But the probing of matter has often left us with, ironically, the immaterial: voids and fields — StreetlightX

In my view, that part is a mistake. Insofar as It's the case that physics sees such things as somehow fundamental, it's an upshot of the instrumental, mathematical approach to physics. That's fine insofar as it goes--basically as an instrumental, practical approach to making predictions, but it shouldn't be taken literally as ontology.

It only becomes a problem under a monist guise, because those non-dimensional points which are separated by matter must be given some real existence, as other than matter, otherwise "medium' has no meaning here. So, to say the medium is "all there is" is really contradictory, because "medium" implies the middle, between that which is not the medium. — Metaphysician Undercover

Media and form are two sides of one coin. I'm not sure about matter separating non-dimensional points. I've never heard of that.

I'm not sure about matter separating non-dimensional points. I've never heard of that. — frank

It's only a suggestion of how one could try to conceive of matter as a medium, and also as "all there is". However, the problem I described remains, how to account for those non-dimensional points, with matter remaining as all there is. And without those points, matter is not a "medium".

A monistic materialist will have to show that the immaterial is an illusion. As you say, the immaterial is part of the concept of materiality, so the materialist can't just dispense with it.

One of the big issues with any metaphysical ism, material or otherwise is how it handles emergence.

You’re stretching to make materialism the messiness it rightly is, which I’ll give you. Perhaps I was too harsh on my assessment of abstraction. But it could be said that even the messy ecological view that pervades your materialism, can be said to be even too “formal” (in the literal sense). Of course then it remains to be said whether the thing at hand can be discussed intelligently without these abstractions. This is probably your basis for calling my claim “mysterian”. The fact remains that it is a line of reasoning to be explored as the point is that material is itself before it is the abstracted concepts applied after the fact.

I agree with much of the above stated, with this nature of matter being of relatively significant value in the face of the materialistic society we live in today.

To understand "matter", not necessarily limited physics specifically, is to understand not just the nature of our reality, and the inherent problems it curtails, but society itself.

To equate matter as a medium, or center point of origin, leaves us with a necessary understanding of point space being the foundation of any concept of the atom.

If we look at the atom, as strictly a part which is composed of and composes further parts, as evidenced by physics (with fields taking on the same nature due to their existence and relation to further fields) we are reduced to point space.

Take an atom, or part, observe it from a distance and it is reduced to a point. Look at the atom closer and we see it, due to its curvature/angulature, it is composed of further atoms/parts that effectively equate to point space. Look at these atoms/parts closer and the point space continues.

What we understand of the atomist perspective is continual point space as the foundation for not just the atom but relativistivally is the atom as well. Where atoms are composing/composed of further atoms, points exist in the same function and manner.

One point inverts to many and many invert to one, with the point and atom simply being a median of inversion or change through which movement occurs. The point/atom as composed of and composing further points necessitate a relativistic nature of a field where the point composed of further point effectively acts as a boundless field or void conducive to a 0d point.

The point/field acts as a means of inversion between a unity/multiplicity which is the foundation for all phenomenon.

0d Point space would give logical foundation to dark matter, black holes, but elements of the human psyche that exists through this material medium; hence a far reaching effect occurs that gives a hopeful notion of unity within the sciences.

However the 0d point, or void conducive to the presocratic notion of the apeirion, as nothingness necessitates a form of relation as nothingness cannot be observed on its own terms except relative to being. The 0d point/darkmatter/blackholes/void is the foundation of relativity in these regards considering as "inversive" it is nothing or "mass" on its own terms which cannot be observed without contradiction.

As inversive of being, 0d point space exists as a dual to being with being being necessitated through directed movement requiring an "inversion of inversion" as an ethereal point space. This ethereal point space, as pure infinite movement as unchanging can be equated to not just a foundational glue to being (reminiscent of the Hindu akashic record) but being itself through a 1d point.

The 0d point effectively inverts the 1d point to many points, with the 1d point existing as one point considering void is nothing (which takes into account relativity and quantum connection simultaneously) and what exists as 1 through many is effectively the same. A point in locality A is still the same point in locality B considering the composition of both points is still composed of the same points and existing within a singular point field.

And I will cut it off here to keep it short.

One of the big issues with any metaphysical ism, material or otherwise is how it handles emergence. — schopenhauer1

If one is to speak in terms of "emergence", then the first order would be to determine what emerges, and what does it emerge from. The different "isms" might treat these fundamental principles differently, so that talking "emergence" without first determining these principles might be very confusing.

As inversive of being, 0d point space exists as a dual to being with being being necessitated through directed movement requiring an "inversion of inversion" as an ethereal point space. This ethereal point space, as pure infinite movement as unchanging can be equated to not just a foundational glue to being (reminiscent of the Hindu akashic record) but being itself through a 1d point.

The 0d point effectively inverts the 1d point to many points, with the 1d point existing as one point considering void is nothing (which takes into account relativity and quantum connection simultaneously) and what exists as 1 through many is effectively the same. A point in locality A is still the same point in locality B considering the composition of both points is still composed of the same points and existing within a singular point field. — eodnhoj7

How could there be a 1d point? Wouldn't that be a line, and therefore a multitude of points marking a specific order? And if the point, instead of being 0d is infinitesimally small, without that specific order, then it occupies a 3d area, not a 1d point, though it may be ordered as a sphere or something else. So it cannot be correct to represent the emergence of being with a 1d point.

While I'd like to think that yes, materialism does entail more mature, more elaborate theorizing than the various idealisms which it arrays itself against, I think you're vastly understating the influence and pervasiveness of the latter. If one accepts materialism in the sense outlined here, people like Richard Dawkins and Steven Weinberg become nothing other than arch-Idealists; searches for reductive 'theories of everything', where all the universe follows from a small handful of first principles, turn out to be idealist desiderata par excellence. — StreetlightX

I am not really seeing the opposition that you are setting up here. I can understand you pitting reductionist physicalism against non-reductionist physicalism, but that's a different debate. What does this have to do with the question of matter?

