Scrutinizing Equality "=" more closely

[chikoka]

A dog is a dog because it is identified as a dog.

If you think this is a literally a math equation, then there's nothing else I can tell you, other than: you've really got to work on your understanding on the basics of philosophy.

Wow!!...you really at the lowest level of abstraction there. The OP is several layers of Abstraction above mentioning instances..i see why its so hard for you to keep up.

Lets break down your analysis.
Are you aware that the greeks wrote all their mathematics with words and did not use a single symbol even for numbers?

i'll break this down...this is from an excerpt of a mathematical proof done in ancient greece;

"the square root of two is therefore to be identified with irrationality"

I dont expect to to have the slightest idea of the whole story behind this statement ...but since you are so sure you understand everything at least tell me this ...is that not a mathematical equation?

Isnt it strange that you say such bold statements about equivalences when you dont even know ...lord forbid...what an orderd pair is...or what the properties of symmetry , transitivity or reflexivity ARE?!?!

If i said those last 3 define equivalence ..i know..you wouldnt understand in the slightest.

Your caught up in order ...i mentioned infinite regresses, cartesian products, relations...none of that came out from you..was the word order the only word in the OP?

Diebert help me out here, your single post mentioned transitivity, something i didnt mention..a valuable contribution thats why i was commpeled to acknowledge it and all your other points with the word "Nice". Theres been nothing Nice about russels contributions. Please just say something to russel , maybe he just doesnt (want to) understand because its me.

[chikoka]

I see you replied :)

[chikoka]

Obviously if you'd stop asserting the axion (hold it as true) a logical system will not function. That's why it's called axiom! So are you trying to prove a logical system does not function without its axioms to be true?

I never said anything about "truth". I mentioned consistency.I am fully aware that an axiomatic sytem is a statement "if this then that" and nothing more. "if axioms are true then theorems a to z are also true. Truth can only be established within a larger system with its own axioms.

Even if it is inconsitent it can still function. #godel

The question you should ask is what remains after doing that, since you don't have a system anymore to organize your thoughts or definitions in.

My aim is one only , to show that there is an objective reality, i havent fully done that but i'm toying with the idea that there are no minds..only disposition to behave.coupled with objective reality..lets not hijack this thread tho..i dont know how the "concept" disposition itself is objective

Quote:
Quote:
In practice nothing is totally or absolutely equivalent to anything unless it would equal totality


What do you mean by this? Are you admiting that nothing can be absolutely equivalent to itself?

This is about the truth of change, which is also part of causality. There will always be differences between a thing and whatever it is one is comparing it to. So the equivalence is approximation, like everything else that is being observed. The abstract realm consist of idealized reality where the normal flux of reality is artificially suspended. But that is because you accept the approximation of the abstract, like you accept a drawing as representation only.

these are words so horribly far from conceptualisation in the mind of Russel.<sigh>

[Bobo]

If we assume that something has a relation and show it to have no-relation we could define the relation: relation=>no-relation. Of course a relation with NO-relation wouldn't possibly be a relation, that's why we assume it to be a relation too. There are two assumptions that things can have this relation and that it is a relation, if it is that it is not a relation and things can't have this relation it can be explain it the same way relation=>no-relation, without it can we make suppositions?

[chikoka]

The abstract realm consist of idealized reality where the normal flux of reality is artificially suspended

The abstract realm can never be totally suspended, because the concept of suspension involves a viscious infinite regress.

[chikoka]

If we assume that something has a relation and show it to have no-relation we could define the relation: relation=>no-relation. Of course a relation with NO-relation wouldn't possibly be a relation, that's why we assume it to be a relation too. There are two assumptions that things can have this relation and that it is a relation, if it is that it is not a relation and things can't have this relation it can be explain it the same way relation=>no-relation, without it can we make suppositions?

If you assume something has a relation and show it has no relation you have effectively just said A != A there. That is the first half of the OP.
That a relation must itself be related to itsef , and this new relation is also related to itself is the only alternative , which is no alternative because it is a viscous infinite regress.

You catch on quick :)

[Bobo]

Take related-to-itself, no-relation and relation=>no-relation to mean the same thing, to say that it is a viscous relation is saying relation=>no-relation. It is not an strict relation as it also is a no-relation. When you define a strict relation you have it as a consequence of more relations.

[chikoka]

Take related-to-itself, no-relation and relation=>no-relation to mean the same thing, to say that it is a viscous relation is saying relation=>no-relation. It is not an strict relation as it also is a no-relation. When you define a strict relation you have it as a consequence of more relations.

Understand that the underlined can also be read as relation=>no-strict-relation.

