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### Aristotelian Paradox of Place Counter Argument

Posted: Wed Nov 22, 2017 6:41 pm

From Aristotle:

"if everything that exists has a place, place too will have a place, and so on ad infinitum."[15]

Presented argument:

1) If everything that exists has a place, place too will have a place, and so on ad infinitum.

2) Place exists if and only if there is Place. Places exist if and only if there is infinity: (P1 ↔ P2) ↔ ∞

3) Place exists if and only Place is gradient. This in turn exists if and only if there is infinity: (P ↔ (1,2,x)) ↔ ∞

4) Gradation is an element of Place and is relative to other grades: ∫(1,2,x) ∈ P

5) Place divides itself infinitely as a direct product of its elemental relative grades: (P/P ≜ ∞) ∏ ∫(1,2,x)

6) As self-divisive, Place manifests itself as both potential unity and multiplicity. In these respects Place is a dimensional limit (boundary, Ω) manifested as individuation through division. (Place is a dimension/boundary through division as a constant, as boundaries/dimensional limits act as dividing lines)

(P/P → P ^ P(1,2,x)) = Ω

7) Place as a dimensional limit is infinite because Place is proportional to self - division equal in definition to infinity.
((P = Ω) = ∞) ∵ P ∝ (P/P ≜ ∞)

Agree/Disagree?

### Re: Aristotelian Paradox of Place Counter Argument

Posted: Thu Nov 23, 2017 3:05 am
2) No,

3) Neither Scalar nor Gradient, but it can be resolved Scalar (if you really want to, but that is tedious) if you ∉ person and place in simultaneous time. Stoics were the first to resolve this, in their categories rejecting Aristotle. You'll likely more aware of Einstein's simplification that no two objects can occupy the same place at the same time, and the time travel paradoxes that hit science fiction in the late 80s and 90s of people touching one another outside of time.

https://en.m.wikipedia.org/wiki/Stoic_categories
Aristotle solved the problem in proposing that accidental attributes are non-substantial beings that inhere in substances. He defines this presence saying "By being 'present in a subject' I do not mean present as parts are present in a whole, but being incapable of existence apart from the said subject." (The Categories 1a 24–26)

Such incorporeal presence caused problems to the Stoics in saying that the οὐσία of a thing is its matter. It is easy to understand the problem. If there is an insubstantial being, in Athens somehow present in Socrates, causing him to be substantially present in Athens we seem to be faced with an infinite regression, for there would seem to be an insubstantial Socrates in the insubstantial Athens in Socrates, in Athens, etc. Ultimately, who is to say who is the real Socrates and what is the real Athens? Similar arguments can be made of Aristotle's other categories. Was there an insubstantial running in Archimedes causing him to run naked through the streets of Syracuse, shouting out his immortal "Eureka"? Was there an insubstantial fist in Athena causing her to strike Aphrodite as the Iliad recounts?
When I eventually got around to reading parts of Nietzsche's Will To Power (I didn't like reading it as he didn't want it published, but was surrounded by Nietzscheans on forums so eventually took a look over) shortly after I studied the categories, and noticed he was more or less trying the same thing, but failed to resolve some of these problems. People treat it like it is a esoteric wisdom text, he was just trying to build his own categories, which is fine, but very difficult. Some of the problems are inherent in how we do Calculas, not easy to resolve, and his concept of power was based on earlier works like Machiavelli, don't think he got to Clausewitz when he was speculating on the nature of such thinking.

It is a minor issue, causes more problems in Indian philosophy, trying to determine a state of This and That relative to Self on a dual, non-dual, qualified non-dual basis (and more that that) than our own western schools. Existentialists will hiccup occasionally with Dasein, but since nobody takes them seriously, problem will resolve itself over time.

