Logical deduction (religion, the PoE)

[ratiocinator]

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.

Do you think that the Russell and some of the best mathematical minds who considered the problem he raised in the early 20th century, were less intelligent than you or didn't understand the examples you've given here, like taxonomies and other hierarchies? Because unless you do think that, then it's a 100% safe bet that you haven't understood the problem.

Remember this was all before formal axiomatised set theories, so they were just thinking in 'naive' or informal 'sets', i.e. just unrestricted groupings. The paradox was spotted as soon as you try to form a group of all groups, which directly relates to your 'all-inclusive' LI. You are suggesting that there is a solution that is as simple as dealing with a hierarchy. That is, you think they were stupid and/or ignorant and they painstakingly and carefully developed systems of axioms for formal set theory that retained the usefulness but got around the problem, for nothing. All they had to do was think about a hierarchy....

First. Please be honest. I told you the problem would be a loop condition, didn't I?

You were talking about a loop in constructing or representing LI, I'm talking about if you try recurse through the concepts it represents.

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

FALSE

Since P is the concept of all concepts that don't contain themselves, then if you set CONTAINS-ITSELF=FALSE for P, then it is missing a concept that doesn't contain itself. That concept is P.

No, I don't. The results are their own individual objects.

And that is self-contradictory. Since the result of any query is itself a concept, (as is the query, for that matter), the results of all possible queries must be in the database, otherwise it doesn't contain all concepts and is not all-inclusive. You called it an 'object' and all objects are concepts.

And frankly the analogy of a database and programming is not helping because it is not directly comparable with the abstract logic approach that you need to properly understand this sort of thing. You seem to have convinced yourself that you could 'code around' the problem, which just means that you haven't grasped how fundamental it is.

 

[ratiocinator]

Just to add a few more comments.

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.

This perfectly illustrates why the programming/database analogy is not helping. You are confusing the representation with the concept. It's easy to represent self-inclusion with a relationship or flag, but it doesn't change the concept.

I only brought up the representation because you'd misunderstood where the paradox was. and that was because you were thinking exclusively in terms of databases. If you think in abstract terms, self-inclusion is simple and doesn't, of itself, directly create a paradox.

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".

If you don't have the results of all possible queries in the database already, then you've given me a ready made set of concepts that aren't to LI, that I can add to it and not create duplicates, and the whole concept of something you can't add to collapses.

 

[timothy1027]

How are you able to be so certain about what people experienced and whether or not any gods made themselves known to them before reliable record keeping methods were invented?

Nobody has provided ANY evidence before, during or after reliable record keeping was invented and used.

 

[mikkel_the_dane]

Nobody has provided ANY evidence before, during or after reliable record keeping was invented and used.

Well, that is unknown in effect, because the truth of your claim rests on the absolute universal state of everything being nautral and that has no proof.
You are in effect as dogmatic as some religious people are.

 

[timothy1027]

Well, that is unknown in effect, because the truth of your claim rests on the absolute universal state of everything being nautral and that has no proof.
You are in effect as dogmatic as some religious people are.

I am not understanding your statement. Following is the pasted definition of the word "dogma"
------

"dogma​

noun​

dog·ma ˈdȯg-mə
ˈdäg-
plural dogmas also dogmata ˈdȯg-mə-tə
ˈdäg-
Synonyms of dogma
1
a: something held as an established opinion
especially : a definite authoritative tenet

b: a code of such tenets
pedagogical dogma

c: a point of view or tenet put forth as authoritative without adequate grounds

2: a doctrine or body of doctrines concerning faith or morals formally stated and authoritatively proclaimed by a church"

 

[mikkel_the_dane]

Nobody has provided ANY evidence before, during or after reliable record keeping was invented and used.

It is c: a point of view or tenet put forth as authoritative without adequate grounds.

In effect there is no reason to accept ANY as before, becuse that amounts to unknown as it is not reliable record keeping.
In straigth words it is unknown if anybody before reliable record keeping has given evidence.

Now for God in general and even wider religion as such, the Abrahamic Gods are not the only versions of gods and not all religions rely on theistic gods.
Rather a given religion is in practice refuted by simply holding another understanding of what the world is and what matters.
But that is not limited to religion, as you run into the same problem with evidence, reason, logic and so on.

So for critical thinking it in a sense ends here:

Cognitive Relativism | Internet Encyclopedia of Philosophy

iep.utm.edu

 

[Hermit Philosopher]

Well, this God supposedly does not want man to suffer. Yet there is suffering.

Dear @an anarchist,

Man makes his mark on earth and the earth reacts. Man makes his mark on the ecosystem and his fellow species react. Man makes his mark upon his brother and his brother reacts. Man makes his mark upon himself and he, himself reacts.