You were talking about "the principle of the irreducibility of the medium," but what your examples suggested was that all you wanted was for your reductive explanations to incorporate more of the underlying messy details. Which is fine; as I said, this is the trajectory that sciences take anyway as they explore their domains in-depth. But there is also a place for big-picture, high-concept theorizing of the likes of Dawkins and Gould - and Darwin for that matter.

It is a key feature of our world that regularities emerge at multiple levels of detail. The picture does not dissolve into noise as we step back and take it in at a larger scale; instead, new patterns come into focus as we scale up or down. This is why we have multiple sciences, all of them more-or-less viable as empirical models. And even within one science, such as evolutionary biology, we can grasp general outlines of a theory, even if they are not exceptionless and do not afford a very precise fit. How else could Darwin have made his great discovery without the benefit of genetics and molecular biology and evo-devo, if the patterns that he noticed were not there to be seen with a naked eye?

For that matter, how could we ever have any "special sciences," anything other than what we call "fundamental physics" if we could not idealize the medium, neglect and smooth out messy details - and still end up with an acceptably accurate model? How could there be evolutionary biology if we could not (mostly) ignore the medium of chemistry and physics? How could we have so much success with the Big Bang theory if we could not ignore the medium of stars and pretty much everything else and idealize it as a perfect fluid?

Besides, what is medium at one level is the nuts and bolts at another, more fine-grained level. You acknowledge this yourself when you pick examples from different sciences that look at the world at different levels of detail. So where exactly is that medium that you are talking about? What is it?

Yes and No.



The point projecting to a point as point results in a 1d point. For example if projected in one direction it becomes a 1 directional line. The one directional line project in all directions in one direction becomes the circle. The nature of the point is defined by its projection in one direction, in both cases.

So point A projecting to point B Results in this extradimensional nature.

Point B projecting to point A Results in this same extradimensional nature.

Point A to Point B and Point B to point A shows a from of alternation in time where The line changes directions through a form of repetition. Now this repitition is dependent upon the point as extradimensional.

If point A and Point B are directed towards eachother simultaneously, with this alternation occurring at a rate of infinity the line takes one an intradimensional nature through the points. It is not a two directional line, as this would require the two directional line to extend from a center point of 0 (like the number line) and the issues of alternation continues.

So A and B are directed towards eachother simultaneously and the line acts as a connector between the points, where prior the projection shows the point moving away from the point resulting in the line. The point moving towards the point, as a point, connected through the line:

1) observes the point existing through Points as 1 pure direction. The point exists through the point as point and exists on its own terms.

2) The multiple points, connected through the line, as 1 point observes the 1 unified point being observed through multiplicity as an approximation of it. This cannot occur for the 0d point as it is strictly void. The 1d point would be pure being. This line, as a connector, does not have any directional qualities in itself except through the point being directed towards itself as itself; hence the line as absent of direction takes an -1 dimensional nature.

3. The 0d point as nothing inverts completely to everything as 1d pure movement.

The 1d line as directional inverts to the -1d line as negative directional. The 1d line does not invert back to the 0d point specifically because the 1d line is not pure direction. It's extradimensional nature, projecting away from itself, necessitates a dual intradimensional counterpart. Projecting away from origin and project too origin are inversive duals. Hence the intradimensional line, as negative dimensional, exists as the points moving towards eachother as point.

The 1d line, as projective/extradimensional, exists as a dual to the -1d line as non-projective/intradimensional.

The circle, composed of infinite -1d lines, observes infinite points existing through 1 point as a point.

Besides, what is medium at one level is the nuts and bolts at another, more fine-grained level. You acknowledge this yourself when you pick examples from different sciences that look at the world at different levels of detail. So where exactly is that medium that you are talking about? What is it? — SophistiCat

I think there's a misunderstanding here: I'm not against 'big picture claims' (Gould is wonderful, as is Darwin!), and I invoked Weinberg and Dawkins not as avatars of 'big picture thinking' but because the specific ways in which they theorize the 'big picture' are severely misguided. Each, in their own way, attempts to assign full explanatory power (in physics and biology respectively) to a privileged ontological stratum so that certain parts of reality are simply reduced to epiphenomena that have no material agency.

That's the point: I'm not at all trying to furnish a 'non-reductionism physicalism' - whatever that might mean - but rather, give full 'ontological rights', if we can speak that way, to all of what is often simply dismissed as medial. The equation of the material with the medial isn't meant to reduce the medial to the material. Quite the opposite: it is meant to expand our understanding of what counts as material. So to these kinds of questions:

How could there be evolutionary biology if we could not (mostly) ignore the medium of chemistry and physics? How could we have so much success with the Big Bang theory if we could not ignore the medium of stars and pretty much everything else and idealize it as a perfect fluid?

I want to answer: precisely because - and not in spite of - the fact that the material is not exhausted by chemistry and physics, nor by the stars. Recall again the etymology of media: the state of being-in-the-middle; the point is to rethink materialism not as origin (arche) or as fundament, but as being-in-the-middle of things. Or better yet, the idea is to rethink what it means to be fundamental, where what is fundamental is precisely all that is often thought of as 'accidental' (hence the inversion of Aristotle I briefly invoked at in the OP). Your questions seem to make it as though I disagree with you on the reality of 'larger scales', as it were. But this is just the opposite of what I'm attempting.

The point projecting to a point as point results in a 1d point. For example if projected in one direction it becomes a 1 directional line. The one directional line project in all directions in one direction becomes the circle. The nature of the point is defined by its projection in one direction, in both cases. — eodnhoj7

No. no. this is all wrong. Producing 1d lines in all directions from a point will never make a circle. That's very obvious. A circle requires that the lines from the point are all the same length, and are connected with a curved line. Where does the necessary curved line come from? That curved line, which connects through the medium between the individual straight lines, is essential. Likewise, a point projected to another point does not make a 1d line segment. The line segment requires a connection through the medium, between the points. That's why people say, no matter how many 0d points you put together, they will never make a line, because you cannot get to 1d from 0d in that way.

