Kepler and the Epistemological Distinctions of Modern Science

November 10, 2015




The following report is a kind of advisory sent to some of my colleagues engaged in investigations of Kepler's works. Despite that the content is thus presented in the form typical of such a communication, I have decided to make it publicly available. For the epistemological subject matter is of great scientific importance, and the elucidation of that subject matter in this report is relatively unique- particularly in the sections on the "First Issue" and "Fifth Issue".



Clarifications of Certain Points Regarding Kepler’s Theories and Epistemological Methods


Ian Brinkley






Since becoming acquainted with Kepler’s work The New Astronomy -through the LaRouchePAC class series on that book- I have had some time to ruminate on the methods of investigation which Kepler utilized in that work, as well as on the epistemological principles upon which the various stages of his investigation were based. Over that time period I had, of course, attentively listened to all of the Basement presentations and discussions, and that with particular attention paid to the discussions regarding Kepler’s discoveries. I found, however, that my own thoughts on Kepler’s work would often differ from the points made by others in the course of these presentations- primarily with respect to material from The New Astronomy. This, naturally, led me to consider the points at issue more carefully, but, after doing so, I always found that I only became more reaffirmed in my conviction respecting the correctness of my own understanding. Naturally, I have thought it in the best interest of our commitment to scientific rigor and honesty to raise issue with certain tendencies of discussion concerning Kepler’s work which serve, I believe, only to obscure the beautiful accomplishments of Kepler and the significance of these accomplishments, thereby making them less accessible to people who are eager to learn about them. In this paper I have compiled a few arguments which will hopefully make clear the reasons as to why I disagree with some assertions frequently made about Kepler’s methods, epistemology and discoveries, as well as the relationship of these discoveries to Newton’s work.


This compilation is not intended to be exhaustive, but will, I think, suffice to make the some points clear for now. This paper should be considered as a partner to another paper which I published a few months ago on LaRouchenet titled “Thoughts on the Scientific Import of Metaphor”. That paper was born out of a debate I entered into with a colleague on some of the issues addressed in the following pages. Below I have included a list of the points at issue in their basic formulations which are commonly heard in discussions on Kepler, followed by my arguments of objection. When they were convenient to find, I included links and quotes from the various basement presentations.



First Issue: “Kepler’s vicarious hypothesis is an example of the coincidence of opposites and metaphor.”(Fn.1)


Since the topic of the “Coincidence of Opposites”, or more inclusively “Metaphor”, is one of the most fundamental epistemological tenets of our organization, the refutation -if refutation it is to be called- of this first assertion requires a slightly longer response in order to render clear the distinctions to be made.


The short argument is this: Kepler concluded that at least one of the axioms of the vicarious hypothesis was false.(Fn.2) It was found that the propositions of the theory implied that the eccentricity of the orbit had two values, which is a logical contradiction. He did not try to find a way by which metaphor or the Coincidence of Opposites could be invoked in order to understand how these theoretical propositions were still  true, in some sort of metaphorical way, despite the fact that they were in logical contradiction to the observations.


Now for the long argument.


Legitimate Uses of Deduction and Logic


Due to the vociferous (and justified) attacks by LaRouche on Aristotle’s theory on human knowledge - a theory which states that truthful thinking is rooted in rooted in deduction(Fn.3) - members of our organization sometimes tend to get a little uneasy when they speak about the use of deduction in science. There is no need for this as we will show. Deductive reasoning, or reasoning which is reliant upon the laws of logic, is a valid aspect of the way in which humans understand the universe around them and their relationship to it, despite its significant limitations.(Fn.4)


The three laws of logic which we will point to are as follows: The law of contradiction (which says that any proposition cannot be both true and false), the law of excluded middle (which says that any proposition must be either true or false), and the law of identity (which says that no thing can be itself and something else). From now on I will refer to these laws together as the “Principles of Logic” (abbreviated henceforth as “POL”). As will be seen very quickly and easily, the POL are quite useful in a large number of situations, and are perfectly legitimate for many purposes. For example: Say someone is on trial for a crime. The prosecution attorney asks the defendant “Where were you on January 13th? And who were you with?” If the defendant replies “I was at home with my brother” then it is immediately know to everyone in the courtroom, by the POL, that the defendant is not telling the truth (for whatever reason) if, for instance, it was revealed earlier that the defendant’s brother was out of town that day. The POL have been violated, and because we recognize this, we are able to come closer to the truth in the trial. As another example: The study of geometry is largely reliant on the POL. Say we assume certain values for two related magnitudes in some geometrical construction- magnitude A and magnitude B. If we carry out a mathematical determination of another (third) magnitude (or angle), magnitude C, in the same figure using the assumed value of A as our starting point, then we arrive at some value for C. If we make the same determination of C again, but instead start with the assumed value of B, then we arrive again at the value necessarily implied for C in a different way. If these separately determined values are not equal, then we know, by the POL, that one of our assumed values for A and B are incorrect.(Fn.5) The POL have been violated.


