A hidden assumption

[Bodhi Dharma Zen]

Sadly, he seems to have some difficulty with the whole "explain" concept.

Indeed, I believe part of the problem is that English is not her/his native language, another is the meaning of key words. Still, from time to time, I can see a couple of interesting concepts behind the gibberish. That's why I ask, to see if the concepts are really there or are simply a byproduct of the wording.

 

[jsfisher]

Indeed, I believe part of the problem is that English is not her/his native language, another is the meaning of key words. Still, from time to time, I can see a couple of interesting concepts behind the gibberish. That's why I ask, to see if the concepts are really there or are simply a byproduct of the wording.

The ESL excuse is a little too convenient. The posts here, the posts in other fora, and the other writings show a basic gap in the ability to reason. There have been just too many examples of "since X therefore Y" with no traceable path between premise and conclusion.

The most recent posts have been very revealing. For doronshadmi, this is a mystical religion, not a science and definitely not Mathematics. It is all true simply because s/he believes it to be true.

Concrete core with 4" rebar, anyone?

 

[Apathia]

Indeed, I believe part of the problem is that English is not her/his native language, another is the meaning of key words. Still, from time to time, I can see a couple of interesting concepts behind the gibberish. That's why I ask, to see if the concepts are really there or are simply a byproduct of the wording.

Earlier on, even before he got to metaphysics, I thought I was seeing an interesting direction to it all. But on closer examination, I'm not finding consistancy. So, it seems to me I was merely reading some concepts in.

I sympathze with his metamathematical quest, but I'm not seeing any solid foundation to anything he's presented so far.

 

[doronshadmi]

I sympathze with his metamathematical quest, but I'm not seeing any solid foundation to anything he's presented so far.

You cannot get that without using your consciousness, and a consciousness
gets the researchable if and only if both the memory without thoughts (the symmetrical side of the consciousness) and a thought without memory (the asymmetrical side of the consciousness) complement each other into a one_of many_faces realm, which is open by nature (it has an evolution).

I am not talking about any subjective experience here but about Symmetry\Asymmetry complementation, which is the universal principle of the researchable, whether it is abstract or not.

Without this fundamental understanding, you will not be able to understand that any researchable result (abstract or not) is actually the reflection of Symmetry\Asymmetry complementation, which stands in the basis of the researcher and the researched thing as a one organic realm.

The dichotomy between the researcher and the researched is nothing but a partial understanding of the organic realm of researcher \ researched complementation.


This partial understanding of the organic realm (Symmetry\Asymmetry complementation) gives the illusion that and object is something that is disconnected from our consciousness, where our consciousness is no more than some subjective (and partial point of view) of the real thing (the object itself).

I am also against some subjective (and partial point of view) of the real thing (the object itself), and the dichotomy between the researcher and the researched is exactly such a partial (and subjective point of view) of the researcher \ researched complementation.

No dichotomist approach can explain how the researcher (the subjective pert of this dichotomy) enables to get the researched (the objective part of this dichotomy).

Actually subject\object dichotomist is nothing but the result of the ignorance of the Symmetrical side of the consciousness, where this dichotomy does not exist.

If the consciousness gets itself right from the non-dichotomist state, then and only then different points of view are generalized into a one simple (atomic and timeless) meaning.

Logic is timeless exactly because it is based on Symmetry\Asymmetry complementation (the universal principle), and this universal principle is exactly our consciousness (Symmetry\Asymmetry complementation that aware of itself).

Symmetry\Asymmetry complementation reinforces the Copernican principle ( http://en.wikipedia.org/wiki/Copernican_principle ) because the concept of consciousness is not understood any more in terms of a subjective point of view ( mysticism ) but in terms of a fundamental principle which stands in the basis of both abstract and non-abstract modern science.


If the consciousness is not aware of itself as Symmetry\Asymmetry complementation, it can easily get some partial point of view of it as some objective thing.

Objectivity is not gotten by some agreement between scholars that are not aware of Symmetry\Asymmetry complementation.

I am, by definition, aware of my own consciousness, so you fail again.

No, your consciousness is directly aware of itself without any need of any definition.
Definitions are a collection of many (maybe infinitely many) different ways in which this direct experience can be expressed.

The community of the mathematicians of the past 2500 years are a community of people that tries as a group to agree on expressions of this direct experience, instead of to get the direct experience of Symmetry\Asymmetry complementation, as the timeless principle of the mathematical science.

 

[PixyMisa]

(Usual drivel snipped.)

No, your consciousness is directly aware of itself without any need of any definition.

No. Something is directly aware of itself without any need of definition, but without definition, we don't have a word for it and can't talk about it.

