“They saw their injured country's woe;
The flaming town, the wasted field;
Then rushed to meet the insulting foe;
They took the spear, - but left the shield.”
―Philip Freneau
.
And by a prudent flight and cunning save A life which valour could not, from the grave. A better buckler I can soon regain, But who can get another life again?
Archilochus
Monday, December 22, 2025
On Platonic Space and Transcendence
55 comments:
Anonymous
said...
Credible. Truthful. Known by the sages of antiquity without the modern scientific tools of today.
Tibetans refer to it as the heart-mind connection. Looking more like we're heading in a full circle back.
In Beyond Good and Evil, Nietzsche critiques traditional philosophy's reliance on absolute truths, exposing hidden prejudices (like the "I think" assumption and simplistic dualisms) and arguing that morality stems not from pure reason but from underlying drives, especially the Will to Power, leading to a revaluation of values where "good" becomes associated with strength/health, and "evil" with weakness/decadence, paving the way for "free spirits" to create new values beyond conventional good/evil.
Core Logical & Philosophical Shifts
Critique of Metaphysical Dualisms: Nietzsche attacks the idea of pure opposites (good/evil, mind/body, truth/error), seeing them as philosophical constructs, not inherent realities, often arising from linguistic habits like subject-predicate grammar.
Will to Power as Primary Drive: He posits that the fundamental force isn't a search for truth but the Will to Power – a drive for growth, mastery, and self-overcoming, influencing philosophers' seemingly objective inquiries.
Revaluation of Values: He challenges the "herd morality" (Christian/Socratic) valuing altruism, sympathy, and selflessness, suggesting these mask a life-denying weakness, and proposes a new "master morality" valuing strength, nobility, and creativity.
Perspectivism: There are no absolute truths, only interpretations from different perspectives, and even the pursuit of truth serves underlying drives, not pure knowledge.
Critique of the "I" and Consciousness: The idea of a unified, rational "I" thinking is an illusion; consciousness is a small part of a larger, instinctual psyche, and logic often serves unconscious needs, not pure reason.
There are no absolute truths in realative realty. On that Nietzsche was correct. The difference between samsara and Nirvana lies in our views and awareness if reality.
There is NO "relative reality". That is OUR human inherent misconception. Because... that is how OUR dumb monkeys brains was built. For the needs of Evolution -- for us to continue frolicking.
But.
There IS -- *OBJECTIVE*REALITY*. And IT IS the Absolute Truth. To anyone who'd try to oppose to that notion I do propose Catch a Brick with Your Head experiment.
//In Beyond Good and Evil, Nietzsche critiques traditional philosophy's reliance on absolute truths, exposing hidden prejudices (like the "I think" assumption and simplistic dualisms) and arguing that morality stems not from pure reason but from underlying drives
Yap. He was creation of his times. And as such his oversight was limited. "Wisdoms of the Past do grow incorrect/incomplete and even OUTdated... with time" Yawn.
That was not mentioned explicitly. As I thought there's no need. But. I do not despise Nietzsche. Or disagree with him. Think he's dumb. Or anything. Just pointing to that fact -- him living in his times... and me AFTERWARDS. Makes MY horizons WIDER. NOT because I smarter and he dumber. Just by the nature of thing called Time.
That is perfectly like two people -- one standing at the foot of a hill and one up on that hill slope -- WHO will have better view? But same time -- it opens MY mind to that truth -- that anybody standing at the TOP of that hill, WILL have even BETTER view. And there's are MOUNTAINS too.
So... it makes all very simple for me -- why not BECAME *THAT*ONE* who standing on the top of that hill? Top(s) of that mountain(s)????
Isn't it DAMN GOOD ENOUGH idea in itself -- to grow smarter... with time... ;-)
//and "evil" with weakness/decadence, paving the way for "free spirits" to create new values beyond conventional good/evil.
In terms of having no claws, no fangs... with our loosy bipedalism. No furr. We are inherently weaker then any other animal. And inherently evil. Yawn.
You know about "Did Diogenes really run into Plato's Academy with a plucked chicken saying "Behold, a man!" when Plato defined Man as a featherless biped?"