Your analogies are leaving out a very important point, the connection through the medium. You cannot get "intradimensional nature", from the 0d point, in this way, because there is a fundamental incompatibility between 0d and 1d, which we might call the medium. The same incompatibility is what gives us the irrational ratios between 1d and 2d. The two perpendicular sides of a square, representing two distinct dimensions produce an irrational ratio. The ratio between the diameter of a circle, and its circumference, being the relation between a 1d line, and a 2d curve, is also irrational. The medium, that which lies between the dimensions, is fundamentally unintelligible to us, because we understand space in terms of dimensions. So whatever it is which separates the dimensions ( and there necessarily is a separation according to the incompatibility described above), the medium, is fundamentally unintelligible, because it lies outside of our understanding (between the dimensions).

I understand long posts are not smiled upon, however your point is not entirely accurate.

Point 8 specifically deals with the nature of the line and 0d point.

Point 11 observes the interdimensional nature of the 1d point and the paradox of the 0d point and 1d point.


1) Pi is the foundation for the circle as infinite lines stemming from a center point, for Pi can be measured from infinite positions within the same circle. Pi as a line, varies in length with the circle however is always the same measurement. The line always exists as one directional and 3.14159.

2) The circumference of a circle as infinite points stemming from a center point, observes the circumference being formed from that center point being infinite lines. The circle as composed of a curved line, with the line being composed of infinite points, still necessitates this definition. However this leads to point 3:

3) The radian, as a curved line which gives the premise of the circle being formed from a curved line, is founded in Pi as a straight line. The line projects to another line of the same length, which exists at 90 degrees to the original line and is curved to the circumference to produce and angle of 57.3 degrees. Considering the radian is premise in an angle, and the angle can be applied in infinite variations within the circle, the circle is composed of infinite lines.

4)All straight lines are Pi and give the foundation of not just the circle as infinite lines, considering Pi can be held in infinite positions within the same circle, but with the circle as a constant infinite lengths of Pi as well with Pi existing as a line. The line is both 1 directional and 3.14159...

5) The circle, through infinite Pi's observes the circle composed of infinite angles with these angles equivalent to degrees as a number much less than one approaching 0. The angle as a degree of "much less than one approaching zero" observes the angle being equivalent to the line where all lines are angles of quantum degrees.

6) The line as a quantum angle, observes the width (not length) of the line as perpetually approaching point zero and hence is sizeless. The circumference of the circle as infinite points, which is still necessitated by a curved line defintion which further necessitates the infinite angles observed in point 3, observes these points connected to the center point of the circle and hence infinite lines.

7) The curved line, as infinite points, can be observed as composed of infinite straight lines forming infinite angles.

8) The line is the projection of a point in one direction, where the 0d point as formless exists as a directive quality. The line takes the nature of directed movement being the foundation of all limits, considering the Pi nature of each line necessitates the line not being infinite but perpetually changing hence moving. The 0d point is strictly void or nothing, hence is given form by direction and movment where direction and movment is the foundation of all limits.

So a line between two points observes the alternation between being and nonbeing (void) where void (0d point) as the inversion of being (where being exists if and only if there is directed movement) into multiple being as multiple lines.

9) To observe the line as a connector between points is to observe the line as non directional. The line as directional observe a projection of one point away from its origins resulting in multiple points. However if the line connects the points, it necessitates that through the line the points are directed towards eachother simultaneously and the line becomes non directional considering the points are directed towards eachother through eachother as eachother. The line is absent of directional qualities (negative dimensional) and the point exists pure direction through itself as itself as 1d.


10)Where one line may be infinitely smaller than another line, where relativistically it may equate to a point, each line observed as a line between two point only is still the same infinite line between two points where size is merely a relation between the lines as a relation between multiple infinities. All lines as Pi are infinite.

11) The 1d point as pure being, pure direction, existing through eachother as eachother observes the 1d point as existing through infinite points as an infinite point. The 0d point acts as an inverter of unity/multiplicity and is not anything other than an observation of relation where the 1d point can only be observed in multiples. The 1d point as direction through itself, by its inherent negative dimensional connection, observes this multiplicity by its inversion through the 0d point point. The negative dimensional line in turn is composed of infinite 1d points.

Being appears in a fractured statement when viewed through 0d point space (void) as a veil equivalent to darkness.

The 1d line is an inversion of the negative dimensional line into a line of direction.

However the 1d line cannot connect points because of its one directional nature necessitates a projective nature of point away from point, hence the 1d point cannot project away from itself (as it exists through itself as itself) therefore it must be the 0d point. The 0d point cannot only project past itself by inverting through itself into a 1d nature of the line.

Void must be void of itself, so the 1d line observes the void of void or the 0d point dividing itself as infinity through the line. This 1d line is an inversion of the of both the 0d point through 0d point (or an inversion of inversion) and the -1 dimensional line.

Now the 0d point as nothing, necessitating it as inversive considering it is nothing in itself, inverts itself into the 1d line as a 1 directional unit considering the line is a unit. All units exists through further units as the projective nature of the line occurs if and only if there is somewhere to project to...This necessitates further units. We can see this with the degree existing in relation to further degrees.

The 0d point cancels itself out to units as multiplicity, but also Unity as pure directed movement. Nothing cancels itself out into pure being. However considering this 1d point, as the inversion of inversion, still occurs through the 0d point as an inverter, the 1d point is observed as multiple points existing through eachother as the -1d line. The 0d point, by inverting the 1d point into multiple connected points (still existing as one) inverts the -1d line (as absent of direction in itself resulted from the 1d point observed in multiple position) into 1 directional and seperative.

***will continue.

View it this way:

1 is a function through the line, hence 1 is a equivalent to a process of directed movement where the line and 1 are the same through Pi.

