Logical deduction (religion, the PoE)

[dybmh]

There's 3 replies in total in this batch. None of the answers are too long. Just a few sentences, no multi-paragraph explanations. I needed to break it up because I reposted the definition for literal infinity.

As usual, please read all three posts before replying. Thank you,

As I pointed out, the whole point was to add elements that weren't in the original set, thereby getting a set that was the same cardinality but a different set. Hence demonstrating the irrelevancy of infinity + something else = infinity and the confusion you seem to have between contents and cardinality.

By definition, everything is already included. If you want to find a flaw in what I said, you need to find that flaw with a member of the infinite set. Not with a non-member.

As I said, relationships make exactly no difference, A relationship is just another concept. You seem to think that making it a relational database makes a difference but you have provided no logic to support the idea.

They aren't just concepts in categories.

But it does. You can have two entirely disjoint sets with the same (infinite) cardinality.

Sure, those are different sets. And cardinalty is a quantity. So what? My turn: Non-sequitur!
In each of the examples you brought, regardless of the infinite set chosen. The relationship of the member of the set to the entire set is absolutely insignficant.

I'm not arguing that functions sometimes produce the same result, or that different sets can't do the same thing, or different things, or that somehow different sets cannot have the same countable-infinite cardinality.

The number of dimensions make no difference at all. The cardinality of ℕⁿ is the same as the cardinality of ℕ, the same is true of ℝ, or ℂ, for that matter.

Non-sequitur. The quantity of the cardinalities of different sets doesn't matter. It's completely irrelevant. I am talking about the relationship between a member of the infinite set with the totality of the same infinite set. When that is a simple quantity, then the example is also simple. When this same idea is generalized, it gets a little more complicated, and the member is a similarity/difference compared to something which is literally all-inclusive.

But it's all the same idea.

 

[dybmh]

That's a bit of a problem then, because what we need is a proper and rigorous definition of this 'literal infinity' - otherwise we have nothing that can be analysed and properly considered.

I gave you the definition. Here it is again. It's a method.

Spoiler: a method for producing literal infinity

• has lived, is living, will live, and could possibly live for a list of items of all the physical objects, physical actions, ideas, and symbols they can imagine

• review the list of items eliminating duplicates

• fully define each item in the list with a series of attributes

• review the list of attributes removing duplicates

• fully define each of these attributes with a list of attributes

• combine the list of attributes and remove duplicates

• repeat steps 5 and 6 until no new attributes are being added to the list, only duplicates

• survey each and every person that has lived, is living, will live, and could possibly live asking them to review the list of attributes looking for missing attributes

• review the list of missing attributes removing duplicates

• repeat steps 5 and 6 until no new attributes are being added only duplicates

• make a list of the compliments/negations of every item in the list

• fully define each of these compliments/negations using attributes

• repeat steps 5 and 6 until no new attributes are being added only duplicates

• review the list of attributes removing duplicates

• survey each and every person that has lived, is living, will live, and could possibly live asking them to review the list of attributes of the compliments/negations looking for missing attributes

• repeat steps 5 and 6 for the missing attributes

• review the list of attrbutes removing duplicates

• make a list of the compliments/negations of the combined list of attributes

• fully define each of these attributes using attributes and repeat steps 5 and 6 until no new attributes of the compliments/negations are added to the list

• make a list of the compliments/negations of these attributes

• repeat steps 19 and 20 until no new attributes of the compliments/negations and no new compliments/negations of those attributes are added, only duplicates

• remove the combined list of attributes and the corresponding compliments/negations of the attributes and the corresponding attributes of the compliments/negations and the compliments/negations of those attributes removing duplicates

• survey each and every person who has lived, is living, will live, and could live asking them to review this list of attributes of the compliments/negations looking for missing attributes

• review the full list of attributes of the corresponding compliments/negations removing duplicates

• survery each and every person who has lived, is living, will live, and could possibly live asking them to review the list of items, the compliments/negations of the items, the attributes of the items, and the compliments/negations of the attributes looking for similarities and differences

• review the list of similarities and differences removing duplicates

• survery each and every person who has lived, is living, will live, and could possibly live asking them to review the list of similarities and differences looking for similarities and differences between the similarities and differences

• review the combined list of similarities and differences removing duplicates

• repeat steps 27 and 28 until no new similarities and differences are found, only duplicates

• these similarities and differences are called catagories

• fully define each catagory using attributes

• repeat steps 6-24 for these the attributes of the catagories developing a complete list of all the attributes and corresponding compliments/negations of the attributes of the catagories

• review the list of items, their corresponding compliments/negations, attributes, and their corresponding compliments/negations, and catagories removing duplicates

• survery each and every person who has lived, is living, will live, and could possibly live asking them to review the list from the above step looking for relationships between each and every entry in the list

• fully define each relationship using attributes

• repeat steps 6-24 for these attributes of the relationships developing a complete list of all the attributes and corresponding compliments/negations of the attributes of the relationships

• review the list of relationships removing duplicates

• survery each and every person who has lived, is living, will live, and could possibly live asking them to review the list from the above step looking for similarities and differences between each and every relationship

• review this list of of similarities and differences removing duplicates and calling them catagories

• repeat the steps for for fully defining the catagories and relationships using attributes, then repeat the steps looking for catagories and relationships of these attributes, removing duplicates after each iteration.

• Contnue repeating the search for new attributes, compliments/negations, catagories, and relationships until no new items are found, only duplicates

• Make a list of the compliments/negations for each catagory and relationship.

• Fully define each compliment/negation for each catagory and relationship using attributes

• repeat the steps above looking for attributes for the attributes, their corresponding compliments/negations, catagories of these attibutes and corresponding compliments/negations, and relationships and their corresponding compliments/negations, until each of these is fully defined using attributes and no new items are being added, only duplicates

• Do a final review of every physical object, physical action, idea, symbol, catagory, relationship, their corresponding compliments/negations, the attributes which fully define them, the attributes' corresponding compliments/negations, the catagories that define those attributes and their corresponding compliments/negations, the relationships of those attributes and their corresponding compliments and negations removing duplicates

• develop a relational database which includes each item, its full definition of attributes, its compliments and negations, all associated catagories and relationships. Also include each attribute with its full definition of attributes, its complments and negations, all assocaited catagories and relationships. Also include each catagory with its full defintion of attributes, its compliments and negations, all associated catagories and relationships. Also include each relationship, its full definition of attributes, its compliments and negations, its catagories and relationships. Each of these items are tables in the database. Each attribute catagory and relationship is a row in each of the tables. Catagories and relationships are junction tables linking each attribute in many-to-many joins so that all the tables are linked together and the relationships between every row of every table and every other row of every other table is maintained

 

[dybmh]

But how can we tell when you haven't actually defined your concept? If this 'literal infinity' includes every concept, then it will contain itself and you run right into the Russell's paradox.

It's defined above. It's because the "set of all sets", the concept, doesn't have members. "Literal infinity", the concept, doesn't have members. They have attributes and relationships.

Nothing in all this properly defines your concept and none of it resembles a logical argument.

I brought it earlier.

the limit of a/x, where 'a' is an individual relationship or group of relationships of similarities and/or differences, and 'x' is approaching the absolute complete total of all possible similarties and differences that have ever and will ever exist, and 'a' is not 'x'. As 'x' approaches full inclusion, the similarities and differences approach insignificance. If this inclusion is absolutely infinite, then all similarities and differences will be absolutely insignficant.

And you haven't brought a logical disproof. So put your money where your mouth is.

Literal infinity ----> nullification.

Bring a logical disproof.

As I've pointed out, adding relationship changes nothing - a relationship is just another concept.

No, it's more than that in category theory. Signifcance is a relationship. And similarities and differences are relationships. Set theory has no tools for this It only does inclusion/exclusion. In order to show nullifcation, it is the relationship that is zero.

This is the relationship becoming zero: lim(x->∞) a/x AND a=/=x
'a' are the similarities and differences of any member or group of members of 'x'
'x' is the absolutley all inclusive literal infinity defined above

a/x=0

That's nullification. Regardless of whether the member is considered from an inclusive perspective or an exclusive perspective the similarities and differences are insignficant. And from the exclusive perspective they are absolutley insignificant.

No, it isn't. A thought experiment should be logically precise or it's useless.

It is precise. And it's being generalized.

You haven't provided a proper definition.

I did. Please read it again. Or you can simply accept a simple english definition: Absolutely all inclusive. From that, nothing new can be added and we can move on.

Because there is no definition.

You were given one. Now you have it again. The spoiler has the definition of literal infinity. Nullification has the definition of the limit of a/x as x approaches absolute inclusion.

As I said above, adding dimensions literally changes nothing. The set ℚ (rational numbers), which are effectively ordered pairs, has exactly the same cardinality as ℕ. The same goes for ℝ² (ordered pairs of real numbers) and ℝ.

Cardinality is just a quantity. Comparing different sets to each other who happen to have the same cardinality is irrelevant. It all just a quanitity which happens to be the same.

Which isn't the same as 'nullification'.

I know. The absolute nullification happens when the similarities and differences ( the relationships ) of an included member or members of the infinite set is related to the same infinite set. That's nullification.

By defintion this can't happen anyway, because nothing is excluded. But even if that is ignored, nullifcation happens.

Pairs make no difference.

Naturally! And your strawman remains standing as a result.

This is just another, apparently nonsensical, assertion with no supporting logic.

It makes perfect sense. Squares and circles are both shapes. Cats and Dogs are both animals. (1,1) and (2,4) are both in the domain y = x². You're not seeing the relevance, either because you're being stubborn or because you're ignoring the relationship.

It's the relationship between the similarities/differences of the member with inclusive set which is zero.

I'm not. You haven't properly defined 'literal infinity' and you have provided no logic at all for nullification.

I did. Your objections needed rebuttal, and you either forgot or are ignoring the definitions and logic given.

 

[ratiocinator]

By definition, everything is already included. If you want to find a flaw in what I said, you need to find that flaw with a member of the infinite set. Not with a non-member.

You seem to be randomly flipping between talking about standard infinite sets and your own concept of "literal infinite" (which I still think is a confusing name), I'll just use LI for now. In the example I was responding to, you used ℕ (strictly, you actually used {ℕ}, which is a set with one element, that element being the set of natural numbers) and I was making the point that you could add other members to the set to make a different set with the same cardinality. This example really had nothing to do with LI, I was just addressing your frequent use of ∞ + ∞ = ∞ as if this meant that you, generally speaking, couldn't add to an infinite set to get anything different, which you obviously can.

They aren't just concepts in categories.

What's the significant difference? They are concepts in the category of 'relationships'.

Sure, those are different sets. And cardinalty is a quantity. So what? My turn: Non-sequitur!

Again, you seem to be flipping from concept to concept without keeping track. You have made a great deal of this ∞ + ∞ = ∞ throughout as an example of why you can't add to infinity to get anything else, but generally speaking, you obviously can. You may argue that you can't with LI but that is entirely non-standard and just your own idea. You need to be clear what it is you're talking about.

In each of the examples you brought, regardless of the infinite set chosen. The relationship of the member of the set to the entire set is absolutely insignficant.

Now we're suddenly back to nullification - they are infinitesimal which is not the same a non-existent.

You were given one. Now you have it again. The spoiler has the definition of literal infinity.

First, a procedure isn't a definition. Second, and as I explained before, since your procedure involves systematically adding lists of things, I really don't see how it's going to produce anything other than a standard set with cardinality ℵ₀. What you need is a proper, rigorous definition.

Non-sequitur. The quantity of the cardinalities of different sets doesn't matter. It's completely irrelevant.

You're the one who brought up the 2-d plane because you didn't like my 1-d function. If it was irrelevant, why mention it?

I am talking about the relationship between a member of the infinite set with the totality of the same infinite set. When that is a simple quantity, then the example is also simple. When this same idea is generalized, it gets a little more complicated, and the member is a similarity/difference compared to something which is literally all-inclusive.

