Deeper than primes

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doronshadmi said:
No problem, enjoy your ignorence.
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Sorry Doron if you think that berating your ignorance is something I enjoy or could possibly miss, you again over estimate your significance. I would much rather have you able to discuss the topics you claim to be supplanting with at least some semblance of knowledge. This is one of the reasons I still continue to actively engage you on this thread. If you want to consider your inability to explain your paradigm shifting notions without directly contradicting yourself as the ignorance of others, that is you prerogative. I am certain you will continue to provide such inconstancies to address without looking at what you have surreptitiously added to a pervious post.
 
sympathic said:
can you show us a mathematical problem solved using your approach? for example provide us with a proof using your approach that the sum of two even integers is always even.
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I see you prefer ignoring posts that involve more than just hand-waving and drawings.
 
The Man said:
Sorry Doron if you think that berating your ignorance is something I enjoy or could possibly miss, you again over estimate your significance. I would much rather have you able to discuss the topics you claim to be supplanting with at least some semblance of knowledge. This is one of the reasons I still continue to actively engage you on this thread. If you want to consider your inability to explain your paradigm shifting notions without directly contradicting yourself as the ignorance of others, that is you prerogative. I am certain you will continue to provide such inconstancies to address without looking at what you have surreptitiously added to a pervious post.
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The Man, you are an ignorant because you cannot distinguish between true/false REIs or meaningful\meaningless REIs, for example:

'/ / /' is a meaningless REI

'x/y' is a meaningful REI, where 'x','y' are Elements and '/' is Relation.

Also I show that REI stands at the basis of any meaningful representation method, for example Lisp:

(= a b) = a=b, where 'a','b' are Elements and '=' is Relation.

(/ x y) = x/y, where 'x','y' are Elements and '/' is Relation.

(/ (/ a b) c) = (a/b)/c where '(a/b)','c' are Elements and '/' is Relation.

(= (/ a b) c) = (a/b)=c where '(a/b)','c' are Elements and '=' is Relation.

'/ = /' is true

'= = =' is true

'≠ ≠ ≠' is false

'≠ = ≠' is true

'= ≠ =' is false

'= = ≠' is false

In other words, I invite you to define a Well Formed Formula which is not a meaningful REI.

If you can do that, then and only then my theory does not hold.
 
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doronshadmi said:
I invite you to define a Well Formed Formula which is not a meaningful REI.

If you can do that, then and only then my theory does not hold.
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Looking past your obtuse misuse of the word, define, we already did this.

Looking past your circular justification for REI's, we already pointed out that you belabor the trivial.
 
jsfisher said:
Nope. That would be your summary post of all your twisted ramblings trying to make the trivial X=X some how vitally important and at the same time identical to the semantically distinct X.
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Nope, that is your inability to get http://www.internationalskeptics.com/forums/showpost.php?p=4529310&postcount=2227 and your twisted ramblings that forcing A alone as WFF.

To say that A alone in A=A is a Well Formed Formula, is similar to "the hand alone of some body is an organ of this body".

In both cases the word alone is meaningless because in both cases the examined thing has a meaning only if it is inseparable of the whole (A=A in the case of A, or the body in the case of the hand).

Since we are talking on the atomic level, only A(Element) or only =(Relation) are too weak (isolated Element) or too strong (isolated Relation) for research.

If you agree that A is WFF only if it is an organ of A=A, you actually agree with Relation Element Interaction as the minimal basis of any WFF.

In this case the minimal WFF is A=A, where A refers to itself by =, as follows:
AAA.jpg


A=A is simple, not trivial (and you do not distinguish between the simple and the trivial).

You still do not get that 2 alone is not the same as 2 as a member of some set, notated at least as {2}.
 
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doronshadmi said:
The Man, you are an ignorant because you cannot distinguish between true/false REIs or meaningful\meaningless REIs, for example:

'/ / /' is a meaningless REI

'x/y' is a meaningful REI, where 'x','y' are Elements and '/' is Relation.

Also I show that REI stands at the basis of any meaningful representation method, for example Lisp:

(= a b) = a=b, where 'a','b' are Elements and '=' is Relation.

(/ x y) = x/y, where 'x','y' are Elements and '/' is Relation.

(/ (/ a b) c) = (a/b)/c where '(a/b)','c' are Elements and '/' is Relation.

(= (/ a b) c) = (a/b)=c where '(a/b)','c' are Elements and '=' is Relation.

'/ = /' is true

'= = =' is true

'≠ ≠ ≠' is false

'≠ = ≠' is true

'= ≠ =' is false

'= = ≠' is false

In other words, I invite you to define a Well Formed Formula which is not a meaningful REI.

If you can do that, then and only then my theory does not hold.
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We continue to invite you to show that you ‘REI’ is meaningful in and of itself. Without ‘relations’ you have no ‘interaction’ since your ‘REI’ can not exhibit your minimal requirement of definition a ‘self-reference’ of a ‘relation’ as a ‘relation’ you have no ‘relations’ in your ‘REI’. As your ‘REI’ can only relate ‘elements’ your ‘relations’ have no ‘self-reference’ as ‘relations’ within your ‘REI’ and thus remain indefinable by your ‘REI’.

