Logical deduction (religion, the PoE)

[ratiocinator]

No a concept is a singleton.

I can have a concept that is the concept of a group of concepts.

Please precisely describe the conceptual difference between LI and {LI}?

Okay.

It's easier to see from the finite examples but LI has some sort of infinite cardinality because it contains an infinite number of concepts, {LI} has a cardinality of 1 because it contains just one element. That element is LI.

A finite example is P = {1, 2, 3}, Q = {4, 5}. Q has cardinality 2 but {Q} = {{4, 5}} has cardinality 1.
Now P ∪ Q = {1, 2, 3, 4, 5} (cardinality 5), but P ∪ {Q} = {1, 2, 3, {4, 5}} (cardinality 4).

My signature asserts the existence of an infinite set, starting with just the empty set, ∅ = {}, using exactly this process.
We start with ∅ ∈ x, so the empty set is in x, but then we have ∀y ∈ x((y ∪ {y}) ∈ x).

So, if we work through building x, we start with ∅ ∈ x
so x = {∅, ...} = {{}, ...}
Then take ∀y ∈ x((y ∪ {y}) ∈ x), with y = ∅ from above,
∴ ∅ ∪ {∅} = {∅} = {{}} ∈ x,
∴ x = {∅, {∅}, ...} = {{}, {{}}, ...}
Now repeat with y = {∅}
∴ {∅} ∪ {{∅}} = {∅, {∅}} ∈ x
∴ x = {∅, {∅}, {∅, {∅}}, ...} = {{}, {{}}, {{}, {{}}}, ...}
...and so on.

Fun, eh?

 

[Ella S.]

I hope you don't mind that I've cut down your reply to this particular segment, as I think it's the most interesting point of disagreement and the only part that I feel like responding to. I did read the rest of your reply and found it well-written and well thought out and, even though I don't fully agree with it, it's not the part of the discussion that interests me.

If there is an eternal, infinite, tri-omni god, then, there must be an "otherness" and there must be "others" in order for the material world to exist. And, everything material that exists are those others. The ones you described in your earlier post? If they exist, I propose, they are a part of everything, but have no will of their own. It's a dirty little secret, but, if so, it explains a great deal. Particularly divine hiddeness.

But none of that compromises omnibenevolence if the others are vessels of omnibenevolence which is flowing, emanating, into each and every material thing which exists. The omnibelevolence ( nurturing ) is invested inside the otherness. And it requires the otherness. Without it, everything reverts back to the source. So the omnipotent could pull the plug on individual things, or on the whole material world. So it's not that the omnipopent cannot interfere with free-will. But there is a point where everything collapses.

The Kabbalistic understanding of God is a remarkably coherent and self-consistent one. I agree with you that it allows for the compatibility of an almighty and all-loving God with natural suffering thanks to its key concepts like reflection and alienation.

I can understand how you could describe that model of God as omnimax. That's something that slipped my mind entirely, I'm sorry.

Normally, when the topic of an omnimax God arises, I'm thinking particularly of Aquinas and other Church fathers who are attributed with formalizing these concepts in the Western canon. In fact, "omnipotence" and "omnibenevolence" are Latin terms, which are used Ecclesiastically by the Roman Catholic Church, and so that's the model I tend to think these ideas invoke.

You're right that these terms have been borrowed in English by other theologies and can have completely different meaning from what the church fathers defined. In that sense, I think we're arguing past each other, and I think that's something I should have thought about earlier.

 

[dybmh]

I can have a concept that is the concept of a group of concepts.

{"the concept of a group of concepts"}

If you notice I defined it this way earlier. Each object in Literal Infinity are defined as a statement, singular, of conjunctions, disjunctions, and/or negations. Just 1 statement per object. That's it.

To use your literal example: L = { 1,2,3,4 } = the concept of { "1 AND 2 AND 3 AND 4" }

Okay.

It's easier to see from the finite examples but LI has some sort of infinite cardinality because it contains an infinite number of concepts, {LI} has a cardinality of 1 because it contains just one element. That element is LI.

First, please note, you said it was easier to show with finite examples. That means I should be able to use finite examples too without objections.

You're pointing to cardinality.... Please remember what I said, and what you said. I said:

It is irrelevant when considering the cardinality. Because 1 concept can include many other concepts by abstraction. That is the definition of a concept.

Then you said:

But we're not.

Actually you were. You just didn't realize it at the time. And here you are doing it again.

The fact that |{LI}| > |LI| is irrelevant. {"dreams","REM"} are conceptually included in {"things that happen when asleep"} That is what a concept means. That is its definition.

A finite example is P = {1, 2, 3}, Q = {4, 5}. Q has cardinality 2 but {Q} = {{4, 5}} has cardinality 1.
Now P ∪ Q = {1, 2, 3, 4, 5} (cardinality 5), but P ∪ {Q} = {1, 2, 3, {4, 5}} (cardinality 4).

My signature asserts the existence of an infinite set, starting with just the empty set, ∅ = {}, using exactly this process.
We start with ∅ ∈ x, so the empty set is in x, but then we have ∀y ∈ x((y ∪ {y}) ∈ x).