It's defined above. It's because the "set of all sets", the concept, doesn't have members. "Literal infinity", the concept, doesn't have members. They have attributes and relationships.

And for those of us looking for logic expressed in English or mathematics....?

I brought it earlier.

the limit of a/x, where 'a' is an individual relationship or group of relationships of similarities and/or differences, and 'x' is approaching the absolute complete total of all possible similarties and differences that have ever and will ever exist, and 'a' is not 'x'. As 'x' approaches full inclusion, the similarities and differences approach insignificance. If this inclusion is absolutely infinite, then all similarities and differences will be absolutely insignficant.

And you haven't brought a logical disproof. So put your money where your mouth is.

Literal infinity ----> nullification.

Bring a logical disproof.

See:

Burden of proof (philosophy) - Wikipedia

en.wikipedia.org

You are proposing something (nullification) with is entirely new (as far as I can see) and is contradicted by literally everything else that uses either limit infinity or actual transfinite numbers.. It really isn't up to me to disprove it, the burden of proof is entirely yours. So far, all you have is some hand-waving, using a fairly standard limit process, like here, and some vague and largely irrelevant stuff about ∞ + ∞ = ∞.

The absolute nullification happens when the similarities and differences ( the relationships ) of an included member or members of the infinite set is related to the same infinite set. That's nullification.

It really isn't. That's just making the elements infinitesimal compared to the whole. This is entirely standard and you're trying to force an entirely non-standard interpretation onto it.

[Edited for typos]

 

[dybmh]

Just 1 reply this time. It is rather long. But some of that is due to formatting.

You seem to be randomly flipping between talking about standard infinite sets and your own concept of "literal infinite" (which I still think is a confusing name), I'll just use LI for now. In the example I was responding to, you used ℕ (strictly, you actually used {ℕ}, which is a set with one element, that element being the set of natural numbers) and I was making the point that you could add other members to the set to make a different set with the same cardinality. This example really had nothing to do with LI, I was just addressing your frequent use of ∞ + ∞ = ∞ as if this meant that you, generally speaking, couldn't add to an infinite set to get anything different, which you obviously can.

No. I'm not flipping. I'm just addressing your strawmen in the order that you are presenting them. And I'm saying 1) I'm not defining a set. 2) Even if I were, the objection is invalid.

When I say "∞ + ∞ = ∞" I'm talking about a quantity that is produced from adding numbers. It's an example.
And I'm saying "∞ + ∞ = ∞" can be generalized if each version of "∞" is identical. Consistency is required. Consistency is included in the statement.

I understand |ℕ| =/= |ℝ| but that fact is irrelevant to "∞ + ∞ = ∞"
I'm not saying "|ℕ|+|ℝ|=|ℕ|", that's false.
I'm not saying "|ℕ|+|ℕ|=|ℝ|", that's false.

When I say "∞ + ∞ = ∞" I am saying:
"∞ + ∞ = ∞", this is true.
|ℕ|+|ℕ|=|ℕ|, this is true.
|ℝ|+|ℝ|=|ℝ|, this is true.

Please notice the consistency above.
It get's a little wonky if |ℤ| and |ℂ| are introduced since |ℤ|=|ℕ| and |ℂ|=|ℝ|. But, it's still consistently true.

I'm saying:
"∞ + ∞ = ∞", this is true.
Countable-infinity + Countable-infinity = Countable-infinty, this is true.
Uncountable-infinity + Uncountable-infinity = Uncountable-infinity, this is true.

I'm NOT saying:
Countable-infinity + Countable-infinity = Uncountable-infinty, this is false.
Uncountable-infinity + Countable-infinity = Countable-infinty, this is false.

So, even if |ℤ| and |ℂ| are introduced, what I'm saying is still true, if the consistency is maintained. "∞ + ∞ = ∞" includes that consistency.

When you flip what I'm saying from something which is consistent into something which is not consistent, your're flipping what I'm saying, which is true, into something that is false.

What I'm saying is true.
What you're saying is false.
You're changing what I'm saying into something that's false.
Please don't change what I'm saying.

From this fact, "∞ + ∞ = ∞", I can logically state: "a + ∞ = ∞", where 'a' is anything included in '∞'. Included.

So... when you start flipping what I'm saying into something inconsistent, ( where a is not included ) I flip it back into something that is true.

If you want to consider |ℕ| and |ℝ|, because |ℕ| =/= |ℝ|, then I say:
"a + ∞ = ∞", which is true
|ℕ| + |ℝ| = |ℝ|, which is true

If you claim I'm saying "|ℕ|+|ℝ|=|ℕ|", I will repeatedly tell you, "I'm NOT saying that" |ℝ| is NOT included in |ℕ|. Don't change what I'm saying.

(And, anytime you want to consider an aleph number or a beth/bet number or any cardinality of an infinite set.. that is { |the-infinite-set| }. That's it. A singleton. Nothing more, nothing less.)

What's the significant difference? They are concepts in the category of 'relationships'.

In category theory, there's objects, morphisms, and functors. Morphisms and functors are intra-category relationships and inter-category relationships. In the super-category of all categories, there will be objects describing the intra/inter-category relationships. That's what you're calling a concept. But this does not replace or duplicate the morphisms/functors that are intrinsic to the super-category's structure.

And eventhough I'm using the category theory framework, I'm really just describing a relational database and object oriented programming languages. It's a framework. A structure. Those relationships are important to the defiintion.

It's important when discussing nullification, because the nullifcation is a/∞. 'a' is not nullified, but the relationship is. An absolutely omnipotent, literally infinite, being creating something distinct and other than itself is a relationship. That relationship is not possible, yet.

Again, you seem to be flipping from concept to concept without keeping track. You have made a great deal of this ∞ + ∞ = ∞ throughout as an example of why you can't add to infinity to get anything else, but generally speaking, you obviously can. You may argue that you can't with LI but that is entirely non-standard and just your own idea. You need to be clear what it is you're talking about.

I am not flipping. I am following your strawmen. You can't add anything which is included in infinity to infinity. It's already included. When you try to add something which is not included, that's an irrelevant strawman.

Now we're suddenly back to nullification - they are infinitesimal which is not the same a non-existent.

It's not sudden. Nullification is the point. It's what you are objecting to.

They are infinitesimal when considered as included. They are non-existent when considered as excluded.
From the perspective of an included object, they, the relationships, are infinitesimal as all-inclusion is approached.
From the perspective of an excluded object, eventhough this violates the defintion, they, the relationships, are completely non-existent, because Literal-Infinity IS all-inclusive.

This proves that the definition is logically consistent.
"a/∞ =0" AND "lim(x-->∞) a/x-->0"
If 'a' is a new creation, "a/∞ =0"
If 'a' is included in 'x', "lim(x-->∞) a/x-->0"

So, there it is ^^. A logical statement and definition. If you are saying it is illogical, it is your burden to show that.

First, a procedure isn't a definition.

Sure a procedure is a definition. Define a sine-wave. "A sine wave is what happens when..."

Second, and as I explained before, since your procedure involves systematically adding lists of things, I really don't see how it's going to produce anything other than a standard set with cardinality ℵ₀. What you need is a proper, rigorous definition.

There are several steps in the definition which establishes relationships between all the objects. Certainly you can see the difference between counting and developing a database.

You're the one who brought up the 2-d plane because you didn't like my 1-d function. If it was irrelevant, why mention it?

Let's see... let me scroll back and figure that out. ... .... .... OK!

The point I was making several posts back was that the cardinality is a one dimensional attribute. The set which produces it only has 1 relationship. 1 function. And that function produces 1 thing, it's not even a collection. It's barely a set. It's very very different from what I'm describing. But, if you want to consider it, the same nullification occurs as long as consistency is maintained.

And for those of us looking for logic expressed in English or mathematics....?

I've given it you. You keep changing it.

In english:

LI:

absolutely all-inclusive relational database​

Nullification:

"external similarities and differences between objects and LI" = 0​

"internal similarities/differences between objects and LI" = infinitesimal​

In logic:

LI ----> Nullification

See:

Burden of proof (philosophy) - Wikipedia

en.wikipedia.org

You are proposing something (nullification) with is entirely new (as far as I can see) and is contradicted by literally everything else that uses either limit infinity or actual transfinite numbers.. It really isn't up to me to disprove it, the burden of proof is entirely yours. So far, all you have is some hand-waving, using a fairly standard limit process, like here, and some vague and largely irrelevant stuff about ∞ + ∞ = ∞.

No.... you haven't brought anything that contradicts the definitions. And the burden is on you to do so. You're saying that I have brought something which is illogical. You have the burden to show that. We had an agreement; you would consider the god concept I defined ,if it was not contradictory.

Please make a list of the contradictions you brought. You don't need to explain them, just a simple list. And then I'll breifly list each of my rebuttals. Throughout the conversation, you haven't undermined any of my rebuttals. Sometimes you'll say "nonsense" or "word salad". Then I'll explain the revelance and the "sense" of what I'm saying. And nothing more comes of it. That's why it's time to move on unless you can bring anything new which is relelvant and valid.

Please make a list. And then I'll very briefly attach my rebuttals. Then you can rebut the rebuttals. But, be ready to see "this is changing the definition" repeatedly.

It really isn't. That's just making the elements infinitesimal compared to the whole. This is entirely standard and you're trying to force an entirely non-standard interpretation onto it.

No. That would be the quantity of the included objects compared to the quanitity of all the included objects is infinitesimal. The included objects themselves remain unchanged.

lim(x-->∞) a/x-->0 is describing 'a/x'. It is not describing 'a'
a/∞ is describing 'a/∞' not 'a'

'a' is not changing. Nullification is a ratio, *points to your screen name*

What this means in english, how it is interpretted depends on how 'a' and 'x' and '∞' are defined.

I have defined 'x' as a relational database.
I have defined '∞' as all-inclusion
I have defined 'a' as the similarities and differences between the included objects in the relational database.

This results in absolute nullification of any similarities and differences which are excluded. This is consistent with the definition.
This results in approaching absolute nullification of any similarities and differences which are included. This is consistent with the definition.

 

[ratiocinator]

When I say "∞ + ∞ = ∞" I'm talking about a quantity that is produced from adding numbers. It's an example.
And I'm saying "∞ + ∞ = ∞" can be generalized if each version of "∞" is identical. Consistency is required. Consistency is included in the statement.

LOL. You jusr said consistency is required right after you posted the ambiguity of the "∞ + ∞ = ∞" statement you've used repeatedly without qualification or clarification.

I understand |ℕ| =/= |ℝ| but that fact is irrelevant to "∞ + ∞ = ∞"
I'm not saying "|ℕ|+|ℝ|=|ℕ|", that's false.
I'm not saying "|ℕ|+|ℕ|=|ℝ|", that's false.
...
... [etc., etc., etc,...]

Now whose using a straw man? I never suggested that you did say any of the incorrect statements you've gone to great lengths to 'refute'.

In category theory, there's objects, morphisms, and functors. Morphisms and functors are intra-category relationships and inter-category relationships. In the super-category of all categories, there will be objects describing the intra/inter-category relationships. That's what you're calling a concept. But this does not replace or duplicate the morphisms/functors that are intrinsic to the super-category's structure.

And eventhough I'm using the category theory framework, I'm really just describing a relational database and object oriented programing languages. It's a framework. A structure. Those relationships are important to the defiintion.

You didn't answer my question in relation to infinite sets. You have all these different sorts of things, some of which are relationships of various kinds, some of which are objects and categories. There are still a certain number of distinct things that make up the whole, so what difference does it make?

I know about relational databases - I've written a few - and I see no significant difference at all in this context.

It's important when discussing nullification, because the nullifcation is a/∞. 'a' is not nullified, but the relationship is.

Why?

An absolutely omnipotent, literally infinite being creating something distinct and other than itself is a relationship. That relationship is not possible, yet.