//Critique of Metaphysical Dualisms: Nietzsche attacks the idea of pure opposites (good/evil, mind/body, truth/error), seeing them as philosophical constructs, not inherent realities, often arising from linguistic habits like subject-predicate grammar.
//Will to Power as Primary Drive: He posits that the fundamental force isn't a search for truth but the Will to Power – a drive for growth, mastery, and self-overcoming, influencing philosophers' seemingly objective inquiries.
Well... he was living in times of Industrial Revolution. That showed to anyone that limits CAN be overcome... with means of techs. And his predecessors he rightfully, but unfairly, criticized -- just was living in other times...
//Revaluation of Values: He challenges the "herd morality" (Christian/Socratic) valuing altruism, sympathy, and selflessness, suggesting these mask a life-denying weakness, and proposes a new "master morality" valuing strength, nobility, and creativity.
Yap. Only one cavit. Nobody can became stronger, nobler and more creative. Especially more creative. By just declaring it. Stupid error. But well, it was impossible to understand that it was inherently an error... in his times.
//Perspectivism: There are no absolute truths, only interpretations from different perspectives, and even the pursuit of truth serves underlying drives, not pure knowledge.
This too. An error.
As LOGIC claims """A "logic explosion," or Principle of Explosion (ex falso quodlibet), is a rule in classical logic stating that a contradiction (like "P and not-P") allows you to logically prove any statement, trivializing truth and falsity within that system, like dividing by zero breaks math;"""
Means, if you allowed JUST ONE error in your thinking... you recieving WHOLE LOT of em as a freebie. And all your thinking proces turns into BS flood.
BTW genius, I'm constantly learning new things, or, a different nuance on old things. My life today is plentiful in every way. Now that I understand non-duality, interconnectedness of everything, dependent origination, and emptiness.
The fact I do not accept everything you or the man says is irrelevant to me or my intelligence.
I realize how much I don't know, do you know how much you don't know? But, realizing the above does not mean I or you must accept views that are in opposition to our changing understanding.
//I realize how much I don't know, do you know how much you don't know?
If you'd not be so idioticly persistent, monkey-brain, you could try and recognise that simple really truth -- it's NOT possible to know what you don't know.
That's why it's so important to keep one's mind open, free-thinking and inquireous.
The "platonic mathematical world" refers to Mathematical Platonism, the philosophy that numbers, sets, and geometric shapes exist as real, abstract entities in a timeless realm, independent of human minds, language, or the physical world, meaning mathematicians discover pre-existing truths, not invent them, much like finding a perfect circle that's always been there, even if our physical drawings are imperfect copies.
Core Concepts of Mathematical Platonism
Existence: Mathematical objects (like numbers, sets, functions) are real things, not just human creations.
Abstractness: These objects aren't physical; they have no location in space or time and are non-material.
Independence: They exist regardless of whether humans think about them, talk about them, or even exist at all.
Discovery: Because they are real and independent, mathematical truths are discovered, not invented, by mathematicians.
How It Works (Example)
The Perfect Circle: In the Platonic world, there's a perfect, ideal circle. Any circle you draw on paper is just a flawed, physical approximation of that perfect Form.
Numbers: The number '3' isn't just a symbol or a concept in our heads; it's an abstract entity that exists eternally, and we discover its properties.
Key Figures & Ideas
Plato: The ancient Greek philosopher who first proposed this idea, suggesting mathematical truths reside in an eternal "World of Forms".
Modern Platonists: Philosophers and mathematicians like Kurt Gödel and Roger Penrose believe we access this world through mathematical intuition, similar to sense perception.
Contrast with Other Views
Formalism: Views math as a game of manipulating symbols according to rules, without inherent meaning.
Intuitionism: Believes mathematical objects are mental constructions.
In essence, Platonism provides a way to explain the objectivity and power of mathematics, suggesting it describes a fundamental, external reality.