So, if we work through building x, we start with ∅ ∈ x
so x = {∅, ...} = {{}, ...}
Then take ∀y ∈ x((y ∪ {y}) ∈ x), with y = ∅ from above,
∴ ∅ ∪ {∅} = {∅} = {{}} ∈ x,
∴ x = {∅, {∅}, ...} = {{}, {{}}, ...}
Now repeat with y = {∅}
∴ {∅} ∪ {{∅}} = {∅, {∅}} ∈ x
∴ x = {∅, {∅}, {∅, {∅}}, ...} = {{}, {{}}, {{}, {{}}}, ...}
...and so on.

Fun, eh?

It is fun, and TBH, it's beautiful. But it's not relevant to concepts. The included concepts will ALWAYS be greater that the concept which includes it. So proving that the cardinality of {LI} is greater than LI does not represent a contradiction or a lack of inclusion. It's actually perfectly consistent and describes all-inclusion.

 

[dybmh]

I hope you don't mind that I've cut down your reply to this particular segment, as I think it's the most interesting point of disagreement and the only part that I feel like responding to. I did read the rest of your reply and found it well-written and well thought out and, even though I don't fully agree with it, it's not the part of the discussion that interests me.

No problem-o

The Kabbalistic understanding of God is a remarkably coherent and self-consistent one. I agree with you that it allows for the compatibility of an almighty and all-loving God with natural suffering thanks to its key concepts like reflection and alienation.

I can understand how you could describe that model of God as omnimax. That's something that slipped my mind entirely, I'm sorry.

Normally, when the topic of an omnimax God arises, I'm thinking particularly of Aquinas and other Church fathers who are attributed with formalizing these concepts in the Western canon. In fact, "omnipotence" and "omnibenevolence" are Latin terms, which are used Ecclesiastically by the Roman Catholic Church, and so that's the model I tend to think these ideas invoke.

You're right that these terms have been borrowed in English by other theologies and can have completely different meaning from what the church fathers defined. In that sense, I think we're arguing past each other, and I think that's something I should have thought about earlier.

Ah. I thought you had considered it based on the specific words you had chosen.

 

[ratiocinator]

{"the concept of a group of concepts"}

If you notice I defined it this way earlier. Each object in Literal Infinity are defined as a statement, singular, of conjunctions, disjunctions, and/or negations. Just 1 statement per object. That's it.

To use your literal example: L = { 1,2,3,4 } = the concept of { "1 AND 2 AND 3 AND 4" }

Not only are you again scrabbling around making things up as we go along, but that's going to give you a bigger and more immediate problem, well, more than one, actually, and that's before we get to the semantic nonsense it generates.

Firstly, LI itself would then have to be a conjunction of every possible concept, and, as it is a concept, it would have to include itself, which would lead to an immediate infinite regress (forget Russell's paradox).

Secondly, it becomes trivially easy to create concepts that aren't in LI, let's to the disjunction of all possible concepts, or just one or two, for that matter, just for fun.

You're pointing to cardinality....

I was trying to point out the differences between LI and {LI}, as you asked me to. It is still irrelevant to the point of adding new things to LI, you still don't need to change the cardinality. Assuming LI ∉ LI,

LI ∪ {LI} ≠ LI, but |LI ∪ {LI}| = |LI|.

The fact that |{LI}| > |LI| is irrelevant.

Did you read what I said? This is backwards and irrelevant. In fact |{LI}| = 1 < |LI|.

That's unless you go with your bizarre conjunction idea above and then we have |{LI}| = 1 = |LI|, which is trivially easy to add to, just on that basis. I could just and any separate concept at all to it.

{"dreams","REM"} are conceptually included in {"things that happen when asleep"} That is what a concept means. That is its definition.

Now you've gone back to hand-waving. I note from before that you wanted to define set of all sets which do not contain themselves as:

{ "the concept of the set of all sets which do not contain themself" }

If you mean this in some sort of literal way, then we could just do this:

LI = {"all possible concepts"}

It has a cardinality of one, it tells us nothing, and it's trivially easy to add to.

The included concepts will ALWAYS be greater that the concept which includes it.

No idea what you're trying to say here. Greater in what way?

So proving that the cardinality of {LI} is greater than LI does not represent a contradiction or a lack of inclusion.

Clearly you've not understood what I said at all. Again, the cardinality of {LI} is one.

 

[dybmh]

Not only are you again scrabbling around making things up as we go along, but that's going to give you a bigger and more immediate problem, well, more than one, actually, and that's before we get to the semantic nonsense it generates.

I'm not making things up as we're going along. The definition was given several times. And if you're refering to easily including any contradiction, that was all part of the plan.

Firstly, LI itself would then have to be a conjunction of every possible concept, and, as it is a concept, it would have to include itself, which would lead to an immediate infinite regress (forget Russell's paradox).

No. The any infinite conjunction can be represented by a singleton. No different than {ℕ}, {ℤ}, {ℝ}, or any function { "x=y"}. There are infinite examples of this. It is no different for LI.

Secondly, it becomes trivially easy to create concepts that aren't in LI, let's to the disjunction of all possible concepts, or just one or two, for that matter, just for fun.

All negations and compliments are included in LI as part of the defintion I brought. The "compliments/negations" are discovered 30 times in the nested loop procedure I brought. It's in post #311 - June 15th, a little over 2 weeks ago. First revision.