Random assertion?

This proves that the definition is logically consistent.
"a/∞ =0" AND "lim(x-->∞) a/x-->0"
If 'a' is a new creation, "a/∞ =0"
If 'a' is included in 'x', "lim(x-->∞) a/x-->0"

This is nothing like a proof, it's just some standard limits of the sort that are routinely used in calculus (for example). At any point in a curve the gradient = 0/0, i.e. undefined (or, in computer jargon, NaN - Not a Number), yet the gradient at every different point is still defined via the limit process, and is distinct at every point. You can't just take limits at face value and say they mean that the distinctions are lost.

Sure a procedure is a definition. Define a sine-wave. "A sine wave is what happens when..."

That would be a terrible way to try to define the sine function. You can (most simply, but not very comprehensively) define it as ratios in a right-angle triangle, or (much better), in terms of complex exponentials, or as an infinite series.

There are several steps in the definition which establishes relationships between all the objects. Certainly you can see the difference between counting and developing a database.

Not in a way that is relevant in this context. Every time you add an object or a relation (say an entry in an SQL database), just assign it a number that's one greater than the last entry you made.

The point I was making several posts back was that the cardinality is a one dimensional attribute. The set which produces it only has 1 relationship. 1 function. And that function produces 1 thing, it's not even a collection. It's barely a set. It's very very different from what I'm describing. But, if you want to consider it, the same nullification occurs as long as consistency is maintained.

All irrelevant. The cardinality isn't one dimensional, it's one number that represents a magnitude. Whether what you're 'counting' is arranged in one dimension, two (which is what you then suggested), or 5,000 dimensions, for that matter, doesn't make a jot of difference. Neither does whether you're counting objects or relationships or both.

And you have still given not one single example of nullification outside of your own personal imagination. Neither have got anywhere near defining how it could possibly work.

LI:
absolutely all-inclusive relational database
Nullification:
"external similarities and differences between objects and LI" = 0
"internal similarities/differences between objects and LI" = infinitesimal

In logic:

LI ----> Nullification

LI is still completely undefined and now you're talking about internal and external differences, where did that distinction suddenly spring from. and what exactly do you mean by it? If you've still some infinitesimal difference, then you've still got differences and you haven't got rid all borders.

No.... you haven't brought anything that contradicts the definitions. And the burden is on you to do so. You're saying that I have brought something which is illogical You have the burden to show that. We had an agreement, you would consider the god concept I defined ,if it was not contradictory.

I've pointed out that an infinite process that systematically adds lists of items into something is exactly the same as countable infinity. I've also pointed out that a procedure, doesn't really count as a proper definition, especially when it's just written in (imprecise) English and hence open to a certain amount of interpretation.

I've also pointed out Russell's Paradox in relation to any idea of 'all inclusive' infinity.

You have addressed none of these.

To be explicit about Russell's Paradox, if your list is 'all inclusive' then it has to include itself, otherwise, there is clearly something (very important to your argument) that isn't included. Once you have lists (sets, categories, database, or whatever else you call it, it makes no difference) that contain themselves, you arrive at Russell's Paradox. That is, you then have lists that do include themselves (at least one) and those that don't (an all inclusive list must also include other lists). So what about the concept of all those lists that don't contain themselves? Does it contain itself or not? If it doesn't then it's a list that doesn't contain itself, so should be in itself, but then it would be a list that does contain itself, so it shouldn't be in itself.

See the problem?

Not calling it a set doesn't help (formal set theories were basically introduced to get around this sort of thing), neither does making it a database. Your own procedure will inevitably trip over this problem too, if it really does end up capturing every concept, which is one good reason why a procedure is not a good definition because there can be problems lurking in a procedure that are far from obvious just by looking at it.

lim(x-->∞) a/x-->0 is describing 'a/x'. It is not describing 'a'
a/∞ is describing 'a/∞' not 'a'

'a' is not changing. It's a ratio, *points to your screen name*

What this means in english, how it is interpretted depends on how 'a' and 'x' and '∞' are defined.

I have defined 'x' as a relational database.
I have defined '∞' as all-inclusion
I have defined 'a' as the similarities and differences between the included objects in the relational database.

This results in absolute nullification of any similarities and differences which are excluded. This is consistent with the definition.

That's just an assertion or a non sequitur (depending on how you look at it). You don't seem to get the concept of proof. You actually have to take logical steps that lead inevitably to the conclusion - or alternatively (reductio ad absurdum) - assume the negation of what you want to prove and take logical steps the inevitable lead to a contradiction.

I understand your limiting process but it simply doesn't prove anything remotely like nullification. You've just posted some basic limit taking and then, like a magician pulling a rabbit out of a hat, exclaimed "See!!! Nuffification!!". Sorry but, no, I don't - there is not rabbit.

 

[dybmh]

@ratiocinator,

Sadly, there is nothing new here being brought. And I had hoped for more of a list of objections. Anyway... I'll post my line by line replies in another post. Honestly, very little of it matters. There are 3 things that are relevant. 1) can I use a method for a definition? 2) is that defintion self-referential leading to a paradox? 3) what is a formal proof of the nullification behavior?

That's it. All the other stuff is irrelevant.

1) Any definition that includes an operator is a method. Any function is a method. Only the most rudimentary definitions are not methods, they are strict identities. Euler's formula is a method for producing a sine wave. It is still derived from a procedure of manipulating the sides/angles in a right triangle. So, name dropping the "complex exponential" definition, doesn't exclude it from being a method.

2) I have already refuted this, "but, but, set theory doesn't permit a set of all sets". Yes, it does. There are several set theories that do permit it, and there is no paradox. You are working off an old set theory, ZFC, which was developed in the 1900s. It is NOT the only set theory. I gave you a list of others that do permit it. They're more modern. And, I'm defining a structure. S-T-R-U-C-T-U-R-E. You've written relational databases? Then you know that the structure is different than the content. The concept of "category of all category", or "set of all sets", can easily exist in the structure I have defined without self-reference. It's defined by its attributes and relationships, not by its members.

So, I don't need to put the entire structure of "the category of all categories" in the concept of "the category of all categories". A concept is its attributes and relationships. The "category of all categories" concept has the attribute of "the category of all categories=true". All other objects have the attribute "category of all categories=false". That attribute "category of all categories" has attributes. But none of those attributes contains the entire structure. And all of those attributes combined do not equal the entire structure.

All I need is 1 counter example to prove that the self-reference doesn't exist. And there are many. The concept "category of categories" does not contain the attributes of the concepts of "dream", or "bicycle", or "dog whistle". The structure that I have defined, "the category of all categories" contains those objects. But the concept, "category of all categories"? No. It doesnt contain the entire structure. It's actually a simple concept.

And that's the end of your objection to the structure I have defined, which you keep calling a list, but, it's not.

3) The proof you are wanting is so simple. I can make it stupid-simple. And then we can definitely move on. This really should be it. It's all part of the definition.

Definitions:

1. An object is defined by its attributes and the similarities and differences of these attributes to the attributes which define all other objects that can exist and cannot exist
2. A category is a structure of objects, their defining attributes, similarities, and differences
3. A category of all categories is an all inclusive structure which includes all objects, attributes, similarities and differences as objects and all the similarities and differences of all the objects. These similarities between the objects are called relationships.
4. Nullification is when there are no defining similarities or differences of an object which are not included in the total similarities and differences of all the objects in a categorical structure.
5. Nullification is described as: 'a' is nullified in 'x' or '{ a } ⊆ { x } is true' where:
   • 'a' are the similarities and differences in the defintion of the object
   • 'x' are the total similarities and differences included in the categorical structure
6. For the category of all categories, no object can ever exist which has any similarities or differences which are not included in it.

• If 'x' are the total similarities and differences of an all inclusive category, then any 'a' are always nullified in 'x'?
  1. For an all inclusive category nothing is excluded. '{ a } ⊆ { x } is always true'. There are no defining similarities or differences of the object which are not in the all inclusive category.
  2. The propostion is always true.

• Case 2: If 'x' are the total similarities and differences of a non-all inclusive category, then any included object is always nullified in 'x'?
  1. For a non-all inclusive category, if the object is included then '{ a } ⊆ { x } is true'. There are no defining simlarities or differences of the object which are not included in the non-all inclusive category.
  2. The propostion is always true.

• Case 3: If 'x' are the total similarities and differences of a non-all inclusive category, then any excluded object is never nullified in 'x'?
  1. For a non-all inclusive category, if the object is not included then '{ a } ⊆ { x } is false.' There is at least one similarity or difference of the object which is not included in the non-all inclusive category.
  2. The proposition is always true.

There you have it. It's all in the definition. Using the definition, it's 2 steps to prove the nullification.

{ a } ⊆ { x } = nullification
infinity+infinity=infinity is nullification because { infinity } ⊆ { infinity }
any finite number or numbers + infinity = infinity is nullification because { any finite number or numbers } ⊆ { infinity }
any object or objects + the all inclusive category = the all inclusive category is nullification because { any object or objects } ⊆ { the all inclusive category }

This means 3 things. 1) Nothing new can be added to the all inclusive category. 2) In order for an object to be excluded, it requires similarities and differences which are excluded. 3) If this excluded object loses those excluded similarities and differences it ceases being excuded.

That's nullification. Nothing new can be created without excluding similarities and differences. If those excluded differences are removed, thn the object is included.

 

[dybmh]

Here is my reply to post#326

Spoiler: none of this stuff matters

LOL. You jusr said consistency is required right after you posted the ambiguity of the "∞ + ∞ = ∞" statement you've used repeatedly without qualification or clarification.

I did clairfy in the previous post. And there is no ambiguity until you insert it. If these were different types of infinity being added, then different notation would be used. You're creating a problem that doesn't exist.

Now whose using a straw man? I never suggested that you did say any of the incorrect statements you've gone to great lengths to 'refute'.

You have been changing what I have been saying, bringing non-members to an infinite set and then adding them saying "see, see, they're different".

It doesn't really matter if you were or weren't; as long as it doesn't happen from here forward.

You didn't answer my question in relation to infinite sets. You have all these different sorts of things, some of which are relationships of various kinds, some of which are objects and categories. There are still a certain number of distinct things that make up the whole, so what difference does it make?

So what? That's a quantity. I'm not talking about the quantity.

I know about relational databases - I've written a few - and I see no significant difference at all in this context.

There's tables and there's joins. You are talking about a list, which is 1 table with an infinite number of rows. That's not what I'm talking about.

Why?

Why what?

Random assertion?

No. That's the purpose of all of these posts.

This is nothing like a proof, it's just some standard limits of the sort that are routinely used in calculus (for example). At any point in a curve the gradient = 0/0, i.e. undefined (or, in computer jargon, NaN - Not a Number), yet the gradient at every different point is still defined via the limit process, and is distinct at every point. You can't just take limits at face value and say they mean that the distinctions are lost.

I have never once in this thread claimed anything was 0/0.

That would be a terrible way to try to define the sine function. You can (most simply, but not very comprehensively) define it as ratios in a right-angle triangle, or (much better), in terms of complex exponentials, or as an infinite series.

Fine. If a sine wave can be defined it as ratios in the right triange, that means I can define literal infinity as a process.
If there is something missing from the definition I brought, then indicate that.
You already tried to do that and it failed. The unthinkable objects and relationships are already included. And even if they aren't, then they can be added explicitly.

And... your objection is yet again, moot, because the definition you're using is still a process involving the manipulation of the sides/angles in a right trangle through all their infinite iterations. It's still a ratio, and that is still a method. Any operation is a method. That means any function excluding an identity is a method. No matter how you slice it, I can define literal infinity as a method.

Not in a way that is relevant in this context. Every time you add an object or a relation (say an entry in an SQL database), just assign it a number that's one greater than the last entry you made.