Plato's "Divided Line," presented in The Republic, is a metaphor illustrating the hierarchy of knowledge and reality, dividing existence into the visible world (images, physical objects) and the intelligible world (mathematical concepts, Forms/Ideas) and corresponding levels of understanding (imagination, belief, thought, intelligence), moving from murky perception to pure reason and knowledge of the eternal Forms. This analogy maps our mental states to different degrees of clarity and truth, showing how true understanding comes from grasping abstract Forms, not just sensory data.
The Structure of the Line
The line is divided into two main sections, each further subdivided:
Visible World (Lower Section): Our world of sensory experience, less real than the Forms.
Physical Objects (Pistis): Real things we see, but which are copies of the Forms (e.g., a chair, a tree).
Intelligible World (Upper Section): The realm of pure reason and perfect concepts.
Mathematical Objects (Dianoia): Concepts like numbers, shapes, understood through hypotheses.
The Forms (Noesis): The ultimate realities, the perfect essences (e.g., Justice, Beauty, the Good) (most clear, true knowledge).
What It Means
Hierarchy of Reality: The upper section (Forms) is more real and true than the lower (Visible World).
Hierarchy of Knowledge: Our minds progress from imagination (shadows) to belief (objects) to reasoning (math) to pure intellect (Forms).
Path to Truth: The goal of philosophy is to ascend the line through reason, moving beyond mere opinion (doxa) to true knowledge (episteme) of the Forms, especially the Form of the Good, notes informationphilosopher.com.
Connection to the Cave: It parallels the Allegory of the Cave, describing the prisoner's journey from shadows to the world outside, paralleling the move from the visible to the intelligible realm, says Wikipedia.
"Noumenal" refers to the world of things as they are in themselves, beyond human perception, a key concept in Immanuel Kant's philosophy, contrasting with the phenomenal world (how things appear to us). It signifies a true, underlying reality that is unknowable by our senses but is the necessary basis for our experienced world, involving concepts like God, the soul, or true reality, existing outside space, time, and causality.
Key aspects of noumenal:
Inaccessible: The noumenal realm (or the "thing-in-itself") cannot be directly experienced or understood through our senses or intellect.
The "Real" World: It's the essential, true nature of reality, whereas the phenomenal world is just our subjective interpretation of it.
A Limit Concept: We know the noumenal world exists as a theoretical necessity, but we can't know what it is like.
Examples: Questions of free will, morality, the soul, or the ultimate meaning of life are noumenal concepts, as they can't be empirically proven.
In simple terms:
Phenomenal: The world you see, touch, and experience (e.g., a chair).
Noumenal: The "chair-in-itself," its ultimate essence, which you can never truly grasp, only its appearance (phenomenon).
Other uses:
Brand Names: "Noumenal" is also used as a brand name for clothing, beauty products, and even 3D modeling software, leveraging the philosophical term's depth.
"Nous" (νοῦς) is a multifaceted Greek concept meaning mind, intellect, understanding, or intuition, referring to the faculty that grasps first principles, divine truth, or immediate perception, distinct from mere sense data, found in philosophy (Anaxagoras, Aristotle) and Christian theology (spiritual perception of God's will). It's the capacity for profound insight and reason, distinguishing humans and connecting them to universal intelligence, as well as a spiritual faculty for understanding divine things.
Key Aspects of Nous:
Philosophical Nous (Greek Philosophy):
Anaxagoras: Saw Nous as the cosmic intelligence that sets the world in motion, a pure, unmixed principle.
Aristotle: Defined Nous as the highest part of the soul, grasping the fundamental first principles (starting points) for all knowledge and reasoning (both theoretical & practical), essential for wisdom and prudence.
Function: It "sees" with the mind's eye, understanding universal truths and ethical salience beyond just sensory input.
Theological Nous (Christianity):
Spiritual Perception: It's the spiritual capacity, opened by God's Spirit, allowing believers to understand spiritual realities and God's will, which natural intellect cannot grasp.
"Mind of Christ": Believers develop the nous of Christ through the indwelling Spirit, enabling spiritual discernment.
Example: In Luke 24, Jesus "opened their mind (nous)" so the disciples could understand the Scriptures.
Don't you read the Nous-papers? ;) Or hear the Good Nous (religion).
