I did, but you ignored it. The common-ground should be set theory since you are using set theory consistently here.
The distinction is ∈ ≠ ⊂. To which you answered: "I know."
I then went on to point out why is doesn't help because this has to be a case of element of: ∈. If a concept is just a subset then it can be added as an element and I've added to LI without duplication.
It's not arbitrary. It's orderly. I have already shown that the construct I have defined can produce results that a naive set cannot produce.
You've misunderstood again. What you put into LI (any and every concept) has to be
unrestricted, i.e. I have to be able to arbitrarily choose anything and include it.
This is the essence of how naive set theory works and how axiomatic set theories don't because they
have to restrict what counts as a set to avoid the paradoxes. You are caught in a catch-22. To avoid the paradoxes, you have to restrict what is allowed but if you restrict what is allowed, then you can't have something that's all-inclusive.
All you've added is a structure. Organising the constants of the naive set of all sets so it looks like a database can't change anything fundamental. I can still pull out every single concept (including the concept of the organisation itself) and demonstrate the same contradictions. The phrase "reorganising the deckchairs on the Titanic" could have been made for this exercise.
No. the concept of all the quantity of groups of concepts in LI is going to be bigger than the quantity of LI itself.
So it will contain concepts that LI doesn't. This is unavoidable. You can add to a set and keep the cardinality the same, but you can't increase the cardinality without adding new items. That's exactly what the proof shows; you can't do a one-to-one map, there will always be items in the power set that are not in the original.
Yes literal containment is literally impossible for any concept by definition.
Going back to what you said before about ∈ and ⊂. You
must have LI ∈ LI, otherwise it doesn't contain every concept. You're basically saying LI is impossible. I agree.
The proposition can be valid, but not sound
Arguments (specifically deductions) are sound or valid,
not propositions. You need to provide a sound argument that shows that you've done what you think you have.
The way to disprove what I'm saying is to take what I'm actually saying and undermine it.
Technically I don't need to because it's up to you to prove it. Nevertheless, I have done just that.
That's the difference between math and engineering. Engineers know which tools to use to make stuff that works. I've contructed a tool that works.
Unfortunately, even the best engineer cannot engineer away fundamental problems. They are restricted by mathematics an physics. Your problem seems to be that you won't accept that and are placing far too much confidence in an engineering approach.
As I said before, this is supposed to be the most fundamental concept of all. Engineering is completely the wrong approach. There can be no engineering at this level. Who do you think will engineer the basis for God? That's exactly why endless bodges, flags, and work-arounds undermine the whole idea.
Actually I could be pendantic and pick apart what you've written in the same way you are trying to pick apart what I'm saying, eventhough, you *actually* understand what I mean.
Please do, if you want, but I'm afraid that I don't understand what you mean because I keep on raising issues and sometimes you'll add a flag (e.g. the new contradiction flag a few posts back) or some other programming hack, sometimes you'll make apparently contradictory statements, sometimes you misuse terms so I'm not sure what you're getting at, and sometimes I get a lot of words that don't seem to say much. Even when you add detail, you don't seem to have thought it through (physical actions, physical events, ideas, and symbols).
Ignoring that, there are at least two things which you haven't precisely defined. And I think precisely defining them would resolve all or most of the debate, either in my favor or against: Incomplete and Inconsistent. You have asserted that the construct I have defined will be either one or both. But these terms have not been defined; I think the failure condition you are asserting is a semantic fault. But I could be wrong.
In this context, 'incomplete' means that not everything that should be included is included and 'inconsistent' means that there is a contradiction.
What matters is, name dropping a programming language...
It's not a programming language, it's a specification language. I raised it to make the point about being precise.
...which contains the same limitations as naive set theory is not helpful.
Nope. Naive set theory has very few limitations, it's problem is that it contains paradoxes. Z is not based on naive set theory.
I am thinking in those terms. That's exactly what I did when defining the concept "all concepts which do not contain themself".
What!? You tried to make it into a query, then tried to add a flag to bodge round the basic self-contradiction. You apparear to be making things up as we go along. You clearly don't seem to have been thinking in these terms when you came up with physical actions, physical events, ideas, and symbols.
Anyway, the picture above is just a triggered event.
What!? It's an inheritance relationship that says that an action
is an event - like a cat
is an animal.
But one of the ways I avoid the contradiction is by abstraction. And that is what a concept does by definition. And technically, there's nothing that says a naive set cannot employ this same technique. Here is a naive set which contains the concept of the set of all sets which do not contain themself. Ready?
{ "the concept of the set of all sets which do not contain themself" }
It's just a concept. There really is not problem including it in any set as long as it is just a concept.
Wow. What is this? I've lost count. The third or fourth attempt to get around this problem?
Unfortunately this doesn't either and is, yet again, telling everybody that the people who identified the paradoxes and dealt with them with axiomatic set theories were idiots, and that you're way more clever than them. If you
really believe this, publish, and collect your Nobel prize.
If you're allowing this sort of thing in your LI, then it is rich with opportunities to add more items without duplication.
So, in summery, you still haven't provided any significant difference from naive set theory, as a consequence, you still haven't explained how you would avoid Russell's paradox, and you haven't addressed the ability to always constrict a larger group of concepts than LI, via the power set process.