All fractals are composed of further fractals as evidence by Pi.

1) Pi is: the symbol π denoting the ratio of the circumference of a circle to its diameter

b : the ratio itself : a transcendental number having a value rounded to eight decimal places of 3.14159265

http://www.bing.com/search?q=Pi+definit ... 1B982EA403


2) Pi is a line between two points that exists from the center point of the circle to the circumference. All lines in turn exists as center points of a circle towards is circumference where all lines exist as the ratio of Pi as 3.14159...


3) The line as composed of infinite points is composed of infinite lines, hence the line is composed of infinite circles as all lines exist as Pi.


4) The line is composed as infinite circles projecting, hence the line is equivalent not just to infinite points but infinite quantum circles as well.


5) Each line, as composed of infinite further lines, is composed of infinite "pi's" where the line as Pi is composed of further Pi's. Hence Pi is divided by an infinite number of Pi being divided by Pi. All functions exists through further functions as 1 function, hence 1 is equivalent to a function that is a continuum. 1 is a continuous function.

Hence Pi dividing itself observes Pi as its own function of self-division conducive to 1 through the line where 1 is Pi as a function of perpetual self division.

f(x)= 3.14159→(x→∞)
............f(x)= (3.14159→(x→∞) =1
................f(x)= (3.14159→(x→∞)
.........................f(x)=...

or


f(x)= (3.14159→(x→∞))/( f(x)= (3.14159→(x→∞))/(f(x)= (3.14159→(x→∞))/…)) = 1


X= a continuous series to infinity where the counting of Pi has stop. X= the limit of Pi as a finite rounded number.


Hence “x = all number with all number equivalent to 1.”

2) Pi is a line between two points that exists from the center point of the circle to the circumference. All lines in turn exists as center points of a circle towards is circumference where all lines exist as the ratio of Pi as 3.14159... — eodnhoj7

Pi is not a line, it is the relation between two measurements. As it is an irrational ratio, we can conclude that the two measurements are actually incommensurable.

1. The radius is the center point of the circle to its circumference.

2. Dividing the circumference by pi results in the diameter

3. It would be equivalent to me saying c/3.141... = d.

4. The radius is half of the diameter.

5. Each radius in itself is a diameter, of another circle.

6. Now if I divide the circumference by Pi, like I said before, I get the diameter.

7. If I multiply the diameter by Pi, I get the circumference.

8. Pi results in both diameter and circumference base upon its relation to each respectively.

9. Now the diameter and circumferance are based upon relative units of measurement (cm, inches, feet, whatever) with these units of measurement being lengths. One length is merely a ratio of the number of time one line fits in or contains another line.

10. The division of circumference by pi, resulting in diameter, observes the circumference as a length being divided by pi into another length of diameter. The diameter, as a length, is multiplied by pi into another length equating to circumference.

11. Pi respectively multiplies/divides lengths into further lengths.

As the mutiplication/division of a length requires another length, Pi is a constant length of a line as regardless of the size of a line relative to another line, a line is always a line.

So I may multiply a 1 line 3 times and get 3 lines as 1 line which is 3 times larger than the original. So in multiplying the original line I fundamentally divided it it 1/3 of a line.

I may divided 1 line into three 1/3 lines. In dividing the line I multiply the original line into being three times larger than the new lines, while multiplying the number of lines.

Regardless of whether the line is multiplied/divided, it stays as a line.

Now considering the line of x is multiplied/divided, in accords with itself, where the line effectively folds inwards (through division) into fraction of itself, or folds outwards (through multiplication) the line is the constant standard for the ratios.

12. For the line to multiply by 3.141... would require the line to contain a set number of ratios in it as other lines in one respect with the number of these ratios existing as one in itself. So I may have a diameter of x, multiply it by pi, and get circumference y, however this new measurement is still one length composed of a specific number of ratios. What changes is the number of lines the line is composed of, as a line is still a line on its own terms.



Therefore in another respect 1 constant line, multiplied by 3.141 would cause a line of length 3.141.

With the original line as 1/Pi of the new line where pi as a length divides the one line into many.

In these respects each line, as a unit defined by its directional qualities is both 1 and Pi and Pi and 1. Pi is a unit of length as one is a unit of length, with both being continuous. All lines as 1 unit of length observes Pi as a unit of length.

As the mutiplication/division of a length requires another length, Pi is a constant length of a line as regardless of the size of a line relative to another line, a line is always a line. — eodnhoj7

No. Pi is not itself a length. It is the number that a length is divided, or multiplied by. The length of the diameter is multiplied by 3.14... to give the length of of the circumference. But 3.14... is not itself a length, it represents a ratio, a relationship between the circumference and diameter which is constant for any circle. You can know that Pi is not a length because it's always the same number no matter what size the circle is.

I am fully aware it is a ratio, but this does not negate it from being a line as well. All lines exists as x length relative to the lines the are composed of or compose. Each line however as composed of infinite lines or composing infinite lines is 1.


A ratio is the number of times one phenomena fits in another, in these respects we can use a line.

Pi = c/d.


The diameter fits into the circumference 3.141... times; Hence a diameter of one observes a circumference of 3.141... .

The diameter is a determined ratio of parts. To say it is x units, with each unit being composed of further units to infinity, observes the diameter as 1 length composed of x units. However as one length, determined by the number of units composing it, with the number of units further composing it resulting in not just infinite units but a number of units approaching infinity, the diameter can be observed as 1 unit as one 1d line.

The diameter as one fitting into the circumference 3.141... times observes the circumferance as 3.141...

The circumferance, as a length of 3.141, when unraveled, observes a line in itself that is equivalent to a diameter for one circle, with the diameter being a relative radius of another circle.

So a diameter of Pi results in a circle with a circumference of 9.8696

And a radius of Pi results in a circle with a circumferance of 19.739.

In these respects the diameter of 1 results in a circumferance of Pi, hence a line equivalent to Pi where Pi becomes a length.