So what? I'm not talking about the quantity of objects and joins. YOU want to talk about the quantity of objects, but it's not relevant.

All irrelevant. The cardinality isn't one dimensional, it's one number that represents a magnitude.

Hee. 1 number that represents a magintude.. 1 number is 1 dimensional.

Whether what you're 'counting' is arranged in one dimension, two (which is what you then suggested), or 5,000 dimensions, for that matter, doesn't make a jot of difference. Neither does whether you're counting objects or relationships or both.

I'm not counting. I'm not listing. I'm defining and joining.

And you have still given not one single example of nullification outside of your own personal imagination. Neither have got anywhere near defining how it could possibly work.

Sure I have. You're too focused on the strawman of a list. And you are not considering what happens when a new item ( eventhough that cannot exist by definition ) is added to an all inclusive category. You keep considering it as an included item.

LI is still completely undefined and now you're talking about internal and external differences, where did that distinction suddenly spring from. and what exactly do you mean by it? If you've still some infinitesimal difference, then you've still got differences and you haven't got rid all borders.

I have been taking about adding something new to an all inclusive category from the very beginning. Please, please try to focus on what is happening outside the all inclusive category when a member of the all inclusive category is attempted to be added.

It is not possible by definition of the words "all inclusive". And that is comfirmed simply by a/∞, where a is included in ∞. But it's not because 'a' becomes nothing, it's because the relationship of 'a' to '∞' is nothing.

I've pointed out that an infinite process that systematically adds lists of items into something is exactly the same as countable infinity. I've also pointed out that a procedure, doesn't really count as a proper definition, especially when it's just written in (imprecise) English and hence open to a certain amount of interpretation.

Adding items to a list is not even half of what I have defined.

I've also pointed out Russell's Paradox in relation to any idea of 'all inclusive' infinity.

And I have pointed out that there are quite a few logical frameworks which do not have any paradox when considering all inclusivity. So just name dropping "Russel's paradox" doesn't work, because then I can name drop 5-6 other logical frameworks which do not have that paradox and have an all inclusivity problem.

You have addressed none of these.

I did. You keep ignoring it.

To be explicit about Russell's Paradox, if your list

I can stop you right there. It's not a list.

is 'all inclusive' then it has to include itself, otherwise, there is clearly something (very important to your argument) that isn't included.

It can be included as a concept, but not as a list with members.

Once you have lists (sets, categories, database, or whatever else you call it, it makes no difference)

It does make a difference, because a catagory is not a list. It's a structure, not a collection.

that contain themselves, you arrive at Russell's Paradox.

It doesn't contain itself. it contains a concept which is defined by attributes and relationships, not membership.

That is, you then have lists that do include themselves (at least one) and those that don't (an all inclusive list must also include other lists).

It's not a list. It's a structure.

So what about the concept of all those lists that don't contain themselves?

The concept doesn't contain iself.

Does it contain itself or not?

It's not a list, it doesn't contain itself. It's a structure where the concept is defined but it does not a self reference to do that.

If it doesn't then it's a list that doesn't contain itself, so should be in itself, but then it would be a list that does contain itself, so it shouldn't be in itself.

It's not a list, this is not set theory. It's a structure, it doesn't have the limitations of a set. There is nothing in category theory that prevents a super category of all categories.

"If all you have is set theory, everything looks like a set."
"If all your objections are about sets, then all your objections are strawmen"

I'm not defining a set.

See the problem?

Yeah. The problem is, you're talking about a set, but I have defined a structure.

Not calling it a set doesn't help (formal set theories were basically introduced to get around this sort of thing)

I'm not only saying "It's not a set", I'm telling you what it is, and I have defined it. It's a structure. The concepts do not need to have self-references in order to be complete. Those self-references have been filtered out.

, neither does making it a database.

Sure it does. The structure does not require self-references to be complete.

Your own procedure will inevitably trip over this problem too,

That's a claim. That's your burden.

if it really does end up capturing every concept, which is one good reason why a procedure is not a good definition because there can be problems lurking in a procedure that are far from obvious just by looking at it.

Every function that is not an identity is a procedure.

That's just an assertion or a non sequitur (depending on how you look at it). You don't seem to get the concept of proof. You actually have to take logical steps that lead inevitably to the conclusion - or alternatively (reductio ad absurdum) - assume the negation of what you want to prove and take logical steps the inevitable lead to a contradiction.

No, it's the purpose. Anyway, it's a really simple concept. Nothing new can be added without some differences and similarities which are not included in the all inclusive category.

 

[ratiocinator]

I have already refuted this, "but, but, set theory doesn't permit a set of all sets". Yes, it does. There are several set theories that do permit it, and there is no paradox. You are working off an old set theory, ZFC, which was developed in the 1900s. It is NOT the only set theory. I gave you a list of others that do permit it.

Yes, you mentioned them but then said you didn't know how they worked, so it's rather irrelevant. I don't know how they work either but I'd happily work through one if you were actually using one instead of fumbling around trying to bodge your own ideas to get round the problems.

Presumably they have some way around Russell's paradox but nothing you've said does.

ZFC gets round it by making sure that the set of all sets isn't a set but that has the side-effect of making something like LI impossible. I don't know how the other versions work but, unless you do, and can explain how something like LI can exist in those systems, then they are irrelevant.

It's also irrelevant when ZFC was first developed. It's not like people have stopped considering it. Why do you think it is that we both know ZFC and not the others?

1) Any definition that includes an operator is a method. Any function is a method.

It's a map, actually. What's perhaps more important is that it rigorously defined without ambiguity, not a long list of English descriptions of a procedure.

And, I'm defining a structure. S-T-R-U-C-T-U-R-E. You've written relational databases? Then you know that the structure is different than the content. The concept of "category of all category", or "set of all sets", can easily exist in the structure I have defined without self-reference. It's defined by its attributes and relationships, not by its members.

Yes. I know how relational databases work but it really doesn't help.

So, I don't need to put the entire structure of "the category of all categories" in the concept of "the category of all categories". A concept is its attributes and relationships. The "category of all categories" concept has the attribute of "the category of all categories=true". All other objects have the attribute "category of all categories=false". That attribute "category of all categories" has attributes. But none of those attributes contains the entire structure. And all of those attributes combined do not equal the entire structure.

It really doesn't matter whether it contains the entire structure or not. In order for LI to be all inclusive, it has to contain every concept (even if that's done by a reference or relationship). Tagging with an attribute doesn't help either. Since LI is a concept in your mind now, your procedure will inevitably pick it up and add it to itself. It will also pick up the concept of the 'all things that don't contain themselves' because that is a concept in my mind now. As soon as it tries to fit that into its database, it will run straight into Russell's paradox because its contents cannot be consistently defined. If you want to look at it in terms of relationships, then the 'included' relationship to other concepts would be impossible to compete in a self-consistent way.

Again, Russell's paradox does not arise because you are defining something as a set in some formal set theory, quite the opposite. Formal set theories have to address the problem. ZFC does, and so, presumably, do the other theories you mention, but your procedure and LI concept don't.

Nullification is when there are no defining similarities or differences of an object which are not included in the total similarities and differences of all the objects in a categorical structure.

Which doesn't do what you want. You seem to have lost sight of what you want to do. Your concept of nullification is there so that you can turn LI, that contains everything, into some sort of unity with no borders. Nothing you've said can possibly achieve that. You simply can't turn everything into one thing. Infinity (of any kind) isn't going to help you to do that, because it's basically self-contradictory.

For the category of all categories, no object can ever exist which has any similarities or differences which are not included in it.

Which just doesn't turn it into one thing. That's it. If you want to define it like that, then fine, 'nullification' works but then it doesn't do what you want, i.e. turn everything into a unity.

You can't have it both ways. You can define it as you've said above and it exists, but doesn't achieve what you want, or your definition isn't nullification.

Take your pick....

 

[dybmh]

Yes, you mentioned them but then said you didn't know how they worked, so it's rather irrelevant. I don't know how they work either but I'd happily work through one if you were actually using one instead of fumbling around trying to bodge your own ideas to get round the problems.

Presumably they have some way around Russell's paradox but nothing you've said does.

ZFC gets round it by making sure that the set of all sets isn't a set but that has the side-effect of making something like LI impossible. I don't know how the other versions work but, unless you do, and can explain how something like LI can exist in those systems, then they are irrelevant.

It's also irrelevant when ZFC was first developed. It's not like people have stopped considering it. Why do you think it is that we both know ZFC and not the others?

All I'm saying by bringing those examples is the objection "the set of all sets was disproven" is invalid. It was only disproven in 1 framework from the 1900s. So that specific objection doesn't work.

It's a map, actually. What's perhaps more important is that it rigorously defined without ambiguity, not a long list of English descriptions of a procedure.

But you can't actually produce the sine wave without using the map ( the function, formula, whatever ) in a step by step procedure / method that is repeated. Since that is what I have done in the definition I brought, the objection "it's a method, not a definition" is invalid.

Yes. I know how relational databases work but it really doesn't help.

It does. And I apologize. For me, this is simple to imagine. Because I've been working with databases and categories and topologies for a very long time. I remember writing my first database at 12 in dbase3. I don't remember how I did it. But it was fun. I remember when Novell introduced its first directory structure. Then microsoft copied it. Schema >>> Leaf objects >>> containers ( branches ) >>> trees >>> forests... all part of a master directory. And at that time, poor unix/linux was stuck with flat files in bind.

Anyway. Let me try to make it very simple. I've been thinking about this. And had a nice chat about it last night over supper.

The main difference between a "set of all sets", and a "category of all categories" is that the set lacks any hierarchy. It lacks the structure. This means that as the sets are nested, the "set of all sets" becomes more and more and more complicated. The opposite is happening with the "category of all categories". Because it has a structure, the all inclusive category is becoming more and more general. But the all inclusive set is becoming more and more detailed. Can you imagine it? They are literally flip-flopped. It's another inverse relationship, a recipricol, just like the classic limit(x-->infinity) 1/x ---> 0.

The all inclusive set is starts with {}, then it gets filled. {} is like a point. Then as each set is added and added and added, and the sets get nested, layer on layer, it's an upside-down triange. The set of all sets is at the top, but, it never ends. The all inclusive category is the opposite. It starts with literally everything ( even {} is included ). That's the base of the triangle. Then as each category is nested, layer after layer, the number of categories are reducing and reducing and reducing until it eventually resolves into just 1 all inclusive, absolutely-general category at the tippy-top.

And that's why I keep saying, "I'm not defining a list", "I'm not defining a set". It's because I'm defining the opposite of a set. A set only has 1 relationship, inclusion/exclusion. The category has every possible relationship you can imagine. The "set of all sets" is the top of an every expanding upside-down triangle. The "category of all categories" is the top point of a right-side-up triangle.

Put most simply: the category of all categories is all-inclusive and that makes it absolutely general. That's a simple concept. The set of all sets is the opposite of this. It is infinitely specific, and, it never ends. It is a forever more and more and more complicated construct.

Do you see the difference now? Do you see how I have avoided the paradox? It's not just because I filtered out the self-reference. ( but that avoids the problem as well ). It's built in to category theory. There does exist a completely general all inclusive category of all categories. And this is because categories have the tools to establish the hierachy which avoids the repeated self-reference.

A long as you hold these words "absolutely general" in your mind while considering the "category of all categories" you should be able to easily see why it is completely different from a "set of all sets". OK?

It really doesn't matter whether it contains the entire structure or not. In order for LI to be all inclusive, it has to contain every concept (even if that's done by a reference or relationship). Tagging with an attribute doesn't help either. Since LI is a concept in your mind now, your procedure will inevitably pick it up and add it to itself. It will also pick up the concept of the 'all things that don't contain themselves' because that is a concept in my mind now. As soon as it tries to fit that into its database, it will run straight into Russell's paradox because its contents cannot be consistently defined. If you want to look at it in terms of relationships, then the 'included' relationship to other concepts would be impossible to compete in a self-consistent way.