Am i losing you Bobo ? :)

[Bobo]

That's what I was trying to express ,an ordered pair is in some sense lesser or stronger than relationship, or yet relationship is more expressive, even when you define something like an ordered pair you would assume a relation between the things and verify if it is the case of it having the relation or not having it.

[chikoka]

That's what I was trying to express ,an ordered pair is in some sense lesser or stronger than relationship, or yet relationship is more expressive, even when you define something like an ordered pair you would assume a relation between the things and verify if it is the case of it having the relation or not having it.

The orderd pair is the defining and the defining is the orderd pair. When you include more to defining ,i.e. defining futher you are just introducing more orderd pairs.
Do you see that once we have defined something (established an orderd pair) we still have to define what the relationship is between this defintion and its orderd pair, this second defining's relationship with the orderd pair it establishes also needs to be defined and so on...
This is the infinite regress.

[chikoka]

LOl..

The relation between; going through russels left ear and out his other ; must be an equivalence relation. It goes thru unchanged or processed.

#just_kidding

But seriously tho dont you wonder how everyone else is beyond the first line of the OP that mentions "order" and is onto the meaningful other stuff in the rest of It.
Dierbert mentioned *not a single* complaint on order or any of the other prerequisites.Bobo's doing good too.

you did mention elsewhere that you never went to college...i see that now.
try picking up a book on logic and explore the definitions of meaning and the theory's on it..juicy stuff to be had too, and its simple like so you'll totaly get it, i hope.

When you get to group theory which the OP uses heavily implied concepts of then you've begun. like how the fractal statement borrows the concept of isomorphism from there were each level (part) of the statement is related to the next isomorphicaly. I know from D's other posts that he aslo infuses material "suggestive" of various different branches of math i dont know if knowingly.
If i was to strip all the layers of some of my posts <smurk> maybe you'ld understand all the "double speak" involved..i thought of doing that then i realised it would probably make even less sense.

#reversing_the_game

[Diebert van Rhijn]

So are you trying to prove a logical system does not function without its axioms to be true?

I never said anything about "truth". I mentioned consistency.

Consistency remains the realm of the factual but the axiomatic is the generalized realm of truth. Truth therefore as being derived from some higher order system and not derivable or provable within the confines of the used system. This is why the only consistency that counts is the consistency with the axioms.

Logical systems are just one formalized instance of a generalized principle. Perhaps it's tempting for some to try to reverse that?

Even if it is inconsitent it can still function. #godel

Provability is a weaker notion than truth. #Hofstadter

[Diebert van Rhijn]

The abstract realm consist of idealized reality where the normal flux of reality is artificially suspended

The abstract realm can never be totally suspended, because the concept of suspension involves a viscious infinite regress.

That might be so but it's just as easy to say that the abstract realm involves all the infinite regress and tautologies. It might explain the confusion when addressing the concrete world through the abstract. It's true that the very act of accessing the world involved abstraction. Suspending the abstraction then also annihilates the world. But it's not necessarily so that the thing we refer to always equals our abstraction of it: a reference remains open-ended.

[chikoka]

This is why the only consistency that counts is the consistency with the axioms.

But the axioms are not consistent ..thats what i'm saying. For the AOI to be the AOI there must be ,included in the "process", a viscous infinite regress. But if we do not allow for that arent we admititing that the AOI cannot be the AOI. And if we have both the "fact" of the AOI and what is in fact a violation of that fact i.e. that the AOI is not the AOI we are left with no consistensy.
I feel you are going to say that the statement AOI != AOI is a theorem not axiom. But Hahaha.....for the theorem to not be an axiom there has to be an ordered pair for that relation "not.." which involves an infinite regress so that relation cannot hold meaning that the statement AOI!=AOI is not not an axiom,or in other words is an axiom.

You could do the same trick with the relation "is an axiom" and derive an infinite regress but then again thats my point that no axiom can also participate in "is an axiom_ing"

Youve just strenghtened my case :)

Quote:
Even if it is inconsitent it can still function. #godel

Provability is a weaker notion than truth. #Hofstadter

Hahaha..the relation "is weaker......".......

[chikoka]

The abstract realm consist of idealized reality where the normal flux of reality is artificially suspended

The abstract realm can never be totally suspended, because the concept of suspension involves a viscious infinite regress.

That might be so but it's just as easy to say that the abstract realm involves all the infinite regress and tautologies. It might explain the confusion when addressing the concrete world through the abstract. It's true that the very act of accessing the world involved abstraction. Suspending the abstraction then also annihilates the world. But it's not necessarily so that the thing we refer to always equals our abstraction of it: a reference remains open-ended.