It's the "Holy Ghost" in the Xtian Trinity Father-Son-Holy Ghost/ Spirit. It "transcends" time in our human-cyborg existence, as memories/ information stored "outside" of our DNA and accessible through books/ scrolls/ written information and symbolic figures (ie - sacred geometry in architecture)..
The "noumenal fallacy" isn't a standard philosophical term, but it refers to the error of applying our mind's categories (like space, time, cause) beyond possible experience to the noumenal realm, the unknowable world of "things-in-themselves" (Ding an sich) that underlies appearances (phenomena). Immanuel Kant warned against this: we can only know phenomena, but reason tempts us to make claims about noumena (God, soul, true essence), which leads to metaphysical confusion, mistaking the limits of our understanding for objective knowledge of ultimate reality.
Key Concepts:
Phenomena (Appearance): The world as we experience it, structured by our minds (space, time, categories).
Noumena (Thing-in-itself): Reality as it exists independently of our perception, which we can't directly know.
The Fallacy: Using concepts like substance, causality, or being to describe noumena, which are concepts only applicable to phenomena.
Why it's a Fallacy (Kant's View):
Limits of Understanding: Our cognitive tools (intuitions, categories) are designed for sensory experience (phenomena), not for grasping things outside of it.
Transcendental Illusion: Reason naturally seeks completeness, leading it to posit noumena as the foundation, creating an illusion that we can know these ultimate realities.
Unknowable Nature: We can conceive of noumena as the source of phenomena, but we cannot have theoretical knowledge (science) about their actual nature; any such assertion is speculative.
Example:
We perceive a carrot as colored, sweet, and spatial (phenomena).
The "noumenal fallacy" would be claiming to know the carrot's "true color" or its "inherent sweetness" as it exists before our mind processes it, which Kant says is impossible.
In essence, the "noumenal fallacy" is the mistake of treating the unknowable, ultimate reality (noumena) as if it were another knowable object within our experience (phenomena).
/ Transcendental Illusion: Reason naturally seeks completeness, leading it to posit noumena as the foundation, creating an illusion that we can know these ultimate realities.
"Philosophy is the translation of Eros into Logos" - Byung-Chul Han "...and the desire and pursuit of the whole is called, "Love"" - Plato "Symposium" (Aristophanes' Speech)
Love... a transcendent force beyond "Reason". Welcome to Station 11. ;)
Goedel's Incompleteness Theorum: Gödel's Incompleteness Theorems, published by Kurt Gödel in 1931, reveal fundamental limits of formal mathematical systems, proving that any sufficiently powerful, consistent system (like arithmetic) will always contain true statements that cannot be proven within the system itself (First Theorem) and that such a system cannot prove its own consistency (Second Theorem). These theorems shattered dreams of creating a single, complete set of axioms for all mathematics, showing a permanent gap between mathematical truth and formal provability.
55 comments:
Credible. Truthful. Known by the sages of antiquity without the modern scientific tools of today.
Tibetans refer to it as the heart-mind connection. Looking more like we're heading in a full circle back.
"...and the desire and pursuit of the whole is called, "Love""
- Plato "Symposium" (Aristophanes' Speech)
Love "transcends" rather than "Emerges".
Your love/ desire for the whole is 'transcendent".
Truth is a reconciliation process.
As the Sikhs say... all is oneness with life's divine energy. Realizing the falseness of duality is critical to seeing truth.
"If One is not, then Nothing is." Plato, "Parmenides"
e pluribus unum
Yup. Perhaps one day the world will recognize non-duality. But won't be crossing my fingers anymore.
And I can do FFT to discern how it works in details. ;-p
While you'll play your silly games in alchemy. Yawn.
Pft. )))))
"Philosophy is the translation of Eros into Logos" - Byung-Chul Han
Alchemy is the reverse
FFTs are pure Logos. So have at it.
In Beyond Good and Evil, Nietzsche critiques traditional philosophy's reliance on absolute truths, exposing hidden prejudices (like the "I think" assumption and simplistic dualisms) and arguing that morality stems not from pure reason but from underlying drives, especially the Will to Power, leading to a revaluation of values where "good" becomes associated with strength/health, and "evil" with weakness/decadence, paving the way for "free spirits" to create new values beyond conventional good/evil.