The question then arises: “When we find such contradictions what do we do?” This is a good question because the answer is not as simple as one might expect. There are, in fact, two ways of “solving” logical contradictions.


Two Different Approaches to Contradictions


  • First Approach: Adoption of New Propositions Which Satisfy the POL


By maintaining that no logical contradictions could be permitted into any set of propositions (axiom set), Aristotle implicitly admitted of only one way of “dealing with” contradictions should they be found in a theorem lattice. This bring us to the first way (and only way to Aristotle) in which logical contradictions can be addressed: To modify the propositions (axiom set) which implied the contradictions, by either adding or subtracting axioms, until consistency is established. We see this done regularly in science, for example, through the continual adjustments made to physical theories. By modifying our propositions, we eliminate the contradictions implied by our old ones (since those old propositions no longer exist). As the progress of physical science has shown, this method works very well in certain circumstances.


As a brief example of this: If someone were to say that they love Obama while simultaneously maintaining that they do not love people who wage war and genocide, then, by the POL, their propositions are contradictory since (they must admit) Obama wages war and genocide. They can modify their propositions to make them consistent by saying that Obama is not a person, or by saying that they don't love Obama etc. Thus they eliminate the contradiction by abandoning the propositions (axioms) which implied it, in favor of new ones.


So, again, the first way of responding to propositions which imply a logical contradiction is to demand that the propositions be changed such that logical consistency is attained.


  • Second Approach: Coincidence of Opposites


There is, however, a second way to address propositions which imply logical contradictions. It is called the principle of “Coincidence of Opposites” (abbreviated “CO”). It is also known as the principle of “Metaphor”. In this case, contradictories are said to be “resolved” through a unification within a higher intellectual concept while remaining contradictories from the logical standpoint (that is, by the standards of the POL). That is to say, that two separate things, even things which are in diametrical logical opposition to each other, or which logically preclude each other, can both be considered as simultaneously true (in contradiction to the POL) by virtue of an associative concept which supersedes the confines of logical relationships.


It should be re-emphasized again that, even when mutually exclusive propositions are said to be unified by the principle of the CO, they remain mutually exclusive when considered logically. This is altogether different from the way in which contradictory propositions are dealt with by the first method listed above- namely, the method of axiomatic modification. For when axiomatic modification results in a new self-consistent theorem-lattice, the contradictions which existed in previous (since abandoned) theorem-lattice no longer exist.(Fn.6)


As an illustration of this principle, which seems to be strange when described in words (as above), let’s examine a case in which the mind, in order to comprehend what it is presented with, is clearly beckoned to utilize the principle of CO/Metaphor.(Fn.7) We will then find it to be not so strange, but very familiar.


Here we have the first sonnet from William Shakespeare's collection. Let's read it.


From fairest creatures we desire increase,

That thereby beauty's rose might never die,

But as the riper should by time decease,

His tender heir might bear his memory:

But thou contracted to thine own bright eyes,

Feed'st thy light's flame with self-substantial fuel,

Making a famine where abundance lies,

Thy self thy foe, to thy sweet self too cruel:

Thou that art now the world's fresh ornament,

And only herald to the gaudy spring,

Within thine own bud buriest thy content,

And, tender churl, mak'st waste in niggarding:

 Pity the world, or else this glutton be,

 To eat the world's due, by the grave and thee.


If you haven't already made a judgement as to which line has the logical contradiction which best beckons the utilization of the CO then think about it a little longer before moving on (this is better than just saying it immediately).


Ok. Now, we see that there is a logical contradiction in line seven(Fn.8): Surely it is possible to have a famine near an abundance, that is not a contradiction. But to have an famine precisely where (or in the same subject in which) an abundance lies is a logical contradiction.(Fn.9) By the POL we found an inconsistency. Now, Aristotle would have demanded that Shakespeare change this line such that the propositions therein would satisfy the POL!(Fn.10) But Shakespeare was smarter than Aristotle; he realized that the concept in his mind which was intended to be conveyed to his audience could not have been communicated in any other way than the (logically contradictory) way in which he wrote it. (Try and you will surely fail). What's more, if we understand Shakespeare’s meaning, we see that the concept itself is the conjoining of the contradictories- it has no existence otherwise. The two contradictory propositions are unified in the mind through the CO, a metaphorical concept, even while they remain contradictory when subjected to logical scrutiny.


