That hasn't happened yet. That's why these examples are good. They don't need the literal objects included. I have been saying they are all inclusive of the concepts included in them.

I am defining an all inclusive conglomerate of concepts. And all concepts are included. You need to bring one that isn't. The concept of all concepts that don't contain themselves is included, accuratley. And I can list those concepts. And I can store a copy of those results literally included in the infinite relational database.

Literal Infinity also IS the instance of itself and all it contains. But if you need a replica, that can happen too. I think it's silly to diplicate it, but if it's important to you, it can be done. You need to show me it can't be done. I already showed you how it can be done.

Just because it doesn't work in a naive set, doesn't matter, because a naive set doesn't have a way to establish:

Hierarchy, Inheritance, and Relevance

but the concept of all concepts is a concept?​

Yes, it's a simple concept to include in literal infinity. Regardless of how you choose to define the word "include". It's included as a concept defined by attributes+relationships. And if you need an exact replica of all the contents spawned inside itself, that is also possible. I dont think it's needed, but if you do, then poof. Infinite memory permits it.

 

[ratiocinator]

1. I am not defining a naive set, because a naive set does not have a way to establish hierarchy, inheritance, and relevance. Naive set theory was developed in the 1600s, more modern set theories have these capabilities, at least hierarchy and inheritance along with other axioms to permit the set of all sets.
2. The examples of org charts, family trees, etc, are good examples because the topic is concepts. The periodic table does not need drops of mercury to be all inclusive of the concepts.
3. Literal Infinity does include the concept of "all concepts which do not contain themself." These concepts can be listed, and a copy of that list can be literally stored in Literal Infinity.
4. Literal Infinity does include the concept of itself and all its contents. All of these concepts can be listed, and a copy of that list can be literally stored in Literal Infinity.

That refutes all you arguments.

1. You haven't established a hierarchy and there is nothing at all to stop you doing so within naive set theory. That's the point; you can include anything, and that's exactly what you need for LI. You couldn't make it all-inclusive if you couldn't include anything. That's why it basically has to be naive set theory.
2. Missed the point yet again. Concept of all concepts is a concept. Periodic table isn't an element. The first contains itself, the second doesn't. The is really, really easy!
3. Then it will be inconsistent.
4. Ditto.

 

[dybmh]

You haven't established a hierarchy there is nothing at all to stop you doing so within naive set theory.

Yes, I have. Attributes+relation pairs define objects. Objects go into categories, categories nest into other categories. Each category becomes more and more general, until at the top there is one all inclusive conglomerate. I accomplish this by using an infinite relational database to define the structure and produce the results of any category.

I listed 3 things that are missing in naive set theory. You're only focusing on one. If there is nothing stopping me from defining a conglomerate of all concepts in naive set theory, then I guess your objections are none.

That's the point; you can include anything, and that's exactly what you need for LI. You couldn't make it all-inclusive if you couldn't include anything. That's why it basically has to be naive set theory.

I am including everything, anything, and, technically, "nothing" the concept is included too.
And you haven't given any reasons why it MUST be naive set theory.
Your claim, your burden: "it basically has to be naive set theory" needs reasons.

Missed the point yet again. Concept of all concepts is a concept. Periodic table isn't an element. The first contains itself, the second doesn't. The is really, really easy!

The periodic table is a concept.

Literal infinity is more than a list of all concepts.
The concept "concept of all concepts" is included in Literal Infinity.
The concept of "Literal Infinity" is included in Literal Infinity.

You need to find something, anything which is not included.

Then it will be inconsistent.
Ditto.

No, they're not inconsistent. You made a semantic argument which was fallatious.

Listing Literal Infinity would be a "FIND / -print".
You need to find an inconistency in this.

Listing all the concepts which do not contain themself would be "SELECT * WHERE CONTAINS-ITSELF=FALSE.
You need to find an inconsistency in this.

I can produce results from my structure that you cannot in naive set theory.
Even if you bring a literal contradiction, I can include that too.

---

So you have made 3 claims, you have 3 burdens:

1) "it basically has to be naive set theory"
2) listing "all concepts that don't include themself" will be inconsistent
3) listing "all concepts" will be inconsistent

Please start with #1. Yes I know that #3 is only because of #2. So you're really only making 2 arguments.

 

[ratiocinator]

The periodic table is a concept.

But not the concept of an element.

The periodic table is not something that belongs in the periodic table.

The same goes for all the other examples you listed. They are all defined in such a way that they don't belong among their contents. None of them are instances of the things they are supposed to contain.

You idea of LI is that it is defined to include every single idea and concept that has ever existed, will ever exist, or could ever exist - that's basically what your procedure was looking for - so it very much does belong among its contents because it is a concept that is actually in human minds now. It is an instance of the things it is supposed to contain.

