A hidden assumption

[doronshadmi]

A deck of punched cards doesn't have self awareness. So? You asked if this thread could exist independently of any consciousness. The answer is yes.

An unconscious thing (let us call it a mathematician) made a deck of punched cards that doesn't have self awareness.

By the way: How do you know that?

Given that your lack of any sound grasp on even basic mathematics and logic has led you into multiple absurdities, I suppose we should be grateful for this.

How do you know that? (after all you are an unconscious thing)

Symbolic representation.

How do you know that?

It's a tautology. You may find trivial statements of logic boundlessly entertaining; others do not.

How do you know that?

The definition. You know, definitions, those things you are apparently fatally allergic to?

How do you know that?

Yes, yes. You realise that this is philosophy, right? I mean, once you're finished with it it's gobbledegook, but it started out as philosophy - not mathematics.

How do you know that? How you are able to distinguish between Philosophy and Mathematics?

 

[PixyMisa]

An unconscious thing (let us call it a mathematician) made a deck of punched cards that doesn't have self awareness.

Mathematicians are conscious. Some of the time, anyway.

By the way: How do you know that?

How do I know what?

How do you know that?

You presented truth tables showing only the inputs. And you seem to consider that meaningful. You can't get much more absurd than that.

(after all you are an unconscious thing)

Why do you make that claim?

How do you know that?

Simple. That's what you do when you need to discuss or explore a concept.

How do you know that?

I asked them.

How do you know that?

As I said, it's an assumption. It's one plausible explanation for your total failure to provide definitions for any of your non-standard terminology despite repeated requests from everyone in this thread.

How do you know that? How you are able to distinguish between Philosophy and Mathematics?

By - ta da - knowing how they are defined.

Anyway, if you are looking for a rigorous, formal, and provably consistent basis for mathematics, you're out of luck. Kurt Gödel nailed that door shut long ago. If you're looking just to babble about mystical symmetries, Religion and Philosophy is, as I said earlier, over there.

 

[doronshadmi]

Anyway, if you are looking for a rigorous, formal, and provably consistent basis for mathematics, you're out of luck. Kurt Gödel nailed that door shut long ago.

I agree with you. Mathematics is an open framework that can be changed by paradigm-shifts (it is under Evolution).

This paradigm-shift is actually Hilbert's organic paradigm of the mathematical science.

Since formal definitions are only some reflections of our consciousness, they are accessible to us.

The motivation of Gödel was actually to show that the framework of formal definitions is unable to fully capture the Platonic realm.

I agree with him, because the Platonic realm is not a collection of ideal objects, but it is Symmetry itself as total unity which is totally invariant and its completeness cannot be defined by any collection of infinitely many objects.

As a result any given collection (finite or not) is incomplete by definition in comparison to total symmetry.

Total symmetry is the common basis of all there is including the personal aspect of our consciousness, and the paradigm-shift of the mathematical science is exactly the awareness of each person to the objective and invariant (non-local) basis of its (local) personality.

How do I know that?

Very simple: Try to avoid the invariant basis of the different faces of your personality, and there is nothing that keeps you together.

You presented truth tables showing only the inputs.

No, I presented the universal principle of Logic itself, which is not less than Symmetry\Asymmetry complementation.

 

[Don At Work]

Sorry. My brain shattered on post #248

No, I mean superposition of identities\distinct identities complementation.

At first I thought that he was interpreting { A,B } as "the curly braces are the rules that define the members of the set". Reading most of the thread, however, has made my brain pack up and leave.

 

[ArmillarySphere]

I think part of what he means is that you can't tell if an object is identical to itself without comparing it. Which makes a sort of half-assed sense in computer science, but no sense at all in mathematics.

 

[doronshadmi]

I think part of what he means is that you can't tell if an object is identical to itself without comparing it. Which makes a sort of half-assed sense in computer science, but no sense at all in mathematics.

No.

Symmetry itself is not any object, but it enables to compare between objects and define their self identities and the infinitely many relations that can be defined among them.

A particular case of such a relation is classical logic, which is based on the universal principle of Symmetry\Asymmetry complementation.

 

[doronshadmi]

Sorry. My brain shattered on post #248




At first I thought that he was interpreting { A,B } as "the curly braces are the rules that define the members of the set". Reading most of the thread, however, has made my brain pack up and leave.

A set is not less than "{" and "}" (represent the invariance) and some objects that are identified according to it.

Also "{" and "}" can represent a domain, where Locality(the variant) cannot be in more than one relation with it, and Non-locality(the invariant) ignores it.

 

[jsfisher]

My incorrect statement?

Exactly right. Your statement was that a set is equal to the union of its members. That statement is flatly incorrect, and it is yours. So, yes, your incorrect statement.