So, the second way of responding to propositions with logical contradictions is to identify a metaphorical kind of concept in which the contradictories are unified while remaining contradictory to logic (as opposed to demanding that the propositions are changed such that logical consistency is attained).



Comparison of the Two Different Approaches to Contradictions by Examples


For further clarification, let us examine a few different situations in which logically inconsistent propositions are found, and compare how we might address them on the basis of the two different epistemological approaches outlined above.


  • Say you lose your house key and then ask your roommate if he knows where it is. He says that it is on the living room coffee table and on the kitchen counter. Obviously these propositions violate the POL. What do you do? Should you use the second approach -the CO- and try to generate a higher intellectual concept in the mind of how your housekey might be in both places in some metaphorical way? No. You should resort to the first approach: demand that he provide you with new propositions (new information on where your key is) which do not violate the POL so that you can get to work!  

  • Next, let's say you read Keat’s “Ode on a Grecian Urn” and finish the last lines confronted by “Beauty is truth, truth beauty…”  The two different words have different denotations and thus the statement is in violation of the POL. What do you do? Do you take the first approach by demanding that Keats change the propositions in this line to satisfy the POL? Do you rewrite the line such that it has no contradictions with something like “Beauty is beauty, truth truth...”? (Aristotle would be proud). Perhaps you should change the denotation of the word “beauty” such that truth=beauty and then substitute the alternative word equivalents back into the statement thus rendering: “Beauty is beauty, beauty beauty…”?  No, no. This won’t do. The first method won't work here. You would rather adopt the second approach, and allow yourself to be led to understand how it is that these two things, which you normally consider different from (or opposed to) each other in your experience, are also equal, their equality and difference being conjoined in a deeper unity- a unity which can be accessed through metaphorical reasoning- only through the CO.

  • James Clapper states, in testimony before Congress, that the NSA does not intentionally collect any private data from unknowing citizens of the USA, but, later, he reveals that he was the one leading the program to do exactly that. This is a clear violation of the POL and we have a contradiction. Which approach should we adopt? Should the congress adopt the second approach (that of the CO/metaphor) to address the contradictions and interpret Clapper’s propositions as meaning that the NSA somehow, metaphorically, does and simultaneously does not knowingly collect private data, and thus forgo a perjury charge? No. The first approach should be taken to satisfy the POL: The congress should demand a set of propositions from Clapper which have no contradictions- either he did, or did not know about the spy program. Clearly, if the congress were smart enough to understand the POL then James Clapper would be sitting in a prison cell right now.

  • You hear Shakespeare admonish his friend thus:  “Profitless usurer, why dost thou use so great a sum of sums, yet canst not live?” Now, since a usurer, by definition, is someone who lends out money at unreasonably high interest, a “profitless usurer” is a contradiction, since, if the money lender isn't even turning a profit, his interests can’t be exorbitant. This is a violation of the POL and therefore represents a contradiction. First or second approach- propositional modification for POL, or higher concept with CO/metaphor? First approach: Shakespeare is a fool and we should rewrite his propositions in this sentence to exclude contradictory descriptions of people. No, that won't do. Rather we should take the second approach -adopt the CO- and understand that Shakespeare is accusing his friend of being -precisely- a “profitless usurer”. We understand that the higher concept here employed depends on the union of the propositions as contradictories.

  • Obama says that the United States will support “moderate terrorists” to further the interests of global peace and democracy. Now, the concepts of “moderate” and “terrorist” are in diametrical opposition to each other- they preclude each other in a single subject. Thus we see, by the POL, that Obama has stated a contradiction. Which approach? Should we take the second approach (as we did with Shakespeare’s contradictory description in the previous example) and try to come to understand a more profound truth which Obama is trying to enable us to understand, metaphorically, about these “moderate terrorists”? No, that won’t do. We would rather adopt the first approach and recognize that Obama’s statement proves his insanity and invoke the 25th amendment accordingly.

  • An astronomical theory states that the planets move in circular orbits with the sun at the center, but then it is found out, through observation and calculation, that the distance from the sun to a planet is different at different times of the planet’s year- A contradiction according to the POL. Which approach do we take? Try the second one: The orbit of the planet is, metaphorically, both circular and not circular simultaneously, there is no need to alter the propositions. No, that won't do. First approach: The calculated distances do not correspond to those of a circular orbit, therefore, the orbit is not circular, so change the propositions (theory). Simple enough.



So we see that when we find contradictory propositions, we can either change our propositions and establish logical consistency (first approach) , or we can leave the propositions as they are and seek out a metaphorical resolution (second approach).