I was trying to point out the differences between LI and {LI}, as you asked me to. It is still irrelevant to the point of adding new things to LI, you still don't need to change the cardinality. Assuming LI ∉ LI,

LI ∪ {LI} ≠ LI, but |LI ∪ {LI}| = |LI|.

I asked you for a conceptual difference, since we're discussing concepts. From what you are telling me, there is no conceptual difference, because a concept does not need to be a member inorder to be included. The example I brought {"dreams","REM"} are included in {"things that happen while asleep"} proves this, but there are infinite examples.

Did you read what I said? This is backwards and irrelevant. In fact |{LI}| = 1 < |LI|.

Yes, I read it backwards.

That's unless you go with your bizarre conjunction idea above and then we have |{LI}| = 1 = |LI|, which is trivially easy to add to, just on that basis. I could just and any separate concept at all to it.

That would be adding a duplicate. Duplicates are filtered out.

Now you've gone back to hand-waving. I note from before that you wanted to define set of all sets which do not contain themselves as:

{ "the concept of the set of all sets which do not contain themself" }

If you mean this in some sort of literal way, then we could just do this:

LI = {"all possible concepts"}

What you're calling handwaving is me, restating the definition you have been provided.

And you have LI defined wrong above. LI = {all possible concepts + all impossible concepts}. Nothing is excluded, by defintion. I'm quite sure this issue of impossible concepts was addressed already.

It has a cardinality of one, it tells us nothing, and it's trivially easy to add to.

Only if you change what I've defined.

No idea what you're trying to say here. Greater in what way?

In the way that |{cars,trucks,buses}| > |{transportation}|. That's what we were talking about.

Clearly you've not understood what I said at all. Again, the cardinality of {LI} is one.

So is LI.

 

[ratiocinator]

The definition was given several times. And if you're refering to easily including any contradiction, that was all part of the plan.

I don't recall you ever posting anything remoty like { 1,2,3,4 } = the concept of { "1 AND 2 AND 3 AND 4" }. And of course it wrong, the general group is not the same concept as the conjunction.

No. The any infinite conjunction can be represented by a singleton. No different than {ℕ}, {ℤ}, {ℝ}, or any function { "x=y"}. There are infinite examples of this. It is no different for LI.

Again, you don't seem to get that "all possible concepts" is a concept itself. It's impossible to be complete without including itself. That is fundamentally different to all the other examples you've brought up.

All negations and compliments are included in LI as part of the defintion I brought. The "compliments/negations" are discovered 30 times in the nested loop procedure I brought. It's in post #311 - June 15th, a little over 2 weeks ago. First revision.

You keep on posting endless different snippets that don't seem to add up to a whole picture. If you're going to represent things like { 1,2,3,4 } as { "1 AND 2 AND 3 AND 4" }, then why not LI itself {c1, c2, c3,......} as {"c1 AND c2 AND c3 AND...."} (c1 etc. being concepts)? If not,, then what criteria are being used? The point basically is that a group of concepts is not the same as the conjunction of its elements. The grouping is one concept and the conjunction is another. Hence within all concepts, you have to have both, so we're back at square one with Russell's paradox.

I asked you for a conceptual difference, since we're discussing concepts. From what you are telling me, there is no conceptual difference, because a concept does not need to be a member inorder to be included.

Of course there's a fundamental conceptual difference, and pointing the different cardinality was a way to try and get this across. This is exactly why I can add to LI if it doesn't include itself as an element by doing this: LI ∪ {LI}. That is not a duplicate unless LI ∈ LI and then we get Russell's paradox.

So is LI.

If |LI| = 1, then it's easy to add to without duplicating anything. LI ∪ {cat} would do it. It doesn't matter if cat is included in whatever the single element of LI is, it isn't included as a separate element, so I can add it.

 

[dybmh]

I don't recall you ever posting anything remoty like { 1,2,3,4 } = the concept of { "1 AND 2 AND 3 AND 4" }. And of course it wrong, the general group is not the same concept as the conjunction.

I defined the concept as a single statement of conjunctions disjunctions and negations 3 times. The first time was post #332, immediately after you asked for precise definitions. Almost 3 weeks ago. I restated the same thing in post #336 and #358.

Yes, {1,2,3,4} is the same concept as {"1 AND 2 AND 3 AND 4"}. Any concept can be described as a singleton. This is why set theory is inappropriate for this.

Again, you don't seem to get that "all possible concepts" is a concept itself. It's impossible to be complete without including itself. That is fundamentally different to all the other examples you've brought up.

It does include itself. {"all possible concepts"} = {"all possible concepts"}

You're making a big deal out of nothing. This is why set theory is inappropriate for this.

You keep on posting endless different snippets that don't seem to add up to a whole picture. If you're going to represent things like { 1,2,3,4 } as { "1 AND 2 AND 3 AND 4" }, then why not LI itself {c1, c2, c3,......} as {"c1 AND c2 AND c3 AND...."} (c1 etc. being concepts)? If not,, then what criteria are being used? The point basically is that a group of concepts is not the same as the conjunction of its elements. The grouping is one concept and the conjunction is another. Hence within all concepts, you have to have both, so we're back at square one with Russell's paradox.

Not at all. {transportation} does not need {cars,trucks,buses} as members. This is why set theory is inappropriate for this.