So the circle fundamentally observes three lengths:

Radius as 1/2 Diameter as 1 line

Diameter as 2 radius as 1 line.

Circumferance as 1 Pi as one line.

So while pi = c/d or c/2r we are left with the circumferance being pi if the diameter is one infinity and the radius is 2 infinities as one infinite.

The circumferance in turn equates to a length which can be applied as both diameter and radius considering both are lengths.

Pi is a length, not just a ratio and alternates with 1 as the foundation of length.

All lines are equivalent to Pi just as all lines are equivalent to one in themselves.

I am fully aware it is a ratio, but this does not negate it from being a line as well. All lines exists as x length relative to the lines the are composed of or compose. Each line however as composed of infinite lines or composing infinite lines is 1. — eodnhoj7

Each line is one line, as an identified thing, a line. But a line is not the number one. Nor is the number one a line, except as a numeral, you might make a line to signify the number one.

A ratio is the number of times one phenomena fits in another, in these respects we can use a line. — eodnhoj7

"Line" has no such definition, which would allow you to say that a ratio is a line.

The circumferance, as a length of 3.141, when unraveled, observes a line in itself that is equivalent to a diameter for one circle, with the diameter being a relative radius of another circle. — eodnhoj7

This assumption is itself problematic. You cannot "unravel" the circumference of a circle. If you took the circumference and made it into a straight line, it would no longer be the circumference of the circle, it would be a straight line. This is why PI has an issue, which makes it irrational, it assumes that a curved line (2d) can be measured as a straight line (1d), as if the circumference of a circle were like a string, which could be cut and laid out in a straight line.

In reality though, a curved line is necessarily two dimensional while a straight line is one dimensional. And, there is an incommensurability between two dimensions, expressed by the irrational ratio between two perpendicular side of a square, which indicates that a two dimensional line, the curved line of a circumference, is fundamentally not a measurable as a straight line. The curved "line" of a circle is fundamentally irrational, and not a "line" at all, because it requires (or assumes as a premise) that the irrational ratio between two dimensions has been resolved, and that a two dimensional line is measurable in the same manner as a one dimensional line. But this is clearly false, the nature of the relationship between two dimension has not between understood, and therefore not resolved.

In these respects the diameter of 1 results in a circumferance of Pi, hence a line equivalent to Pi where Pi becomes a length. — eodnhoj7

To say that a line may have a length which is equivalent to pi, is not to say that pi is a length. It is actually nonsense. It is nonsense because pi has no units of measurement, metres, or centimetres, it is just a value for the "number of times" the diameter goes into the circumference. So to say that a line has the length of pi is nonsense, because no unit of measurement has been specified. And, if a unit of measurement were indicated, we must respect the unresolved (irrational) nature of pi, which would indicate that the exact number of units, or exact length of the line is really undeterminable. This is due to the incommensurability of one dimension in relation to another. A curved line cannot be measured as a straight line.

Pi is a length, not just a ratio and alternates with 1 as the foundation of length.

All lines are equivalent to Pi just as all lines are equivalent to one in themselves. — eodnhoj7

Nonsense. "Pi" is unresolved, irrational, while "one" is resolved, rational. Therefore there is a fundamental difference between "one" and "pi". To say that there is one unit which has the length of pi, is nonsense because it would render your unit as undeterminable. That's fundamentally contradictory, to determine an undeterminable unit of measurement.

I think there's a misunderstanding here: I'm not against 'big picture claims' (Gould is wonderful, as is Darwin!), and I invoked Weinberg and Dawkins not as avatars of 'big picture thinking' but because the specific ways in which they theorize the 'big picture' are severely misguided. Each, in their own way, attempts to assign full explanatory power (in physics and biology respectively) to a privileged ontological stratum so that certain parts of reality are simply reduced to epiphenomena that have no material agency.

That's the point: I'm not at all trying to furnish a 'non-reductionism physicalism' - whatever that might mean - but rather, give full 'ontological rights', if we can speak that way, to all of what is often simply dismissed as medial. The equation of the material with the medial isn't meant to reduce the medial to the material. Quite the opposite: it is meant to expand our understanding of what counts as material. — StreetlightX

What I would call reductive physicalism envisions a unique (but so far only hypothetical) Theory of Everything, usually identified with fundamental physics, that fixes everything in existence. All other theories and explanations, from chemistry to psychology, at best supervene on and approximate this TOE. The TOE thus has a unique status. Its ontology is the only true ontology, and its causality is the only true causality - everything else being illusory and epiphenomenal. With some variations, this is a pretty popular view among physical scientists (especially physicists, natch) and scientifically-minded laymen.

Those who reject this view, but still adhere to a broadly empiricist epistemology, which moreover does not privilege mental phenomena in its explanatory scheme, often stake their position as non-reductive physicalism. But there are different ways that one can oppose the thoroughgoing reductionism that I just outlined. One can reject the premise of a single TOE and propose instead a patchwork of theories that operate in different regimes, scales and domains. (Clearly, these theories cannot be entirely independent of each other, but presumably their interrelationship does not amount to a straightforward top-down reduction.) One can take an issue with epiphenomenalism (and here too there are different options). You seem to be rejecting the primacy of some fundamental physical ontology and instead insisting on a multiplicity of coequal ontologies.

I am sympathetic to this view, but I might be coming to it from a somewhat different direction, one that deemphasizes ontology in favor of epistemology. To my mind, ontology is theory-dependent.Theory comes first, and whatever entities it operates with, that is its ontology.

The definitions you argue are correct under standard axioms of mathematics. The problem, as axioms, is that they are subject to a multitude of fallacies: authority, bandwagon, no true scotsman (pseudo fallacy for some), straw man (the axioms form a position not previously held), red herring (each axiom diverts to another axiom), etc.

The axioms are determined as true because of the arguments, as strucutures, which stem from them. These argument/structures, in turn are justified according to there symmetry with symmetry being the replication of certain qualities/quantities that show a common bond.

