The Paradox of Understanding

[Eodnhoj7]

I said you can redefine them that way if you really want to, since they are abstract concepts. Just don't expect others to accept your version.

If it is all abstractions are subjectively oriented does anyone really accept eachother's axioms considering noone truly knows another's subjective experience?

Wtf tends to disagree from my experience, on regards to infinitely small spaces.

As to the rest:

They are not redefined, they are applied to themselves as their own context.

The world more or less agrees on mathematics even though it's abstract. You don't have to 100% know someone else's subjective experience for that, duh.

[Atla]

Applying there own nature to themselves is not random, it is a system, just like infinite progress from an axiom is a system.

Let's take a point, which by definition can't be divided. So I "apply" the indivisible point to the invisible point, and that somehow turns it into being infinitely divisible? How does that work?

A single point is divided by a line into two points. A single point alone is indistinct thus not a distinction. A point only occurs when it is individuated, simultaneously multiplied and divided by the act of the single point occurring as many.

But a point by definition can't be divided by a line into two points. Its coordinates in abstract space make it distinct from other points.

[Eodnhoj7]

I said you can redefine them that way if you really want to, since they are abstract concepts. Just don't expect others to accept your version.

If it is all abstractions are subjectively oriented does anyone really accept eachother's axioms considering noone truly knows another's subjective experience?

Wtf tends to disagree from my experience, on regards to infinitely small spaces.

As to the rest:

They are not redefined, they are applied to themselves as their own context.

The world more or less agrees on mathematics even though it's abstract. You don't have to 100% know someone else's subjective experience for that, duh.

Yeah and the western world was predominantly catholic at one point and agreed with catholicism and look how that turned out. Assumptions and beliefs change.

Mathematical axioms are an assumption, math is built on assumptions.

[Eodnhoj7]

Let's take a point, which by definition can't be divided. So I "apply" the indivisible point to the invisible point, and that somehow turns it into being infinitely divisible? How does that work?

A single point is divided by a line into two points. A single point alone is indistinct thus not a distinction. A point only occurs when it is individuated, simultaneously multiplied and divided by the act of the single point occurring as many.

But a point by definition can't be divided by a line into two points. Its coordinates in abstract space make it distinct from other points.

They are not completely distinct if they are both points just like two cars are not completely distinct if they are both cars.

A single point divided becomes a line. A single point is a quantifiable distinction of 1. There is 1 point, it is divided then there are 2. The division of space allows localities to be divided. If the locality of a state is divided then there are two localities as a locality is a context.

[Atla]

A single point is divided by a line into two points. A single point alone is indistinct thus not a distinction. A point only occurs when it is individuated, simultaneously multiplied and divided by the act of the single point occurring as many.

But a point by definition can't be divided by a line into two points. Its coordinates in abstract space make it distinct from other points.

They are not completely distinct if they are both points just like two cars are not completely distinct if they are both cars.

A single point divided becomes a line. A single point is a quantifiable distinction of 1. There is 1 point, it is divided then there are 2. The division of space allows localities to be divided. If the locality of a state is divided then there are two localities as a locality is a context.

What does "completely distinct" mean when it comes to abstractions? Cars are concrete.

[Eodnhoj7]

But a point by definition can't be divided by a line into two points. Its coordinates in abstract space make it distinct from other points.

They are not completely distinct if they are both points just like two cars are not completely distinct if they are both cars.

A single point divided becomes a line. A single point is a quantifiable distinction of 1. There is 1 point, it is divided then there are 2. The division of space allows localities to be divided. If the locality of a state is divided then there are two localities as a locality is a context.

What does "completely distinct" mean when it comes to abstractions? Cars are concrete.

And what does concrete mean?

A car is as much of an abstraction as evidenced by its occurence in memory as well as the schematics that form it.

Complete distinctions of points do not exist, so there is no necessity in arguing such a term. One point exists by its relationship to another and thus relationship necessitates the point as composed of its relations. If point a exists because of point b than point a is composed of its relations to b, and vice versa, thus the point contains itself through its own context: A leads to B which leads back to A thus A contains itself through B.