Of course there's a fundamental conceptual difference, and pointing the different cardinality was a way to try and get this across. This is exactly why I can add to LI if it doesn't include itself as an element by doing this: LI ∪ {LI}. That is not a duplicate unless LI ∈ LI and then we get Russell's paradox.

Concepts can be included other concepts without being a member of it AND without being a subset of it. This is why set theory is inappropriate for this.

If |LI| = 1, then it's easy to add to without duplicating anything. LI ∪ {cat} would do it. It doesn't matter if cat is included in whatever the single element of LI is, it isn't included as a separate element, so I can add it.

Cat is a concept included in LI already. This was defined in post#331. This is why set theory is inappropriate for this.

 

[ratiocinator]

I defined the concept as a single statement of conjunctions disjunctions and negations 3 times. The first time was post #332, immediately after you asked for precise definitions. Almost 3 weeks ago. I restated the same thing in post #336 and #358.

You said in #332: "A concept is a statement of conjunctions, disjuctions, and negations of attributes which fully establishes its similarities and differences to all other concepts." which is just vague hand-waving. It certainly doesn't imply an equivalence between an unstructured grouping and a conjunction. Same applies to #336.

In #358, we have "...the concept is a statement of conjunctions, disjunctions, and negations of attribute+relationship pairs which defines the results." This just sounds like some sort of basic germ of an idea. Not something that is fully worked out.

Yes, {1,2,3,4} is the same concept as {"1 AND 2 AND 3 AND 4"}.

No it isn't. For example, {"The earth is flat", "The earth is approximately spherical"} is just two concepts, whereas {"The earth is flat" AND "The earth is approximately spherical"} is a contradiction.

It does include itself. {"all possible concepts"} = {"all possible concepts"}

You can't just switch abstraction levels like this. If all you're going to do is say that you have a concept of all concepts, i.e. {"all possible concepts"}, then it's been abstracted to the point of being trite and worthless for what you want to achieve. Your whole aim was (have you changed your mind?) that we have something that couldn't be added to. All you are doing in posting things like this is adding to lack of clarity about what you're actually proposing. For all I know, all this is perfectly clear in your own mind, but it really isn't translating into your written posts.

Not at all. {transportation} does not need {cars,trucks,buses} as members.

See above about abstracting to the point of being useless. Unless you include all the details, LI is not all-inclusive.

This is why set theory is inappropriate for this.

If you're going to reject the use of even the unrestricted, intuitive notion of sets (naive set theory), then you'll have to use another formally defined system or define something yourself that is precise and good enough to be used to construct the concept of LI with the properties you need it to have.

By all means give it a go, but I'll not be holding my breath.

 

[dybmh]

You said in #332: "A concept is a statement of conjunctions, disjuctions, and negations of attributes which fully establishes its similarities and differences to all other concepts." which is just vague hand-waving. It certainly doesn't imply an equivalence between an unstructured grouping and a conjunction. Same applies to #336.

In #358, we have "...the concept is a statement of conjunctions, disjunctions, and negations of attribute+relationship pairs which defines the results." This just sounds like some sort of basic germ of an idea. Not something that is fully worked out.

It is fully worked out. The words I used in those posts combined with the finite examples fully describe what I mean.

No it isn't. For example, {"The earth is flat", "The earth is approximately spherical"} is just two concepts, whereas {"The earth is flat" AND "The earth is approximately spherical"} is a contradiction.

What you posted above does not match what I said precisely. Regardless:

{"The earth is flat", "The earth is approximately spherical"} are 2 contradicting concepts.
{"The earth is flat AND The earth is approximately spherical"} are 2 contradiction concepts.

You can't just switch abstraction levels like this. If all you're going to do is say that you have a concept of all concepts, i.e. {"all possible concepts"}, then it's been abstracted to the point of being trite and worthless for what you want to achieve. Your whole aim was (have you changed your mind?) that we have something that couldn't be added to. All you are doing in posting things like this is adding to lack of clarity about what you're actually proposing. For all I know, all this is perfectly clear in your own mind, but it really isn't translating into your written posts.

What you're noticing is, it is an easy concept. It has been easy from the beginning. When you asked me to define it precisely, it becomes very complicated, but at the end of that precise definition it returns to being just like I said at the beginning, a very simple idea.

But you do keep changing what I'm saying. {"all possible concepts"} is incorrect. That is not what I'm saying. If I had to limit it to a set, it is {"all possible concepts AND all impossible concepts"}. That is absolutely all inclusive.

See above about abstracting to the point of being useless. Unless you include all the details, LI is not all-inclusive.

All the details are included. The same as {ℕ}, {ℤ}, {ℝ}, or any function { "x=y"}. Are any integers missing from {ℤ}? It's the same thing.

If you're going to reject the use of even the unrestricted, intuitive notion of sets (naive set theory), then you'll have to use another formally defined system or define something yourself that is precise and good enough to be used to construct the concept of LI with the properties you need it to have.

That system is a relational database.

By all means give it a go, but I'll not be holding my breath.

It's already been done. Your challenge was to find anything that was not included.

 

[ratiocinator]

It is fully worked out. The words I used in those posts combined with the finite examples fully describe what I mean.

It may be in the confines of your own mind but you've totally failed to communicate it to me. I have no idea at all what you're proposing. You seem to endlessly contradict yourself.