If the structure, does not contain itself, then russel's paradox is avoided, and, what I have defined does contain every concept.

LI, as a concept, can be included in the structure without paradox. The concept "all things that that don't include themselves" can also be included in the structure without paradox.

Both of these concepts can be consistently defined in the same way that any infinite concept can be consistently defined. The concept simply defines something which is infinite. One is all inclusion, the other is all exclusion. I don't need to list all of the objects which saticfy these conditions to have a consistent definition. Again, look at the sine wave or any other infinite phenomena that is well defined.

Again, Russell's paradox does not arise because you are defining something as a set in some formal set theory, quite the opposite. Formal set theories have to address the problem. ZFC does, and so, presumably, do the other theories you mention, but your procedure and LI concept don't.

I have addressed it. Russel's paradox results from 2 conditions in the most basic set theory. 1 is an endless loop, and the other is a violation of the definition. Either there is an endles loop and the set is never completed, or it's not actually a set of all sets. I have addressed this in two ways.

First the counter-examples. This shows there is no loop condition.

The concept for LI does not require inclusion of the concept for "dream" or "ball bearing". The all inclusive structure includes those concepts. But the concept of LI does not. LI, the concept, is included, but the entire structure is not forever and ever and ever re-embedding itself in the structure itself. If there was an endless loop, then I would need to include those in the concepts, "dream" and "ball bearing", in the concept. Then that concept would need to be included in itself, over and over and over. That would be the endless loop condition. But that loop does not occur.

Second the definition is not violated. The definition of a category of all categories is a completely all inclusive, absolutely general category where the objects are defined by attributes and their similarities and differences to all other objects. The all inclusive category contains categories and structure which establish a hierarchy of categories. Eventually the categories all resolve into 1 completely general category.

So there is no paradox. There is no loop condtion. The definition is not violated. It's nothing like Russel's paradox. Nothing. Set theory does not have the tools to establish the hierachy. That prevents an absolutely general "set of all sets". And Cantor could not produce a god concept out of absolute-infinity in set-theory. And... depending on who you ask... maybe that contributed to his conversion to Christianity. IDK. He couldn't justify strict monotheism; felt he was inspired by the divine; and so... he ends up with a god concept which is triune, not strictly mono.

Which doesn't do what you want. You seem to have lost sight of what you want to do. Your concept of nullification is there so that you can turn LI, that contains everything, into some sort of unity with no borders. Nothing you've said can possibly achieve that. You simply can't turn everything into one thing. Infinity (of any kind) isn't going to help you to do that, because it's basically self-contradictory.

1) That's a claim, and the burden is on you to show the self-contradiction.
2) I haven't lost sight of the goal. I still think the recipricol is a better way to understand what I'm saying, big picture. But it's not needed. There are three goals. 1) An object requires similarities and differences to exist apart from God. 2) While God is only literally infinite, nothing new can be created. 3) Because God is literally infinite, God is solitary before creation.

All three goals are acheived from the definition and the very simple 2 step proofs. I like the recipricol better. But I did say that the nullification can be observed in many ways. One of those examples I brought was the union of an included element of an infinite set with the same infinite set. So, since you are stuck on set theory, that's what I'm using.

Which just doesn't turn it into one thing. That's it. If you want to define it like that, then fine, 'nullification' works but then it doesn't do what you want, i.e. turn everything into a unity.

I don't need the absolute unity. It's still true, but, it's not needed to acheive the goals. Infintesimal differences when considered internally works fine.

You can't have it both ways. You can define it as you've said above and it exists, but doesn't achieve what you want, or your definition isn't nullification.

Take your pick....

YAY!!!!! It looks like we have winner!!!! You have accepted my definition? Everything is included, and no object can exist apart from LI without any similarities or differences? Nothing new can be created while God is only-literally infinite?

If so, we can move on!

 

[ratiocinator]

All I'm saying by bringing those examples is the objection "the set of all sets was disproven" is invalid. It was only disproven in 1 framework from the 1900s. So that specific objection doesn't work.

As I said before, trying to somehow belittle standard set theory because it was developed in 1900 doesn't work because mathematicians haven't stopped thinking about it. Further, many theorems are way older than that, and are still considered to be solid.

However, the point is that we can't draw any conclusions from these other set theories because neither of us knows how they resolve Russell's paradox and hence whether something remotely like LI would be possible.

And, yet again, Russell's paradox does not arise from assuming ZFC. It's a problem ZFC avoids.

Do you see the difference now? Do you see how I have avoided the paradox?

No, because what preceded it was just English assertions, basically waffle. You need to be more precise.

If the structure, does not contain itself, then russel's paradox is avoided, and, what I have defined does contain every concept.

As I said before, it's not a question of how you represent it, it's a question of the concepts themselves. The paradox is 'out in the world' (of concepts). Conceptually, LI has to contain itself as 'the concept that consists of all concepts'. Likewise the concept of 'every concept that doesn't include itself' has to be included.

The way you represent it seems irrelevant and you have not described in any detail how you'd represent these concepts anyway.

I have addressed it. Russel's paradox results from 2 conditions in the most basic set theory. 1 is an endless loop...

It really has nothing to do with an infinite loop. You seem to be seeing everything in terms of programming and procedures. What was it you were saying? Oh, yes: "If all you have is a hammer, everything looks like a nail."

The concept for LI does not require inclusion of the concept for "dream" or "ball bearing". The all inclusive structure includes those concepts. But the concept of LI does not. LI, the concept, is included, but the entire structure is not forever and ever and ever re-embedding itself in the structure itself

You seem to be contradicting yourself and trying to answer a problem that was never a problem. You've given LI the structure of a database, fine, but it's still a concept, and, as such it's 'in' its own structure. That doesn't mean that you literally have to endlessly add the whole structure, you just define an 'included' relationship to the whole of LI. This is not a problem. Also if you want the "structure" to be somehow separate from LI, then you've created another concept that needs adding.

Second the definition is not violated. The definition of a category of all categories is a completely all inclusive, absolutely general category where the objects are defined by attributes and their similarities and differences to all other objects. The all inclusive category contains categories and structure which establish a hierarchy of categories. Eventually the categories all resolve into 1 completely general category.

That just looks like some sort of assertion. You haven't addressed the conceptual problem at all. As I said above, Russell's paradox is a problem with the basic concept of LI as you've described it. That is, it is itself a concept.

Russell's paradox is not resolved.

1) That's a claim, and the burden is on you to show the self-contradiction.

0 ≠ ∞, applied to the number of 'borders' in your LI. That is your basic problem.

2) I haven't lost sight of the goal. I still think the recipricol is a better way to understand what I'm saying, big picture. But it's not needed. There are three goals. 1) An object requires similarities and differences to exist apart from God. 2) While God is only literally infinite, nothing new can be created. 3) Because God is literally infinite, God is solitary before creation.

But with an infinite number of internal borders. The other problem (of the many still to come) is that you can't just go from LI (if you can get over Russell's paradox), which is basically nothing but an abstract concept, to something like a 'God' that can think, make choices, and act.

All three goals are acheived from the definition and the very simple 2 step proofs.

I've not actually seen any proofs in your posts, either logical or mathematical. Both require particular structures and steps that have been absent in all that you've written.

I don't need the absolute unity. It's still true, but, it's not needed to acheive the goals. Infintesimal differences when considered internally works fine.

So you are backing off from your previous claim that there are no borders in the 'non-material domain'?

YAY!!!!! It looks like we have winner!!!! You have accepted my definition?

I'll accept the definition of 'nullification' that you gave because it's basically trivial if you manage to construct LI in a self-consistent way that avoids Russell's paradox (which you haven't yet achieved). In fact, it's hardly worth giving it a name.

 

[dybmh]

As I said before, trying to somehow belittle standard set theory because it was developed in 1900 doesn't work because mathematicians haven't stopped thinking about it. Further, many theorems are way older than that, and are still considered to be solid.

However, the point is that we can't draw any conclusions from these other set theories because neither of us knows how they resolve Russell's paradox and hence whether something remotely like LI would be possible.

And, yet again, Russell's paradox does not arise from assuming ZFC. It's a problem ZFC avoids.

None of this changes that "a set of all sets is disproven" is false. It WAS disproven in ONE version of set theory. And there are several others that have been developed since that time that permit a set of all sets. A never said Russel's paradox came from ZFC. Just that it came from an old version. Technically I suppose the paradox existed from the beginning in the1600s when the first set theory was developed.

And a category of all categories does exist, it's just called a quasi-category. It's a just a tiny shift in nomenclature.

​

"The category Cat is itself a large category, and therefore not an object of itself. In order to avoid problems analogous to Russell's paradox one cannot form the “category of all categories”. But it is possible to form a quasicategory (meaning objects and morphisms merely form a conglomerate) of all categories."​

​

It's a conglomerate. A blob. An absolutely general all inclusive category. I'm avoiding the words "absolute infinity" because it reminds you of a "set of all sets". Maybe I need to avoid using the words "category of all categories" because that too reminds you of a "set of all sets". I'll start using the words "all inclusive conglomerate". There is a category of all categories. Technically it's a quasi-category which is merely, simply, a conglomerate.

Category of small categories - Wikipedia

No, because what preceded it was just English assertions, basically waffle. You need to be more precise.

As the categories are nested, the relationships in each higher level category reduce until they resolve into 1 absolutely general category conglomerate.

This is easy to see. Just look at a taxnomy table.

There are many species, then fewer genus, then fewer families, then fewer classes, then fewer phylum, then fewer kingdoms, then the fewest are domains. And all of them are in the absolutley general category conglomerate of taxonomy.

If there was a real paradox, there would be no taxonomy.

As I said before, it's not a question of how you represent it, it's a question of the concepts themselves. The paradox is 'out in the world' (of concepts). Conceptually, LI has to contain itself as 'the concept that consists of all concepts'. Likewise the concept of 'every concept that doesn't include itself' has to be included.

Literal infinity is a structure which contains concepts and relationship. Literal infinity is also a concept which is included in the structure. This is easily resolved if you stop using LI unqualified. From now on, please use the precise terms LI-structure and LI-concept. Thank you. The LI-concept does not need to include itself.

The way you represent it seems irrelevant and you have not described in any detail how you'd represent these concepts anyway.

I did. But I'll do it again and this time I'll do it in one sentence. A concept is a statement of conjunctions, disjuctions, and negations of attributes which fully establishes its similarities and differences to all other concepts.

InB4: If you start asking about the definition of an attribute, that is foolish. It's either a noun, any noun or an adjective, any adjective. No formal definition requires that every word be defined. There is an accepted expectation that the reader knows the language that they are reading.

It really has nothing to do with an infinite loop. You seem to be seeing everything in terms of programming and procedures. What was it you were saying? Oh, yes: "If all you have is a hammer, everything looks like a nail."

Yes, it does. If there is set of all sets, then that set needs to include itself, which needs to include itself, and needs to include itself, and everytime it includes itself, a new set is produced which needs to be added, and because of this, there cannot be a set of all sets. As soon as the set of all sets is added to itself, that has produced a new set which is not included in the set of a sets. That's a loop condition.

You seem to be contradicting yourself and trying to answer a problem that was never a problem. You've given LI the structure of a database, fine, but it's still a concept, and, as such it's 'in' its own structure. That doesn't mean that you literally have to endlessly add the whole structure, you just define an 'included' relationship to the whole of LI. This is not a problem. Also if you want the "structure" to be somehow separate from LI, then you've created another concept that needs adding.

Yes, the concept is in the structure. No, there isn't a problem. So why are you making it a problem? All your'e doing is name-dropping Russel's paradox because the words "category of all categories" reminds you of it. But it doesn't apply. It's MERELY a conglomerate. The concept, "structure" is included in the structure as a concept. There's still no problem.

