Select Tractate Abstract Introduction Contents The Error of Zeno The Error of Aristotle The Error of Boethius The Error of Copernicus The Error of Leibniz The Error of Kant

---

The War & Peace of a New Metaphysical Perception : Book 1
Resolving Paradoxes of the Distant Past - An Alien Conversation

Tractate 1 : The Error of Zeno

490 BC Zeno - The Error of: Physical Distance - a new perception 2000 AD



The Error: The paradox of Distance: The System is filled with increments of distance
The perception: Zeno moves our perceptual understanding of the system into that of being a system filled with both multiplicity and seamlessness. As such, multiplicity and seamlessness, with the help of Zeno, now have a location within which they can be found. However, the understanding regarding the role of multiplicity and seamlessness as well as the understanding regarding the interrelationship between multiplicity and seamlessness not only remain in a state of confusion but even more disconcerting, the existence of such a interrelationship is not recognized as a significant aspect of the ‘larger’ system.

It is this state of confusion which will be specifically addressed within this tractate.

Contents:

Part I: The Paradox of seamlessness and multiplicity
Introduction
Zeno’s paradoxes
The scholarly confusion regarding Zeon’s Paradoxes:
Zeno’s paradox of space/distance:

Part II: Resolving the issue with a new metaphysical perception
Zeno: The appearance of the ‘real’ and the ‘real illusion’
A ‘New Metaphysical Perception’ regarding Zeno’s paradox:
Reversing perceptions – counter view
The point – individuality
The ‘real’ and the ‘real illusion’ illustrated
Working backward to Zeno:
Zeno’s Paradox of Motion revisited
The Greek concept of increments
Calculus is but a tool – it does not eliminate what is
Incrementalism and the Individual
Concrete/Physical Functionality
Removing the physical while leaving the abstract intact
The truth ‘I exist.’ vs. the truth ‘You exist.’
Abstract Functionality
Being a Part of ‘Being’ is not a new idea
Zeno Himself Says It:
The multiplicity of individuality:

Terms/concepts:
Abstract
Abstract Functionality
Concrete
Concrete Functionality
Incrementalism
Illusion
Multiplicity
Real
Real Illusion
Seamlessness
Silent conspiracy of collusion
Singularity of location
Totality/Whole

Part 1: Zeno – The Error of Physical Distance

Introduction:

Zeno: So near and yet so far
Faltering on the brink of understanding the nature of man
Zeno is where the perception of physical distance (Physical distance: 1. distance found ‘within’ the physical, 2. distance subject to the characteristics of multiplicity, 3. distance subject to the parameters of time and space) split from abstract distance (Abstract distance: 1. distance found ‘within’ the abstract, 2. distance subject to the characteristics of seamlessness, 3. distance subject to the parameters of timelessness and the absence of space). Zeno, and for that matter philosophers throughout the past two thousand five hundred years, were not aware of what it was they were on the verge of understanding. The understanding eluding philosophers was not to reveal itself until after Einstein and his concept of ‘relative’ time was verbalized. Even then, even with the concept of ‘relative’ time being verbalized, the potential understanding regarding the relationship of ‘being’, ‘Being’, and being (vb) (1. ‘being’: individuality, individual knowing. 2. ‘Being’: the whole being (vb): action, process/reality) was not to be immediately understood.

And why would understanding the relationship of ‘being’, ‘Being’, and being (vb) not be understood when Einstein revealed the concept of relative time? It was not understood because philosophers had proclaimed the demise of Metaphysics and having done so, buried Metaphysics deep within the most inaccessible realms of the philosophical subconscious. As such, the tool needed to understand the concept of individuality/‘being’, the whole/‘Being’, and action, process/reality/being (vb) was to languish until the time when Metaphysics was once again brought forth from the dark sub-sub conscious realm of philosophy. After all Metaphysics is by its most primal definition, the understanding of fundamental, universal, truths and their interrelationship in the active sense (Question: What is ‘active’ sense? Answer: The ‘active’ sense refers to how the agreed upon universal truths interact with each other, affect each other) of their coexisting as opposed to the previously perceived passive sense (Question: What is ‘passive’ sense? Answer: The ‘passive’ sense refers to the simple existence of the universal truth without regard to the actions they ‘affect’ upon each other.) of their coexisting.