That's your problem right there. Well, one of your problems.

The community of the mathematicians of the past 2500 years are a community of people that tries as a group to agree on expressions of this direct experience, instead of to get the direct experience of Symmetry\Asymmetry complementation, as the timeless principle of the mathematical science.

No.

 

[doronshadmi]

No. Something is directly aware of itself without any need of definition, but without definition, we don't have a word for it and can't talk about it.

So, it is not less than direct awareness\definition complementation.

That's your problem right there. you are not aware of this complementation that can easily be understood as Symmetry\Asymmetry complementation.

There is nothing subjective here but simply invariant\variant complementation of a one organic realm that can be defined by infinitely many definitions that not one of them is possible without the universal principle of invariant\variant complementation.



Here is some concrete example of your misunderstanding of the invariant\variant complementation.

NN
NS
SN
SS

Yes. You have just discovered that two times two is four. Congratulations!

1. Without a loss of generality (http://en.wikipedia.org/wiki/Without_loss_of_generality ) we get:

1. NN
2. NS
3. SN (the inverse of #2)
4. SS (the inverse of #1)

that is reduced to Symmetry (NN or SS)\ Asymmetry(SN or NS) complementation:

For example:

NN (Symmetry)
N  (Asymmetry)

is equivalent to

SS (Symmetry)
S  (Asymmetry)

which is exactly Symmetry\Asymmetry complementation as the universal principle of Standard Logic itself.

2. Furthermore. By standard Logic there is no answer to this question:

How True AND False share the same realm without contradict each other?

It must be understood that without this simultaneous shareness no True or False conclusion can be found.

You maybe claim that there is not AND between True\False shareness but OR.

OR is:

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

and we get (without a loss of generality) again Symmetry\Asymmetry complementation as the universal principle of Standard Logic.

 

[PixyMisa]

Here we go again.

So, it is not less than direct awareness\definition complementation.

No, it is not more than a complementary rabbit\carrot direction.

That's your problem right there. you are not aware of this complementation that can easily be understood as Symmetry\Asymmetry complementation.

I might be more aware of it if you ever bothered to say what any of this is supposed to mean.

There is nothing subjective here but simply invariant\variant complementation of a one organic realm that can be defined by infinitely many definitions that not one of them is possible without the universal principle of invariant\variant complementation.

Sorry, that's entirely nonsensical.

Here is some concrete example of your misunderstanding of the invariant\variant complementation.

Waiting.

1. Without a loss of generality (http://en.wikipedia.org/wiki/Without_loss_of_generality ) we get:

1#.NN
2#.NS
3#.SN (the inverse of 2#)
4#.SS (the inverse of 1#)

that is reduced to Symmetry (NN or SS)\ Asymmetry(SN or NS) complementation:

Meaningless.

For example:

NN (Symmetry)
N  (Asymmetry)

Is equivalent to

SS (Symmetry)
S  (Asymmetry)

which is exactly Symmetry\Asymmetry complementation as the universal principle of Standard Logic itself.

Meaningless.

2. Furthermore. By standard Logic there is no answer to this question:

How True AND False share the same realm without contradict each other?

What do you mean by "share"? What do you mean by "realm"? What do you mean by "contradict"?

It must be understood that without this simultaneous shareness no True or False conclusion can be found.

Nope.

You maybe claim that there is not AND between True\False shareness but OR.

No thanks.

OR is:

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

And we get (without a loss of generality) again Symmetry\Asymmetry complementation as the universal principle of Standard Logic.

An astounding new discovery! All truth tables look alike if you leave out the result!

 

[doronshadmi]

I might be more aware of it if you ever bothered to say what any of this is supposed to mean.

Since you simply refuse to be aware of yourself when you are doing mathematics, you are unable to get it.

No, it is not more than a complementary rabbit\carrot direction.

Cynicism is the tool of persons that are afarid of evolution.

Here we go again.

No PixyMisa.

You have never moved from your point of view, which is the ignorence of yourself when you are doing mathematics.

Result: You get exactly nothing again and again and again ... ad infinitum.

 

[PixyMisa]

Since you simply refuse to be aware of yourself when you are doing mathematics, you are unable to get it.

Unable to get what?

Cynicism is the tool of persons that are afarid of evolution.

I thought that was religion.

No PixyMisa.

You have never moved from your point of view, which is the ignorence of yourself when you are doing mathematics.

What does this "ignorence of yourself" have to do with mathematics?

Result: You get exactly nothing again and again and again ... ad infinitum.

You are supposed to get the same answer every time. Indeed, that's rather the point. If you disagree, then you're simply not doing mathematics any more. You've moved on to mysticism.