Core Logical & Philosophical Shifts
Critique of Metaphysical Dualisms: Nietzsche attacks the idea of pure opposites (good/evil, mind/body, truth/error), seeing them as philosophical constructs, not inherent realities, often arising from linguistic habits like subject-predicate grammar.
Will to Power as Primary Drive: He posits that the fundamental force isn't a search for truth but the Will to Power – a drive for growth, mastery, and self-overcoming, influencing philosophers' seemingly objective inquiries.
Revaluation of Values: He challenges the "herd morality" (Christian/Socratic) valuing altruism, sympathy, and selflessness, suggesting these mask a life-denying weakness, and proposes a new "master morality" valuing strength, nobility, and creativity.
Perspectivism: There are no absolute truths, only interpretations from different perspectives, and even the pursuit of truth serves underlying drives, not pure knowledge.
Critique of the "I" and Consciousness: The idea of a unified, rational "I" thinking is an illusion; consciousness is a small part of a larger, instinctual psyche, and logic often serves unconscious needs, not pure reason.
There are no absolute truths in realative realty. On that Nietzsche was correct. The difference between samsara and Nirvana lies in our views and awareness if reality.
There is NO "relative reality". That is OUR human inherent misconception.
Because... that is how OUR dumb monkeys brains was built.
For the needs of Evolution -- for us to continue frolicking.
But.
There IS -- *OBJECTIVE*REALITY*. And IT IS the Absolute Truth.
To anyone who'd try to oppose to that notion I do propose Catch a Brick with Your Head experiment.
//In Beyond Good and Evil, Nietzsche critiques traditional philosophy's reliance on absolute truths, exposing hidden prejudices (like the "I think" assumption and simplistic dualisms) and arguing that morality stems not from pure reason but from underlying drives
Yap.
He was creation of his times.
And as such his oversight was limited.
"Wisdoms of the Past do grow incorrect/incomplete and even OUTdated... with time" Yawn.
That was not mentioned explicitly. As I thought there's no need.
But. I do not despise Nietzsche. Or disagree with him. Think he's dumb. Or anything.
Just pointing to that fact -- him living in his times... and me AFTERWARDS. Makes MY horizons WIDER.
NOT because I smarter and he dumber.
Just by the nature of thing called Time.
That is perfectly like two people -- one standing at the foot of a hill and one up on that hill slope -- WHO will have better view?
But same time -- it opens MY mind to that truth -- that anybody standing at the TOP of that hill, WILL have even BETTER view.
And there's are MOUNTAINS too.
So... it makes all very simple for me -- why not BECAME *THAT*ONE* who standing on the top of that hill? Top(s) of that mountain(s)????
Isn't it DAMN GOOD ENOUGH idea in itself -- to grow smarter... with time... ;-)
//and "evil" with weakness/decadence, paving the way for "free spirits" to create new values beyond conventional good/evil.
In terms of having no claws, no fangs... with our loosy bipedalism. No furr.
We are inherently weaker then any other animal.
And inherently evil.
Yawn.
You know about "Did Diogenes really run into Plato's Academy with a plucked chicken saying "Behold, a man!" when Plato defined Man as a featherless biped?"
//Critique of Metaphysical Dualisms: Nietzsche attacks the idea of pure opposites (good/evil, mind/body, truth/error), seeing them as philosophical constructs, not inherent realities, often arising from linguistic habits like subject-predicate grammar.
Exactly what Lem was pointing too. BTW.
//Will to Power as Primary Drive: He posits that the fundamental force isn't a search for truth but the Will to Power – a drive for growth, mastery, and self-overcoming, influencing philosophers' seemingly objective inquiries.
Well... he was living in times of Industrial Revolution. That showed to anyone that limits CAN be overcome... with means of techs.
And his predecessors he rightfully, but unfairly, criticized -- just was living in other times...