Did you just say "concrete"...shame on you :)

and accessing the world?

But hahaha The relation between "the thing" and "the abstraction of it" , i.e. "not necessarily always equal" involves an infinite regress

[chikoka]

This haha trick realy is cheap :)

We just need to scrap this idea that minds exist.
Isnt that another idea.
its not because once we have scrapped minds other ideas have nowhere to exist.
What if its the same idea?
Then it must be related to itself--->infinite regress so it cannot be the same idea.

I would like to see someone break through that "pre-nup".

[Diebert van Rhijn]

This is why the only consistency that counts is the consistency with the axioms.

But the axioms are not consistent ..thats what i'm saying.

How would you prove the axion "is not consistent"? It's the consistency which is a given. The facts and theories are gathered around the axioms, as it were. You seem to insist axioms need some kind of proof derived from those same axioms. And it's that insistence that's causing regression. Like cutting the anchor and let the boat spin around on the current, going nowhere.

We just need to scrap this idea that minds exist. Isnt that another idea.

If you keep thinking destructively, that is, denying the simple assertion of the axiom, then everything becomes indeed highly doubtful. But in a way you're proving the point to yourself that you cannot have anything without going with the axiom or in this case, reflexive identity and equivalence relations.

[Russell Parr]

A dog is a dog because it is identified as a dog.

If you think this is a literally a math equation, then there's nothing else I can tell you, other than: you've really got to work on your understanding on the basics of philosophy.

Wow!!...you really at the lowest level of abstraction there. The OP is several layers of Abstraction above mentioning instances..

That's exactly my point: you are trying to apply the concept of equivalence from math, which is indeed layers above the simple logical truth of the law of identity, to something that is more fundamental and not yet mathematical. When it comes to the law of identity, it is not yet time to ponder about equivalence, in the mathematical sense.

Lets break down your analysis.

Let's see it...

Are you aware that the greeks wrote all their mathematics with words and did not use a single symbol even for numbers?

i'll break this down...this is from an excerpt of a mathematical proof done in ancient greece;

"the square root of two is therefore to be identified with irrationality"

I dont expect to to have the slightest idea of the whole story behind this statement ...but since you are so sure you understand everything at least tell me this ...is that not a mathematical equation?

Isnt it strange that you say such bold statements about equivalences when you dont even know ...lord forbid...what an orderd pair is...or what the properties of symmetry , transitivity or reflexivity ARE?!?!

If i said those last 3 define equivalence ..i know..you wouldnt understand in the slightest.

Your caught up in order ...i mentioned infinite regresses, cartesian products, relations...none of that came out from you..was the word order the only word in the OP?

What is this?! More math. You skip the intro and go straight for the plot. You can't build a house without a solid foundation.

While you can know math without understanding philosophy in the slightest *ahem*, just as you can do the woodwork on a house without knowing anything about laying concrete, you first have let the concrete layers do their job before you start erecting walls. It's as if you don't even know the concrete slab is there, or its purpose. Then you go about telling the concrete layers about their job, using woodwork terms and ideas.

[Russell Parr]

Another link from that website: Logic

Math exists in the realm of logic. Note the first sentence from that link. The law of identity is the axis (axiom) upon which logic can be performed.

Law of identity = solid foundation, math = walls. No solid foundation, no walls. No Law of identity, no math.

Diebert has been telling you the same thing, albeit perhaps more eloquently.

Put the math pipe down and think more philosophically, chikoka :)

[Russell Parr]

you did mention elsewhere that you never went to college...i see that now.

There's a lot to be said about the ways that academia can ruin peoples' ability to perform philosophy in simple, yet profound ways. David Quinn vs the Ne Ultra Plus forum comes to mind.

[chikoka]

Another link from that website: Logic

Math exists in the realm of logic. Note the first sentence from that link. The law of identity is the axis (axiom) upon which logic can be performed.

Law of identity = solid foundation, math = walls. No solid foundation, no walls. No Law of identity, no math.

Diebert has been telling you the same thing, albeit perhaps more eloquently.