Whether agency is viewed as choice or/and causality, Man’s suffering is causes by Man.

Thus, the meaningful question is instead: why would a potential creator have chosen things to be governed by choice or/and causality and not by [creator’s] own “hand”?

Abrahamic faiths look to their scriptures for answers to that question and come up with many different reasons. Some choose to accept that they may not be able to identify one specific cause and instead say that they trust that their god knows what it’s doing.

I’m not omni x3 but I’d still ask myself: if I were to set up a mini ecosystem in my yard and let it run for itself; what reasons would I have for doing so? Would it be to cause it suffering?

Humbly,
Hermit

 

[ratiocinator]

Whether agency is viewed as choice or/and causality, Man’s suffering is causes by Man.

Whereas some of it is, what about natural disasters and disease? What did 'Man' do to cause childhood leukaemia, for example?

 

[Hermit Philosopher]

Whereas some of it is, what about natural disasters and disease? What did 'Man' do to cause childhood leukaemia, for example?

Natural disasters and deseases are not “curses” sent by a divine, to make us suffer. They too are -indirectly and/or directly- caused by our interaction with environment.

Specifically cancers are caused by mankind; by our use of natural resources, our innovations, the artefacts we produce and promote, our current way of life in general.

We very literally reap what we collectively sow.


Humbly,
Hermit

 

[ratiocinator]

Natural disasters and deseases are not “curses” sent by a divine, to make us suffer. They too are -indirectly and/or directly- caused by our interaction with environment.

In what way, exactly, do you think humans cause earthquakes or volcanic eruptions, for example?

Specifically cancers are caused by mankind; by our use of natural resources, our innovations, the artefacts we produce and promote, our current way of life in general.

That's a bold assertion. Obviously some of the things we do put carcinogens into the environment but I've never heard the suggestion that all cancers are due to human activity, let alone all diseases.

 

[dybmh]

Nobody has provided ANY evidence before, during or after reliable record keeping was invented and used.

My question is about before reliable record keeping was invented. I understand the reasons for being certain after that. Is it possible you are speaking with certainty, but you actually mean, extremely unlikely? And this comes from the assumption that there are no circumstantial differences between people now and people way back then which would be prohibitting contact with the divine and obtaining the evidence, here and now, which would be reliable?

What I mean is: is there an assumption that modern people should be able to produce evidence of the divine at least as well as primitive people? Could it be that there is a substantive difference between modern and primitive people such that evidence would be much more readily available to the primitive person, while at the same time virtually impossible to preserve this evidence for a modern person to review several 1000s of years later?

If this assumption is made, then the lack of evidence now, is considered a lack of evidence then, and all of it is blended together as if the circumstances way back then are identical to the circumstances now, as if the people way back then were identical the people now. But it is highly unlikely that this is the case. Therefore, the assumption is highly unlikely to be true, and the absolute certainty is also highly unlikely to be true.

 

[dybmh]

Do you think that the Russell and some of the best mathematical minds who considered the problem he raised in the early 20th century, were less intelligent than you or didn't understand the examples you've given here, like taxonomies and other hierarchies? Because unless you do think that, then it's a 100% safe bet that you haven't understood the problem.

This is irrelevant. I already addressed it. No I'm smarter, just had access to computers and these concepts from a relatively early age. And I've spent many many hours working with these concepts and ideas. Maybe take a look at the book Outliers. Outliers (book) - Wikipedia

There really is no mystery how to avoid the paradox. I brought you the wiki-article showing this. It's super simple.

Remember this was all before formal axiomatised set theories, so they were just thinking in 'naive' or informal 'sets', i.e. just unrestricted groupings. The paradox was spotted as soon as you try to form a group of all groups, which directly relates to your 'all-inclusive' LI. You are suggesting that there is a solution that is as simple as dealing with a hierarchy. That is, you think they were stupid and/or ignorant and they painstakingly and carefully developed systems of axioms for formal set theory that retained the usefulness but got around the problem, for nothing. All they had to do was think about a hierarchy....

Ummmm, I don't think you're accurately describing the sequence of events here, nor the amount of time between development of set theory and the discovery of Russell's paradox. But, it really isn't relevant.

You were talking about a loop in constructing or representing LI, I'm talking about if you try recurse through the concepts it represents.

It's exactly the same thing. Recursing through the concepts IS constructing LI.

Since P is the concept of all concepts that don't contain themselves, then if you set CONTAINS-ITSELF=FALSE for P, then it is missing a concept that doesn't contain itself. That concept is P.

Duuuuuude, you're stuck in a semantic loop that doesn't actually exist in the structure itself. All of this is coming from misinterpretting the words used. It's a semantic fault.