The point is its own context in this respect while in another respect the infinite points between points A and B observe the points exist because of points and the context of the point becomes self referential, the point exists because of variations of itself.

[Atla]

They are not completely distinct if they are both points just like two cars are not completely distinct if they are both cars.

A single point divided becomes a line. A single point is a quantifiable distinction of 1. There is 1 point, it is divided then there are 2. The division of space allows localities to be divided. If the locality of a state is divided then there are two localities as a locality is a context.

What does "completely distinct" mean when it comes to abstractions? Cars are concrete.

And what does concrete mean?

A car is as much of an abstraction as evidenced by its occurence in memory as well as the schematics that form it.

Complete distinctions of points do not exist, so there is no necessity in arguing such a term. One point exists by its relationship to another and thus relationship necessitates the point as composed of its relations. If point a exists because of point b than point a is composed of its relations to b, and vice versa, thus the point contains itself through its own context: A leads to B which leads back to A thus A contains itself through B.

The point is its own context in this respect while in another respect the infinite points between points A and B observe the points exist because of points and the context of the point becomes self referential, the point exists because of variations of itself.

Do you subscribe to some sort of metaphysical antirealism where only our mental content is the "real world"? Or do you subscribe to metaphysical realism but really don't see the difference between the abstract and the concrete?

Human understanding is inherently "self-referential" but that still doesn't mean that a line can divide the indivisible point.

[Age]

So

There are other words that MEAN and/or REFER TO the EXACT SAME thing OF 'subjective aspects of brains and/or bodies'.

Which, by the way, ARE FAR MORE Accurate when SEEN in the light of, or in the perspective of, the G.U.T.O.E

So
Everyone lives in their own unique universe, their own head so to speak...

ONLY 'those' who CHOOSE TO DO SO, DO. As for the REST OF 'us', 'we' DO NOT. So, your CLAIM, here, that 'Everyone' lives in their OWN UNIQUE universe IS False AND Wrong, from the outset.

Oh, and by the way, there IS ONLY One Universe, ONLY, ACTUALLY. And, WHO and/or WHAT are 'the ones', EXACTLY, which you CLAIM, here, HAVE or OWN 'their own heads'?

Now, OBVIOUSLY, 'you' separate AND unique human beings DWELL in separate AND unique human heads, and separate AND unique human bodies, HOWEVER, and OBVIOUSLY, 'you' do NOT HAVE TO LIVE 'there', 'so to speak', as some might say.

What meaning means to someone is built on their own unique understanding, or interpretation, based on their personal past experiences, preferences and knowledge, while allowing meaning, the text to change them and their convictions at the same time.

Which IS EXACTLY, more or less, what 'I' HAVE BEEN SAYING, and POINTING OUT, here. Which, by the way, is ALSO THE REASON WHY 'I' HAVE ALSO BEEN SAYING, and CLAIMING, that 'you' older human beings KEEP MISUNDERSTANDING, and MISSING, WHAT the ACTUAL Truths, in Life, REALLY ARE.

Which, for 'those' who HAVE BEEN FOLLOWING, here, EXPLAINS WHY 'these human beings', back when this was being written, WERE, STILL, SO LOST AND, STILL, SO CONFUSED, here.

We form a unique relationship with it that ultimately results in a unique interpretation.

If 'you' MEAN and are REFERRING TO 'you human beings', with and by the 'we' word, here, then what is the 'it' REFERRING TO, EXACTLY, which 'you' CLAIM you human beings form a unique relationship WITH?

It's different that's all.

'What', EXACTLY, IS 'different'?

And, what do 'you' ACTUALLY MEAN BY, 'that is all'? 'What', EXACTLY, IS 'all'?

Doesn't mean it's wrong or right in someone else's mind.

1. There is NO one's 'mind'.

2. IF 'meaning', itself, is, SUPPOSEDLY, 'different', AND 'that is all', AND 'meaning', itself, being, SUPPOSEDLY, 'different' does NOT mean that 'meaning', itself, is wrong, nor right, ANYWHERE, then HOW do ANY of 'you' KNOW, FOR SURE, that 'you' HAVE and HAVE OBTAINED the IRREFUTABLE True, Right, Accurate, AND Correct Knowledge, HERE, EXACTLY?