//Revaluation of Values: He challenges the "herd morality" (Christian/Socratic) valuing altruism, sympathy, and selflessness, suggesting these mask a life-denying weakness, and proposes a new "master morality" valuing strength, nobility, and creativity.
Yap.
Only one cavit.
Nobody can became stronger, nobler and more creative. Especially more creative.
By just declaring it.
Stupid error. But well, it was impossible to understand that it was inherently an error... in his times.
//Perspectivism: There are no absolute truths, only interpretations from different perspectives, and even the pursuit of truth serves underlying drives, not pure knowledge.
This too. An error.
As LOGIC claims """A "logic explosion," or Principle of Explosion (ex falso quodlibet), is a rule in classical logic stating that a contradiction (like "P and not-P") allows you to logically prove any statement, trivializing truth and falsity within that system, like dividing by zero breaks math;"""
Means, if you allowed JUST ONE error in your thinking... you recieving WHOLE LOT of em as a freebie.
And all your thinking proces turns into BS flood.
Yawn.
Words, words, words...™
Absolutely disagree. But, your training/conditioning differs. That's okay. Whatever works for you is fine. Its easy to walk away.
Of course. Yawn.
Because your monkey brain tells you that you already too smart (for a monkey) and do not need to learn anything new.))))
Yawn. You're merely projecting anon. Have a sparkling day.
Well... at least your monkey brain learned word "projecting"... thought unable to use it correctly))))
Be happy, monkey.)))))
BTW, my inquiring human mind tells me that I need to learn, I need to know more newthings.
That's why your miserly try to use word you barely if even understanding. Is totally self-revealing of your monkey-brain idiocy. ;-p
BTW genius, I'm constantly learning new things, or, a different nuance on old things. My life today is plentiful in every way. Now that I understand non-duality, interconnectedness of everything, dependent origination, and emptiness.
The fact I do not accept everything you or the man says is irrelevant to me or my intelligence.
I realize how much I don't know, do you know how much you don't know? But, realizing the above does not mean I or you must accept views that are in opposition to our changing understanding.
//BTW genius, I'm constantly learning new things...
Like meaning of word "projecting"? ))))))))
//Now that I understand non-duality, interconnectedness of everything, dependent origination, and emptiness.
Yeah. You just admitted that you proficient in... nothing.)))))))
//The fact I do not accept everything you or the man says is irrelevant to me or my intelligence.
THE FACTS being irrelevant. Very usual, even ordinary thing.
For idiots.))))))
//I realize how much I don't know, do you know how much you don't know?
If you'd not be so idioticly persistent, monkey-brain, you could try and recognise that simple really truth -- it's NOT possible to know what you don't know.
That's why it's so important to keep one's mind open, free-thinking and inquireous.
//But, realizing the above does not mean I or you must accept views that are in opposition to our changing understanding.
Yep.
That's what our monkey brains do tell us -- be scared of anything new.
Yawn.
Yada, yada, yada... happy you're happy.
When monkey unhappy and/or in fear... it throwing shit.
And your reaction authentically the same.
With verbal shit.
Sorry, words are all I've got...
"You are my sister"©
Means... so do I. Only, I looking for a way to have something more then just words...
Yeah, monkey, yeah.)))))
:-)
)))))))
Acta non Verba! ;)
In the beginning was the Word... ;-p
Naaah... the "Platonic Realm". ;)
You mean programming? ;-p
Nah, already built/ "run-able" programs.
The "platonic mathematical world" refers to Mathematical Platonism, the philosophy that numbers, sets, and geometric shapes exist as real, abstract entities in a timeless realm, independent of human minds, language, or the physical world, meaning mathematicians discover pre-existing truths, not invent them, much like finding a perfect circle that's always been there, even if our physical drawings are imperfect copies.
Core Concepts of Mathematical Platonism
Existence: Mathematical objects (like numbers, sets, functions) are real things, not just human creations.
Abstractness: These objects aren't physical; they have no location in space or time and are non-material.
Independence: They exist regardless of whether humans think about them, talk about them, or even exist at all.
Discovery: Because they are real and independent, mathematical truths are discovered, not invented, by mathematicians.