"contains" has 2 meanings.
Contains could be literal membership, or it could be a subset relationship.
∈ =/= ⊂

{A} ∈ {A} = FALSE
{A} ⊂ {A} = TRUE

P=∀Concept (Concept ∉ Concept → (Concept ∈ Concept = FALSE))
P ∉ P
P ⊂ P
The concept "All concepts that do not contain themself" is defined as a query.
A query is evaluating a subset relationship not literal membership.

P is included, belongs to the concept, but is not literally contained in, a member of, the concept.

And that is self-contradictory. Since the result of any query is itself a concept, (as is the query, for that matter), the results of all possible queries must be in the database, otherwise it doesn't contain all concepts and is not all-inclusive. You called it an 'object' and all objects are concepts.

No, the concept is a statement of conjunctions, disjunctions, and negations of attribute+relationship pairs which defines the results. Each individual result which is described by the concept is already included elsewhere. It doesn't need to be included twice.

But if this is a roadblock for you, queries in databases are stored in memory. In theory an infinite database would have infinite memory and could store infinte queries simultaneously. And this is what happens temporarily anytime I take a full backup (snapshot) of a database while it is online. The database spawns a new temporary offline database and populates it with absolutely everything including the schema definitions, all the permissions. Literally everything. But it's only temporary.

And the offline version is .. offline. It doesn't actually do anything. It doesn't spawn anything, it doesn't run the backup, it's not... omnipotent. Not the way the master database is. It has all the bits and pieces, all the relationships, but it is never online.

If this wasn't possible, if this paradox exists, universally, the way you say it does, I would never get an absolutely full backup. It used to be that way. I would have to take a server offline to do a complete backup. But, compression algorithms and journaling make it possible to take snapshots and full backups of a server while it's online.

So, if you literally need the results to be omnipresent, OK, we can do it, Boss. We have the technology. But that doesn't mean that the concept = the results. The concept produces the results the same as any function.

And frankly the analogy of a database and programming is not helping because it is not directly comparable with the abstract logic approach that you need to properly understand this sort of thing. You seem to have convinced yourself that you could 'code around' the problem, which just means that you haven't grasped how fundamental it is.

Or, it's the opposite. Maybe you haven't grasped how miniscule the problem is when all the power of an omnipotent GOD is combined with nearly unlimited imagination.

 

[dybmh]

Just to add a few more comments.

I really appreciate the time you're taking with this.

This perfectly illustrates why the programming/database analogy is not helping. You are confusing the representation with the concept. It's easy to represent self-inclusion with a relationship or flag, but it doesn't change the concept.

I only brought up the representation because you'd misunderstood where the paradox was. and that was because you were thinking exclusively in terms of databases. If you think in abstract terms, self-inclusion is simple and doesn't, of itself, directly create a paradox.

I suppose that's the literal definition of paradox. I see the loop condition included in that. And there IS a loop condition when contructing an all-inclusive set as it would have been imagined by Leibniz and Cantor and others. I include this in my understanding of Russel's paradox. I don't think I'm incorrect to do so. Perhaps you are only focused on one "deal-breaker", but I see at least 2.

If you don't have the results of all possible queries in the database already, then you've given me a ready made set of concepts that aren't to LI, that I can add to it and not create duplicates, and the whole concept of something you can't add to collapses.

They ARE included already, or they wouldn't be returned by the query. I said: "All would be returned as results from the query without themself being included in the concept directly." Directly. All the results from any possible query are already included.

Your challenge is to find one that isn't or can't be. If you do, then, you win.

 

[ratiocinator]

This is irrelevant. I already addressed it. No I'm smarter, just had access to computers and these concepts from a relatively early age.

And that is clearly colouring everything you say. And it's completely irrelevant. Turning it into a program cannot change a fundamental logical problem. It's not like people in the early 20th century didn't know about hierarchies or formal procedures.

Contains could be literal membership, or it could be a subset relationship.
∈ =/= ⊂

{A} ∈ {A} = FALSE
{A} ⊂ {A} = TRUE

P=∀Concept (Concept ∉ Concept → (Concept ∈ Concept = FALSE))
P ∉ P
P ⊂ P

This is set notation gibberish. I mean, each line means something but there is no connecting logic.

∈ ≠ ⊂
I know.

{A} ∈ {A} = FALSE
{A} ⊂ {A} = TRUE
In what context?

P=∀Concept (Concept ∉ Concept → (Concept ∈ Concept = FALSE))
P is a truism!? No.

P ∉ P
P ⊂ P
No context again.

P is defined (using 'set' in the informal sense) as the set of all sets A for which A ∉ A (you shouldn't put brackets round a symbol that represents a set). Also P ∈ LI.