The category of relationships, as concepts exists in the structure. This is the "schema" of a directory structure or a database. You said you've developed databases, were you aware of the schema, that's it's literally called, which came bundled in the framework you were using. When you type the commands CREATE, SELECT, JOIN, where do you think those commands came from?

In category theory the category of the structure are the types of morphisms and functors with their corresponding attributes and relationships. It looks like there are around 140 different types of morphisms and around 20 types of functors.

That just looks like some sort of assertion. You haven't addressed the conceptual problem at all. As I said above, Russell's paradox is a problem with the basic concept of LI as you've described it. That is, it is itself a concept.

But it's not a problem because LI-structure =/= LI-concept. There is no paradox. If this were a real problem, there would be no taxonomy.

Russell's paradox is not resolved.

It is avoided. It can be ignored the same way taxonomy ignores it. A hierarchy permits infinite lower-order categories to be nested into higher-order categories resolving into one highest order category conglomerate.

0 ≠ ∞, applied to the number of 'borders' in your LI. That is your basic problem.

Ahhhhh. Thank you. It's not 0, it's 1. I never made the claim this way, gratefully. I am talking about a unity. Absolutely all inclusive means: ∞=∞, which is an identity. The relationship is ∞/∞=1. The borders are the differences which are infinite. The similarites are also infinite. They cancel each other out. ∞-∞=0. No borders. That's when LI-structure is absolutley all inclusive, when infinity has been acheived.

But, when considering each individual object, or a group of objects, in isolation from the LI-structure, that consideration is removing it from the stucture. That's what consideration means. When this happens, LI-structure is approaching all inclusion. Now the borders are infinitesimal.

So, the absolutely general category conglomerate has no borders. The included individual categories and their objects have infinite infinitesimal borders.

But with an infinite number of internal borders. The other problem (of the many still to come) is that you can't just go from LI (if you can get over Russell's paradox), which is basically nothing but an abstract concept, to something like a 'God' that can think, make choices, and act.

Thinking, making choices, and acting are included in omnipotence. So before creation ( yes "before", we'll get to the time issue later ) God is literally infinite and omnipotent. Then, God chooses to be omnibenevolent. This sets up the premise of the PoE. "How can God be both omnipotent AND omnibenevolent if evil and suffering exist?"

I've not actually seen any proofs in your posts, either logical or mathematical. Both require particular structures and steps that have been absent in all that you've written.

I brought a few, but they're really just restating the definitions.

So you are backing off from your previous claim that there are no borders in the 'non-material domain'?

Nope. There are no borders in the absolutely infinite all inclusive general category conglomerate.

I'll accept the definition of 'nullification' that you gave because it's basically trivial if you manage to construct LI in a self-consistent way that avoids Russell's paradox (which you haven't yet achieved). In fact, it's hardly worth giving it a name.

I know, I know, it's a very simple concept. All inclusive means nothing is excluded. If it's included, that means it satisfies the same conditions all the other included members satisfied. In that way, it's equal to all the others. The differences it has between itself and all the others is totally insignificant regarding its inclusion. All inclusion MEANS all inclusion. Pretty simple.

In order for something to be excluded, existing outside of the absolutely infinite all inclusive general category conglomerate, something has to happen. And if that something is reversed... bye-bye exclusion, bye-bye existence outside of the category conglomerate.

If you want to continue to pursue Russel's paradox as a defeater, you need to show the paradox in taxonomy.

 

[ratiocinator]

It WAS disproven in ONE version of set theory.

Yet again, Russell's Paradox is nothing to do with a particular set theory. It is something any set theory has to avoid somehow.

And a category of all categories does exist, it's just called a quasi-category. It's a just a tiny shift in nomenclature.

"The category Cat is itself a large category, and therefore not an object of itself. In order to avoid problems analogous to Russell's paradox one cannot form the “category of all categories”. But it is possible to form a quasicategory (meaning objects and morphisms merely form a conglomerate) of all categories."

So how, exactly, does that relate to your ideas? How does it allow the construction of LI? Please be precise.

This is easy to see. Just look at a taxnomy table.

There are many species, then fewer genus, then fewer families, then fewer classes, then fewer phylum, then fewer kingdoms, then the fewest are domains. And all of them are in the absolutley general category conglomerate of taxonomy.

If there was a real paradox, there would be no taxonomy.

This is nothing like what you're trying to do because the taxonomy is not a species, genus, family or any of the other groupings that it includes. There is no reason it needs to include itself. It's irrelevant.

Literal infinity is a structure which contains concepts and relationship. Literal infinity is also a concept which is included in the structure. This is easily resolved if you stop using LI unqualified. From now on, please use the precise terms LI-structure and LI-concept. Thank you. The LI-concept does not need to include itself.

How do you think that helps? Now we have two concepts: LI-concept and LI-structure. Both of them will need to be included into whatever the thing is that that is supposed to include all concepts, and that will need to include itself, and the concept of "all concepts that don't include themselves". You don't appear to have changed anything.

I did. But I'll do it again and this time I'll do it in one sentence. A concept is a statement of conjunctions, disjuctions, and negations of attributes which fully establishes its similarities and differences to all other concepts.

So how does that help? I was asking specifically about the concepts of "all concepts" and "all concepts that don't include themselves" because that is where the paradox is. I wasn't asking a general question. How specifically does this scheme represent those two concepts without contradiction?

Yes, it does. If there is set of all sets, then that set needs to include itself, which needs to include itself, and needs to include itself...

That just isn't the problem, and never was, as I already explained. You just need an 'included' relationship back to the whole "concept of all concepts" (it's container). You only get a loop problem if you think as a procedure and you require some sort of literal, as opposed to conceptual, inclusion. I never suggest that. That is nothing to do with Russell's Paradox.

Thank you. It's not 0, it's 1.

Eh? I thought you said one object, zero borders. I was (as I said) talking about borders.

I never made the claim this way, gratefully. I am talking about a unity. Absolutely all inclusive means: ∞=∞, which is an identity. The relationship is ∞/∞=1. The borders are the differences which are infinite. The similarites are also infinite. They cancel each other out. ∞-∞=0. No borders. That's when LI-structure is absolutley all inclusive, when infinity has been acheived.

You can't just assert that an infinite number of things somehow cancels out and is equivalent to ∞/∞ or ∞-∞. You actually have to show your working.

Thinking, making choices, and acting are included in omnipotence. So before creation ( yes "before", we'll get to the time issue later ) God is literally infinite and omnipotent. Then, God chooses to be omnibenevolent.

Even if you'd manages to construct your LI, there'd be a massive conceptual leap to this God. But let's not go there until you've done the basics of LI.

All inclusive means nothing is excluded. If it's included, that means it satisfies the same conditions all the other included members satisfied. In that way, it's equal to all the others.

Another bare assertion with no working. You haven't shown any sort of equality at all.

 

[dybmh]

Yet again, Russell's Paradox is nothing to do with a particular set theory. It is something any set theory has to avoid somehow.

The paradox existed, past tense, at a time when there was only one version of set theory. The fact that it is avoided in multiple ways means I can avoid it too.

So how, exactly, does that relate to your ideas? How does it allow the construction of LI? Please be precise.

It relates to the objection you are raising about Russel's paradox. Avoiding the paradox is nothing more, that's why the wiki article says "merely", than a minute shift in the label of the top level category.

Bye-bye Russel's paradox. Hellooooooo conglomerate!

This is nothing like what you're trying to do because the taxonomy is not a species, genus, family or any of the other groupings that it includes. There is no reason it needs to include itself. It's irrelevant.

And LI-structure is not a concept or a relationship. Taxonomy is not a species, genus, family, etc... LI-structure is not the concepts or the relationships. A species is included in the conglomerate "taxonomy". The LI-concept is included in LI-structure.

Again, there is no problem. And taxonomy is a great example. If there was a paradox, there would be no taxonomy.

How do you think that helps? Now we have two concepts: LI-concept and LI-structure. Both of them will need to be included into whatever the thing is that that is supposed to include all concepts, and that will need to include itself, and the concept of "all concepts that don't include themselves". You don't appear to have changed anything.

It doesn't need to include itself. You said that in the other post. The all inclusive conglomerate "Taxonomy" doesn't need to be included in itself.

So how does that help? I was asking specifically about the concepts of "all concepts" and "all concepts that don't include themselves" because that is where the paradox is. I wasn't asking a general question. How specifically does this scheme represent those two concepts without contradiction?

I answered it in a previous post, and you said it yourself earlier this morning.

My answer was, the attribute+relationship "all-inclusive=true" is applied to the concept "all-concepts" and the attribute+relationship "all-inclusive=false" is applied to everything else ( including the concept "all concepts which don't include themself" ). Conversely the concept "all concepts which don't include themself" has the attribute+relationship "all-exclusive=true" applied to it. And all other objects have the attribute+relationship "all-exclusive=false" ( including the concept "all-concepts" ). It's really no problem. Just a few rows and a few joins to a junction table. These are simple concepts to define.

Your answer was: "... you just define an 'included' relationship to the whole of LI[-concept]."

So why are you flippig back and forth on this? You already said it wasn't a problem. I already said it wasn't a problem. We don't actually disagree, unless you flip-flop.

That just isn't the problem, and never was, as I already explained. You just need an 'included' relationship back to the whole "concept of all concepts" (it's container). You only get a loop problem if you think as a procedure and you require some sort of literal, as opposed to conceptual, inclusion. I never suggest that. That is nothing to do with Russell's Paradox.

There you go. You just said it again. There is no problem defining these concepts in the structure. So, please stop manufacturing a problem that doesn't exist. You're just name dropping Russel's paradox. You need to undermine taxonomy and the wiki article I brought which shows a conglomerate is somehow a problem.

Just a few lines ago, you said: "Both of them will need to be included into whatever the thing is that that is supposed to include all concepts, and that will need to include itself, "

But here you are confirming: "You just need an 'included' relationship back to the whole "concept of all concepts"

So why are you flipping and flopping? It's time to simply admit, the objection based Russel's paradox is dead.

Eh? I thought you said one object, zero borders. I was (as I said) talking about borders.

If there is only 1 thing. There are no borders. There needs to be at least two to have one border. That's the definition of a border.

You can't just assert that an infinite number of things somehow cancels out and is equivalent to ∞/∞ or ∞-∞. You actually have to show your working.

All inclusive / All inclusive = 1. This is just the defintion of an identity. There is no "working" an identity that is this simple. All inclusive MEANS no borders. Both the similarities and the differences are countable infinity. I don't need "work" something you have already agreed is true. Countable Infinity - Countable infinity = 0, just the same as anything subracted from itself.

Even if you'd manages to construct your LI, there'd be a massive conceptual leap to this God. But let's not go there until you've done the basics of LI.

Why? Are you still imagining a sky-daddy cartoon god wth a magic wand?

Another bare assertion with no working. You haven't shown any sort of equality at all.

Do you know what the words "All inclusive" mean? If so, that's all the "working" that's needed.

 

[ratiocinator]

The paradox existed, past tense, at a time when there was only one version of set theory.

It pre-dated ZFC and was one of the reasons that motivated it's development.

Zermelo–Fraenkel set theory - Wikipedia

en.wikipedia.org

Under the History section: "The modern study of set theory was initiated by Georg Cantor and Richard Dedekind in the 1870s. However, the discovery of paradoxes in naive set theory, such as Russell's paradox, led to the desire for a more rigorous form of set theory that was free of these paradoxes."

It relates to the objection you are raising about Russel's paradox. Avoiding the paradox is nothing more, that's why the wiki article says "merely", than a minute shift in the label of the top level category.

Oh for goodness sake! I'm asking exactly how the one set of concepts you posted is related to your construction of LI. That is, I want a map to see how the correspondence works, so that I can be sure that the solution to the paradox carries across. Just citing formal systems that avoid the paradox somehow, doesn't mean we can apply the same solution to your 'all-inclusive' concept.

It doesn't need to include itself.