All axioms, therefore, are composed of further axioms, and there are infinite further axioms considering all axioms are justified according to there replicative symmetry. Instead of the word replication, one may use the word "mirroring" or "recursion".

1) Each line exists because of its directional qualities. It's quantifiable nature is inseparable from its direction. All empirical phenomena, as the premise for quantity, exist because of the directional nature in time. All quantity exists because of time, hence it directional.

2) A ratio, as how many times a phenomena can fit into another phenomena, with all phenomena as directional due to time, necessitates that ratio as existing as linear. How many times 3 lines can fit into one still necessitates the three lines as 1. The same applies for how many time 3 lines can fit into 6 lines as two lines.

3. The circumferance unraveled into a straight line, as 3.141 Diameter as one line, is still a length through the 1 diameter as 3.141... .Pi is also transcendental number with any line as Pi necessiting all lines as infinite. This is symmetrical to further definitions of the line as infinite between 0d points.

4. A curved line can be composed of infinite 1d lines as quantum angles, a curved line is multiple straight lines as an approximation of the straight line. The line exists because of its directional qualities, and the curved line exists if and only if there are Euclidian axioms, with the Euclidean axioms necessitating the line as having a directional quality as point directed to point..

5. Pi as a line observes the line, at minimum as three dimensional where it is three directions in one, with the fractal nature observing infinite directions through these three. The line can exist as:

A. 1 line
B. 1 quantum angle.
C. 1 quantum frequency as multiple angles
D. Points A,B,C as individuating (multiplying/dividing) through eachother, into infinite directions reference itself back to a circle.

***due to lack of diagrams, I may have to expound on this point further.

6. To say pi is a length is not nonsense, considering all lengths are premised in a relation of parts. 1 unit relative to another unit is the foundation for all length, and this in itself leads to an infinite regress where 1 as a unit is one as a length. Pi as a length is composed of units already, where 1 length can be argued strictly as 1. If the diameter is 1, then the circumferance is of a length equivalent to Pi. It is not a problem in math but rather a problem in establishing units of measurement.

7. If the curved line of a circumferance is not as measurable as a straight line, then Pi is wrong because the measurement of the circumferance and diameter/straight line cannot form a ratio.

8. The curved line of a circle as irrational, neccessitates a continuum in that it is not finite. A line a 1 unit is equally irrational as a continuum.

9. Two dimensionality is opposition as contradiction, where what is "even", effectively is without boundary as no center source gives balance, and therefore unit to the number. All even numbers, as premised in 1 as a medial point, is an opposition of medial points necessitating an inherent seperation. 2 is the beginning of any form of multiplicity where a structure cannot be observed, considering all structure is dependent upon an inherent form of unit as premise in the odd number always having a center medial point which gives balance to the number.

10. The number of times a diameter goes into a circumferance necessites the circumferance as Pi. Pi is 1 line as one lemgth where 1 (diameter) and Pi (circumferance) are interchangeable. All diameters act as pi, amd we can observe the Pi replicates itself into further circles as further circumferance. 1 and Pi are strictly interchangalbe lengths relative to context, and act as foundational measurements.

11. Pi is transcendtal, as it is continuous, and as a foundational measurement give premise to recursion as an element within math, logic, science, etc.

The definitions you argue are correct under standard axioms of mathematics. — eodnhoj7

I don't believe that there is a standard axiom of mathematics which states that pi is a line, or a length. If there is, maybe you can produce it.

2) A ratio, as how many times a phenomena can fit into another phenomena, with all phenomena as directional due to time, necessitates that ratio as existing as linear. How many times 3 lines can fit into one still necessitates the three lines as 1. The same applies for how many time 3 lines can fit into 6 lines as two lines. — eodnhoj7

That something is linear doesn't mean that it is a line, it means that it can be represented by a line. A thing, and its representation are two distinct things. If something is represented by a line this does not mean that it is a line. You argue by equivocation.

7. If the curved line of a circumferance is not as measurable as a straight line, then Pi is wrong because the measurement of the circumferance and diameter/straight line cannot form a ratio. — eodnhoj7

It does not necessitate that pi is wrong, it necessitates that pi is irrational. I could argue that being irrational is a case of being wrong, if I argued by equivocation like you. It cannot form an intelligible ratio, that's what "irrational" signifies, it's a ratio which has been determined as real, and existent, but which is unintelligible.

8. The curved line of a circle as irrational, neccessitates a continuum in that it is not finite. A line a 1 unit is equally irrational as a continuum. — eodnhoj7

I don't understand this, it appears as nonsense. Why do you assume a continuum? That assumption appears to be unwarranted.

10. The number of times a diameter goes into a circumferance necessites the circumferance as Pi. — eodnhoj7

This is nonsense. how do you think that "the circumferance [sic] as Pi" is necessitated?

The axioms of mathematics are still subject to the fallacies observed, thus negating them as a single stand alone quality with the exception of the proof of these axioms under the frameworks through which they exist. Proof is structure as framework, ie Proof is existence.

You are correct there is no standard axiom in math, that observes Pi as a line (let alone a length), however this not negate the principle the axiom is possible, therefore must exist given a continuum of further axioms.

1. Something that is linear is a line, even the linear movement of a particle from point A to point B exists through a line from point A to point B. A line is a localization of directed movement in 1 direction. A curved line, as an approximation of a straight line, can be constituted as infinite straight lines composing and composed of infinite angles.

2. Pi is transcendental and gives both proof and framework, as a number, that numbers exist through continuums. All lines exist as infinite continuums as well. A line can be both a quantity and quality. So can a circle and point. Numbers as spatial qualities have a trifold nature, due to there directed capacity where no number can exist unless directed to another number.

3. The curved line as a continuum observes the curved line as the continuous projection of 0d points (no form) as a line (directed movement as form). All lines and circles are composed of infinite 0d points, necessitating the line and circle existing as not just continuums but having inherent directional qualities as well.