How It Works (Example)
The Perfect Circle: In the Platonic world, there's a perfect, ideal circle. Any circle you draw on paper is just a flawed, physical approximation of that perfect Form.
Numbers: The number '3' isn't just a symbol or a concept in our heads; it's an abstract entity that exists eternally, and we discover its properties.
Key Figures & Ideas
Plato: The ancient Greek philosopher who first proposed this idea, suggesting mathematical truths reside in an eternal "World of Forms".
Modern Platonists: Philosophers and mathematicians like Kurt Gödel and Roger Penrose believe we access this world through mathematical intuition, similar to sense perception.
Contrast with Other Views
Formalism: Views math as a game of manipulating symbols according to rules, without inherent meaning.
Intuitionism: Believes mathematical objects are mental constructions.
In essence, Platonism provides a way to explain the objectivity and power of mathematics, suggesting it describes a fundamental, external reality.
Plato's "Divided Line," presented in The Republic, is a metaphor illustrating the hierarchy of knowledge and reality, dividing existence into the visible world (images, physical objects) and the intelligible world (mathematical concepts, Forms/Ideas) and corresponding levels of understanding (imagination, belief, thought, intelligence), moving from murky perception to pure reason and knowledge of the eternal Forms. This analogy maps our mental states to different degrees of clarity and truth, showing how true understanding comes from grasping abstract Forms, not just sensory data.
The Structure of the Line
The line is divided into two main sections, each further subdivided:
Visible World (Lower Section): Our world of sensory experience, less real than the Forms.
Images (Eikasia): Shadows, reflections, illusions (least clear).
Physical Objects (Pistis): Real things we see, but which are copies of the Forms (e.g., a chair, a tree).
Intelligible World (Upper Section): The realm of pure reason and perfect concepts.
Mathematical Objects (Dianoia): Concepts like numbers, shapes, understood through hypotheses.
The Forms (Noesis): The ultimate realities, the perfect essences (e.g., Justice, Beauty, the Good) (most clear, true knowledge).
What It Means
Hierarchy of Reality: The upper section (Forms) is more real and true than the lower (Visible World).
Hierarchy of Knowledge: Our minds progress from imagination (shadows) to belief (objects) to reasoning (math) to pure intellect (Forms).
Path to Truth: The goal of philosophy is to ascend the line through reason, moving beyond mere opinion (doxa) to true knowledge (episteme) of the Forms, especially the Form of the Good, notes informationphilosopher.com.
Connection to the Cave: It parallels the Allegory of the Cave, describing the prisoner's journey from shadows to the world outside, paralleling the move from the visible to the intelligible realm, says Wikipedia.
"Noumenal" refers to the world of things as they are in themselves, beyond human perception, a key concept in Immanuel Kant's philosophy, contrasting with the phenomenal world (how things appear to us). It signifies a true, underlying reality that is unknowable by our senses but is the necessary basis for our experienced world, involving concepts like God, the soul, or true reality, existing outside space, time, and causality.
Key aspects of noumenal:
Inaccessible: The noumenal realm (or the "thing-in-itself") cannot be directly experienced or understood through our senses or intellect.
The "Real" World: It's the essential, true nature of reality, whereas the phenomenal world is just our subjective interpretation of it.
A Limit Concept: We know the noumenal world exists as a theoretical necessity, but we can't know what it is like.
Examples: Questions of free will, morality, the soul, or the ultimate meaning of life are noumenal concepts, as they can't be empirically proven.
In simple terms:
Phenomenal: The world you see, touch, and experience (e.g., a chair).
Noumenal: The "chair-in-itself," its ultimate essence, which you can never truly grasp, only its appearance (phenomenon).
Other uses:
Brand Names: "Noumenal" is also used as a brand name for clothing, beauty products, and even 3D modeling software, leveraging the philosophical term's depth.
"Nous" (νοῦς) is a multifaceted Greek concept meaning mind, intellect, understanding, or intuition, referring to the faculty that grasps first principles, divine truth, or immediate perception, distinct from mere sense data, found in philosophy (Anaxagoras, Aristotle) and Christian theology (spiritual perception of God's will). It's the capacity for profound insight and reason, distinguishing humans and connecting them to universal intelligence, as well as a spiritual faculty for understanding divine things.