Thus we can see that it is natural that in certain cases in which we find contradictories the POL should be used, and in other cases the CO (or metaphor) (Fn.11) should be used. Just as with deductive reasoning, metaphorical reasoning should not be indiscriminately used in human inquiry.(Fn.12)


Kepler's Vicarious Hypothesis


Now that we have clarified the different approaches to addressing contradictions, we now ask the question: Was Kepler’s use of the vicarious hypothesis and subsequent development of a new theory of planetary motion in his New Astronomy an instance of the first or second approach- an instance of resolving contradictions by changing his propositions (theory), or of maintaining his propositions and seeking a way to metaphorically understand the contradictions embedded within them?


What were the propositions with which Kepler was dealing? Kepler was trying to find the eccentricity of Mars’ orbit. After some calculations, Kepler found himself confronted with these two propositions: The eccentricity is A, and the eccentricity is B (and A doesn’t equal B). That is to say, that the eccentricity was found to be two different values- a violation of the POL. (This came as a necessary consequence of the original propositions that the vicarious theory was true in conjunction with the proposition that the calculated eccentricity from observation was also true.)


Now, when confronted with these contradictory propositions, which approach did Kepler take? Did Kepler resort to the second approach and leave these propositions as they were while trying to demonstrate how it could be that -somehow- the orbit really could have two different eccentricities in some sort of metaphorical way?- that the eccentricity really could be both the longer and shorter magnitude simultaneously when considered from the standpoint of the Coincidence of Opposites and metaphor? No. Not at all. Kepler knew that the orbit had only one eccentricity; that two implied eccentricities therefore presented a contradiction; and that a logical resolution needed to be found. Therefore he took the first approach and sought out to change the propositions (find a new theory) respecting the planetary orbit which did not lead to contradictions (as when compared with observations). By doing this, Kepler established a new theory which matched observations in full correspondence with the POL: Elliptical orbits and the Area/Time law.(Fn.13)


Indeed Kepler himself tells us which approach he took: “Something among those things we have assumed must be false. But what was assumed was: that the orbit upon which the planet moves is a perfect circle; and that there exists some unique point on the line of apsides at a fixed and constant distance from the center of the eccentric about which point Mars describes equal angles in equal times. Therefore, of these, one or the other or perhaps both are false, for the observations used are not false.”(Fn.14)


Nothing about Kepler’s procedure (here) contradicts Aristotle’s implicit rejection of the Coincidence of Opposites or his insistence to only utilize theories in correspondence with the POL.(Fn.15) Kepler’s use of the vicarious hypothesis is in no way an example of the CO,(Fn.16) and we are thankful that it isn't, else Kepler would have never discovered the orbits of the planets (or their harmonies later) because he would have inappropriately forsaken the attempt to eliminate the contradictory propositions he was confronted with in order to find a logically consistent theory- this by (inappropriately) contenting himself with the CO. It would have been just as silly for Kepler to use the CO/metaphor at this stage of his investigation as it would have been for you, in our first comparative example above, to try to use the CO/metaphor to interpret the proposition about your housekey that it was truly and metaphorically on on both the kitchen counter and on the living room table.(Fn.17)



Second Issue: “The vicarious hypothesis showed that Kepler needed to go beyond geometry and adopt a physical principle. Kepler’s physical principle was not mathematical.”


Throughout the course of presentations given by the basement, there have been many different points made which serve as elaborations of this general formulation just stated. This has resulted in a multiplication of corollary assertions which are also erroneous in their own right. Thus I will attempt to rectify a number of different points which all have the same general flavor of this second issue within the following treatment.


On the Need for a Physical Principle In Light of the Results of the Vicarious Hypothesis


Take this quote from “Metaphor: An Intermezzo”:

“In this case, this failure was Kepler’s goal, this was the metaphor he created. The only unification, the only resolution [to the contradictions found when using the vicarious hypothesis], lay outside sense-based modeling. The abstract shape of a circular orbit, and the angular rotation of the equant would have to give way to something unseen, and, indeed unseeable: they must give way to Kepler’s hypothesis of universal physical gravitation, and the power of the sun to cause the motion of the planets. Like the previous examples of combining different viewpoints, knowledge only comes from combining the different evidence of two different perceptions. But this time, the resolution does not exist in the domain of any viewpoint, since it cannot be “seen” at all!”