So,

P = {x ∈ LI | x ∉ x} and P ∈ LI.
The problem is that P ∈ P ⇒ P ∉ P and P ∉ P ⇒ P ∈ P.

The concept "All concepts that do not contain themself" is defined as a query.
A query is evaluating a subset relationship not literal membership.

Both a query and its result (when run on LI) are concepts. If you put the concepts into LI then you have the above problem and if you don't, I can take any result of any query and add it to LI without a duplication and the whole idea of it being all-inclusive breaks down.

You really, really need to give up the idea that making this a program and a database is going to make any difference at all to the underlying logic.

They ARE included already, or they wouldn't be returned by the query. I said: "All would be returned as results from the query without themself being included in the concept directly." Directly. All the results from any possible query are already included.

Either the results of all queries are literally already in the database you're querying or they aren't and can therefore be added without duplication.

 

[dybmh]

And that is clearly colouring everything you say. And it's completely irrelevant. Turning it into a program cannot change a fundamental logical problem. It's not like people in the early 20th century didn't know about hierarchies or formal procedures.

Maybe they simply weren't motivated to apply the ideas the way I'm applying them. And since I brought an unbiased source supporting this idea, this is not about me. Unless you can show where the wiki article is wrong, then a conglomerate is a logically consistent, all inclusive structure with the same properties of a category of all categories. But that is not the same as a set of all sets.

Anyway, crying out "Blasphemy! This is a fundemental problem." isn't a valid argument. You are claiming that what I have defined is not all-inclusive. I am arguing it is. You have been repeatedly redefining what I've brought saying it's a list, it's a set, and there is no difference. Because of that I brought examples that are different: Taxonomy tables, Org charts, Family trees, Directory structures, File Systems, the periodic table, online full backups ( snapshots ), ACL (Access Control Lists). All of these show that all inclusive structures do exist. Even a book, any book, is an all-inclusive conglomerate of the concepts contained in the book.

What have brought shows:

1) What I am defining is not a set. Comparing it to a set is a false equivilance.
2) An all inclusive conglomerate is logically possible. It has not been disproven by anyone.

To refute #1, you need to show that what I'm defining is equivilant to a set. It can't be done. To refute #2, you need to show that the wiki article is wrong. Maybe you can do it, but I doubt it. I have many strong reasons to believe I am right and you are wrong about this. So far you have only brought "Blasphemy".

We're starting to get into some actual attempts at refutation. But the redefining of Literal Infinity into a set is a failed dead argument. And claiming it can't be done on principle is also a failed argument. Considering the concept "all concepts which don't contain themself" is basically dead. Unless there is something more than semantics, you'll need another example of a concept which cannot be included.

OK?

This is set notation gibberish. I mean, each line means something but there is no connecting logic.

Not really. It looks like you've lost, or are ignoring, the context. That's not my fault.

∈ ≠ ⊂
I know.

Great. ( Not gibberish then )

{A} ∈ {A} = FALSE
{A} ⊂ {A} = TRUE
In what context?

The context is: Self-reference. {A}={A}.
This reminds me of your objection to ∞+∞=∞, as if I didn't intend for ∞=∞.

( Not gibberish, is it? What I wrote is true, if the context is maintained from our conversation. )

P=∀Concept (Concept ∉ Concept → (Concept ∈ Concept = FALSE))
P is a truism!? No.

That's a claim. I disagree. It's always true. And ( if you can evaluate it as "Not a truism" then it's not gibberish, is it? )

The burden is on you. Please bring an example where P as defined above is false AND holding the necessary condtions:

P=P
Concept=Concept
False=False
P AND Concept AND False =/= {}

IOW, Please bring 1 example where it is false. Please no pedantic nonsense. The context is self-reference. All of these concepts exist. Each word means 1 and only 1 thing.

P ∉ P
P ⊂ P
No context again.

The context is self reference. P=P. What I wrote is true. It's not my fault the context is ignored or lost. It's not gibberish; it's 100% true.

The point of these examples is to show:

1) There is an important difference between "literal membership" and "included in the concept".
2) "IS-CONTAINED=FALSE" describes NOT "literal membership". But that does not necessarily mean that it is NOT "included in the concept".

P is defined (using 'set' in the informal sense) as the set of all sets A for which A ∉ A (you shouldn't put brackets round a symbol that represents a set). Also P ∈ LI.

Just because you can define a concept in a way that produces a paradox doesn't mean it needs to be defined that way. You would need to take what I defined and show that it, infact, is equivalent to what you are defining. So far it's just been "If I define P like this, it produces a paradox." But I can define the concept and produce the the results which match the condition without the paradox.