Under First Order Predicate Logic True and False are both well formed formulas as is the atomic formula P(x,y) where P is the predicate name with x and y as variables, which are all themselves well formed formula as well under the requirements of First Order Predicate Logic .

It is up to you, Doron, to establish the language and grammar of your ‘REI’ to determine what is or is not a WFF in your ‘REI’. So far the requirements you have given are ‘relation’, ‘element’ and ‘interaction’ with ‘self-reference’ as the basis of definition within your ‘REI’ and the fundamental ‘interaction’. Unfortunately you also require ‘elements’ to be the only things that can be ‘related’, so you have defined a language that does not permit the ‘relations’ it requires to be defined or ‘self-referenced’ as ‘relations’ within that language.
 
I think it is quite evident that Doron's ideas have no mathematical substance whatsoever. Maybe we should all take Skeptic's advice and stop wasting Doron's time and ours. There is no real dialog here, just a huge waste of time.
 
The Man said:
We continue to invite you to show that you ‘REI’ is meaningful in and of itself. Without ‘relations’ you have no ‘interaction’ since your ‘REI’ can not exhibit your minimal requirement of definition a ‘self-reference’ of a ‘relation’ as a ‘relation’ you have no ‘relations’ in your ‘REI’. As your ‘REI’ can only relate ‘elements’ your ‘relations’ have no ‘self-reference’ as ‘relations’ within your ‘REI’ and thus remain indefinable by your ‘REI’.

Under First Order Predicate Logic True and False are both well formed formulas as is the atomic formula P(x,y) where P is the predicate name with x and y as variables, which are all themselves well formed formula as well under the requirements of First Order Predicate Logic .

It is up to you, Doron, to establish the language and grammar of your ‘REI’ to determine what is or is not a WFF in your ‘REI’. So far the requirements you have given are ‘relation’, ‘element’ and ‘interaction’ with ‘self-reference’ as the basis of definition within your ‘REI’ and the fundamental ‘interaction’. Unfortunately you also require ‘elements’ to be the only things that can be ‘related’, so you have defined a language that does not permit the ‘relations’ it requires to be defined or ‘self-referenced’ as ‘relations’ within that language.
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If we use Lisp as an example, then X is the function where y is the parameters (where the parameters can be also functions),
such that (X y1 y2 y3 ...)

The function is a form of Relation where the parameter is a form of Element, even if some parameter is a function.

Furthermore, the parameter can be the function in the case of recursion, such that (X y1=X)

It does not change the fact that the fundamental form is (Relation Element1 Element2 Element3 …)

True is WFF, or False is WFF exactly because it is based on REI, where where 'True' OR 'False' are Element(s) and 'is' is Relation.

So is P(x,y), where P is Relation and x,y are Element(s).


"under the requirements of First Order Predicate Logic" is based REI as shown in http://www.internationalskeptics.com/forums/showpost.php?p=4512946&postcount=2153
 
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sympathic said:
I think it is quite evident that Doron's ideas have no mathematical substance whatsoever. Maybe we should all take Skeptic's advice and stop wasting Doron's time and ours. There is no real dialog here, just a huge waste of time.
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I think it is quite evident that you do not wish to read http://www.internationalskeptics.com/forums/showpost.php?p=4528548&postcount=2225 and do not with to research the philosophical foundations of the mathematical science, which is OK with me.

You are a participator of a philosophy forum here. No one forces you to do that.
 
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doronshadmi said:
Ho yes you do in http://www.internationalskeptics.com/forums/showpost.php?p=4518092&postcount=2178 , where you write:


In other words: "A in A = A is a formula" = "A is an organ of A = A, and it is WFF only if A in A=A"

You simply don't get http://www.internationalskeptics.com/forums/showpost.php?p=4512946&postcount=2153 .
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No. You continue to twist and warp simple declarations into odd and unidentifiable claims. My claim is a simple one; please stop trying to contort it into something it is not. The rules for what constitute well-formed formulae accept a lone term as a formula. Something as simple as A, therefore, can be a well-formed formula, just as A=A can be. And there is no dependence on the latter for the former.
 
jsfisher said:
The rules for what constitute well-formed formulae accept a lone term as a formula.
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These rules cannot avoid Relation Element Interaction in order to do that, for example:
Well Formed Formula - Wikipedia said:
Each propositional variable is, on its own, a formula.

http://en.wikipedia.org/wiki/Formula_(mathematical_logic)
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Element = "propositional variable"

Relation = "is"

In other words, this rule cannot be expressed unless REI is used, and it is used by you as a hidden assumption as clearly explained in http://www.internationalskeptics.com/forums/showpost.php?p=4496540&postcount=2035 .

AGAIN:

In this case the minimal WFF is A=A, where A refers to itself by = (it is not less than REI) as follows:
AAA.jpg


A=A is simple, not trivial (and you do not distinguish between the simple and the trivial).

You still do not get that 2 alone is not the same as 2 as a member of some set, notated at least as {2}.

You simply don't get http://www.internationalskeptics.com/forums/showpost.php?p=4512946&postcount=2153

jsfisher said:
You continue to twist and warp simple declarations into odd and unidentifiable claims.
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You continue to use REI as a hidden assumption of your simple (formal) declarations.
 
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