New Paradigm Show 3/18/15 @ about 20 minutes (rough transcript):

“Reflect on where do these conceptions [the circle and the equant] come from? Where does the circle come from? The equant? They come from geometry, the geometry of visual space, of sense perception... He asks if the physical cause of the motions of the planets exist in a system of circles and equants? In the framework sense perceptual concepts? Is science mediated through sense perception? He shows it is not. So he shows that there is nothing you can do in this sense perceptual geometry of circles and equants that can even model or reflect the actual motion of the planets….So he shows that there is nothing you can do in this sense perceptual geometry of circles and equants that can even model or reflect the actual motion of the planets….Here he shows an incommensurability between the nature of physical cause and sense perception. Nothing in the framework of sense perception can ever even reflect or model the actual nature of the planetary motion, or the nature of the cause of the motion”


As noted in footnote 13, the consistency of Kepler’s new theory of planetary motion with the observed motions of the planets is in no way dependant upon the addition of a causal factor into his theory. The results of Kepler’s Vicarious procedure demanded(Fn.18) a new geometrical model of the planetary orbit but not a reason why that model is necessary. (Although it is great that Kepler took that question up too, we need to recognize that it is a separate question- Eliminating a contradiction by establishing new propositions is different than providing a reason as to why those propositions should be preferred to any others which might satisfy logical consistency) Thus, a set of axiomatic parameters which the orbits should correspond to was established: elliptical orbits and the area time law. These postulates can be tested against observations, and they always reveal consistency (and this without any consideration of physical cause).(Fn.19)


From this we can see why the quotes about the vicarious paradox requiring something unseeable or non-sense perceptual for its resolution are confused. Also, an ellipse is just as seeable as a circle- it is no more or less a “sense perceptual geometric concept” than a circle. These quoted passages could thus be nothing but confusing.


On Whether or Not Kepler’s Principles are Anti-Mathematical


Now, on the other side of the issue, consider this quote:

New Paradigm 10/21/15

“So what Kepler did instead, was to create something  totally different. He had a physical principle of gravitation, that the Sun caused the planets to move. It wasn’t  just sitting in the central seat watching them as a bystander. He had a physical hypothesis. Not only was it  not based on mathematics, it couldn’t even be expressed  in mathematics. The Kepler problem: If you try to express Kepler’s principle as to where will a planet be on  a certain day, you can’t even solve the math for it exactly. So his approach was non-mathematical. It was anti-mathematical: It was physical. It was metaphorical”


This statement is quite confusing. Firstly, we shouldn’t say that Kepler “had a principle of gravitation” in this context, since, what Kepler called gravity (see quote in the Third Issue below) was not the same thing as his idea of the emanating influence originating in the sun which caused the planet’s circular component of motion. Now, was this idea of the power emanating from the sun and idea which was capable of being “expressed in mathematics”? Why yes, in fact. Kepler stated that the power of this influence on the planets was effective in proportion to the distance which the planet was from the sun. Kepler said that this would mean that the speed of the planet would be in inverse proportion to the distance from the sun, or, said another way Power(or Speed)=(proportionality value)/(distance) or S=c/r. Looks pretty mathematical to me. But, what about the path implied by this force in the sun? Is that mathematically expressible? Why yes, in fact. As mentioned before, Kepler hypothesized that the emanating influence rotates with the sun and thereby produces the circular motion of the planet. Thus, if there were no other forces acting on the planet besides this one, the shape of the orbit determined by this force is defined -mathematically- as a circle (or y=±(sqrt)(r2-x2)if you please).


Now, none of this is to deny the fact that Kepler attempted to provide a non-mathematical cause -a hypothetical physical basis- as to why and how such an influencing force would be brought about; He devotes a whole chapter to the search for such a physical theory- one which would reveal how such a mathematically regular effect might be produced on the planet's motion. But, as said before, this causal concept was not necessary to resolve the contradictions posed by the vicarious hypothesis


This is, of course, is not the whole story. For Kepler didn’t hypothesize only one physical influence which moved the planets in circles (he knew that the orbits were not circular), he also proposed another physical factor which influenced the orbit. This hypothetical factor was created in order to account for the deviations from the circular path (implied by his first hypothesized force) which the planets exhibited through their elliptical orbits. This new force was considered to act like a magnet- by attracting under certain orientations to the sun, and repelling under others. However, this factor was also defined mathematically just as was Kepler’s first one. Since the mathematical characteristics of this force were tailored to provide for the necessary correction Kepler needed to obtain an elliptical orbit, the final mathematical theory respecting this force seemed a bit complex and contorted. But, nonetheless, it was mathematically defined, just as the first force, and it did a good job at filling out the total theory of planetary motion.(Fn.20)


Now that we have shown that both of Kepler’s physical concepts were in fact mathematically formulated, perhaps we should ask the following question: What about the final effect resulting from the confluence of these two forces- was that mathematical? It seems that, again, we must answer in the affirmative. As mentioned before, an ellipse is a definable mathematical entity, (just as much, in fact, as any circle). So, the path of the planet is mathematical. What about the motion? Well, the area/time law is a mathematical law just as much as any other mathematical law of physics. The fact that the law does not permit a determination of where the planet will be on a given day does not make the law any less mathematical. A mathematical law of physics is not required to provide information on future states of a system they describe -many laws of physics don’t and they are no less mathematical because of it- they are only required to be testable (and the area/time law is).