And where does all this ‘being’, ‘Being’, being (vb), active, passive, demise of Metaphysics, Metaphysics resurrection, incrementalism, abstract functionality, concrete functionality, ad infinitum begin? It begins with Zeno because Zeno expressed ‘a’ good point from which we can begin the discussion. Zeno verbalized the long and arduous task of understanding the development regarding the technicality of a radically new metaphysical perception. Zeno initiated a discussion regarding the multiplicity of distance vs. the seamlessness of distance, which, after twenty-five hundred years of philosophical debate, has lead us to the development of a new metaphysical perception.

It was Zeno who established an excellent ‘beginning’ point from which the most primal understanding of the universe, our home, could begin. It is through the paradoxes of Zeno that we were to learn the difference between the abstract and the physical, the concrete.

So who is this solitary man standing at this point we call ‘a’ beginning rather than ‘the’ beginning of the journey traveled by this thing we call humanity, this thing we call ‘a’ human?

There were many Zeno’s in Greek history. This Zeno is Zeno of Elea. This man is like you and I, a simple human with a simple idea which when added to ideas, perceptions, emerging over the next twenty-five hundred years would create a metaphysical picture capable of answering three questions which were to trouble our specie since time began: ‘Where am I?’ ‘What am I?’ And, ‘Why do I exist?’

In order to begin we must know what this man called Zeno had to say.

Zeno’s paradoxes describe a puzzle regarding the concept of ‘actually’ passing ‘through’ distance as opposed to ‘being unable’ to pass through distance. We might better describe the paradox as simply a means of illustrating the difference between the concrete and the abstract.

How does one make the leap from a second, a third, a fourth, and finally infinitesimally small quantities of distance to another quantity of distance? Science and mathematics, through Calculus, believe they have answered the question to the satisfaction of humankind. In truth, however, science and mathematics have not addressed Zeno’s paradox. Science and mathematics have just covered up the paradox in order to ward off the annoying ramifications of the paradox regarding actuality vs. perception. This was not a negative action on the part of science or mathematics for it has allowed science to do what it is science is intended to do and that is expand our understanding of the physical. (Clarification. The universal acceptance on the part of science regarding Calculus being the resolution to Zeno’s paradox, allowed science the means of ‘moving on’ with its intended function, which is to observer the physical universe, observe multiplicity itself. It was philosophy’s function to examine seamlessness but because philosophy could not resolve Zeno’s paradoxes of motion, philosophy followed the lead of science and mathematics and declared Calculus to be the solution to Zeno’s paradoxes. This was philosophy’s error not the error of science and mathematics.)

The paradox of space and time is not solved by the limits of Calculus. Calculus simply becomes a tool, which allows us to move on with out lives and leave the paradox behind, unsolved.

Zeno was on the verge of understanding the nature of man and incremental aspects of reality. Zeno, however, fell short of his goal. Zeno did not make the necessary leap needed to solve his paradox. Science through mathematics thought it made the leap but in fact it did not. Science using the language of mathematics only swept Zeno’s paradox under the rug. As such, Zeno’s paradox remains and until it is rationally understood, we, humanity, will continue to remain as we are mentally and spiritually confused, perplexed, mystified, empty… Until we resolve Zeno’s paradox, we, humanity, will continue to act as we do, saying one thing and doing another.

To place such a heavy emphasis upon the correlation of the solution to Zeno’s paradox and the change in human nature would seem to be a ludicrous parallel. But resolving Zeno’s paradox holds the key to understanding our reality, understanding a new metaphysical perception, understanding why we exist.

One cannot ignore the impact ideas, perceptions, have had, do have upon actions we as individual, we as a specie initiate towards our own selves, our environment, our specie. This past history of action is not to be taken lightly for we are about to venture into space and this in turn means we will not only continue to impact our own selves, our own environment, and our own specie, but we are about to impact environments that are not our own. We are about to affect other species throughout space, a region we presently call ‘our’ universe.

The concept of ‘falling short’ is not a failing of Zeno; rather it is a part of our make-up as specie. We have a difficult time being what we are not and one thing we, as a specie, are not, is being capable of perceiving what lies beyond our ability to perceive.

This inability, this limitation, is the very reason one must never accept any model we develop of a universal philosophy as a fact, as an absolute, as ‘the’ model. Whatever universal philosophy we decide or decide not to develop must always have a label attached to it reading:

‘A Universal Philosophy’ - as best we are able to determine based upon our perceptions ‘today.’ A universal philosophy must never be taken to be an absolute for there are no such things as absolutes. There are only perceived absolutes, which we, humankind, attempt to define based upon perceptions we develop through our limited means of observation, faith, and reason – science, religion, and philosophy.