Sometimes you seem to have some sort of spider's web of interconnecting relationships, attributes, conjunctions, disjunctions, negations and so on, then it's suddenly all within some kind of neat hierarchy. One time it includes everything at every level of detail, then it's abstracted to the point that "transportation" doesn't need the details like "cars", "trains", etc. It's a mess.

{"The earth is flat", "The earth is approximately spherical"} are 2 contradicting concepts.
{"The earth is flat AND The earth is approximately spherical"} are 2 contradiction concepts.

One is a list of concepts that correspond to different views and the other is a solid contradictory statement. The fact that you consider them the same shows exactly why you think this is all worked out and I disagree.

Consider the disjunction: {"The earth is flat" OR "The earth is approximately spherical"}. Now it's not contradictory at all. To have all concepts, you'd need to include all three.

But you do keep changing what I'm saying. {"all possible concepts"} is incorrect. That is not what I'm saying. If I had to limit it to a set, it is {"all possible concepts AND all impossible concepts"}. That is absolutely all inclusive.

What's an "impossible concept"? You can have concepts that refer to impossible things (e.g. "square circle") but the concepts aren't impossible, it isn't impossible to construct them. Anyway, that misses the point. Neither {"all possible concepts"} or {"all possible concepts AND all impossible concepts"} will do for your purpose simply because they are high-level abstractions, hence I can easily add to them by adding concrete detail.

All the details are included. The same as {ℕ}, {ℤ}, {ℝ}, or any function { "x=y"}. Are any integers missing from {ℤ}? It's the same thing.

It's nothing like it at all. All these sets are exactly defined. We can immediately tell whether something some item is in any of them or not. You can't do the same with general concepts.

That system is a relational database.

Totally wrong level of detail.

A relational database just adds structure to some data. That tells me nothing about the data it's adding structure to. A naive set is something you could put in a relational database but you've rejected that, so you've got to think of some other idea to express the data you're going to put in your database.

And, as I said before way back, the relations in a database would just be further concepts to it doesn't logically change a thing. Database or not, all you've got is a big old bunch of concepts. The organisation couldn't be less relevant.

 

[dybmh]

It may be in the confines of your own mind but you've totally failed to communicate it to me. I have no idea at all what you're proposing. You seem to endlessly contradict yourself.

There is no contradiction. The only way you produce one is by changing what I'm saying.

Sometimes you seem to have some sort of spider's web of interconnecting relationships, attributes, conjunctions, disjunctions, negations and so on, then it's suddenly all within some kind of neat hierarchy. One time it includes everything at every level of detail, then it's abstracted to the point that "transportation" doesn't need the details like "cars", "trains", etc. It's a mess.

The answer to the question depends on the question being asked. The top level concept is absolutely general and all inclusive. As you have tried to pick apart what I'm saying, I have followed you and showed that picking it apart does not produce any fault in what I have defined. The way I did that is to show how the infinte concepts are connected and setup into a hierarchy which resolves back into an absolutely general all inclusive concept.

Several times I've said it's both a structure and a concept. When you try to pick apart the structure, I explain the stucture, that has detail. When you try to pick apart the concept, I explain the concept which is absolutely general.

One is a list of concepts that correspond to different views and the other is a solid contradictory statement. The fact that you consider them the same shows exactly why you think this is all worked out and I disagree.

It's a category error. A set is not a logical proposition. A set is a collection. Nothing more nothing less.

Consider the disjunction: {"The earth is flat" OR "The earth is approximately spherical"}. Now it's not contradictory at all. To have all concepts, you'd need to include all three.

First, you're changing what I said. The quotes are in the wrong place. Second, all three concepts are included. There's nothing wrong with including all three. They don't all need to evaluate as "true" to be included.

What's an "impossible concept"? You can have concepts that refer to impossible things (e.g. "square circle") but the concepts aren't impossible, it isn't impossible to construct them. Anyway, that misses the point.

Because of all the circling back that's happening in this discussion, I would prefer that you do not change what I'm saying even if you don't see the difference. I think it's important to phrase it the way I am phrasing it because it defeats this whole flat vs. round earth problem you seem to be having.

Neither {"all possible concepts"} or {"all possible concepts AND all impossible concepts"} will do for your purpose simply because they are high-level abstractions, hence I can easily add to them by adding concrete detail.

Not true. The concrete detail is included in the general concept. The general concept is not limited to individual concrete details. It includes them all.

It's nothing like it at all. All these sets are exactly defined. We can immediately tell whether something some item is in any of them or not. You can't do the same with general concepts.

Sure you can. Is an amoeba included in transportation?

Totally wrong level of detail.

But you cannot actually show any fault in it.

A relational database just adds structure to some data. That tells me nothing about the data it's adding structure to. A naive set is something you could put in a relational database but you've rejected that, so you've got to think of some other idea to express the data you're going to put in your database.

Not true. I did not reject that.

And, as I said before way back, the relations in a database would just be further concepts to it doesn't logically change a thing. Database or not, all you've got is a big old bunch of concepts. The organisation couldn't be less relevant.

It doesn't matter if YOU can see the relevance. Whether or not YOU see it says nothing about its consistency or all inclusion. The simple truth is: Neither ∪, nor ∈, nor ⊂ are valid tests for whether or not a concept is all inclusive.