 

[doronshadmi]

What does this "ignorence of yourself" have to do with mathematics?

You think that Mathematics is well-defined definitions.

You cannot define anything without your consciousness.

In that case it is inevitable to ask what are the minimal terms that enable to define anything (formal or not, it does not matter) if you wish to avoid hidden assumptions.

 

[PixyMisa]

You think that Mathematics is well-defined definitions.

No, but formal definitions are essential to mathematics.

You cannot define anything without your consciousness.

A definition is merely the attaching of a symbol to a concept. You don't need to be self-aware to do this.

In that case it is inevitable to ask what are the minimal terms that enable to define anything (formal or not, it does not matter) if you wish to avoid hidden assumptions.

I'm not entirely sure what that's supposed to mean. Mathematics is an abstract system derived from propositional logic. Do you have a problem with propositional logic? Because if that is sound, all of mathematics is sound, and your argument (as near as I can make it out) falls flat.

 

[doronshadmi]

No, but formal definitions are essential to mathematics.

And consciousness is essential to formal definitions.

Be aware that a computer or any other mechanic formal method that enables to get premises and produce conclusions is no more than an agent of your consciousness.

A definition is merely the attaching of a symbol to a concept. You don't need to be self-aware to do this.

The symbol, the concept and the attachment between them are inseparable of the mathematician's consciousness.

I'm not entirely sure what that's supposed to mean. Mathematics is an abstract system derived from propositional logic.

Propositional logic is inseparable of the mathematician's consciousness.

In all of these cases I am not talking about the subjective interpretation of the concept of Consciousness.

I am talking about the must have terms that enables the existence of a self-aware thing (whether it is mostly made of carbon, like us, or not)

It must be based on Symmetry(invariance)\Asymmetry(variance) complementation that is aware of itself and enables to understand what is researchable what is not researchable and how they complement each other.

Without this complementation no two things (abstract or not) are gathered into a one thing, and no system that is beyond its atomic state (total unification or total isolation) can be found.

 

[jsfisher]

And consciousness is essential to formal definitions.

Be aware that a computer or any other mechanic formal method that enables to get premises and produce conclusions is no more than an agent of your consciousness.

And just how is consciousness relevant to this thread?

What does it have to do with your assertion that a set is the union of its members?

 

[doronshadmi]

And just how is consciousness relevant to this thread?

Please demonstrate the existence of this thread, as something that is totally independent of any consciousness.

In other words, you cannot avoid consciousness (including an indirect agent of it)whether you are doing mathematics or not.

It is simply impossible. Since it is impossible you have no choice but to be aware of it when you are doing mathematics

What does it have to do with your assertion that a set is the union of its members?

Since a set and a member are no more than the reflection of the mathematician's consciousness, it is essential that the mathematician's consciousness will be aware of the fact that its results are nothing but its own reflection.

This is known as the minimal test that checks the intelligence of any creature that enables to get its own reflection in some reflector (some mirror).

You put it in front of a mirror. If the creature does not recognize its own reflection and look at it as another creature, then it does not pass the minimal test of intelligence.

The current community of mathematicians is a group of persons that are trained for the past 2500 years to ignore their own reflection, until they really think that their own reflection is an independent object.

You may say: but what if this is not the mathematician's self reflection, but really a realm that is totally independent of us?

In that case another question arises, which is:

Who you are able to know that there are things that are your own reflection, and on the same realm there are things that are not your own reflection?

In other words, how these two alternatives can be compared with each other, without any common basis?

If you think about it you cannot avoid the conclusion that things are the result of Symmetry(the invariance and the common)\Asymmetry(the variance and the non-common) complementation.

Without this complementation nothing is researchable.

A set is a researchable thing, and it is a researchable thing exactly because it is not less than the common(what you, by mistake, call a set)\non-common(what you call a member) complementation.

Since any researchable thing the result of some complementation, and since a set is a researchable thing, its members are inseparable of it and it is not less than a one thing with many faces (an organic realm).

Again:

Without this complementation no two things (abstract or not) are gathered into a one thing, and no system that is beyond its atomic state (total unification or total isolation) can be found.

-----------------

X={{A,B},{A,C,D}}

There is nothing in {A,B} or {A,C,D} which gives us the knowledge that {A,B} or {A,C,D} are also members of X.

This knowledge is available only if {{A,B},{A,C,D}} exists.

So, a member of X has a meaning only by {{A,B},{A,C,D}} and this knowledge cannot be related to {A,B} or {A,C,D} without the knowledge of {{A,B},{A,C,D}}.