Your "correct" statement is based on reasoning without consciousness, which leads to hidden assumptions of both the premise and the conculsion of the researched.

Irrelevant gibberish.

 

[jsfisher]

At first I thought that he was interpreting { A,B } as "the curly braces are the rules that define the members of the set". Reading most of the thread, however, has made my brain pack up and leave.

That's part of it. Doron has also implied that the braces (and the set) have some sort of physical existence. Sets are some sort of physical container, exclusive of any other container. If 2 is in the set { 2,3,4 } then you cannot use 2 for any other purpose without first cutting 2 out of that set. This lead to his severed body part analogy.

The problem is, though, whenever we play back to doron things he's said, but translated to English, he retreats to more and different gibberish. I've lost count of how many different thing1\thing2 complementations he has thrown at us.

Since I do not think doronshadmi to be a troll, I am left with the belief that his inability to communicate is not his lack of fluency with English, but that his thinking is superficial and fuzzy. His only hope to maintain his fantasy is to bolster it in gibberish.

(Actually, "gibberish" is not the work I had in mind, but eight asterisks could have been misinterpreted.)

 

[PixyMisa]

I agree with you. Mathematics is an open framework that can be changed by paradigm-shifts (it is under Evolution).

No.

This paradigm-shift is actually Hilbert's organic paradigm of the mathematical science.

No. You don't get it. Gödel's incompleteness theorem (specifically, his second incompleteness theorem) proved that Hilbert's goals were impossible.

Since formal definitions are only some reflections of our consciousness, they are accessible to us.

No.

The motivation of Gödel was actually to show that the framework of formal definitions is unable to fully capture the Platonic realm.

Completely wrong. Gödel showed the limitations of any (sufficiently powerful, consistent) formal system. There is no "Platonic realm". There are just formal systems. And any (again, sufficiently powerful, consistent) formal system has the same limitations.

I agree with him, because the Platonic realm is not a collection of ideal objects, but it is Symmetry itself as total unity which is totally invariant and its completeness cannot be defined by any collection of infinitely many objects.

Meaningless.

As a result any given collection (finite or not) is incomplete by definition in comparison to total symmetry.

Meaningless.

Total symmetry is the common basis of all there is including the personal aspect of our consciousness, and the paradigm-shift of the mathematical science is exactly the awareness of each person to the objective and invariant (non-local) basis of its (local) personality.

Extremely meaningless.

How do I know that?

How do you know what?

Very simple: Try to avoid the invariant basis of the different faces of your personality, and there is nothing that keeps you together.

There is no invariant basis to my personality. There can be no invariant basis to my personality. Personality - like consciousness - is a process.

No, I presented the universal principle of Logic itself, which is not less than Symmetry\Asymmetry complementation.

You don't even read your own posts, do you?

Does this look familiar?

OR is:

1#.FF
2#.FT
3#.TF (the inverse of 2#)
4#.TT (the inverse of 1#)

That, right there, is a truth table with only the inputs shown, claiming (somehow) to represent the OR operator. As I said, that's about as nonsensical as you can get. OR actually looks like this:

FF -> F
FT -> T
TF -> T
TT -> T

See the difference? What you presented is simply the state listing for two variables in two-valued logic. It means nothing beyond that.

 

[Apathia]

Pixy said:

There are just formal systems. And any (again, sufficiently powerful, consistent) formal system has the same limitations.

Precisely Pixy.
Doron's unfortunately garbled system will get dashed upon the same rocks.
Unless, of course, it places such sever constraints on Mathematics that it is next to useless.
What reward have ye, if ye worm out of Russell's Paradox by making set elements relative and making Mathematics a eunuch in the process?

Doron, your not the reincarnation of Zeno of Elea are you?

My serious question is what's your take on Nicholas of Cusa?

 

[nathan]

Doron's unfortunately garbled system will get dashed upon the same rocks.

I don't think Goedel's theorem applies to Doron's work, because it addresses sufficiently powerful consistent formal systems. Doron's work is incomplete for an entirely different reason

 

[doronshadmi]

That's part of it. Doron has also implied that the braces (and the set) have some sort of physical existence.

No, in the case of set, this is the invariant side of any given collection (abstract or not). You simply cannot get this generalization.

Sets are some sort of physical container, exclusive of any other container.

No, it is a generalization of any container (abstract or not) understood it terms
of using total Symmetry as the basic point of view of any given collection (abstract or not).

If 2 is in the set { 2,3,4 } then you cannot use 2 for any other purpose without first cutting 2 out of that set. This lead to his severed body part analogy.

Wrong again. for example 2 and {2} are different, and there is nothing in 2 (2 without "{" and "}") that forces us to conclude that it is a member of {2}.