A line may exist in 1 direction relative to another direction (line). A circle may be observed as going in all directions as one direction.

4. The circumference as Pi is necessitated if Pi = C/D and D = 1. I explained this already, multiple times.

What I would call reductive physicalism envisions a unique (but so far only hypothetical) Theory of Everything, usually identified with fundamental physics, that fixes everything in existence. All other theories and explanations, from chemistry to psychology, at best supervene on and approximate this TOE. The TOE thus has a unique status. Its ontology is the only true ontology, and its causality is the only true causality - everything else being illusory and epiphenomenal. With some variations, this is a pretty popular view among physical scientists (especially physicists, natch) and scientifically-minded laymen. — SophistiCat

Yeah, part of what I'd like to argue is that this kind of approach to things simply is idealism par excellence, and an insidious one at that, insofar as it couches itself in the language of the ‘physical’, despite being a metaphysical (in the pejorative sense) chimera through and through. It always amazes me that those who hew to this kind of view don’t recognise just how shot-through with theology it is. And I don’t mean this as a cheap-shot (like ‘oh science is just the new religion'), but in a properly philosophical key: it shares with theology its ‘emanative’ logic wherein, to botch Plotinus, everything flows from the One and returns to the One - and where the ‘flow’ is just so much detritus and debris. What you call reductive physicalism mirrors, exactly, ancient theological tropes and, from my perspective, is more or less indistinguishable from them.

You seem to be rejecting the primacy of some fundamental physical ontology and instead insisting on a multiplicity of coequal ontologies.

I am sympathetic to this view, but I might be coming to it from a somewhat different direction, one that deemphasizes ontology in favor of epistemology. To my mind, ontology is theory-dependent. Theory comes first, and whatever entities it operates with, that is its ontology.

I perhaps wouldn’t say ‘co-equal ontologies’: my basic intuition is that ontology ought to be dictated by both the things and what we want to know about them, as it were, and that both are subject to change. A dynamic, pluralist ontology, maybe, one attentive to historical currents and issues of scope, scale, and interest, but one still with synthetic ambition. The philosopher Reza Negarestani probably put it best:

"We can generally investigate the space of the universal through particular instances or local contexts. But once we carry out this investigation through the synthetic environment that the interweaving of continuity and contingency create, we can arrive at very interesting results. Looking at the space of the universal, through particular instances or local contexts is in this sense no longer a purely analytical procedure. It is like looking into an expansive space through a lens that does not produce zooming-in and zooming-out effects by simply scaling up and down the same image but instead it produces synthetic and wholly different images across different scales of magnification. It then becomes almost impossible to intuitively guess what kind of conceptual and topological transformations the local context—a window into the universal— undergoes as it expands its scope and becomes more true to the universal”. (Negarestanti, Where Is the Concept? [pdf])

But these are very general methodological remarks that are perhaps not quite to the point. I aver to it because I’ve long had a suspicion that the distinction between ontology and epistemology is not a particularly fruitful one, and that both are abstractions from a more general question about how we go about conceptualizing phenomena, with concepts being reducible to neither side of the epistemology/ontology divide. To bring this back to the OP, one of the reasons I think this, is because this approach is itself dictated (I like to think) by the necessity of avoiding what I see as idealist approaches in which the world is made to ‘pre-fit’ certain a priori conceptions of it, or else follow from some eternal, God-given rules from which everything else is just epiphenomena, as with what you referred to ‘reductive physicalism’.

Agree with the above.

1. Something that is linear is a line, even the linear movement of a particle from point A to point B exists through a line from point A to point B. A line is a localization of directed movement in 1 direction. A curved line, as an approximation of a straight line, can be constituted as infinite straight lines composing and composed of infinite angles. — eodnhoj7

The problem here is that under a strict definition of "line", the line from point A to point B must be straight, one dimensional. If there are any angles in that course between A and B we are no longer talking about a line, we are talking about a multitude of different lines at angles to each other. If we try to resolve this issue by changing the angles into curves, and claim that we have one curved line instead of many lines at angles to each other, this is not a real resolution. What we would be doing is hiding the multitude of different lines behind the illusion of a curved line. But a curved line is really not a line at all, so that "hiding" is really a matter of deception.

Pi is transcendental and gives both proof and framework, as a number, that numbers exist through continuums. All lines exist as infinite continuums as well. A line can be both a quantity and quality. So can a circle and point. Numbers as spatial qualities have a trifold nature, due to there directed capacity where no number can exist unless directed to another number. — eodnhoj7

I can see how a line is a continuum but I cannot see how "numbers exist through continuums". Numbers appear to reveal the essence of discreteness by referring to individual units, and discreteness is the converse of continuity. So I really do not see how "numbers exist through continuums", as they are based in the concept of the discrete.

1) There is not a strict definition to a line, or anything for that matter, except through the framework built around it.


2) A line can be both composed of angles (frequency) and exist as an angle within itself without contradiction considering all angles set the premise for size.

For example I may have a frequency of x wavelengths in y length. The frequnecy can ve observed as the repitition of angles.

Now the line appears as a frequency. However if I observe is relative to a much larger angle or frequency, and use that new form as the center point of measurement in which everything is measured against it, then the frequency of x wavelengths and y length "relativistivally" shrinks into a line.

The line, as a unit of relation, is determined by its size relative to other phenomena.

This applies in the same manner to an angle acting as a line. A 1d line exists because of its projection in one direction, this projection from one point to another observes a form of condensation where any phenomenon approaching point 0 (like the number 1) shrinks or turns into a fractal. For the line to shrink would require a previous expansion elsewhere as condensation is a form of shrinking. This shrinking, can be observed in an angle where the apex observes a point of "condensing" where the angle is a projection. Due to size determining the relative nature of the 1d line, an angle of a fractal degree can be observed as a line

3. Keep in mind one phenomena can appear as another due to size which size being the relation of one phenomena to another and using it as a starting point.