In that case {A,B} U {A,C,D} does not have any knowledge of {{A,B},{A,C,D}} unless it is used as a hidden assumption of {A,B} U {A,C,D}.

 

[jsfisher]

Please demonstrate the existence of this thread, as something that is totally independent of any consciousness.

In other words, you cannot avoid consciousness (including an indirect agent of it)whether you are doing mathematics or not.

It is simply impossible. Since it is impossible you have no choice but to be aware of it when you are doing mathematics

I ask about relevance to this topic, and you go off on another irrelevant tangent.

...meaningless and irrelevant claptrap...

Remember, your incorrect statement at hand is that a set is the union of its members. These excursions off into metaphysics and existentialism lend nothing to support your statement.

 

[PixyMisa]

Please demonstrate the existence of this thread, as something that is totally independent of any consciousness.

What do you mean by "the existence of this thread"? This thread can be represented by a series of magnetic domains on a hard disk - or holes in a deck of punched cards, if you want something simple and clearly physical. Does a deck of punched cards exist if no-one is there to put them in a card reader?

Yes.

In other words, you cannot avoid consciousness (including an indirect agent of it)whether you are doing mathematics or not.

No.

It is simply impossible.

No.

Since it is impossible you have no choice but to be aware of it when you are doing mathematics

No, hence also no.

Since a set and a member are no more than the reflection of the mathematician's consciousness

No.

it is essential that the mathematician's consciousness will be aware of the fact that its results are nothing but its own reflection.

No.

This is known as the minimal test that checks the intelligence of any creature that enables to get its own reflection in some reflector (some mirror).

You put it in front of a mirror. If the creature does not recognize its own reflection and look at it as another creature, then it does not pass the minimal test of intelligence.

That's a really bad description of the mirror test, both in terms of procedure and conclusions. What you do is paint a dot on the face of the creature, and then put it in front of a mirror. The reaction of the creature shows whether it can recognise a representation of itself as such. The great apes, elephants, and dolphins - and human children over about 18 months - clearly do. Dogs, cats, lichen, and human babies under about 18 months don't.

Human babies begin to walk and talk, and certainly to recognise faces, voices, rhythms, colours, shapes and numbers well before they pass the mirror test. It's certainly not a "minimal test of intelligence" and it has nothing whatsoever to do with mathematics.

The current community of mathematicians is a group of persons that are trained for the past 2500 years to ignore their own reflection, until they really think that their own reflection is an independent object.

No.

You may say: but what if this is not the mathematician's self reflection, but really a realm that is totally independent of us?

How generous of you.

In that case another question arises, which is:

Who you are able to know that there are things that are your own reflection, and on the same realm there are things that are not your own reflection?

I don't see how any such question arises, nor do I consider it meaningful, as you have still failed to define what you mean by "realm", much less what it has to do with reflections, where you are clearly conflating the physical with the metaphorical.

In other words, how these two alternatives can be compared with each other, without any common basis?

Symbolic representation.

If you think about it you cannot avoid the conclusion that things are the result of Symmetry(the invariance and the common)\Asymmetry(the variance and the non-common) complementation.

You still haven't said what this means.

Without this complementation nothing is researchable.

Or this.

A set is a researchable thing, and it is a researchable thing exactly because it is not less than the common(what you, by mistake, call a set)\non-common(what you call a member) complementation.

And because of that failure (and possibly for other reasons) this is meaningless.

Since any researchable thing the result of some complementation, and since a set is a researchable thing, its members are inseparable of it and it is not less than a one thing with many faces (an organic realm).

And this is double plus meaningless.

Again:

Without this complementation no two things (abstract or not) are gathered into a one thing, and no system that is beyond its atomic state (total unification or total isolation) can be found.

With cream.

-----------------

X={{A,B},{A,C,D}}

There is nothing in {A,B} or {A,C,D} which gives us the knowledge that {A,B} or {A,C,D} are also members of X.

So?

This knowledge is available only if {{A,B},{A,C,D}} exists.

What do you mean by "exists" here?

So, a member of X has a meaning only by {{A,B},{A,C,D}} and this knowledge cannot be related to {A,B} or {A,C,D} without the knowledge of {{A,B},{A,C,D}}.

You just defined X as being the set {{A,B},{A,C,D}}. If X were undefined, X would be undefined. Since X has been defined, X is defined.

This is not particularly interesting.

In that case {A,B} U {A,C,D} does not have any knowledge of {{A,B},{A,C,D}} unless it is used as a hidden assumption of {A,B} U {A,C,D}.

{A,B} U {A,C,D} is a set operation. It doesn't have knowledge. Or assumptions. Or anything to do with X.