Just stick to Einstein, people get it in modern times (well, a big part of it at least) the constradiction Zeno was pointing at, and Aristotle stumbled over. I'm in agreement with Einstein and not Bell that when you look at the moon, you are seeing a moon. It is there, the fault isn't in the knowledge but the approach to measurement of things. Thingness is the subject matter we are worried about here. Too easy to overlook.

### Re: Aristotelian Paradox of Place Counter Argument

Posted: Thu Nov 23, 2017 7:27 pm
EchoesOfTheHorizon wrote:
Thu Nov 23, 2017 3:05 am
2) No,

3) Neither Scalar nor Gradient, but it can be resolved Scalar (if you really want to, but that is tedious) if you ∉ person and place in simultaneous time. Stoics were the first to resolve this, in their categories rejecting Aristotle. You'll likely more aware of Einstein's simplification that no two objects can occupy the same place at the same time, and the time travel paradoxes that hit science fiction in the late 80s and 90s of people touching one another outside of time.

"Place" manifests itself fundamentally a self dividing "form" through perpetual grades with these grades being:
"a particular level of rank, quality, proficiency, intensity, or value".

In these respects "Place" (or anything corresponding to it for that matter) is defined through division as a constant. This division forms the dimensional limits of "place" as "place" as a constant. This observation of gradation does not imply the places existing in the same space at the same time, as each Place manifests itself as a space through various qualities.

The argument breaksdown in many parts to space within space which inevitably manifests further grades. The constant dimension of division is the sole constant that maintains the dimensions of space for what it is. Division acts as a dimensional limit that defines Place as Place through Place.

Division manifests direction through a form of "regress" that is conducive either to circularity or linearity.

https://en.m.wikipedia.org/wiki/Stoic_categories
Stoicism places a heavy emphasis on the control of one's thoughts, as the exterior world is uncontrolable. The problem occurs in the respect that the exterior world is composed of other's thoughts. Reality manifests itself through idea, and the stoic's fall into there own form of contradiction in these respects. In these respects their manifestation of categories are strictly just structural extension of how they see themselves...as out of control.

Their dependence on strict understanding of reality as "corpeal" bodies only, with incorpeality being impossible, in many respects to the conclusion their ideas, as bodies, are temporal and pass. In these respects they are subject to contradiction through temporality, as they can make no truth claims.

There emphasis on strict concrete terminology has not foundation as abstractness is required for any of their statements to be observed.

"It was the effort to solve the problems raised by the Platonists and Peripatetics that led the Stoics to develop their categories, somehow disposed and somehow disposed in relation to something."

Stoicism is founded on self-cycling relativism which has no consistencies. It is strictly a philosophical system based on a percieved absence of control, hence usually adopted by people in high stress situations. It does not provide a solid base for metaphysics without being reduce to an understanding of the universe as strict perpetual movement, in this they contradictory claim a constant.

Aristotle solved the problem in proposing that accidental attributes are non-substantial beings that inhere in substances. He defines this presence saying "By being 'present in a subject' I do not mean present as parts are present in a whole, but being incapable of existence apart from the said subject." (The Categories 1a 24–26)

Place cannot be place without being something else entirely. However "Place" within "Place" inevitably leads to division of place through grades, with these grades (as continual self division) manifesting the dimensional limits of Place as Place. Place is a constant and is not limited to perpetual movement.

Such incorporeal presence caused problems to the Stoics in saying that the οὐσία of a thing is its matter. It is easy to understand the problem. If there is an insubstantial being, in Athens somehow present in Socrates, causing him to be substantially present in Athens we seem to be faced with an infinite regression, for there would seem to be an insubstantial Socrates in the insubstantial Athens in Socrates, in Athens, etc. Ultimately, who is to say who is the real Socrates and what is the real Athens? Similar arguments can be made of Aristotle's other categories. Was there an insubstantial running in Archimedes causing him to run naked through the streets of Syracuse, shouting out his immortal "Eureka"? Was there an insubstantial fist in Athena causing her to strike Aphrodite as the Iliad recounts?
When I eventually got around to reading parts of Nietzsche's Will To Power (I didn't like reading it as he didn't want it published, but was surrounded by Nietzscheans on forums so eventually took a look over) shortly after I studied the categories, and noticed he was more or less trying the same thing, but failed to resolve some of these problems. People treat it like it is a esoteric wisdom text, he was just trying to build his own categories, which is fine, but very difficult. Some of the problems are inherent in how we do Calculas, not easy to resolve, and his concept of power was based on earlier works like Machiavelli, don't think he got to Clausewitz when he was speculating on the nature of such thinking.