So,

P = {x ∈ LI | x ∉ x} and P ∈ LI.
The problem is that P ∈ P ⇒ P ∉ P and P ∉ P ⇒ P ∈ P.

Good. Using this precise definition, P ( which is not the same as the P I defined ) as you have defined it above would not be a category. It would be a concept with the attribute+relationship pair ( among others ):

IS-CONTRADICTION=TRUE

See how simple that is. It would belong to the category with the attribute-relationship-filter: "IS-CONTRADICTION=TRUE" along withthese other contradicting concepts:

Married-Bachelor
Square-Circle
True-Lies
Partial-Circumcision
Military-Intelligence

Both a query and its result (when run on LI) are concepts. If you put the concepts into LI then you have the above problem and if you don't, I can take any result of any query and add it to LI without a duplication and the whole idea of it being all-inclusive breaks down.

No. There is no problem. You defined a contradiction and it fits neatly into Literal Infinity right next to the other contradictions. So far you have not brought any example of a concept which is not included.

Literal infinity is all inclusive. Nothing is missing. Nothing can be excluded. All the results are included. Everything you can think of and more is included.

If you can think of something that isn't, then, you win.

You really, really need to give up the idea that making this a program and a database is going to make any difference at all to the underlying logic.

Why? Your example when properly defined is included as a contradiction. My corresponding concept which Selects for all lacking literal self-reference also works. It produces results which are all the concepts which don't include itself. It does include a link to itself 1 time in these results in the same way that a subset relationship is true for itself. But it's not a literal self reference which will cause any problems.

Either the results of all queries are literally already in the database you're querying or they aren't and can therefore be added without duplication.

The results of all queries are literally already in the database. If you define a contradiction, then there will be no results. For any non-contradicting query, those results are already included. If you need a duplicate copy. That can be accomplished too.

 

[ratiocinator]

Maybe they simply weren't motivated to apply the ideas the way I'm applying them.

Claiming superiority again.

And since I brought an unbiased source supporting this idea, this is not about me.

You're referenced a lot of other formal systems but you aren't actually using any of them, so they are irrelevant. If you want to use another set theory or category theory, then please feel free to reformulate your proposal in terms of one of those and we can see if it then works.

1) What I am defining is not a set. Comparing it to a set is a false equivilance.

It is the absolute epitome a set in the naive, unrestricted sense that gave rise to Russell's paradox. You are trying to put literally everything into it.

2) An all inclusive conglomerate is logically possible. It has not been disproven by anyone.

As I said, if you want to use category theory, then go ahead. You own database and programming approach does not gain any credence from formal mathematics unless you can show direct equivalence.

ETA: It's worth noting that you are up against two mathematically established results. Both the (naive) set of all sets problems (e.g. Russell's paradox) and the 'no largest infinity' result. No matter how you define infinity, you can always construct a larger one.

Great. ( Not gibberish then )

As I said, each line means something by itself. It was the whole lot that amounted to gibberish.

The context is self reference. P=P.

Now we have: P ∉ P, P ⊂ P, and P=P. That basically says that P is itself (wow, is it!?) and that it isn't in itself (which would be wrong).

The point of these examples is to show:

1) There is an important difference between "literal membership" and "included in the concept".
2) "IS-CONTAINED=FALSE" describes NOT "literal membership". But that does not necessarily mean that it is NOT "included in the concept".

And the programming/database approach again shows how flawed it is. How you represent it is irrelevant. The concept is all important.

Good. Using this precise definition, P ( which is not the same as the P I defined ) as you have defined it above would not be a category. It would be a concept with the attribute+relationship pair ( among others ):

IS-CONTRADICTION=TRUE

See how simple that is. It would belong to the category with the attribute-relationship-filter: "IS-CONTRADICTION=TRUE" along withthese other contradicting concepts:

Married-Bachelor
Square-Circle
True-Lies
Partial-Circumcision
Military-Intelligence

*sigh*

This isn't an external contradictory concept that has been included because it's a concept. This has been directly deduced from the very existence of LI.

Once you've got LI, you've got to be able to form (informal) subsets from it in any way you want. So using an arbitrary selection function ψ,

∃y∀x(x ∈ y ⟺ ψ(x))

Now, all we have to do is define ψ(x) as x ∉ x, and we have

∃y∀x(x ∈ y ⟺ x ∉ x)

Then P = y and you have your problem. Unless you start adding logical restriction to the way LI works (which would compromise its necessary generality), then you hit the contradiction.

What's more, you have now added endless bells and whistles to the LI concept, so it now has a structure, queries, and all sorts of flags associated with each concept. All of this makes any sort of 'nullification', i.e. somehow identifying it with a single, borderless unity, even more absurd than it was to begin with.

 

[dybmh]

Claiming superiority again.