So, we see that both of Kepler’s forces, the resulting orbital shape, and the motion of the planet on that shape are all mathematical. Keep in mind though that this is not a bad thing. It is a good thing- for if Kepler’s astronomical theories did not imply any definite mathematical effects then they wouldn't be testable and we wouldn't be here today. (I do not mean to say, however, that all conceivable things in the universe must have mathematically precise (or even approximately precise) effects in order to be considered as scientifically legitimate concepts. Kepler’s investigation in the New Astronomy was of processes which were mathematical; planetary pathways and motions are things which are intrinsically mathematical- at least to the extent you say anything definite about them.)(Fn.21)


All this considered, we see how to repeat these things about Kepler’s intention to go “beyond the mathematical and sense-perceptual” to resolve the vicarious paradox could only result in confusion. This in turn has a tendency to mystify Kepler’s work, and for this there is no need.



Third Issue: “Kepler Discovered Universal Gravitation.”


The alternative formulation of this point would be “Kepler was the first person to hypothesize that all corporeal substances in the universe share a mutual attraction with each other.”(Fn.22)


In Kepler’s New Astronomy, the motions of the planets are not  hypothesized to be caused by a universally operative force. Kepler hypothesizes that there are two physical factors which influence the planet, thereby producing the orbital motion. One physical factor emanates from the Sun and affects all the planets, the other physical factor is hypothesized as existing in each individual planet (Kepler postulates a magnetic like attraction which operates according to certain mathematical rules based on its position to the sun). Neither of these hypothesized physical influences are what is popularly known as “universal gravitation.”


Sometimes the following quote from Kepler is provided as evidence that he did discover universal gravitation:


“Every corporeal substance, so far forth as it is corporeal, has a natural fitness for resting in every place where it may be situated by itself beyond the sphere of influence of a body cognate with it. Gravity is a mutual affection between cognate bodies towards union or conjunction (similar in kind to the magnetic virtue), so that the earth attracts a stone much rather than the stone seeks the earth. ...wheresoever the earth may be placed, or whithersoever it may be carried by its animal faculty, heavy bodies will always be carried towards it. If the earth were not round, heavy bodies would not tend from every side in a straight line towards the centre of the earth, but to different points from different sides. If two stones were placed... near each other, and beyond the sphere of influence of a third cognate body, these stones, like two magnetic needles, would come together in the intermediate point, each approaching the other by a space proportional to the comparative mass of the other….If the attractive virtue of the moon extends as far as the earth, it follows with greater reason that the attractive virtue of the earth extends as far as the moon and much farther; and, in short, nothing which consists of earthly substance anyhow constituted although thrown up to any height, can ever escape the powerful operation of this attractive virtue.”


This statement from Kepler cannot be construed to mean that he hypothesized universal gravitation. The bolded parts of the quote reveal that Kepler considered the gravitational attraction between the earth and a stone to exist only because these bodies are cognate with each other- that is to say: they are like substances. The Sun, and the other planets might be made of something else which does not attract to the earth as a stone does- Kepler does not venture to hypothesize otherwise. Theories of like substances attracting to each other date back to ancient times, and some were probably popular in Kepler’s time. This quote is clearly an elaboration of such a theory, and this is why Kepler didn't venture to consider the possibility that the same attractive force he was describing in this passage could also be the force which makes all of the planets move around the sun.


Fourth Issue: “Kepler introduced physics into astronomy”


Aristotle expounded a physical theory explaining the planetary motions, and it is plausible that there were at least a few other people who lived between Aristotle and Kepler who also had physical theories of the planetary motions. Kepler made use of different physical concepts in his theory than Aristotle had before him, but that doesn’t make Aristotle’s theory non-physical. It should also be noted that the concept of immaterial forces -originating in bodies and exerting influence on other bodies over distances without any apparent material medium of transmission- was one which had been hypothesized and elaborated upon before Kepler, as by Gilbert, for example, in his works on magnetism. Even Aristotle had a similar (although much more vague than Gilbert’s) concept in which he hypothesized that all the elements naturally tend to attract towards their respective sphere’s in the cosmos.(Fn.23)