It is a minor issue, causes more problems in Indian philosophy, trying to determine a state of This and That relative to Self on a dual, non-dual, qualified non-dual basis (and more that that) than our own western schools. Existentialists will hiccup occasionally with Dasein, but since nobody takes them seriously, problem will resolve itself over time.

Just stick to Einstein, people get it in modern times (well, a big part of it at least) the constradiction Zeno was pointing at, and Aristotle stumbled over. I'm in agreement with Einstein and not Bell that when you look at the moon, you are seeing a moon. It is there, the fault isn't in the knowledge but the approach to measurement of things. Thingness is the subject matter we are worried about here. Too easy to overlook.
I am not sure exactly what you are arguing, but in frankness I don't think you do either, as I am simply stating that the perpetual movement which justifies place simultaneously allows for consistency in a seperate respect. In this respect, "Place" maintains itself as both a "Platonic" form and "Aristotelian" function (however that is wording it poorly). The argument fundamentally breaks down to this simple axiom:

1) The continual division of Place (as a Place must exist in a Place ad-infinitum) in itself manifests as the boundaries which form place. All dimensional limits maintain a structure as both stable and seperate from its surrounding environment. This boundary exists within Place as Division through gradation with this gradation not being limited to strictly accidental properties defining it but as an inherent acts of the Place relating to itself as Place.

Place forms Place through itself as a boundary of division.

### Re: Aristotelian Paradox of Place Counter Argument

Posted: Thu Nov 23, 2017 8:27 pm
Try again, reread what was written. This is the primary division between Stoic and Peripatetic Categories. Until you grasp the difference, you will not be able to grasp Zeno's paradox. He isn't referring to a Noumenon, but presumed phenomena prone to contradiction. It also runs up against our modern mathematics a bit, (the fundamental theorem of Calculas primarily) but no fault to the Stoa.

This is one of the more painful aspects of ancient physics that split the two schools apart, and kept one another at their throats. I so strongly recommend instead of a bull headed assertion from a mere glance over a wiki pages, you keep this in mind as you go on in the future. You don't have to grasp it now, but know there is a massive rift, and that it goes deeper than I intuitated so far. You'll have to get into Theories of Mind in Pure Mathematics, when forcing alien mathematical systems together in order to grasp the magnitude of what these two schools were doing and arguing about. It still exists (in many more forms, more schools) today. The Stoa are certainly right in regards to Zeno's position however. It is absolutely obvious they wrote on this very subject from the little I quoted, I did not build a time machine and insert this argument into the past in order to upset your Thanksgiving Day, it really does exist.

Space and Place doesn't exist externally. These are presumptions, nothing more. Stoic picked up on this faster, and solved the paradox. We actually have a fraud in the Catholic Church who exploited this a few decades back (or should I say two, twins) who would appear in two places at once. One would bleed from wounds in the hands, while another wouldn't. Was pushed by many as a miracle, but God doesn't deal in such petty miracles, so easily seen through.

### Re: Aristotelian Paradox of Place Counter Argument

Posted: Fri Nov 24, 2017 12:21 am
EchoesOfTheHorizon wrote:
Thu Nov 23, 2017 8:27 pm
Try again, reread what was written. This is the primary division between Stoic and Peripatetic Categories. Until you grasp the difference, you will not be able to grasp Zeno's paradox. He isn't referring to a Noumenon, but presumed phenomena prone to contradiction.