Then it's not, by definition, all inclusive.

My answer was, the attribute+relationship "all-inclusive=true" is applied to the concept "all-concepts" and the attribute+relationship "all-inclusive=false" is applied to everything else ( including the concept "all concepts which don't include themself" ). Conversely the concept "all concepts which don't include themself" has the attribute+relationship "all-exclusive=true" applied to it. And all other objects have the attribute+relationship "all-exclusive=false" ( including the concept "all-concepts" )

So how does flagging them help? You've still got to be able to access all the contents somehow, otherwise you haven't captured the concept properly.

Look, we're just going in circles here. So I'm going to just set out the problem that you keep dodging.

1. Every single idea you have that you can put into words and post on here is a concept. There is no avoiding that.
2. From 1, the idea of something that is all-inclusive is a concept.
3. If something is all-inclusive, then it must include all concepts. That's what "all-inclusive" means.
4. From 1, 2, and 3, the all-inclusive concept inevitably includes itself.
5. Point 4, is not where the paradox lies. You can represent that in any way you like. An attribute, a self reference relationship, whatever. If you want you can just use "all-inclusive=true", but that has to conceptually mean that it includes itself.
6. Since it is trivially easy to think of concepts that don't include themselves we now have both concepts that do include themselves and concepts that don't. It's quite easy to think of other concepts that would include themselves too.
7. The idea of all concepts that don't include themselves (denoted P, from here on) is also a concept.
8. P must also be in the concept of all concepts.
9. It must be possible (somehow) to enumerate the contents of P, otherwise it hasn't been captured properly.
10. The paradox occurs when you enumerate the contents of P.
11. If the contents of P include P, then they shouldn't because P is supposed to be the concept of all concepts that don't include themselves and P is in itself, so it shouldn't be.
12. If the contents of P don't include P, then they should, because P is supposed to include all concepts that don't include themselves and P doesn't include itself, so it should.

None of that has anything to do with how you represent it all. It is all an inevitable result of trying to have an all-inclusive concept. Flagging P with "all-exclusive=true" doesn't help when we come to enumerate its contents. The list of contents still either has to include itself or not, and both are inevitably wrong.

I'm not interested in category theory or other set theories unless you can show that the solutions to the paradox that they employ are directly applicable to an all-inclusive LI.

[Edited for numbering problem in argument.]

 

[dybmh]

It pre-dated ZFC and was one of the reasons that motivated it's development.

Zermelo–Fraenkel set theory - Wikipedia

en.wikipedia.org

Under the History section: "The modern study of set theory was initiated by Georg Cantor and Richard Dedekind in the 1870s. However, the discovery of paradoxes in naive set theory, such as Russell's paradox, led to the desire for a more rigorous form of set theory that was free of these paradoxes."

Yuuuuuup. I already know that, and I've said that. I think you may be rushing through my posts. Which is totally understandable. No judgements, just say'n.

Oh for goodness sake! I'm asking exactly how the one set of concepts you posted is related to your construction of LI. That is, I want a map to see how the correspondence works, so that I can be sure that the solution to the paradox carries across. Just citing formal systems that avoid the paradox somehow, doesn't mean we can apply the same solution to your 'all-inclusive' concept.

You need a picture of an org chart? You don't know what a taxonomy table looks like? What about a family tree?

You said you've designed databases before. Taxonomy is an all-inclusive conglomerate. I gave you the mapping. There's two attributes involved and two relationships involved. That's it, this is a super simple concept.

Attributes: { All-inclusive, All-exclusive }
Relationships: { true, false }

Mapping: All-inclusive-concept: { All-inclusive=true AND All-exclusive=false }

That's it, it's a "one-liner".

Then it's not, by definition, all inclusive.

Hee. Except that is just a few words cherry picked. All inclusive does not require repeats.

This is what I actually said. And you confirmed that it is correct by your own words.

"It doesn't need to include itself. You said that in the other post. The all inclusive conglomerate "Taxonomy" doesn't need to be included in itself."

And it's true, it doesn't NEED to include itself. When you look at a family tree, is the family tree excluded from itself?

So how does flagging them help? You've still got to be able to access all the contents somehow, otherwise you haven't captured the concept properly.

Flagging them defines the concept. Acessing the contents, traversing the structure, happens by .... drumroll ... accessing the contents, traversing the structure.

Do this, assuming you can:

Login to a linux terminal

type: sudo root -i
type: the root password
type: cd / [enter]
type: cd etc [enter]
type: cd .. [enter]
type: cd root [enter]
type: cd .. [enter]
type: cd home [enter]

WOW! You can access each concept without any problem at all!

Look, we're just going in circles here. So I'm going to just set out the problem that you keep dodging.

LOL. You're the one who's dodging all the examples of org structures with a hierarchy

1. Every single idea you have that you can put into words and post on here is a concept. There is no avoiding that.
2. From 1, the idea of something that is all-inclusive is a concept.
3. If something is all-inclusive, then it must include all concepts. That's what "all-inclusive" means.
4. From 1, 2, and 3, the all-inclusive concept inevitably includes itself.
5. Point 4, is not where the paradox lies. You can represent that in any way you like. An attribute, a self reference relationship, whatever. If you want you can just use "all-inclusive=true", but that has to conceptually mean that it includes itself.
6. Since it is trivially easy to think of concepts that don't include themselves we now have both concepts that do include themselves and concepts that don't. It's quite easy to think of other concepts that would include themselves too.
7. The idea of all concepts that don't include themselves (denoted P, from here on) is also a concept.
8. P must also be in the concept of all concepts.
9. It must be possible (somehow) to enumerate the contents of P, otherwise it hasn't been captured properly.
10. The paradox occurs when you enumerate the contents of P.
11. If the contents of P include P, then they shouldn't because P is supposed to be the concept of all concepts that don't include themselves and P is in itself, so it shouldn't be.
12. If the contents of P don't include P, then they should, because P is supposed to include all concepts that don't include themselves and P doesn't include itself, so it should.

No. P doesn't have contents. It's a concept which is defined by attributes and relationships. If you want to find all objects that meet those requirements, it would be SELECT * WHERE "IS-MEMBER-OF-ITSELF"=FALSE. Or something like that. And you would get infinite results.

So,

10 is false.
11 is false. It P, the concept is defined by 1 attribute+relationship pair. { "IS-MEMBER-OF-ITSELF"=FALSE }. The structure of P, the category, is enumerated by the SELECT statement. ( depending on how the results are formatted )
12 is false. The Select statement will return P. The conglomerate is all-inclusive.

None of that has anything to do with how you represent it all. It is all an inevitable result of trying to have an all-inclusive concept. Flagging P with "all-exclusive=true" doesn't help when we come to enumerate its contents. The list of contents still either has to include itself or not, and both are inevitably wrong.

Enumerating all the concepts is an infinite statement of conjunctions, disjunctions, and negations. But, its not a set. It's one never ending true statement. A conglomerate.

I'm not interested in category theory or other set theories unless you can show that the solutions to the paradox that they employ are directly applicable to an all-inclusive LI.

You already have it. It was stated simply and truly in the wiki-article. Avoiding something analogous to Russel's paradox comes from MERELY considering it a conglomerate and changing the nomenclature from catergory to quasi-category. But all the other relationships and properties are intact. This thing with Russel's paradox is no biggie. It never was a big deal not even when it was discovered.

 

[ratiocinator]

You need a picture of an org chart? You don't know what a taxonomy table looks like? What about a family tree?

None of these are trying to be all-inclusive, so none of them has the same problem. This is obvious. The same goes for a folder hierarchy.

Taxonomy is an all-inclusive conglomerate.

Of course it isn't. A taxonomy is not an instance of the things it includes. An all-inclusive concept is a concept.

If you can't see this simple distinction, I'm just giving up.

P:{all-inclusive=no, all-exclusive=yes}

Unless you can (in principle, and of course it will probably be infinite) tell me all the concepts it contains, and specifically if it contains itself, you have not captured the concept.

P is an object, not a structure. You stated that in #7.

I (quite deliberately) didn't mention either. The whole argument is about concepts that can be objects, structure, sets, categories, zebras, poems, colours, or anything else you care to dream up. P is something (call it whatever you like) that is, essentially, a bunch of other concepts.

11 is false. It contains 2 attribute+relationship pairs.

Nonsense, it is, by the way I've defined it, a number of other concepts that are united by the characteristic that they don't contain themselves. You need to be able to tell me if some given concept is included or not. Otherwise you haven't captured the concept.

12 is false. P is a concept not a structure per #7.

Quite clearly a concept can be a structure. It's something you can think of and explain, hence it's a concept. Whether P is one or not, depends on your exact definition of 'structure'. I didn't call it a structure. It's defined as above.

But, its not a set.

I never called it a set either. You can call it anything you want, it doesn't change the logic I've presented and you've once again ignored and tried to make out you can gloss over the problem with jargon and make invalid comparisons to things that cleanly don't have the same problem.

You can't map an all-inclusive concept to a strict hierarchy.

 

[dybmh]

None of these are trying to be all-inclusive, so none of them has the same problem. This is obvious. The same goes for a folder hierarchy.

They are all inclusive in their respective domains. There isn't even a whiff of self-referential paradox.

Of course it isn't. A taxonomy is not an instance of the things it includes. An all-inclusive concept is a concept.

LOL. A taxonomy IS THE instance of the things it includes. The taxonomy IS The taxonomy. That's an identity.
Yes, the all inclusive concept is a concept. What is the problem?

If you can't see this simple distinction, I'm just giving up.

That's because there is no argument left. Just as the taxonomy can be complete without any paradox, so can literal infinity. They are the same thing just one is smaller. Does a family tree need to somehow include itself in itself to be a family tree?

Unless you can (in principle, and of course it will probably be infinite) tell me all the concepts it contains, and specifically if it contains itself, you have not captured the concept.

Sure. So simple. Here's all the concepts it contains. "SELECT *". Yes the concept "All-inclusive" is returned. All-inclusive is a simple concept.

I (quite deliberately) didn't mention either.

But a concept is defined this way per my defintion. If you aren't using my definition, then your objection is moot.

The whole argument is about concepts that can be objects, structure, sets, categories, zebras, poems, colours, or anything else you care to dream up. P is something (call it whatever you like) that is, essentially, a bunch of other concepts.

Great! Here's your group of concepts: SELECT * WHERE "CONTAINS-ITSELF=FALSE"

Nonsense, it is, by the way I've defined it, a number of other concepts that are united by the characteristic that they don't contain themselves. You need to be able to tell me if some given concept is included or not. Otherwise you haven't captured the concept.

Asked and answered. It is included and I showed you how. Your job is to come up with a concept that isn't included. But they're all included by defintion.

"All inclusive" is included.
"All exclusive" is included
"All that include themselves" is included.
"All that do not include themselves" is included.
"SELECT" is included
"*" is included
"WHERE" is included
"=" is included
"TRUE" is included
"FALSE" is included
"AND" is included
"OR" is included
"XOR" is included
"NOT" is included

Your turn. What's not included, and show me how it's not included. If I can't include it, you win.

Quite clearly a concept can be a structure. It's something you can think of and explain, hence it's a concept. Whether P is one or not, depends on your exact definition of 'structure'. I didn't call it a structure. It's defined as above.

But it doesn't NEED to be a structure. Sure you can define your own model and build in a paradox. I didn't do that. P is a simple concept whether you like it or not.

I never called it a set either. You can call it anything you want, it doesn't change the logic I've presented and you've once again ignored and tried to make out you can gloss over the problem with jargon and make invalid comparisons to things that cleanly don't have the same problem.

What you're missing is, if I can make a comparison to a thing that doesn't have the problem, then I can define something that doesn't have the problem.