The concept of force acting at a distance is a physical concept, but one which is of a different kind than the idea of mechanical interactions which lead to the motion of bodies by contact with other bodies. Whether Kepler thought that the notion of “force acting at a distance” was a legitimate concept in itself for use in physics as Gilbert, or whether he thought that all such forces must be shown as following from kinetic interactions of mechanical contact is not clear to me. Kepler was willing to explain what seemed to be an action-at-a-distance force (from the sun) as arising from the necessary interactions of matter (the planets) with what he called “immaterial species” which he compared to light (something he also seems to consider immaterial) in its diffusion through space- much as we would imagine corporeal matter diffusing through space. But, while Kepler seems to have thus provided, or at least attempted, a hypothetical physical basis(Fn.24) for the force exerted by the sun on the planet, it seems that he sought no physical basis for the second magnetic-like force, and, rather, thought of it in the same way Gilbert thought about magnetic force: a striving tendency acting on one body to another, without the need for any other physical basis to be employed as an explanation for it’s existence. Although I suspect that Kepler might have wanted to find a physical basis for the mathematical character of his second force, he probably didn’t pursue that goal due to the fact that it would be quite difficult, if not impossible, to find such a basis for a mathematical force which was as complicated as the one he proposed in that instance. The extreme difficulty in providing a physical hypothetical basis rooted in kinetic interaction to explain such mathematical regularities is shown by the difficulty in explaining even the simple attraction of objects to the earth- there were many instances of failed theories which were employed for this purpose throughout the centuries.



Fifth Issue: “Kepler rejected the a priori notions of space and time. Newton reintroduced those notions as a fraud.”


New Paradigm 3/18/15 (rough transcript)

“The need to be able to understand this physical cause demanded a new mathematics- calculus. So you see that he went from the investigation of the physical cause, to then develop the necessary geometry and math. Your conceptions of space, time, are not a priori, they come from that physical cause. The nature of time in a planetary orbit is not an equant, it is something which comes from area-time, which comes from investigating the nature of the change of the planet itself. They are secondary considerations, derived from the expression of change governing the motion of the planet. This is a different idea of what science is. Kepler shows us that we must reject these sense-perceptual terms. That the mind can develop conceptions of change which are representative of the principles of change in the universe.


“You see the fraud of Newton- he reintroduces these ideas of space and time as a priori conceptions when Kepler showed that you can't adhere to an a priori sense perceptual conception of the universe. This was the reintroduction of concepts which had already been rejected.”


In this instance, I can see that the disagreement is not with the concept attempting to be conveyed -for that concept, I think, is perhaps one of the most important in all of philosophy- but, rather with what I consider to be the confusing comparison of that concept to the work of Kepler and Newton. The issue, however, is so important that no fault could be found with raising it as an issue -provocative and profound as it is- even if there are differences of opinion. That is what scientific dialogue is all about anyhow.


The short argument is this: Firstly, Kepler did not seem to distinguish the “relationist” or “absolutist” views of space.(Fn.25) However, his theoretical results (respecting the relations of the planets) would have been identical had he made this distinction and taken one side over the other.  Secondly, Kepler’s use of Euclidean geometry in his determination of the planetary relationships and his use of the concept of a causal factor (a force)  show that he never departed from Euclidean geometry or Euclidean notions of space, at least insofar as he considered solely the geometrical relations between the planets.


To say then that “space and time come from the physical cause” is needs to be clarified. What is meant by space? The relations amongst bodies? If so then such statements respecting Kepler’s physical hypothesis should be accompanied by clear statement that the relations implied by that principle do not contradict Euclidean relational axioms. Or alternatively, if “space” here means an absolute medium in which bodies exist and relate to each other, then it should be made clear that Kepler’s physical principle does not imply any other “space” within which the objects which it affects exist other than Euclidean space.(Fn.26) In fact, if we consider what was mentioned before about the mathematical nature of Kepler’s forces, we see that they are tailored to Euclidean space (or relations), for, unless space (or relations) were Euclidean, then the mathematical characteristics of Kepler's forces would not result in the correct orbit.


Despite all this, it seems to me that the intended concept is true: Whatever you may encounter in phenomenal experience, and however you may come to conceive of the rational ordering of the universe, whether it be relational or absolutist, Euclidean or Riemannian, there must be a reason that such orderings are found, there must be some way for the mind of man to come to know why so and not otherwise. These concepts will always partake, more or less, of what Cusa called the intellectual side of our thinking. The principles of change and development which our mind has access to through creative thinking share a common existence with the very principles of change which govern the universe, and hence, all of the rational orderings and perceptible occurrences of the universe.  



The Long Argument


In his De Conjecturis, Cusa elaborates his understanding of the lawful ordering of human thought. His essential conception includes the idea of the four levels of being, or oneness, which mankind has access to knowledge of through the different kinds of thinking. Cusa makes the point that in order for any phenomenal experience to take place (such as sensation), the rational power of the mind must be active, for, without the reason, nothing could be distinguished from anything else, (and thus no distinguished experience would take place). In all of our sense-perceptions, then, we find a rational ordering, which includes distinction (multiplicity), relation (comparison), similarity (equality) etc.