I'm happy to go onto the rest of what you said but there is no point unless I can succeed in communicating this difference to you (if only because it's directly relevant to some of them). This is the very first important point in the very first stage of your argument. If we can't agree about it, we are wasting our time.

[Edited for typos]

 

[dybmh]

You idea of LI is that it is defined to include every single idea and concept that has ever existed, will ever exist, or AND could ever exist - that's basically what your procedure was looking for - so it very much does belong among its contents because it is a concept that is actually in human minds now. It is an instance of the things it is supposed to contain.

Literal Infinity as I have defined it does include "every single idea and concept that has ever existed, will ever exist, and could ever exist".
Literal Infinity also includes their compliments and negations: "every single idea and concept that has never existed, will never exist, or could not ever exist"

Even if we disagree about the relevance of the other examples, what I said above is true. You challenged the idea in several ways, and each time I was able to include the concept you described.

 

[mikkel_the_dane]

Literal Infinity as I have defined it does include "every single idea and concept that has ever existed, will ever exist, and could ever exist".
Literal Infinity also includes their compliments and negations: "every single idea and concept that has never existed, will never exist, or could not ever exist"

Even if we disagree about the relevance of the other examples, what I said above is true. You challenged the idea in several ways, and each time I was able to include the concept you described.

Literal Infinity is an idea included in "every single idea and concept that has ever existed, will ever exist, and could ever exist", unless you can explain how it is not an idea made up of the concepts of literal and infinity.

 

[dybmh]

Literal Infinity is an idea included in "every single idea and concept that has ever existed, will ever exist, and could ever exist", unless you can explain how it is not an idea made up of the concepts of literal and infinity.

Yes, it IS included, and I showed how it is included, and I showed there is no paradox.

 

[mikkel_the_dane]

Yes, it IS included, and I showed how it is included, and I showed there is no paradox.

That is beyound my pay grade. But indeed if you have done to, you should write it up and submit it to a math/logic journal.

 

[dybmh]

That is beyound my pay grade. But indeed if you have done to, you should write it up and submit it to a math/logic journal.

I think Godel already did it. And from what I can tell, he did it in the same way I did it. He established rules of hierarchy and rules which flagged the paradox as "non-constructable". Then plowed forward. The only difference is, I include the paradox as a paradox. It's in the category of "paradoxes" where he excluded it altogether. And that makes sense because he only wanted to work with existence. But I'm talking about pre-existence.

And this is why Godel's set theory includes "the set of all sets". And so does Literal Infinity.

 

[dybmh]

That is beyound my pay grade. But indeed if you have done to, you should write it up and submit it to a math/logic journal.

I also want to say: it's extremely valuable to get the sort of feedback I'm getting in this thread. I had never considered the semantic issues / pitfalls that are inherent in this idea of literal infinity.

Anyway, it's kind of a silly, no-brainer concept. Literal infinity = everything that can exist + everything that can't exist? Duh. Of course it does.

That would be a rather short journal article.

 

[mikkel_the_dane]

I think Godel already did it. And from what I can tell, he did it in the same way I did it. He established rules of hierarchy and rules which flagged the paradox as "non-constructable". Then plowed forward. The only difference is, I include the paradox as a paradox. It's in the category of "paradoxes" where he excluded it altogether. And that makes sense because he only wanted to work with existence. But I'm talking about pre-existence.

And this is why Godel's set theory includes "the set of all sets". And so does Literal Infinity.

Yeah, you are doing philosphy since you include existence. That belongs to metaphysics, ontology and epistemology as much as logic.

In effect you are one of those who do postive logic as if that is all there is to being a human.

 

[mikkel_the_dane]

I also want to say: it's extremely valuable to get the sort of feedback I'm getting in this thread. I had never considered the semantic issues / pitfalls that are inherent in this idea of literal infinity.

Okay, I can refute your idea, but that is not logic that you would accept, because you do logic and the rest of philsophy different than me.

 

[dybmh]

Yeah, you are doing philosphy since you include existence. That belongs to metaphysics, ontology and epistemology as much as logic.

In effect you are one of those who do postive logic as if that is all there is to being a human.

The challenge to my idea is from strict logic; so that is where the argument is happening.

 

[dybmh]

Okay, I can refute your idea, but that is not logic that you would accept, because you do logic and the rest of philsophy different than me.

No, please. I want to hear your refutation. I promise I will have an open mind, and if it's beyond me I'll admit it.

 

[ratiocinator]

Literal Infinity as I have defined it does include "every single idea and concept that has ever existed, will ever exist, and could ever exist".
Literal Infinity also includes their compliments and negations: "every single idea and concept that has never existed, will never exist, or could not ever exist"

Yes, so, since it is an idea or concept itself, it must contain itself.

This is the fundamental difference between all the other examples and LI. This is a characteristic that LI shares with the classic universal set or set of all sets; they must be elements of themselves.

I can't emphasis too much how important this is to the arguments that follow.