 

[doronshadmi]

What do you mean by "the existence of this thread"? This thread can be represented by a series of magnetic domains on a hard disk - or holes in a deck of punched cards, if you want something simple and clearly physical. Does a deck of punched cards exist if no-one is there to put them in a card reader?

A deck of punched cards is some result of a consciousness (its agent).

No consciousness has to currently use it, and still it is the result of a consciousness. The deck of punched cards is a consciousness agent.

Furthermore, both of them are results of Symmetry\Asymmetry complementation, where a consciousness is aware of itself as a complementation and can manipulate it according to this awareness, and a deck of punched cards cannot manipulate Symmetry\Asymmetry complementation according to its self awareness.

That's a really bad description of the mirror test,

Thank you for the details, but is does not change the fact that the community of mathematicians of the past 2500 years is trained to see premises and conclusions as something that is totally disconnected from their consciousness. You are a good example of this training.

As a result they recognize their own results as something that is totally disconnected of them.

If this is the case, then how any mathematician has an access to this isolated realm?

You just defined X as being the set {{A,B},{A,C,D}}. If X were undefined, X would be undefined. Since X has been defined, X is defined.

This is not particularly interesting.

Yes I know, because "interesting" for you is anything that does not have any connection to your consciousness, but still you can get it. What a trick of "pure consistency" we have here.

{A,B} U {A,C,D} is a set operation. It doesn't have knowledge. Or assumptions. Or anything to do with X.

Who told you that, maybe the operation itself?


"The foundational philosophy of Platonist mathematical realism, as exemplified by mathematician Kurt Gödel, proposes the existence of a world of mathematical objects independent of humans; the truths about these objects are discovered by humans. In this view, the laws of nature and the laws of mathematics have a similar status, and the effectiveness ceases to be unreasonable. Not our axioms, but the very real world of mathematical objects forms the foundation. The obvious question, then, is: how do we access this world? (cf Anglin 1991 p. 218)"

"...In a sense, the crisis (My addition: of the foundation of mathematics) has not been resolved, but faded away: most mathematicians either do not work from axiomatic systems, or if they do, do not doubt the consistency of ZFC, generally their preferred axiomatic system. In most of mathematics as it is practiced, the various logical paradoxes never played a role anyway, and in those branches in which they do (such as logic and category theory), they may be avoided."
( http://en.wikipedia.org/wiki/Foundations_of_mathematics )

 

[doronshadmi]

Remember, your incorrect statement at hand is that a set is the union of its members. These excursions off into metaphysics and existentialism lend nothing to support your statement.

My 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.

 

[PixyMisa]

A deck of punched cards is some result of a consciousness

Yes. So?

(its agent).

No.

No consciousness has to currently use it, and still it is the result of a consciousness.

Yes. So?

The deck of punched cards is a consciousness agent.

No.

Furthermore, both of them are results of Symmetry\Asymmetry complementation

You still haven't said what this means.

where a consciousness is aware of itself as a complementation

Meaningless.

and can manipulate it

It? What?

according to this awareness, and a deck of punched cards cannot manipulate Symmetry\Asymmetry complementation according to its self awareness.

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.

Thank you for the details, but is does not change the fact that the community of mathematicians of the past 2500 years is trained to see premises and conclusions as something that is totally disconnected from their consciousness. You are a good example of this training.

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.

As a result they recognize their own results as something that is totally disconnected of them.

Correct.

If this is the case, then how any mathematician has an access to this isolated realm?

Symbolic representation.

Yes I know, because "interesting" for you is anything that does not have any connection to your consciousness, but still you can get it. What a trick of "pure consistency" we have here.

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

Who told you that, maybe the operation itself?

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

"The foundational philosophy of Platonist mathematical realism, as exemplified by mathematician Kurt Gödel, proposes the existence of a world of mathematical objects independent of humans; the truths about these objects are discovered by humans. In this view, the laws of nature and the laws of mathematics have a similar status, and the effectiveness ceases to be unreasonable. Not our axioms, but the very real world of mathematical objects forms the foundation. The obvious question, then, is: how do we access this world? (cf Anglin 1991 p. 218)"

"...In a sense, the crisis (My addition: of the foundation of mathematics) has not been resolved, but faded away: most mathematicians either do not work from axiomatic systems, or if they do, do not doubt the consistency of ZFC, generally their preferred axiomatic system. In most of mathematics as it is practiced, the various logical paradoxes never played a role anyway, and in those branches in which they do (such as logic and category theory), they may be avoided."
( http://en.wikipedia.org/wiki/Foundations_of_mathematics )

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.

 

[PixyMisa]

My incorrect statement?

Yes.

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

Whatever. The point is that you're still wrong.