4. 1 exists as a unit, as a unit it must continue to exist through further units. It exist through 2 and 1/2, 3 and 1/3, 4 and 1/4, etc. One effectively inverts into one state, then into multiple states with each of these states being 1 number in itself. This progression of numbers manifests as a continuum as each number, composed from and as a unit of one, must follow that same nature and exist through further numbers. 1 along with all numbers composed of 1 as 1 in themselves must exist through a continuum where 1 and 1n exist through infinities as infinities.

1) There is not a strict definition to a line, or anything for that matter, except through the framework built around it. — eodnhoj7

Yes there is a strict definition of "line". It is a straight, one dimensional, geometrical figure. If mathematics did not have strict definitions which are adhered to, it would be useless due to equivocation.

2) A line can be both composed of angles (frequency) and exist as an angle within itself without contradiction considering all angles set the premise for size. — eodnhoj7

No, if there is an angle, then there are two distinct lines, because a line is one dimensional.

The line, as a unit of relation, is determined by its size relative to other phenomena. — eodnhoj7

As I explained, relations may be represented as a line, in the sense of "linear", but this does not mean that the relation itself is a line, it is merely represented by a line. You still do not seem to have understood this.

4. 1 exists as a unit, as a unit it must continue to exist through further units. It exist through 2 and 1/2, 3 and 1/3, 4 and 1/4, etc. One effectively inverts into one state, then into multiple states with each of these states being 1 number in itself. This progression of numbers manifests as a continuum as each number, composed from and as a unit of one, must follow that same nature and exist through further numbers. 1 along with all numbers composed of 1 as 1 in themselves must exist through a continuum where 1 and 1n exist through infinities as infinities. — eodnhoj7

No, the progression of numbers does not manifest as a continuum, it is a succession of discrete units. This fact is exemplified by your description referring to "states". If each number represents a different state, then there is a progression of different states, without an active "change" between the states. But that change is necessary to explain why one state is different from the next, and provide continuity between the states. Without the "change" between states, there is no continuity and no continuum. With the change between states, there is a separation and discontinuity between states. Either way, the states are not a continuity.

1. The definition is subject to the framework which proves it. If memory serves in non Euclidean geometry a line is two points on a sphere. Axioms are determined by the frameworks which comes from them and the foundations of mathematics are not universally agreed upon.

The definition of the line is determined by the proofs which follow it, necessitating all axioms as subject to equivocation in light of multiple proofs observing different properties. The agreement of what constitutes a proof is subject to bandwagon and authority fallacies as group agreement determines the nature of the proof.

2. So a line cannot change to a point relative to a much larger line? Geometric forms are determined by the framework of reference, which through the nature of the Monad (point, line and circle), is all forms as size through relation is determined by degree but most specifically quantum degrees (if one gives thought to the nature of fractal degrees). The degree, as one line relative to another, is the foundation of all size.

A line as infinite points can be observed as infinite lines.

3. If a line as infinite points is composed of infinite lines, the line is a continuum of relations...you habe not seem to understood this or much of the above argument for that matter.

4. A succession of units is a continuity of units, from which the word continuum is derived. Look it up in a thesaurus if you don't believe me.

5. Each number is a state of progressive relations.

One state of one, is continual division: 1/1, 2/2, 3/3, to infinity. 1 is a divisive function based upon this continuous nature. Infinite change is no change for change is inversion of unity/multiplicity with continual inversion existing as one continuum.

1. The definition is subject to the framework which proves it. If memory serves in non Euclidean geometry a line is two points on a sphere. Axioms are determined by the frameworks which comes from them and the foundations of mathematics are not universally agreed upon. — eodnhoj7

In non Euclidean geometry, the parallel postulate is negated. This alters the understanding of a "plane" which is a two dimensional construct, from the Euclidean understanding of a plane. It does not change the definition of "line" (1d), it changes the way that one dimension is related to another dimension, as a plane. It is a different definition of "plane".

That one dimension may be related to another dimension through various means (different geometries), and the correct way has not been firmly established, supports my claim that there is a degree of unintelligibility to the relationship between one dimension and another.

2. So a line cannot change to a point relative to a much larger line? Geometric forms are determined by the framework of reference, which through the nature of the Monad (point, line and circle), is all forms as size through relation is determined by degree but most specifically quantum degrees (if one gives thought to the nature of fractal degrees). The degree, as one line relative to another, is the foundation of all size.

A line as infinite points can be observed as infinite lines. — eodnhoj7

No, as I explained earlier, an infinite number of 0d points cannot construct a 1d line. A segment of line is what lies between two points, the medium between points. There is a fundamental incompatibility between 0d and 1d which makes it impossible that a line is composed of points, it is composed of line segments which are marked by points. 0d provides absolutely no spatial extension, while 1d "line" implies spatial extension. Contrary to what you claim above, a line and a point are fundamentally incompatible and one cannot be reduced to the other.

3. If a line as infinite points is composed of infinite lines, the line is a continuum of relations...you habe not seem to understood this or much of the above argument for that matter. — eodnhoj7

It's not that I don't understand your argument, but that I reject it as invalid. A point marks a place on a line. A line is not made of points. That is your invalid assumption, and why I reject your argument.

4. A succession of units is a continuity of units, from which the word continuum is derived. Look it up in a thesaurus if you don't believe me. — eodnhoj7

A thesaurus? Continuous means unbroken, uninterrupted, connected. A unit is an individual thing, bounded and complete. Therefore an interruption is implied between one unit an another. When you say that a "succession of units" is continuous, "continuous" is predicated of "succession". But that such a succession (the activity of one succeeding the other) is continuous is just an assertion. There is nothing inherent within a multitude of units to validate your claim of continuity. Nor is there anything inherent within the concept of succession to validate your claim that a succession is continuous. Therefore you have simply predicated "continuous" of "succession", for absolutely no reason, other than to produce an argument from this axiom. That's begging the question.