Put the math pipe down and think more philosophically, chikoka :)

You talk about the basics of philosophy but you dont seem to realise that its definition...math is knowledge, and philosophy is the love of knowledge...you rat an education ..maybe you could educate yourself on the fact that before 1800 all spheres of knowledge were considered (rightly so..by defn) to be philosophy. Science itself ...based on empiricism was known as natural philosophy.
If you dont trust the education system try get education somehow. Educating yourself gives you knowledge that ,that is included in the defn. of philosophy

There is more to be said for education..the more you push the envelope of your mind the better able you are to grasp abstract concepts.It seems , from your responses that literaly *all* the concepts in the OP escape you.
If you could see so many single instances of things ,you would be better able to understand what the number 1 means. You may glorify dogs and other instances but when you start to see variables..that in a sense dont exist..you will know much more about the rules all other instances participate in than if you observed any large number of dogs or instances. in a sense i made rash saying in a sense they dont exist because in a deeper sense they are *all* that exists..is permanent among the passage of appearances..
That underlined is a formulation of causality if you see it? *or you could make a stab at toilet humour*
So i will lead you through this because it will help you greatly. For "the love of knowledge" what are the properties of the equallity expressed in the abstraction the AOI?

[chikoka]

How would you prove the axion "is not consistent"? It's the consistency which is a given

The word given means an axiom.You need see that axioms are not consistent of themselves. There is actualy an axiom that is implied to be the consistency giver. thats how you go about choosing axioms.you are in fact building up the properties of you system by wisely choosing what you want to add to your system.
The AOI is the "given" that imputes consistency on everything else in a system. Not simply to the other axioms but to the system..and the system..axioms , theorems and all ..is what can then be described as either consistent or not. Once we see that it is inconsistent and all the properties of the system are derived from the "givens" ..then it is also a given responsible for this inconsistency.

You say as if you've never heard of an inconsistency in a system....and a system has as axioms as part of its definition.

You seem to insist axioms need some kind of proof derived from those same axioms

If you have two axioms "a is red" and "a is not red" can you not see that the system is inconsistent. is not the inconsistency of that system derived from its axioms. given that the AOI is a given (axiom) in every system?

[chikoka]

chikoka wrote:
We just need to scrap this idea that minds exist. Isnt that another idea.

If you keep thinking destructively, that is, denying the simple assertion of the axiom, then everything becomes indeed highly doubtful. But in a way you're proving the point to yourself that you cannot have anything without going with the axiom or in this case, reflexive identity and equivalence relations.

The point of this thread is that all thinking is destructive because of the very nature of the "facilitator" of thinking...Which i think we are all in agreement is the AOI

[chikoka]

D

A theorem is a restatement of the axioms.

Inconsistency is really a runaway of *choice* and is related to the base of the natural log "e".

[Russell Parr]

You talk about the basics of philosophy but you dont seem to realise that its definition...math is knowledge, and philosophy is the love of knowledge...you rat an education ..maybe you could educate yourself on the fact that before 1800 all spheres of knowledge were considered (rightly so..by defn) to be philosophy. Science itself ...based on empiricism was known as natural philosophy.
If you dont trust the education system try get education somehow. Educating yourself gives you knowledge that ,that is included in the defn. of philosophy

There is more to be said for education..the more you push the envelope of your mind the better able you are to grasp abstract concepts.

I would think that philosophy preceding science in history, and that it is the basis of science, is common knowledge. At least on this forum.

The modern education system has its uses, namely in preparing people with skills for specific fields of work. However, when it comes to philosophy, particularly in its use in understanding Ultimate Reality, it has done far more bad than good. It more or less completely stunts people in this area.

It seems , from your responses that literaly *all* the concepts in the OP escape you.

I don't engage in your mathematical jargon precisely because it is irrelevant to the point I am making, namely, that you have completely misunderstood and misused the AOI thus far. Due to your attachment to mathematical jargon, I might add.

If you could see so many single instances of things ,you would be better able to understand what the number 1 means. You may glorify dogs and other instances but when you start to see variables..that in a sense dont exist..you will know much more about the rules all other instances participate in than if you observed any large number of dogs or instances. in a sense i made rash saying in a sense they dont exist because in a deeper sense they are *all* that exists..is permanent among the passage of appearances..
That underlined is a formulation of causality if you see it? *or you could make a stab at toilet humour*

The AOI has nothing to do with variables. It simply deals with the manner that consciousness makes distinctions. So you can flush your variables down the drain. (I had to)

So i will lead you through this because it will help you greatly. For "the love of knowledge" what are the properties of the equallity expressed in the abstraction the AOI?

The AOI, complete with its use of the equal sign, is nothing more than another way of saying "you perceive what you perceive". From there, you can begin to make assumptions about what equality really means, or whether or not what you perceive is inaccurate in some way, etc.. Are you ever going to get this?

In one of your replies to Diebert you suggest that axioms can be interchanged and chosen based on perceived consistency. While this is true in the realms of science, this not so for the philosophical understanding of Reality. Fundamentally, the AOI is the only acceptable axiom on which such philosophy is based. Otherwise, we have no solid grounds to stand on, and uncertainty ultimately rules the day.