No. Come on, that's not what I said. I said: "Maybe they simply weren't motivated to apply the ideas the way I'm applying them." IOW, maybe they're not religious, or, they don't care about the problem of evil, or they don't care about strict monotheism, or they do care about these things but they approach it from pure faith, or they do care but approach it from pure mystery...

There's so many reasons why a person would not be motivated to do what I'm doing. And it has nothing to do with intelligence.

Are you motivated to do everything and anything?

You're referenced a lot of other formal systems but you aren't actually using any of them, so they are irrelevant. If you want to use another set theory or category theory, then please feel free to reformulate your proposal in terms of one of those and we can see if it then works.

I quoted a wiki article which states:

​

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.​

​

Category of small categories - Wikipedia

en.m.wikipedia.org

​

This shows that there exists a logical concept which can be called a quasi-category or a conglomerate which has all the properties of a category of all categories with a slighty different name. AND changing the name avoids Russell's paradox.

This is an unbiased source which confirms that I am correct. A category or all categories does exist. It hasn't been disproven. It just needs a minor sift in nomenclature to avoid the paradox. In addtion to this, I brought many examples of all-inclusive concepts. And I listed several set theories which permit "the set of all sets".

So, I have 3 reasons to believe I am correct about the existence of a category of all categories:

1) The wiki article confirms it
2) There are many real life examples
3) There are several set theories which permit a set of all sets

Even if #3 is weak because I don't know how they avoid Russel's Paradox, your objection is equally weak because you don't know it either. Even if we remove #3 from the list. I still have 2 strong reasons. If I were you, I would try to undermine the wiki article somehow.

ETA: This appears to be the #1 extension to naive set theory which permits the set of all sets. But there are also formalized axioms of seperation and limitation defining a class which included all sets. But the function composition is the big ticket item. This is what produces the structure: heirarchy and inheritance. The class definition is only an idea. Function compostion is the mechanics behind it.

Inhertiance is what resolves all the infinte sets into 1 conglomerate.

Function composition - Wikipedia

en.m.wikipedia.org

It is the absolute epitome a set in the naive, unrestricted sense that gave rise to Russell's paradox. You are trying to put literally everything into it.

Thats a claim. All I need is one example of a difference and the claim is false.

1) Sets do not have sequence. { A, B, C } = { C, B, A }

As I said, if you want to use category theory, then go ahead. You own database and programming approach does not gain any credence from formal mathematics unless you can show direct equivalence.

Category Theory (Stanford Encyclopedia of Philosophy)

plato.stanford.edu

First sentence: Category theory has come to occupy a central position in contemporary mathematics and theoretical computer science.

A central position in theoretical computer science. Central. It's the heart of it.

The point of bringing category theory is "the category of all categories" has not been disproven. It is a logically consistent concept wth no paradoxes. It is called either a quasi-category or a conglomerate. Once I have confirmed that the claim "It can't be done because of Naive Set Theory and ZFC has a rule against it." is fallacious, I can move on to define Literal Infinity as an infinite relational database. Your challenge is to find something that is somehow missing from this concept.

ETA: It's worth noting that you are up against two mathematically established results. Both the (naive) set of all sets problems (e.g. Russell's paradox) and the 'no largest infinity' result. No matter how you define infinity, you can always construct a larger one.

Naive set theory is not Category Theory nor is it Computer Science. There are many differences.
Cantor's theorum confirms that Literal Infinity's attributes are infinite. So what? That doesn't mean I can't create an all inclusive category. Watch:

Literal Infintity = All that exists + All that doesn't exist

1 All inclusive conglomerate at the top. 2 massive categories beneath it. Nothing is excluded. The contents of those categories is infinite, but that doesn't mean that there is anything excluded.

As I said, each line means something by itself. It was the whole lot that amounted to gibberish.

No, the context was lost ot ignored. That's not my fault.

Now we have: P ∉ P, P ⊂ P, and P=P. That basically says that P is itself (wow, is it!?) and that it isn't in itself (which would be wrong).

1) P ∉ P, P ⊂ P, and P=P are all true.
2) You lost the context of self-reference forcing me to state the obvious. P=P. The same thing happened with ∞=∞.
3) I didn't say that P is not "in" P. I said that "contains" could mean 2 things.
4) "Included in" is the subset relationship. P is in P. P ⊂ P
5) "Contains" is literal membership. P does not contain P. P ∉ P

And the programming/database approach again shows how flawed it is. How you represent it is irrelevant. The concept is all important.

You need to find a concept which is not contained in Literal Infinity as I have defined it. So far you have failed to do so.

This isn't an external contradictory concept that has been included because it's a concept. This has been directly deduced from the very existence of LI.