Zeno’s paradoxes:
Zeno presents us with our first graphic glimpse of the philosophical paradox regarding ‘a’ location of the abstract and its functionality as opposed to ‘a’ location of the physical and its functionality.

We always assume the two, the physical and the abstract, are one in the same or if not one in the same, then, at the least, located within the same region, namely the universe. But why is it we consider this to be the case? We assume it is the case because we assume there is ‘one’ location of existence. As such, we do not, cannot, look beyond our assumption that the solution to Zeno’s paradox lies in singularity of location. This concept regarding singularity of location historically leads us to resolving Zeno’s paradox in a paradoxically manner. We have resolved Zeno’s paradox through the process of avoiding the paradox rather than solving the paradox. In essence, we attempt to solve the paradox of motion and distance through the process of denial rather than pragmatism. A pragmatic solution to Zeno’s paradox is the essence of this article. The means by which we find a solution to Zeno’s paradox is through the development of a new metaphysical perception.

With this said let’s begin reevaluating Zeno’s paradoxes by first examining Zeno’s paradoxes.

Zeno

The abstract concept of Distance:
What is it Zeno had to say about distance that leads to the concept of distance being an abstract concept and being a physical concept simultaneously yet independently of each other?

In order to begin we must know a little about what it is this man called Zeno had to say, was thinking.

Zeno’s paradoxes, four paradoxes relating to space and motion attributed to Zeno of Elea (fifth century B.C.): the racetrack, Achilles and the tortoise, the stadium, and the arrow. Zeno’s work is known to us through secondary sources, in particular Aristotle

The racetrack paradox:
If a runner is to reach the end of the track, he must first complete an infinite number of different journeys: getting to the midpoint, then to the point midway between the midpoint and the end, then to the point midway between this one and the end, and so on. But it is logically impossible for someone to com- plate an infinite series of journeys. Therefore, the runner cannot reach the end of the track. Since it is irrelevant to the argument how far the end of the track is- it could be a foot or an inch or a Micron Lotion is impossible. Moving to any point will involve an infinite number of journeys, and an infinite number of journeys cannot be completed.

The paradox of Achilles and the tortoise:
Achilles can run much faster than the tortoise, so when a race is arranged between them the tortoise is given a lead. Zeno argued that Achilles can never catch up with the tortoise no matter how fast he runs and no matter how long the race goes on. For the first thing Achilles has to do is to get to the place from which the tortoise started. But the tortoise, though slow, is unflagging: while Achilles was occupied in making up his handicap, the tortoise has advanced a little farther, So the next thing Achilles has to do is to get to the new place the tortoise occupies. While he is doing this, the tortoise will have gone a little farther still. However small the gap that remains, it will take Achilles some time to cross it, and in that time the tortoise will have created another gap. So however fast Achilles runs, all that the tortoise has to do, in order not to be beaten, is not to stop.

The stadium paradox:
Imagine three equal cubes, A, B, and C, with sides all of length I, arranged in a line stretching away from one. A is moved perpendicularly out of line to the right by a distance equal to l. At the same time, and at the same rate, C is moved perpendicularly out of line to the left by a distance equal to I. The time it takes A to travel l/2 (relative to B) equals the time it takes A to travel to I (relative to C). So, in Aristotle’s words, "it follows, he [Zeno] thinks, that half the time equals its double" (Physics 259b35b)

The arrow paradox:
At any instant of time, the flying arrow "occupies a space equal to itself." That is, the arrow at an instant cannot be moving, for motion takes a period of time, and a temporal instant is conceived as a point, not itself having duration. It follows that the arrow is at rest at every instant, and so does not move. What goes for arrows goes for everything: nothing moves. (Cambridge Dictionary of Philosophy, Robert Audi, Cambridge University Press, 1995)

The scholarly confusion regarding Zeon’s Paradoxes:
Scholars disagree about what Zeno himself took his paradoxes to show. There is no evidence that he offered any absolutions" to them. One view is that they were part of a program to establish that multiplicity is an illusion, and that reality is a seamless whole. The argument could be reconstructed like this: if you allow that reality can be successively divided into parts, you find yourself with these insupportable paradoxes; so you must think of Reality as a single indivisible One. (Cambridge Dictionary of Philosophy, Robert Audi, Cambridge University Press, 1995)

Why is it Scholars disagree about what Zeno himself understood his paradoxes to show? Could it be that Zeno lived in a time void of an understanding, void of a perception, void of the concept regarding a limit to the very size of the physical universe itself? As such Zeno may not have been certain regarding what it was he was trying to say other than wanting to say what he did simply because he felt it had to be said, so he said it. If such is the case, without his knowing it, he may have initiated the process of understanding, initiated a truly exciting journey for our specie.