3. By the way, 'the UNIQUE MEANING' that 'you' just GAVE, here, is 'yours' AND 'yours' ALONE, correct?

[Age]

It's less a question of value and more a question of efficiency. I ask a leading question, the AI breaks it down predictably by explaining it and I spend less time doing grunt writing.

Relative to your point about points, WTF tends to disagree with your stance of infinitely small space between points as I sided with your stance. He claims there is no such thing, it is a continuum with no space between them.

So there is an inherent contradiction between you two....and that is the nature of abstract axioms.


But let's go with your stance and say there is infinitely small spaces between points A and B, the direct space between them is linear, as infinitely small is still finite as non-zero...hence a line segment.

I don't think you understand that abstract axioms are assumptions that can be analyzed and broken down into further parts. The self-evident nature of axioms requires subjectivity by the nature of self-evidence alone thus resulting in potential contradiction

You study philosophy and don't question axioms?

Uhh lol? You wrote that there are infinitely small spaces between points A and B on a line segment, not me. I pointed out too that that's just how you arbitrarily redefined the abstract concept of a line segment, that's a main reason why people ignore your works. (The AI was just instructed to work with your hypothetical: IF we redefine line segments so and so, THEN..)

You still don't seem to understand what "abstract" means, which has been your main fatal error over the years. That something is abstract doesn't just mean that we think it, it also means that it doesn't refer to anything in the physical world. So no, you can't contemplate, perceive or question the abstract axioms (definitions) of a line segment or a point, even if Buddhism and Hinduism say that you can. You just posit them, and the commonly accepted definitions of points and lines can't be analyzed and broken down into further parts, because they don't have any further parts, because that's how we defined them.

You didn't discover the true nature of ponts and lines (they don't have a true nature), you just randomly made up a whole alternative system with alternative axioms (and your alternative definitons seem to be fairly nonsensical because they seem to have inherent circularity or infinite regress or whatever built into them).

What we can actually contemplate is for example: I look at a "point, place with a small extension" in the natural world, could one infinitely zoom in there similarly to a fractal and uncover infintie details, or could one only finitely zoom in and there would be a minimum distance to reality?

Questioning the current axioms shows them as paradoxical, if you want to argue they exist because of group acceptance than that is the bandwagon fallacy.

Applying there own nature to themselves is not random, it is a system, just like infinite progress from an axiom is a system.

Seperate the abstract from an experience of thought, it cannot be done.

If points and lines do not have a true nature, according to you, than you cannot argue for or against them without ending in falsity.

If points and lines are analyzed through points and lines they are thier own context. Infinite points between two points is a finite line segment, infinitely small space between points is a finite line segment.

The whole system is intended to be a paradox, don't you read?

WHO and/or WHAT, EXACTLY, INTENDED the WHOLE 'system' to be A so-called 'paradox'?

And, WHICH DEFINITION of the 'paradox' word WAS INTENDED, EXACTLY?

AND AGAIN, BY WHO and/or WHAT, EXACTLY?

That is the title. Points and lines are their own paradox, you accused meaof being nonsensical, when the title already shows that as the conclusion, then while you claim I am nonsensical you claim they have no true nature which is even more nonsensical than saying they are a paradox, then you imply I must accept their nature based off of a created consensus.

AGAIN, 'nonsensical'.

If 'you' NEVER PROVIDE 'the context' of the 'paradox' word, then what 'you' ARE ACTUALLY 'trying to' SAY, and MEAN, here, NO one BUT 'you' KNOWS.

You contradict yourself atla, you make no sense, I at least conclude they are a paradox.

So, one could, more or less, SAY and CLAIM just about ABSOLUTELY ANY thing, and as long as they conclude WITH the words, 'they are a paradox', then ALL is WELL and GOOD, right?

[Age]

Applying there own nature to themselves is not random, it is a system, just like infinite progress from an axiom is a system.