The problem is, though, whenever we play back to doron things he's said, but translated to English, he retreats to more and different gibberish. I've lost count of how many different thing1\thing2 complementation he has thrown at us.

It is one and only one thing, the invariance\variance complementation that enables the researchable. If you get it, you get the other representations of it.

Since I do not think doronshadmi to be a troll, I am left with the belief that his inability to communicate is not his lack of fluency with English, but that his thinking is superficial and fuzzy. His only hope to maintain his fantasy is to bolster it in gibberish.

Symmetry itself is not researchable (total unity). Asymmetry itself is not researchable(total isolation). The researchable cannot be but Symmetry\Asymmetry complementation. This is an axiom.

 

[PixyMisa]

Wrong again. for example 2 and {2} are different, and there is nothing in 2 (2 without "{" and "}") that forces us to conclude that it is a member of {2}.

That contradicts either the standard definition of sets or the law of identity.

Which?

 

[doronshadmi]

No. You don't get it. Gödel's incompleteness theorem (specifically, his second incompleteness theorem) proved that Hilbert's goals were impossible.

I am not talking about Hilbert's program to formalize Mathematics in terms of finite amount of formal terms.

I am talking about his whole\parts organic paradigm of the mathematical science.

It went over the heads of your community.

Completely wrong. Gödel showed the limitations of any (sufficiently powerful, consistent) formal system. There is no "Platonic realm". There are just formal systems. And any (again, sufficiently powerful, consistent) formal system has the same limitations.

I spoke about Gödel's motivation. He proved that any axiomatic system that is sufficiently powerful to deal with the arithmetic of the Natural numbers, cannot be both consistent AND complete.

There is no invariant basis to my personality. There can be no invariant basis to my personality. Personality - like consciousness - is a process.

A process cannot be found without a stable foundation, exactly as any given sound (some variant) is compared to total silence (the invariant).

That, right there, is a truth table with only the inputs shown, claiming (somehow) to represent the OR operator. As I said, that's about as nonsensical as you can get. OR actually looks like this:

FF -> F
FT -> T
TF -> T
TT -> T

See the difference? What you presented is simply the state listing for two variables in two-valued logic. It means nothing beyond that.

Come on PixMisa. What you say is trivial. If you really read my posts you will find that I am talking exactly on what you wrote, but go beyond it and define its universal principle without a loss of generality.

It is clearly written in http://www.geocities.com/complementarytheory/NXOR-XOR.pdf .

 

[doronshadmi]

That contradicts either the standard definition of sets or the law of identity.

Which?

2≠{2}. Simple, isn't it.

 

[PixyMisa]

I am not talking about Hebert's program to formalize Mathematics in terms of finite amount of formal terms.

I am talking about his whole\parts organic paradigm of the mathematical science.

Which exists only in your imagination.

I spoke about Gödel's motivation. He proved that any axiomatic system that is sufficiently powerful to deal with the arithmetic of the Natural numbers, cannot be both consistent AND complete.

Yes.

And on what do you base your claims as to his motivation, and what relevance does it have in any case?

A process cannot be found without a stable foundation

False.

exactly as any given sound (some variant) is compared to total silence (the invariant).

False.

Come on PixMisa. What you say is trivial.

Yes it is. And you got it completely wrong.

If you really read my posts you will find that I am talking exactly on what you wrote, but go beyond it and define its universal principle without a loss of generality.

I really read your posts. Where they are not entirely meaningless they are mostly wrong.

It is clearly written in http://www.geocities.com/complementarytheory/NXOR-XOR.pdf .

Does that PDF contain anything different to the nonsense you have presented here? If so, then why have you not presented that instead?

 

[PixyMisa]

2≠{2}. Simple, isn't it.

Yes, we know that. And it's not what you said. What you said was either:

2≠2

or

2∉{2}

So again, which of these obviously absurd statements are you making?

 

[doronshadmi]

Yes, we know that. And it's not what you said. What you said was either:

2≠2

or

2∉{2}

So again, which of these obviously absurd statements are you making?

2≠{2} and this is exactly what I said.

Which exists only in your imagination.

Formal system is nothing but a dogmatic imagination of some community of people, that thinks that their dogmatic imagination is independent of them.

Your misunderstanding is profound because you are trained to ignore consciousness\object relations, which is the basis of any reasoning (something that is beyond your dogmatic imagination).

 

[PixyMisa]

2≠{2} and this is exactly what I said.

Bzzt! Try again:

for example 2 and {2} are different, and there is nothing in 2 (2 without "{" and "}") that forces us to conclude that it is a member of {2}.

(My emphasis.)

So, what's it to be, 2≠2 or 2∉{2}?

Or was your earlier statement just another bit of nonsense that you immediately abandon when called on it?