So why list these particular paradoxes of Zeno when it is thought he may have outlined as many as forty or more paradoxes. They are listed because they give us a flavor regarding what it was Zeno was attempting to resolve.

This then leads us to the more interesting of Zeno’s paradoxes, the paradox of distance ‘through’ space and the paradox of time ‘through’ space:

Space/distance:
Space is a contradictory notion and reality is indivisible, for the opposite claim leads to absurdity. Suppose that reality is divisible. It will be composed either of a finite or of an infinite number of parts. Reality could have a finite number of parts only if the magnitude of the parts disappeared in a finite number of divisions; but this would lose the finite space with which we began, since a finite number of parts without magnitude cannot produce a magnitude. If, on the other hand, reality has a infinite number of parts, the parts will have magnitude or else they will not. If they do not have magnitude, once again we have lost the space with which we began. If they do have magnitude, and we have an infinite number of them, we can construct a space as much larger than the initial space as we please. Hence, we must give up the idea of space, and of a divisible reality.

Space/time:
Time, likewise, is contradictory. Let us suppose three rows of bodies, one row ("A") at rest, and the other tow ("B" and "C") moving in opposite directions. Beginning from the positions indicated in figure one, by the time they are in the same part of the course (figure two), the B’s will have passed twice as many C’s as A’s. (Consider the matter from the standpoint of the B on the right by way of illustration.) hence, it would take twice as long to pass the A’s as it takes to pass the C’s; but it takes B and C exactly the same time t reach the position of A. Hence, double the time is equal to half.



It is these two paradoxes we will examine in detail. It is the unraveling of these two paradoxes which will leads us to the understanding regarding why our present metaphysical system creates concepts such as inclusion vs. exclusion, either/or. It is the unraveling of these two paradoxes, which will leads us to the understanding regarding a new metaphysical system, a non-Cartesian system powered by a Cartesian system. The resolution of Zeno’s paradoxes will lead us to an understanding regarding the new metaphysical system of ‘being’ being ‘Being’ better known as symbiotic panentheism as opposed to our old metaphysical system of either a Cartesian system or a non-Cartesian system.

To understand Zeno’s paradoxes, however, will require us to take the paradox of space/distance and space/time as they come. Since the paradox of space/distance is presented first, we will begin with Zeno’s paradox of space and distance. We will leave the latter, the paradox of space/time until later, much later. In fact, we will not visit the concept regarding the paradox of space and time until we reach the point of Einstein unknowingly making his contributions to our understanding regarding how a Cartesian system drives a non-Cartesian system: Chapter 9, Einstein: The Error of Abstract Time.

Zeno’s paradox of space/distance:
There are, in essence, two types of distances to which Zeno is unwittingly referring. There is Conceptual/abstract Distance and Concrete/Physical Distance. Zeno referred to them as:

‘…part of a program to establish that multiplicity is an illusion, and that reality is a seamless whole. The argument could be reconstructed like this: if you allow that reality can be successively divided into parts, you find yourself with these insupportable paradoxes; so you must think of Reality as a single indivisible One.

In essence Zeno is implying ‘multiplicity is an illusion…’, physical reality is an illusion, ‘…that the ‘location’ where the physical, ‘multiplicity’, lies is not the real but rather the real is where ‘multiplicity’ does not lie. In short, Zeno is implying the ‘real’ reality lies in the realm, the ‘location’, of the abstract, the abstract world, the ‘larger’ reality (‘Larger’, ‘smaller’, relative size will be addressed elsewhere.)

If Zeno is implying the realm of multiplicity is not what is real, why didn’t he simply state this as his perception? Let’s answer that question with a question. How could Zeno directly come out and state the concept of the physical, the realm of multiplicity, is an illusion unless he had something else with which to replace this illusion, the realm of multiplicity, the realm of the physical? This illusional realm, the physical universe is the location ‘within’ which we find ourselves existing

Zeno had no other alternative to offer as to what is real if the universe is an illusion and therefore Zeno could not rationally declare the universe, the realm of multiplicity, to be an illusion.