Let's take a point, which by definition can't be divided. So I "apply" the indivisible point to the invisible point, and that somehow turns it into being infinitely divisible? How does that work?

A single point is divided by a line into two points. A single point alone is indistinct thus not a distinction. A point only occurs when it is individuated, simultaneously multiplied and divided by the act of the single point occurring as many.

What 'we' can CLEARLY SEE, here, WITH 'this one' is that it PROVIDES PERFECT examples of one who 'TRIES TO' FIND just about ANY words, and then 'TRIES TO' USE them in A WAY, which it HOPES and BELIEVES will align with and prove its ALREADY BELIEVED TRUTH, to be true.

HOWEVER, its ABSOLUTE BELIEF that 'ALL is NOTHING', can NEVER EVER be backed up, supported, NOR PROVED True.

LOL Just ADDING the words, 'they are a paradox', AFTER your OWN words is ALSO NEVER going to help NOR save you, here, either.

[Age]

If it is all abstractions are subjectively oriented does anyone really accept eachother's axioms considering noone truly knows another's subjective experience?

Wtf tends to disagree from my experience, on regards to infinitely small spaces.

As to the rest:

They are not redefined, they are applied to themselves as their own context.

The world more or less agrees on mathematics even though it's abstract. You don't have to 100% know someone else's subjective experience for that, duh.

Yeah and the western world was predominantly catholic at one point and agreed with catholicism and look how that turned out.

Would you like to ENLIGHTEN the readers, here, HOW, EXACTLY, what you just SAID and WROTE, here, CORRELATES WITH what "atla" SAID and POINTED OUT above, which you RESPONDED TO with these words, here?

If no, then WHY NOT, EXACTLY?

Assumptions and beliefs change.

GREAT OBSERVATION and GREAT POINT. Which LEADS me to ASK, 'WHY then HAVE and/or HOLD ASSUMPTION and BELIEFS if they BOTH CHANGE, ANYWAY'?

WHY NOT just 'LOOK AT, and 'SEE', ONLY what IS ACTUALLY IRREFUTABLY True, ONLY. AND, JUST REMAIN WITH 'that' INSTEAD, and ONLY?

Mathematical axioms are an assumption, math is built on assumptions.

Is this what you, ONLY, ASSUME and/or BELIEVE, is true, OR, what IS ACTUALLY IRREFUTABLY True, and SO ABSOLUTELY EVERY one AGREES WITH and ACCEPTS 'this CLAIM' of 'yours', here?

Also, and by the way, you appear to HAVE and/or HOLD a VERY STRANGE definition for the 'ASSUMPTION' word, here. Which is, OBVIOUSLY, HELPING TO LEAD 'you' COMPLETELY ASTRAY, here.

[Eodnhoj7]

What does "completely distinct" mean when it comes to abstractions? Cars are concrete.

And what does concrete mean?

A car is as much of an abstraction as evidenced by its occurence in memory as well as the schematics that form it.

Complete distinctions of points do not exist, so there is no necessity in arguing such a term. One point exists by its relationship to another and thus relationship necessitates the point as composed of its relations. If point a exists because of point b than point a is composed of its relations to b, and vice versa, thus the point contains itself through its own context: A leads to B which leads back to A thus A contains itself through B.

The point is its own context in this respect while in another respect the infinite points between points A and B observe the points exist because of points and the context of the point becomes self referential, the point exists because of variations of itself.

Do you subscribe to some sort of metaphysical antirealism where only our mental content is the "real world"? Or do you subscribe to metaphysical realism but really don't see the difference between the abstract and the concrete?

Human understanding is inherently "self-referential" but that still doesn't mean that a line can divide the indivisible point.

The line is composed of points thus you end up with a self referential paradox of the point dividing itself through points as the line. The points are manifesting points. It's a self referentiality loop.

If human understanding is "inherently self-referential", as you claim, and geometric axioms are the creation of human understanding as human understanding, then geometric axioms result in paradoxes induced by self referentiality.