Once you've got LI, you've got to be able to form (informal) subsets from it in any way you want. So using an arbitrary selection function ψ,

Yes, I am using SELECT FROM WHERE ... to do precisely that. You need to find an example where that fails.

∃y∀x(x ∈ y ⟺ ψ(x))

Now, all we have to do is define ψ(x) as x ∉ x, and we have

∃y∀x(x ∈ y ⟺ x ∉ x)

Then P = y and you have your problem. Unless you start adding logical restriction to the way LI works (which would compromise its necessary generality), then you hit the contradiction.

∃y∀x(x ∈ y ⟺ x ∉ x) is a contradiction, it has no results. It would exist as a contradictory concept. Nothing more nothing less.

You need to show how SELECT FROM WHERE cannot produce what you are calling an "informal subset".

What's more, you have now added endless bells and whistles to the LI concept, so it now has a structure, queries, and all sorts of flags associated with each concept. All of this makes any sort of 'nullification', i.e. somehow identifying it with a single, borderless unity, even more absurd than it was to begin with.

LOL. You cannot object to endless bells and whistles, that is a result of absolute omnipotence.

 

[ratiocinator]

No. Come on, that's not what I said. I said: "Maybe they simply weren't motivated to apply the ideas the way I'm applying them." IOW, maybe they're not religious, or, they don't care about the problem of evil, or they don't care about strict monotheism, or they do care about these things but they approach it from pure faith, or they do care but approach it from pure mystery...

It's really got nothing to do with your faith. Your concept of LI, if it is provable, completely overturns some well established results. You should be sending it to a mathematics journal, not posting here, if you really believed you'd done it rigorously.

Seriously.

1) The wiki article confirms it

It only does so in the context of category theory. You don't appear to be using that here. So, as I said, if you want to relate your whole argument to category theory, then do so. Otherwise, it's as irrelevant as the other set theories.

2) There are many real life examples

Such as?

I don't know how they avoid Russel's Paradox, your objection is equally weak because you don't know it either.

Burden of proof (philosophy) - Wikipedia

en.wikipedia.org

I'm not the one trying to prove something.

3) I didn't say that P is not "in" P. I said that "contains" could mean 2 things.
4) "Included in" is the subset relationship. P is in P. P ⊂ P
5) "Contains" is literal membership. P does not contain P. P ∉ P

I'm not sure why you are finding this hard. Your LI, is the concept of all concepts. It is itself a concept, so LI ∈ LI. Now P (as I defined, and as used in Russell's paradox) is a subset of LI: P ⊂ LI, defined as P = {x ∈ LI | x ∉ x}. The problem is P ∈ P ⇒ P ∉ P and P ∉ P ⇒ P ∈ P. Where is there ambiguity? The problem is that both P ∈ P and P ∉ P are wrong, so LI has to be inconsistent.

Because you are trying to deal with literally everything (all possible concepts) you cannot restrict anything. For example, every single type of grouping from category theory or any different set theories are all going to be concepts, so, despite those systems being able to avoid Russell's paradox using different types of groupings. your LI can't do that. It has to include itself, because it can't be all inclusive if it doesn't.

Yes, I am using SELECT FROM WHERE ...

What difference do you think that makes? It doesn't matter if it's the result of a query, you have already said that all query results are literally already in the database, so the contradiction is inherent regardless.

∃y∀x(x ∈ y ⟺ x ∉ x) is a contradiction, it has no results.

The contradiction is a direct logical consequence of the existence of LI. Again, you're effectively trying to tell me that some of the best minds of the early 20th century were stupid. They should have just ignored the contradiction!

 

[dybmh]

It's really got nothing to do with your faith. Your concept of LI, if it is provable, completely overturns some well established results. You should be sending it to a mathematics journal, not posting here, if you really believed you'd done it rigorously.

Seriously.

The point is, you are lowering your argument and making it about me, personally, and not about what I am saying. I have indulged you and explained myself, eventhough I probably shouldn't. I did not bring up "my faith", I was giving possible reasons why others who are smarter than me may not be motivated to do what I'm doing.

You misinterpretted or misrepresetned my statement about motivation as a statement of my own superiority, and it wasn't. And discouraging me from posting my ideas here is counter to stated the mission of this forum.

I have reasons for posting this here. I also have reasons for not sending it to a journal. Those reasons are irrelevant to whether or not what I'm saying is logically consistent.

It only does so in the context of category theory. You don't appear to be using that here. So, as I said, if you want to relate your whole argument to category theory, then do so. Otherwise, it's as irrelevant as the other set theories.

That cuts both ways. The set of all sets is disproven ONLY in the context of Naive Set theory and ZFC. If you want to disprove Literal Infinity as I have defined it, then you need to relate my whole argument to either Naive Set Theory or to ZFC. It cannot be done.