Even if we disagree about the relevance of the other examples, what I said above is true. You challenged the idea in several ways, and each time I was able to include the concept you described.

No, you are still trying to avoid the point or use some kind of ad hoc programming hack to get round it. However, it really isn't worth getting into that until you've understood the above point.

I think Godel already did it. And from what I can tell, he did it in the same way I did it.

What on earth do you think Gödel did that was remotely like what you've proposed here?

 

[dybmh]

Yes, so, since it is an idea or concept itself, it must contain itself.

There is a semantic issue here. I am defining an all-inclusive structure. Include =/= contain

This is the fundamental difference between all the other examples and LI. This is a characteristic that LI shares with the classic universal set or set of all sets; they must be elements of themselves.

"element of themselves" = "contains"
"include" =/= "contain"

I can't emphasis too much how important this is to the arguments that follow.

I understand.

What on earth do you think Gödel did that was remotely like what you've proposed here?

Constructible universe - Wikipedia

en.m.wikipedia.org

​

L can be thought of as being built in "stages" resembling the construction of von Neumann universe, V. The stages are indexed by ordinals. In von Neumann's universe, at a successor stage, one takes Vα+1 to be the set of all subsets of the previous stage, Vα. By contrast, in Gödel's constructible universe L, one uses only those subsets of the previous stage that are:​

​

definable by a formula in the formal language of set theory,​

with parameters from the previous stage and,​

with the quantifiers interpreted to range over the previous stage.​

There's a hierachy which inherits parameters and quantfiers from the previous stage and excludes the invalid paradoxes. But again, what I'm saying is a simple concept: Literal Infinity = all that exists + all that doesn't exist.

 

[mikkel_the_dane]

The challenge to my idea is from strict logic; so that is where the argument is happening.

No, please. I want to hear your refutation. I promise I will have an open mind, and if it's beyond me I'll admit it.

Okay, it is simple. Combine cause and effect, ontology as something is with the law of non-contradiction. I will use Aristotles' version and remember it is also laungage.
"It is impossible that the same thing belong and not belong to the same thing at the same time and in the same respect."

Okay, a thing is at a given time (and space) as in a respect. Respect is in a sense or property. I.e. e.g. the cat at a given time and space is the respect of being multicolored. In general for a claim of at a given time and space X is Y. Or even shorter P as the proposistion of X is Y or a similar case for phrasing a proposition.

So now comes the falsifaiction of all cases of X is Y for all times and spaces including human behaviour as caused by a given human.
If you say something to the effect of that everthing can be done for all respects of X is Y, you are reducing all respects down to Y. It is caused by you saying that and the refutation is if I can do non-Y. It is that simple.
So if you say only the logical exist, you are saying that all cases of existeince is logic as you think it in a respect and I just answer no!

You have done an overreduction of an respect, namlely that we must all think like you and I just think differently at a different time and space in a different respect.
It is not that the world is not logical as such. It is that the world is not in one respect for all time and space.

 

[ratiocinator]

"element of themselves" = "contains"
"include" =/= "contain"

What do you think the distinction you are making is? Conceptually, both LI and the universal set are elements of themselves. They have to be, otherwise their definitions would not be met.

Constructible universe - Wikipedia

en.m.wikipedia.org

So how does that relate to what you've said here?

 

[dybmh]

So now comes the falsifaiction of all cases of X is Y for all times and spaces including human behaviour as caused by a given human.
If you say something to the effect of that everthing can be done for all respects of X is Y, you are reducing all respects down to Y. It is caused by you saying that and the refutation is if I can do non-Y. It is that simple.

I'm not saying "for all cases of X is Y" I'm saying "for all cases of X is Y or Not Y"

"It is impossible that the same thing belong and not belong to the same thing at the same time and in the same respect."

Is it the "+" sign that's making it look like I'm violating this?

When I write "Literal Infinity = all that exists + all that doesn't exist", do you think I should replace the "+" with "or"?

 

[dybmh]

What do you think the distinction you are making is? Conceptually, both LI and the universal set are elements of themselves. They have to be, otherwise their definitions would not be met.

The distinction is the difference between ∈ and ⊂.
A concept is not literally the thing it describes. It is the opposite of literal. So, when the concept of all concepts is considered the literal "containment" of the all-inclusive is not needed. This is because it is a concept, and a concept by definition is an abstraction, therefore an abstraction of itself is permitted.

This abstraction is "inclusion". It means "fully represented in" which is defined in set theory as a subset relationship which is different than literal membership. Inclusion can mean the same thing as contain, but it doesn't need to, especially in the context of concepts. Either way, a concept is an abstraction, so the "containment" is also abstract. I've been using "inclusive", so for me "include" is the correct word to use. it doesn't matter as long as we agree on what a concept is.

But I am not defining a set, as you have heard me say repeatedly.

So how does that relate to what you've said here?

It doesn't directly. That was a reply to a different person.