So has anything changed? Absolutely, and that is exactly the point of this work

Functional distance lies in the concrete. It is where ‘multiplicity’ lies. Functional, multiplicity of distance is where we see ourselves existing. Incremental distance is found in the reality of our universe, in the concrete, in the physical, where Kant goes with his concept of a Cartesian metaphysical system known as ‘reality’. Functional distance is just that, functional. (More of that in Chapter 6: Kant: The Error of Cartesian Systems.)

Conceptual distance lies in the abstract. Abstraction is where a ‘seamless whole’ lies. Seamlessness is found in the reality of abstract understanding, a place where Hegel goes with his concept of a foundationless metaphysical system, a non-Cartesian system, the ‘greater’ Reality. (More of that in Chapter 7, Hegel: The Error of Non-Cartesian Systems.)

In this chapter, the focus is upon Zeno and the concept of functional distance/incremental distance/ physical versus conceptual distance/seamless distance/abstract distance. These two concepts, multiplicity and seamlessness, will lead us to an understanding regarding conceptual time and functional time as addressed within the chapter reserved for Newton and Einstein, Chapter 9. The four Kant, Hegel, Newton, and Einstein developed independent perceptions of Cartesian systems and non-Cartesian systems or to put it another way: Kant, Hegel, Newton, and Einstein developed independent perceptions of abstract time - constant distance and constant time - abstract distance.

It must also be noted here, in order to avoid the perception that this discussion of Zeno implies the physical is not ‘real’ - is an illusion, that Zeno may have been alluding to an incorrect perception. One does not necessarily need to make a choice between the physical being what is ‘real’ or the abstract being what is real. Physical existence and abstractual existence could both be ‘real’ simultaneously while only appearing to be alternately real and illusional. For the purposes of this chapter, we will remove the concept of ‘time’ in order to remove the complexity time adds to the equation. We will replace the concept of time when we move into Chapter 9.

When time is removed, both realms, that of the ‘real’ and that of the ‘real illusion’, find themselves to be ‘real’ and ‘real illusions’ alternately, depending upon where one ‘stands’ when referring to each. In short, the ‘real’ and the ‘real illusion’ could both be what is ‘real’ depending upon where one stands as one discusses the ‘realness’ of one to the other.

With the concept of the physical existing ‘within’ the abstract:

When one stands within the perception of the physical, the existence of ‘multiplicity’, it is the physical, ‘multiplicity’, that becomes ‘real’ and the abstract, ‘seamlessness’, becomes a ‘real illusion’.

When one stands within the perception of the abstract, the existence of ‘seamlessness’, it is the abstract, ‘seamlessness’, that becomes ‘real’ and the physical, ‘multiplicity’, becomes a ‘real illusion’.

Now what is the difference between an ‘illusion’ and a ‘real illusion’? An illusion is just that: an illusion. It is not real. A ‘real illusion’, on the other hand, is likewise an illusion but it is more than an illusion. It is ‘real’, and as such becomes a ‘place’, an existence, within which one can literally, not figuratively, ‘go’. A real illusion becomes an actuality of which one can literally become a part. A ‘real illusion’ becomes as much a viable entity as that which is ‘real’. In fact, a ‘real illusion’ is what makes what is ‘real’ real.

On the other hand, if something is an ‘illusion’ it is not ‘real’; it is not an alternative ‘location’ of existence.

Zeno had no idea ‘how’ to convert the illusion from the state of being ‘just’ an illusion into that of being a ‘real illusion’ and it is only by performing this conversion that a ‘real illusion’ becomes a viable location for existence. It is only through the process of understanding how ‘seamlessness’ can exist independent of ‘multiplicity’ that we can logically, rationally, begin a discussion regarding the solution to the paradox of ‘seamless’ motion versus motion of ‘multiplicity’. In essence, we must understand Reality as opposed to reality before we can resolve Zeno’s paradoxes of space/distance and space/time.

Because the distinction regarding independent locations of the abstract and the physical has not yet been undertaken, our understanding of Zeno’s paradoxes, our understanding of life remains as it had been for two thousand five hundred years. Until we resolve the paradoxes of space/distance and space/time so aptly expressed by Zeno we will not advance our metaphysical perceptions and metaphysics will remain a mystery.

Are Zeno’s paradoxes relevant topics of philosophical discussion in our modern day era? Absolutely, for we have yet to resolve them as opposed to having glossed over them through the development of mathematical tools.

So how do we begin the process of philosophically resolving Zeno’s paradoxes? We initiate the process through a rational discussion. We begin a rational discussion addressing the relationship between the ‘real’ and the ‘real illusion’.