 

[ratiocinator]

When you try to pick apart the structure, I explain the stucture, that has detail. When you try to pick apart the concept, I explain the concept which is absolutely general.

What you're saying is disjointed and incoherent. It doesn't fit together in any way that I can see. You just seem to jump to a totally different and incompatible concept each time I point out a problem.

Sure you can. Is an amoeba included in transportation?

Is how it moves about?

Regardless, the real point illustrates exactly what I mean about how confused it all is. If you include {"transportation"} as you say, are you also including "car"? First point: how on earth do you think I'm supposed to know that from all the different things you've said? Second point, depending on the answer:

If yes, there is no point at all in brining up {"transportation"} because it's just another concept that has to have an 'include' relationship with "car" and all my points about Russell's paradox that you used abstraction to try to avoid, are right back on the table.

If no, then I could add that detail ("car") without duplication and you'd have no way to include the other attributes of "car" into LI. Things like "things that have wheels", "things with engines", etc., etc, etc.

A naive set is something you could put in a relational database but you've rejected that...

Not true. I did not reject that.

Really??

This is why set theory is inappropriate for this.

This is why set theory is inappropriate for this.

This is why set theory is inappropriate for this.

This is why set theory is inappropriate for this.

 

[dybmh]

What you're saying is disjointed and incoherent. It doesn't fit together in any way that I can see. You just seem to jump to a totally different and incompatible concept each time I point out a problem.

Each potential problem you have raised has been addressed.

Is how it moves about?

An amoeba is not a form of transportation. Yes, there is an assumption that you know and understand the english language when a defintion is given in english. No logical defintion begins with "A, B , C, D..." and reconstructs english from scratch.

Regardless, the real point illustrates exactly what I mean about how confused it all is. If you include {"transportation"} as you say, are you also including "car"? First point: how on earth do you think I'm supposed to know that from all the different things you've said?

Most people do this automatically. But for you, I brought a definition and examples.

Second point, depending on the answer:

If yes, there is no point at all in brining up {"transportation"} because it's just another concept that has to have an 'include' relationship with "car" and all my points about Russell's paradox that you used abstraction to try to avoid, are right back on the table.

No, it doesn't need an include relationship as it is defined in set theory. Neither ∪, nor ∈, nor ⊂ are valid tests for whether or not a concept is inclusive.

If no, then I could add that detail ("car") without duplication and you'd have no way to include the other attributes of "car" into LI. Things like "things that have wheels", "things with engines", etc., etc, etc.

There is a concept "transportation", there is a concept "car", there is a concept "wheels", there is a concept "engine". There is a concept "things with wheels", and "things with engines". All of those concepts are included. This inclusion can be described in multiple ways. When an all inclusive concept is considered, one of those methods showing inclusion produces a paradox, but the others don't.

Really??

Yes. The reason that set theory is not approriate is because what I have defined includes naive sets, but is not limited to being a naive set. Square is a rectangle / rectangle is not always a square. I'm describing a polygon, but you're stuck on a square.

 

[ratiocinator]

Each potential problem you have raised has been addressed.

By changing what you're talking about and contradicting or, at the very least, bringing into question, what you've said before.

An amoeba is not a form of transportation.

I didn't suggest it was, I asked about how it moves. You talked about me "spell checking" what you're doing but this illustrates exactly why details are important because we now have an ambiguity because just don't take care of "dotting i's and crossing t's". How about walking, is that in "transportation"? How about non-human walking? What about herding to transport cattle? See below for more problems with being vague.

Yes, there is an assumption that you know and understand the english language when a defintion is given in english.

There is a very good reason why mathematics and computer code are not written in English (or any other natural language). It's because it's not precise and is riddled with ambiguities, shades of meaning, and multiple senses of the same word. This is why you will never succeed in defining LI rigorously enough if you stick to natural language. That's why you need something like set theory (even in its naive sense) or something else that's just as precise. You need to stop being vague.

No, it doesn't need an include relationship as it is defined in set theory. Neither ∪, nor ∈, nor ⊂ are valid tests for whether or not a concept is inclusive.

So what is? If you say it's a relationship in your relational database, then I can immediately conceptually map that to actual inclusion (∈, in naive set theory) and arrive at the same paradox. This is why you'd need a new and properly defined, underlying concept to deal with the data itself and the relationships you define. Unless you restrict them in some way that is independent of the database, you'll end up with the same problems. Stop being vague.

All of those concepts are included. This inclusion can be described in multiple ways. When an all inclusive concept is considered, one of those methods showing inclusion produces a paradox, but the others don't.

So what, exactly, is the way you are using and how does it avoid the paradox? Stop being vague.

The reason that set theory is not approriate is because what I have defined includes naive sets, but is not limited to being a naive set.

But what it actually is appears to be a closely guarded secret. Stop being vague.

If it literally includes all of naive set theory (if you can do anything that you can do in naive set theory without restriction), then it's included the paradox. Formal set theories avoid it by putting restrictions on naive set theory.

 

[dybmh]

By changing what you're talking about and contradicting or, at the very least, bringing into question, what you've said before.

Not true. I haven't changed a thing.

I didn't suggest it was, I asked about how it moves. You talked about me "spell checking" what you're doing but this illustrates exactly why details are important because we now have an ambiguity because just don't take care of "dotting i's and crossing t's". How about walking, is that in "transportation"? How about non-human walking? What about herding to transport cattle? See below for more problems with being vague.