This "division" between Stoic and Peripatetic Categories provides the dimensionality for these arguments by providing a boundary line. Where you see contradiction, through division, a duality can be comfortably be observed.

These non-noumenon phenomena, are bound by space to Noumenon phenomena and in these respects non entirely separable without ending in contradiction. Noumenon and Non-noumenon are bound through a median of space as both are composed of space. The space they observe, through the stoics is strictly Relativistic and negative in value, which I will cover briefly below.

I reread it, and the categories the stoics apply as axiomatic measurement systems, in themselves are built to end in contradiction (with this contradiction, in itself, equating to a deficiency in stability/structure resulting in an imbalance or flux). All examples requiring measurement systems that are in a state of perpetual movement, justifying the flux in non-noumena phenomenon they argue for. They form the axioms to end in the solution they want.

These categories of Stoic Metaphysics are bound under a nature of Relativity and Particulation and cannot exist without this dualism. I have already observed this in the thread "Relativity, Negation and Atomism" viewtopic.php?f=16&t=23043

These foundations lead to an inherent negation of properties which inevitably result in a contradiction as a deficiency in structure. The categories the stoic's made up naturally lead to the stoic position of negation.

These systems, whose axioms are founded with in the observations of dimensional limits or categories, in themselves form

It also runs up against our modern mathematics a bit, (the fundamental theorem of Calculas primarily) but no fault to the Stoa.

This is one of the more painful aspects of ancient physics that split the two schools apart, and kept one another at their throats. I so strongly recommend instead of a bull headed assertion from a mere glance over a wiki pages, you keep this in mind as you go on in the future. You don't have to grasp it now, but know there is a massive rift, and that it goes deeper than I intuitated so far.

You'll have to get into Theories of Mind in Pure Mathematics, when forcing alien mathematical systems together in order to grasp the magnitude of what these two schools were doing and arguing about. It still exists (in many more forms, more schools) today. The Stoa are certainly right in regards to Zeno's position however. It is absolutely obvious they wrote on this very subject from the little I quoted, I did not build a time machine and insert this argument into the past in order to upset your Thanksgiving Day, it really does exist.

"Zeno's paradoxes are a set of philosophical problems generally thought to have been devised by Greek philosopher Zeno of Elea (ca. 490–430 BC) to support Parmenides' doctrine that contrary to the evidence of one's senses, the belief in plurality and change is mistaken, and in particular that motion is nothing but an illusion."

While the stoics may have agreed with Zeno, there categories of Relativity and Particulation inevitably lead to a form of plurality.

Happy Thanksgiving by the way.

Space and Place doesn't exist externally
"External" is an observation of Space/Place.

. These are presumptions, nothing more. Stoic picked up on this faster, and solved the paradox. We actually have a fraud in the Catholic Church who exploited this a few decades back (or should I say two, twins) who would appear in two places at once. One would bleed from wounds in the hands, while another wouldn't. Was pushed by many as a miracle, but God doesn't deal in such petty miracles, so easily seen through.
I am familiar with Padre Pio, I am assuming you are talking about him, however bilocation has been observed with the Buddha also. I am neither for or against bilocation, however the possibility is there logically at least in certain degrees.
Zeno's Paradoxes of Achilles and the Tortoise and The Dichotomy rely upon a form of division that results in a dualism where both parties (or spaces) are in a perpetual state of flux. Zeno claims this infinite state of flux is impossible, and in turn there is no movement. The problem occurs in that both arguments require a form of dualism through measurement systems that in themselves are in a state of flux (move 1/2 then 1/4, etc.).

The measurement systems themselves are in a constant state of flux resulting in the observable reality as inevitably being "motionless".

The arrow paradox uses time as "durationless" by applying, assumingly, the same constant dualistic division of measurement.

"Whereas the first two paradoxes divide space, this paradox starts by dividing time—and not into segments, but into points.[14]"