[Age]

A single point is divided by a line into two points. A single point alone is indistinct thus not a distinction. A point only occurs when it is individuated, simultaneously multiplied and divided by the act of the single point occurring as many.

But a point by definition can't be divided by a line into two points. Its coordinates in abstract space make it distinct from other points.

They are not completely distinct if they are both points just like two cars are not completely distinct if they are both cars.

BUT, the 'two points' ARE COMPLETELY DISTINCT BY the VERY Fact that 'they' ARE in TWO VERY DISTINCT DIFFERENT PLACES.

Also, IF there ARE 'two cars', then 'they' can NOT be the EXACT SAME 'car'. Therefore, 'they' ARE 'completely distinct', NOT just by 'SEPARATION' but also by their DISTINCT DIFFERENCES, as well.

A single point divided becomes a line.

LOL A 'single point' divided DOES NOT become A 'line'. A 'single point' DIVIDED becomes A 'divided point'.

Just like A 'single elephant' divided DOES NOT BECOME A 'line'. NOR A 'car', for example. A 'single elephant' DIVIDED becomes A 'divided elephant', OBVIOUSLY.

A single point is a quantifiable distinction of 1. There is 1 point, it is divided then there are 2.

BUT, you just SAID and CLAIMED, that 1, or A 'single point', divided becomes A 'line', and 'now' you SAY and CLAIM that 1, or A 'single point' divided becomes 2, or two, 'points'.

you, REALLY, do NEED to STICK to ONE CLAIM, ONLY, if you, REALLY, do want to be HEARD, and UNDERSTOOD, here.

Otherwise, what you are SAYING and CLAIMING, here, WILL come across as NONSENSICAL, to say the least.

I suggest you get RID OF that ABSOLUTE BELIEF of yours that 'ALL, or Everything, IS NOTHING', then you will STOP 'trying to' FIGHT and ARGUE FOR some thing that is NOT even True, NOR Real, to begin with.

The division of space allows localities to be divided.

The CONCEPTUAL 'separation' of ANY thing ALLOWS 'localities' to be divided, CONCEPTUALLY ONLY, but SO WHAT?

If the locality of a state is divided then there are two localities as a locality is a context.

AGAIN, SO WHAT?

'This' WILL NEVER LEAD, LOGICALLY, to 'your' CLAIM, CONCLUSION, and BELIEF, here.

[Age]

They are not completely distinct if they are both points just like two cars are not completely distinct if they are both cars.

A single point divided becomes a line. A single point is a quantifiable distinction of 1. There is 1 point, it is divided then there are 2. The division of space allows localities to be divided. If the locality of a state is divided then there are two localities as a locality is a context.

What does "completely distinct" mean when it comes to abstractions? Cars are concrete.

And what does concrete mean?

A car is as much of an abstraction as evidenced by its occurence in memory as well as the schematics that form it.

Complete distinctions of points do not exist, so there is no necessity in arguing such a term.

LOL So two, SEPARATE and thus DISTINCT, points, LAUGHINGLY, can NEVER be 'complete distinctions' BECAUSE, well to "eodnhoj7" anyway, 'complete distinction of 'points', (with an 's'), does NOT EXIST.

And, this one CLAIMS that it is being SENSIBLE, or NOT being NONSENSICAL, here.

What you have been SAYING and CLAIMING, here, in this post, like MOST of what you SAY and CLAIM, here, is this forum, IS NONSENSICAL, BECAUSE what you SAY and CLAIM does NOT 'logically follow'.

One point exists by its relationship to another and thus relationship necessitates the point as composed of its relations. If point a exists because of point b than point a is composed of its relations to b, and vice versa, thus the point contains itself through its own context: A leads to B which leads back to A thus A contains itself through B.

SO WHAT?

The point is its own context in this respect while in another respect the infinite points between points A and B observe the points exist because of points and the context of the point becomes self referential, the point exists because of variations of itself.

AGAIN, SO WHAT?

What do you PRESUME that 'this' ACTUALLY MEANS, and 'POINTS' TO, EXACTLY?

[Belinda]

It may console you, Age, that I too can't understand Eodnhoj .