There is no ambiguity. An amoeba is not a form of transportation.

There is a very good reason why mathematics and computer code are not written in English (or any other natural language). It's because it's not precise and is riddled with ambiguities, shades of meaning, and multiple senses of the same word. This is why you will never succeed in defining LI rigorously enough if you stick to natural language. That's why you need something like set theory (even in its naive sense) or something else that's just as precise. You need to stop being vague.

Not true. I did define it precisely. I'm not being vague at all.

So what is? If you say it's a relationship in your relational database, then I can immediately conceptually map that to actual inclusion (∈, in naive set theory) and arrive at the same paradox. This is why you'd need a new and properly defined, underlying concept to deal with the data itself and the relationships you define. Unless you restrict them in some way that is independent of the database, you'll end up with the same problems. Stop being vague.

I'm not being vague.

The concept of a bicycle is included in the concept of transportation. This is undeniably true.

But.

{bicycle} ∈ {transportation} is false
{bicycle} ⊂ {transportation} is false

This proves that ∈ and ⊂ are invalid tests for inclusion in a concept.

Therefore, anytime you use those tests to try to show a inconsistency or a lack of inclusion, the test is invalid. It's a category error.

So what, exactly, is the way you are using and how does it avoid the paradox? Stop being vague.

I'm not being vague. I'm just not investing much time in my responses anymore. I've explained, I've defined. In general and in particular. Repeatedly.

In general, the concept of literal infinity includes itself. It is an identity. All of the defining characterstics of Literal Infinity are included in itself because that is what identity means. It is itself.

In particular, an entire replica, each and every concept, can be literally included in itself, but that would be a duplicate.

But what it actually is appears to be a closely guarded secret. Stop being vague.

I'm not being vague. Calling it vague is just a tactic, not an argument.

If it literally includes all of naive set theory (if you can do anything that you can do in naive set theory without restriction), then it's included the paradox. Formal set theories avoid it by putting restrictions on naive set theory.

They way you are defining it, it's simply included as a paradox, and never attempted to be enumerated. Just like any other contradiction.

 

[ratiocinator]

An amoeba is not a form of transportation.

That you repeated this shows that you're just not paying attention.

{bicycle} ∈ {transportation} is false
{bicycle} ⊂ {transportation} is false

This proves that ∈ and ⊂ are invalid tests for inclusion in a concept.

It doesn't prove anything. It's just telling me what it's not - and you still haven't defined what it actually is.

In general, the concept of literal infinity includes itself. It is an identity. All of the defining characterstics of Literal Infinity are included in itself because that is what identity means. It is itself.

An identity is not an inclusion. The concept of all concepts is a concept. Unless it is included it is incomplete and can be added to.

However, let's just assume that identity can be considered inclusion. and see where that leads....

So, you've said that LI itself being itself implies inclusion but it would make no sense for (say) "species" or "atomic elements" or "transportation", for that matter. So it appears to apply to some concepts but not to others. Oh, but wait! What about the concept of "all concepts for which identity is not considered to be inclusion"? Is identity considered inclusion in that case? Oops.

 

[dybmh]

That you repeated this shows that you're just not paying attention.

You editted what I said. Again. That shows my point is valid. You had to omit part of what I said to critisize it.

There is no ambiguity. An amoeba is not a form of transportation. You are manufacturing a problem that does not exist in what I am saying.

It doesn't prove anything. It's just telling me what it's not - and you still haven't defined what it actually is.

And this comment editted what I said. That shows my point is valid. You had to omit part of what I said to critisize it.

No logical defintion includes a dictionary for each word that is used. You know what the words "transportation" and "bicycle" mean. What I said is absolutely true. ∈ and ⊂ are invalid tests for inclusion in a concept.

An identity is not an inclusion.

It is for a concept.

The concept of all concepts is a concept. Unless it is included it is incomplete and can be added to.

It is included. Every characteristic which defines the concept" All concepts" is included in those words.

If it wasn't you could find a concept which isn't included in it. And you've tried, but it's impossible. It's just a definition. All means all.

However, let's just assume that identity can be considered inclusion. and see where that leads....

So, you've said that LI itself being itself implies inclusion but it would make no sense for (say) "species" or "atomic elements" or "transportation", for that matter

Sure it does. What doesn't make sense about it? Transportation is the example I have been using.

. So it appears to apply to some concepts but not to others. Oh, but wait! What about the concept of "all concepts for which identity is not considered to be inclusion"? Is identity considered inclusion in that case? Oops.

Nonsense. All of the characteristics that define the concept of "species" or "atomic elements" or "transportation" are included in those words. That's what words do. You're pretending that you cannot speak or understand english.

 

[ratiocinator]

You editted what I said. Again. That shows my point is valid. You had to omit part of what I said to critisize it.

This is just not true. You said in full "There is no ambiguity. An amoeba is not a form of transportation." My reply, "That you repeated this shows that you're just not paying attention.", stands just as strongly against the whole of your answer as to the part I quoted (which is why I picked out the relevant part). I never suggest that an amoeba was a form of transportation. Hence your assertion that "There is no ambiguity." was irrelevant.

For the record, the exchange was:

Sure you can. Is an amoeba included in transportation?

Is how it moves about?

See?