You're mistaking "glossing over" with restating the definition. It's a huge relational database. And the database doesn't need to repeat it's own contruct in order to have all the elements of the construct included. There only needs to be one version of itself to be complete. It's an identity. It doesn't need to embed the entire structure into the concept of "SELECT *" to be all inclusive. The whole thing = The whole thing.

You can't map an all-inclusive concept to a strict hierarchy.

Sure I can, dude.

"SELECT *" or
"find / -type f -o -type d" or
"Get-ADOrganizationalUnit -Filter * -Recursive"

There's lots of ways to map it. It's just a query.

 

[ratiocinator]

They are all inclusive in their respective domains. There isn't even a whiff of self-referential paradox.

They are not themselves instances of the things they contain. A concept of all concepts is. It is a concept itself. Of course there's no paradox in those things because they are fundamentally different from LI. This really couldn't be simpler.

A taxonomy IS THE instance of the things it includes. The taxonomy IS The taxonomy. That's an identity.
Yes, the all inclusive concept is a concept.

Brilliant. You have absolutely no idea, and zero understanding, of the problem you've created for yourself.

Of course a taxonomy is the things it includes but it doesn't include itself. An all-inclusive concept is a concept so it contains itself. Again, it really couldn't be simpler.

So simple. Here's all the concepts it contains. "SELECT *". Yes the concept "All-inclusive" is returned. All-inclusive is a simple concept.

I wasn't asking about all inclusive, I was asking about P. However queries like this just aren't going to work because they will end up in infinite recursions on an all-inclusive concept because they will have to deal with all the content of all the instances it finds conceptually. So, although you can easily encode it in a with relationships, if you try to recurse down it, you will loop.

It's never going to be a well behaved relational database.

Here's your group of concepts: SELECT * WHERE "CONTAINS-ITSELF=FALSE"

So what is the value of "CONTAINS-ITSELF" for P?

This is exactly where you hit the paradox. If you set it TRUE, it should be FALSE and if it's set FALSE, it should be TRUE. See steps 11 and 12 of my argument.

You actually have to add the result of this query into the database (for it to be all-inclusive) so you must assign a value to the flag. Both TRUE and FALSE would be wrong.

Your turn. What's not included, and show me how it's not included. If I can't include it, you win.

You answered the wrong question yet again. I was asking what's included in P, not the all-inclusive concept. Specifically, if it includes itself.

Sure I can, dude.

You can't have a strict hierarchy that you can navigate down and end up back at the root, or any other higher level, for that matter. You have to be able to do that in an all-inclusive concept. Otherwise it simply can't be all-inclusive.

 

[dybmh]

They are not themselves instances of the things they contain. A concept of all concepts is. It is a concept itself. Of course there's no paradox in those things because they are fundamentally different from LI. This really couldn't be simpler.

And I didn't say they were the instances themself. I said: "They are all inclusive in their respective domains." Their domain is concepts. They ARE themselves the instance that contains all the concepts in their respective domains. The taxonomy table contains all the concepts of taxonomy. The periodic table contains all the concepts of elements and their atomic number. All of them. All those concepts. The are included as a unity, as the periodic table. It's the same for a family tree, or any org chart. They contain concepts. They are the instance, the one instance, of all the concepts they contain. That is what they are. That is their purpose. That is why they are made. And that is what they accomplish. It is their identity.

When you want to gather all the instances of the concepts that are in a book, what do you do? Pick up the book. When you want to gather all the concepts contained in the periodic table, what do you do? Frame it and hang it on the wall.

Brilliant. You have absolutely no idea, and zero understanding, of the problem you've created for yourself.

There is no problem. You'll see. Keep reading.

Of course a taxonomy is the things it includes but it doesn't include itself. An all-inclusive concept is a concept so it contains itself. Again, it really couldn't be simpler.

Now you're making it too simple.

The all inclusive concept will contain the idea of what it means to be a concept in a concept, but that doesn't mean it will contain itself, because the definition is more than just this idea. It also has a structure that goes along with it. Because the concept is more than you are considering, even though I've told you it's more, you keep imagining a self referential paradox that isn't there.

Let's say I define something called "all the numbers 1-10". "All the numbers from 1-10" is a concept, and a sequence, and produced by counting on my fingers. That's 3 attributes. 2 of them are the structure, and 1 of them is what produces "all the numbers 1-10". Are you starting to see it? The concept "all the numbers 1-10" contains more than "all the numbers 1-10". "all the numbers 1-10" is included in the concept. But the concept is not contained in the numbers.

The concept = Criteria 1 + Criteria 2 + the results. The results are in the concept. The concept is not in the results. Why? because criteria 1 and Criteria 2 have been included in the concept, but they are not included in the results. From 1-10 is a sequence, but a sequence is not only 1-10. A square is a rectangle, but a rectangle is not always square. A rectangle includes more than a square. Get it?

I wasn't asking about all inclusive, I was asking about P. However queries like this just aren't going to work because they will end up in infinite recursions on an all-inclusive concept because they will have to deal with all the content of all the instances it finds conceptually. So, although you can easily encode it in a with relationships, if you try to recurse down it, you will loop.

First. Please be honest. I told you the problem would be a loop condition, didn't I? You pushed back repeatedly on that. And here you are, talking about a looping problem. So, I think I should get a little credit for being right about that. And then maybe consider that I actually know what I'm talking about here?

Second: You are saying the concept "all concepts which do not contain themselves" will loop when I select for it. I disagree.

Here is P. It is a nested conjunction, but I'll write it as a bullet list. Take note of all the criteria which define it. There' going to be much more than this, but you should get the idea. It's much more than just the results of the select statement.

All concepts which do not contain themself will have the attribute+relationship pair as defined by the attribute-relationship-filter, "CONTAINS-ITSELF=FALSE". For other concepts, this attribute-relationship-filter could be a much longer statement of chained conditions.

P=:​

• DESCRIPTION="all concepts which do not contain themselves"
• IS-CATEGORY=TRUE
• IS-CONCEPT=TRUE
• IS-RELATIONSHIP=FALSE
• CONTAINS-ITSELF=FALSE
• CATEGORY-DEFINITION='SELECT * WHERE "CONTAINS-ITSELF"=FALSE'
  • DESCRIPTION="Select statement for enumerating All concepts which do not contain themselves"
  • IS-CATEGORY-DEFINITION=TRUE
  • IS-CONCEPT=TRUE
  • IS-RELATIONSHIP=FALSE
  • CONTAINS-ITSELF=FALSE
  • SELECT=TRUE
  • "*" = TRUE
  • "WHERE" = TRUE
  • ATTRIBUTE-RELATIONSHIP-FILTER="CONTAINS-ITSELF=FALSE"

To produce the category and enumerate them: 'SELECT * WHERE "CONTAINS-ITSELF"=FALSE'

So, here is the concept "all concepts which do not contain themself" defined and selected without any loop condition. Your challenge is:

1. to find where this conjunction of all the relationship+attribute pairs in the definition is inside itself, or
2. describe the loop condition when the recursion will repeat starting back at the beginning of the search, or
3. bring an example of a concept which doesn't contain itself and is not returned by the SELECT statement

It's never going to be a well behaved relational database.

That's a claim, you have the burden to show it.

So what is the value of "CONTAINS-ITSELF" for P?

FALSE

This is exactly where you hit the paradox. If you set it TRUE, it should be FALSE and if it's set FALSE, it should be TRUE. See steps 11 and 12 of my argument.

No, there's no reason to set it to be TRUE. It literally doesn't contain itself. Yes, the attribute+relationship pair which is used to filter / identify what it means to be "a concept which doesn't contain itself" is included, but P's definition is much more than that. So, P is not included in itself.

And this is what I've been saying for many posts over many days. It's the structure, itself, the way things are defined which avoids the paradox. Because this concept is more than just an element in a set, the self-reference is seperated from the concept. There is more to this than just inclusion/exclusion. So a concept that identifies a concept which identifies inclusion/exclusion of itself is not a problem. It is sheilded from itself by the hierarchy or by the structure or both. It can be setup in a way which introduces a paradox, but it doesn't need to be that way. Just as a simple change from "category" to "quasi-category" avoids the paradox in category theory, I can just as easily avoid it here by defining the concepts with attribute+relationship pairs which describe more than inclusion/exclusion.

Here it is as a pair of conjunctions.

"All concepts which do not contain themself":
{ DESCRIPTION="all concepts which do not contain themselves" AND IS-CATEGORY=TRUE AND IS-CONCEPT=TRUE AND IS-RELATIONSHIP=FALSE AND CONTAINS-ITSELF=FALSE AND CATEGORY-DEFINITION='SELECT * WHERE "CONTAINS-ITSELF"=FALSE'}

"SELECT * WHERE "CONTAINS-ITSELF"=FALSE":
{ DESCRIPTION="Select statement for enumerating All concepts which do not contain themselves" AND IS-CATEGORY-DEFINITION=TRUE AND IS-CONCEPT=TRUE AND IS RELATIONSHIP=FALSE AND CONTAINS-ITSELF=FALSE AND SELECT=TRUE AND "*" = TRUE AND "WHERE" = TRUE AND ATTRIBUTE-RELATIONSHIP-FILTER="CONTAINS-ITSELF=FALSE" }

Here it is as the bullet list again.

​

P=:​

• DESCRIPTION="all concepts which do not contain themselves"
• IS-CATEGORY=TRUE
• IS-CONCEPT=TRUE
• IS-RELATIONSHIP=FALSE
• CONTAINS-ITSELF=FALSE
• CATEGORY-DEFINITION='SELECT * WHERE "CONTAINS-ITSELF"=FALSE'
  • IS-CATEGORY-DEFINITION=TRUE
  • IS-CONCEPT=TRUE
  • IS-RELATIONSHIP=FALSE
  • CONTAINS-ITSELF=FALSE
  • SELECT=TRUE
  • "*" = TRUE
  • "WHERE" = TRUE
  • ATTRIBUTE-RELATIONSHIP-FILTER="CONTAINS-ITSELF=FALSE"

You actually have to add the result of this query into the database (for it to be all-inclusive) so you must assign a value to the flag. Both TRUE and FALSE would be wrong.

No, I don't. The results are their own individual objects. Dreams, Ball Bearings, Witches, Lint, very small rocks, a duck, and wood. All would be returned as results from the query without themself being included in the concept directly. They're all their own objects who have the attribute+relationship pair: "CONTAINS-ITSELF=FALSE". You're still thinking like this is constructing a set. And I thought you already admitted this simple fact that a direct inclusion wasn't needed.

Yes, you did admit this. You said: "You just need an 'included' relationship back to the whole "concept of all concepts". Great! We agree! It's the same with any concept. All that's needed is the included relationship (technically it's an attribute+relationship pair) back to the concept. And there is no reason to flag the concept as "CONTAINS-ITSELF=TRUE". No reason at all.

As you can see from the definition of P , above, the attribute+relationship pair is included in the concept, but the concept itself is more than that. And all of the results of the query are their own objects with the same attribute+relationship pair. But they're distinct objects seperate and apart from concept. So just because the attribute_relationship pair is shared, that doesn't mean the concept itself is included in itself. And it certainly doesn't mean the results of the query are directly included in the concept. The concept simply contains the method for finding and listing those concepts which match the condition.

It should be all good then right?

If not, I'm guessing you still think the concept is ONLY the attribute+relationship pair which defines inclusion/exclusion, and you're still thinking about this as a set with a function that defines... inclusion/exclusion. But it's more than that. And that is what prevents the problems you keep trying to insert into this.

You can't have a strict hierarchy that you can navigate down and end up back at the root, or any other higher level, for that matter. You have to be able to do that in an all-inclusive concept. Otherwise it simply can't be all-inclusive.

Sure I can. Regardless of whether I am selecting for P recursively, or all included objects recursively, or all categories recursively or any combination of attribute+relationship pairs recursively, I can search the entire conglomerate, and you haven't brought any valid reasons why I can't. All I need is an included attribute+relationship pair or pairs, and I can select for that.