Such as?

Taxonomy
The Periodic Table
Family Tree
Org Charts
Directory Structures
File Systems
Online Full Backups (Snapshots)
Inheritable access control lists
Any book anywhere

Each of these is an all inclusive conglomerate of the concepts it contains.

Burden of proof (philosophy) - Wikipedia

en.wikipedia.org

I'm not the one trying to prove something.

That's not true. You're trying to disprove what I'm saying which is an attemt at proving it cannot be done.

I claimed a category of all categories is logically consistent, and has no inherent paradoxes. I brought evidence to support it.
You claim it cannot be logically consistent and it must contain a paradox. You have not brought any evidence to support it.

I claim that an infinite relational database is logically consistent and has no inherenet paradoxes. The evidence supporting this comes from showing that other logically inconsisent concepts and paradoxes are properly defined in it without problems.
You claim that an infinite relational database is not logically consistent and has inherent paradoxes. You have not brought any evidence to support it.

You keep making claims about Naive Set Theory, but what I am describing extends beyond it. You have not addressed those extensions in spite of my repeated posts about them. Instead you repeatedly reassert, "It can't be done."

Each time you assert, "It can't be done." You have the burden to show it can't be done. My claim is It's possible, and I have shown it's possible.

I'm not sure why you are finding this hard. Your LI, is the concept of all concepts. It is itself a concept, so LI ∈ LI. Now P (as I defined, and as used in Russell's paradox) is a subset of LI: P ⊂ LI, defined as P = {x ∈ LI | x ∉ x}. The problem is P ∈ P ⇒ P ∉ P and P ∉ P ⇒ P ∈ P. Where is there ambiguity? The problem is that both P ∈ P and P ∉ P are wrong, so LI has to be inconsistent.

It's not hard for me. I see your point of view. You are assuming that "concept of all concepts" is literal group membership "LI ∈ LI". But that's not the only way to describe that. That same idea can be derived in multiple ways logically. You are choosing to define it as paradox in Naive Set Theory. But that is not the ONLY way to do it.

Because you are trying to deal with literally everything (all possible concepts) you cannot restrict anything. For example, every single type of grouping from category theory or any different set theories are all going to be concepts, so, despite those systems being able to avoid Russell's paradox using different types of groupings. your LI can't do that. It has to include itself, because it can't be all inclusive if it doesn't.

You said: "your LI can't do that. It has to include itself, because it can't be all inclusive if it doesn't."

Yes, it can. "including itself" is nothing more than an identity. If you need it to be more than that, if you need an exact replica of the entire conglomerate contained in itself, that can be accomplished too. With infinite storage, it could spawn an entire replica of itself.

What difference do you think that makes? It doesn't matter if it's the result of a query, you have already said that all query results are literally already in the database, so the contradiction is inherent regardless.

Please note the claim: "the contradiction is inherent regardless". You have the burden to show that the contradiction is inherenet regardless. Regardless means no matter what I do.

You are asking: "What difference do you think that makes?"

The difference is, you are raising a possible contraditction. I am working around it. That means the contradition is not inherent regadless of what I do. Because of this your claim "the contradiction is inherent regardless" is proven false.

Your challenge is to bring an example of a contradiction that I cannot work around. Some concept, any concept which is not included. If you can do that, you win.

The contradiction is a direct logical consequence of the existence of LI. Again, you're effectively trying to tell me that some of the best minds of the early 20th century were stupid. They should have just ignored the contradiction!

No, I'm not saying that.

All I'm doing is showing you that anything and everything is included in Literal Infinity, including any contradiction and paradox you can imagine.

You're claiming it's blasphemy for me to say what I'm saying. These ideas have been in development for a long time. Take a look at Gottlob Frege, the great grandparent of Functional Composition, which lead to the inheritance that extends Naive Set Theory, avoiding Russel's paradox. If you look at Frege logic, you'll start to see the beginnings of modal logic, relevance logic, things that classical logic and set theory are lacking. And you'll start to see formal mathematical hierarchies forming. This is back in the mid 1800s.

 

[ratiocinator]

I did not bring up "my faith", I was giving possible reasons why others who are smarter than me may not be motivated to do what I'm doing.

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

If you want to disprove Literal Infinity as I have defined it, then you need to relate my whole argument to either Naive Set Theory or to ZFC. It cannot be done.

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

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

Taxonomy
The Periodic Table
Family Tree
Org Charts
Directory Structures
File Systems
Online Full Backups (Snapshots)
Inheritable access control lists
Any book anywhere

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

Each of these is an all inclusive conglomerate of the concepts it contains.

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

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

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

but the concept of all concepts is a concept?​