And this comment editted what I said. That shows my point is valid. You had to omit part of what I said to critisize it.

Again, not true. Here's the exchange in full:

I'm not being vague.

The concept of a bicycle is included in the concept of transportation. This is undeniably true.

But.

{bicycle} ∈ {transportation} is false
{bicycle} ⊂ {transportation} is false

This proves that ∈ and ⊂ are invalid tests for inclusion in a concept.

Therefore, anytime you use those tests to try to show a inconsistency or a lack of inclusion, the test is invalid. It's a category error.

It doesn't prove anything. It's just telling me what it's not - and you still haven't defined what it actually is.

I stand by that too.

Additionally, your claims that "That shows my point is valid. You had to omit part of what I said to critisize it." is a massive non sequitur. Even if I had distorted your claims (which I didn't) and addressed a straw man, that wouldn't show that your point was valid. If wouldn't say anything at all about the validity your point. Unfortunately this shows that you really don't get logic, which explains a lot.

Sure it does. What doesn't make sense about it? Transportation is the example I have been using.

Nonsense. All of the characteristics that define the concept of "species" or "atomic elements" or "transportation" are included in those words. That's what words do. You're pretending that you cannot speak or understand english.

I'm not pretending that I cannot understand English but it is true that you will never achieve a rigorous enough definition of what you mean if you just use natural language. It's just not up to the task, any more than it's up to the tasks of being a programming language or doing mathematics.

And yet again, you've completely missed the entire point. We are back at square one.

"The concept of all concepts" is a concept - so must include itself
"Species" is not a species - so must not include itself.
"Atomic elements" is not an atomic element - so must not include itself.
"Transportation" is not a means of transportation - so must not include itself.

However you choose to represent the difference (considering identity as inclusion, flags, actual inclusion, or whatever else you dream up), it must be represented somehow because it's a fundamental feature of the concepts you're dealing with. As soon as you do represent it, we will run into the paradox.

I really don't know how to make this any simpler.

 

[dybmh]

This is just not true. You said in full "There is no ambiguity. An amoeba is not a form of transportation." My reply, "That you repeated this shows that you're just not paying attention.", stands just as strongly against the whole of your answer as to the part I quoted (which is why I picked out the relevant part). I never suggest that an amoeba was a form of transportation. Hence your assertion that "There is no ambiguity." was irrelevant.

For the record, the exchange was:


See?

You were claiming that the concept of transportation was ambiguous. But it's not and you're still omitting that part of the dialogue. The example of an amoeba shows that "transportation" is not ambiguous. You seem to be confusing "locomotion" with "transportation" eventhough an amoeba is neither of those.

If I'm wrong and you are not, were not, claiming that the general concept is ambiguous, then there is no objection to using the general concept to include all the characteristics which define it. And there shouldn't be any objection. That's what words do. Although you were repeatedly claiming I was being vague. So, again, it's disengenuous to say you weren't.

Again, not true. Here's the exchange in full:


I stand by that too.

Additionally, your claims that "That shows my point is valid. You had to omit part of what I said to critisize it." is a massive non sequitur. Even if I had distorted your claims (which I didn't) and addressed a straw man, that wouldn't show that your point was valid. If wouldn't say anything at all about the validity your point. Unfortunately this shows that you really don't get logic, which explains a lot.

I do get logic. You haven't been able to show a single logical flaw in anything I've said. You omitted the part of my post that showed a bicycle was included. Then you claimed all I said was what "transportation" isn't. That's false. I gave an example of what it is. You cropped that out to try to undermine the simple truth which is, the method you're using to test for consistency and inclusion is invalid.

I'm not pretending that I cannot understand English but it is true that you will never achieve a rigorous enough definition of what you mean if you just use natural language. It's just not up to the task, any more than it's up to the tasks of being a programming language or doing mathematics.

First of all, that's not true. Set theory begins with english language definitions. You would never have any of the fundemental concepts of set theory without english language.

Second, you keep saying this, but you have not brought a single example from what I said where it is true. You are making a principled argument, which does not appear to be true in practice. Even if it is generally true, what I brought could be one of the exceptions.

And this ignores that essentially you are again claiming "blasphemy, this goes against my doctrine". That is not a logical argument.

And yet again, you've completely missed the entire point. We are back at square one.

It's not my fault you keep making category errors.

"The concept of all concepts" is a concept - so must include itself

And it does.

"Species" is not a species - so must not include itself.

Species is a concept, A species is a concept.

"Atomic elements" is not an atomic element - so must not include itself.

Atomic elements is a concept. An atomic element is a concept.

"Transportation" is not a means of transportation - so must not include itself.

Transportation is a concept. A means of transportation is a concept.

However you choose to represent the difference (considering identity as inclusion, flags, actual inclusion, or whatever else you dream up), it must be represented somehow because it's a fundamental feature of the concepts you're dealing with. As soon as you do represent it, we will run into the paradox.

They ARE represented. That's what words do.

I really don't know how to make this any simpler.

The problem is you are stuck in a strongly held belief system that never advanced past 1 specific version of set theory. And you have probably decided that God cannot be logically defined because of this 1 version of set theory. But you never advanced past it. That's the problem with being "certain". Even though it's comforting, it's always and forever incomplete. People don't know what they don't know, and certainty is the death of advancement of knowledge.