Key Aspects of Nous:
Philosophical Nous (Greek Philosophy):
Anaxagoras: Saw Nous as the cosmic intelligence that sets the world in motion, a pure, unmixed principle.
Aristotle: Defined Nous as the highest part of the soul, grasping the fundamental first principles (starting points) for all knowledge and reasoning (both theoretical & practical), essential for wisdom and prudence.
Function: It "sees" with the mind's eye, understanding universal truths and ethical salience beyond just sensory input.
Theological Nous (Christianity):
Spiritual Perception: It's the spiritual capacity, opened by God's Spirit, allowing believers to understand spiritual realities and God's will, which natural intellect cannot grasp.
"Mind of Christ": Believers develop the nous of Christ through the indwelling Spirit, enabling spiritual discernment.
Example: In Luke 24, Jesus "opened their mind (nous)" so the disciples could understand the Scriptures.
Don't you read the Nous-papers? ;) Or hear the Good Nous (religion).
It's the "Holy Ghost" in the Xtian Trinity Father-Son-Holy Ghost/ Spirit. It "transcends" time in our human-cyborg existence, as memories/ information stored "outside" of our DNA and accessible through books/ scrolls/ written information and symbolic figures (ie - sacred geometry in architecture)..
Our Universe is a "mixed" realm (noumenal/ phenomenal)
...and many things in it are beyond our ken...
The "noumenal fallacy" isn't a standard philosophical term, but it refers to the error of applying our mind's categories (like space, time, cause) beyond possible experience to the noumenal realm, the unknowable world of "things-in-themselves" (Ding an sich) that underlies appearances (phenomena). Immanuel Kant warned against this: we can only know phenomena, but reason tempts us to make claims about noumena (God, soul, true essence), which leads to metaphysical confusion, mistaking the limits of our understanding for objective knowledge of ultimate reality.
Key Concepts:
Phenomena (Appearance): The world as we experience it, structured by our minds (space, time, categories).
Noumena (Thing-in-itself): Reality as it exists independently of our perception, which we can't directly know.
The Fallacy: Using concepts like substance, causality, or being to describe noumena, which are concepts only applicable to phenomena.
Why it's a Fallacy (Kant's View):
Limits of Understanding: Our cognitive tools (intuitions, categories) are designed for sensory experience (phenomena), not for grasping things outside of it.
Transcendental Illusion: Reason naturally seeks completeness, leading it to posit noumena as the foundation, creating an illusion that we can know these ultimate realities.
Unknowable Nature: We can conceive of noumena as the source of phenomena, but we cannot have theoretical knowledge (science) about their actual nature; any such assertion is speculative.
Example:
We perceive a carrot as colored, sweet, and spatial (phenomena).
The "noumenal fallacy" would be claiming to know the carrot's "true color" or its "inherent sweetness" as it exists before our mind processes it, which Kant says is impossible.
In essence, the "noumenal fallacy" is the mistake of treating the unknowable, ultimate reality (noumena) as if it were another knowable object within our experience (phenomena).
/ Transcendental Illusion: Reason naturally seeks completeness, leading it to posit noumena as the foundation, creating an illusion that we can know these ultimate realities.
"Philosophy is the translation of Eros into Logos" - Byung-Chul Han "...and the desire and pursuit of the whole is called, "Love"" - Plato "Symposium" (Aristophanes' Speech)
G-d is "Love" (at least in the Xtian religion).
Love... a transcendent force beyond "Reason". Welcome to Station 11. ;)
Goedel's Incompleteness Theorum: Gödel's Incompleteness Theorems, published by Kurt Gödel in 1931, reveal fundamental limits of formal mathematical systems, proving that any sufficiently powerful, consistent system (like arithmetic) will always contain true statements that cannot be proven within the system itself (First Theorem) and that such a system cannot prove its own consistency (Second Theorem). These theorems shattered dreams of creating a single, complete set of axioms for all mathematics, showing a permanent gap between mathematical truth and formal provability.
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