For a long time, a principal method of science has been to hypothesize the existence of a world outside of our sense-perceptions, a world which we can come to understand through rigorous investigation. Contributing to the hypothetical structure of this world have been the rational orderings exhibited in our sense-perceptions- the existence of discrete extensions, the ordering of their relation to each other (space), and the ordering of the changes of their relation to each other (time). Our theories about the constitution and nature of this world are, therefore, extrapolated, in a sense, from our sense-perception. For example, if we look at a book (with sense-perception) and find it to exhibit a certain rational ordering, such as the relationship between its spatial dimensions, we assume that when we turn away, that the book still persists in its existence in a domain outside of our experience, and that, within this domain, the book also exists as an object and maintains the same relative spatial dimensions which it exhibited when we looked at it. Another example: When we observe an object which is moving away from us and becoming smaller and smaller in our field of vision until it is no longer visible, we still imagine that this object exists in the unseen world we hypothesize, and because we hypothesize this unseen world to exhibit the rational orderings we find in our perceptions, we even conclude that the unseen object’s rationally ordered relationship to us is still knowable, - its relative position for example- and we prove this to ourselves by observing the re-emergence of the object into our sensory domain precisely in the way our theory predicted. Because this (our new world) was created using the building blocks of the rational orderings of sense perception, this world “meshes” very well with our perceptual one.


At this point, the concept which we have of the unseen physical world is, as mentioned, purely rational: The space being the rational ordering of objects to each other, it’s time being the rational order of the changes in the relationships between the objects. Since these relationships are, however, not observed (being, as they are, aspects of the unseen world) we must make assumptions about them, for there can be many different ways in which things are rationally ordered.(Fn.27) For example, it may only be possible for objects to be rationally ordered according to the laws of Euclid, or, they may be rationally ordered according to one of the axiom sets of Riemannian geometry. Time, or the changes in the relations of objects, may occur in the same way in different places, or not. Etc.(Fn.28)


That said, let’s look at the following problem. If we establish a rule respecting the lawful ordering of processes in our hypothetical world, then we need to create other reasons as to why we find that law to appear as violated in certain situations. For example: The law of inertia states that all bodies move in a straight line and continue to do so unless acted upon by a force; If we find a body, like a planet, moving in a curved line, then we must provide an explanation as to how the law of inertia is not violated.(Fn.29) How can we do this? It seems that there are three ways: 1.) Resort to a new law or explanation such as by adopting a causal concept like “force” to account for the motion. 2.) Resort to a new characterization of the rational ordering of Space and/or Time such that “curved is the new straight”- as with a Riemannian geometry for example. 3.) Combine both procedures.(Fn.30)


Which method did Kepler use? Well, we see that he used the concept of force as opposed to trying to figure out a new space/time geometry in order to account for the apparent planetary motion- that is, he used the first method listed.


Now we take up the question: Did Kepler’s notions of space and time come from his physical/causal concept? We answer yes and no, depending on the sense with which the question is asked. I would briefly point to Cusa’s De Conjecturis again as providing a useful pedagogy respecting the ordering between sense perception, reason, and the intellect.(Fn.31) The essential point is that causal concepts are, in a certain way, made apparent, or suggested, by the rational ordering we find in our experience or constructions. Thus, to a certain extent, our causal concepts are tailored to our experience and assumptions respecting the rational ordering of nature.


In science we seek out those rational orderings in sense-perceptions or sets of data which seem to enable us to identify a universal causal principle which would make such orderings necessary in those specific circumstances, but which, at the same time, is also not specific to those circumstances, but rather to certain invariant conditions. When we find other effects necessarily implied by such a hypothesized causal principle in different circumstances, we are reaffirmed in our convictions of it’s truthfulness.  


Here is a quote from R.W. Hamilton describing this process:


"And so say I with respect to the observation of phenomena, even when combined with  mathematical calculation: that the visible world supposes an invisible world as its interpreter, and   that in the application of the mathematics themselves there must (if I may venture on the word) be   something meta-mathematical.  Though the senses may make known the phenomena, and mathematical methods may arrange them, yet the craving of our nature is not satisfied till we trace in them the projection of ourselves, or that which is divine within us; till we perceive an analogy between the laws of outward appearance and our inward laws and forms of thought; till   the Will, which transcends the sphere of sense, and even the sphere of mathematical science, but   which constitutes (in conjunction with the conscience) our own proper being and identity, is reflected back to us from the mirror of the universe by an image mentally discerned.  This it is, and not merely the beauty of the mathematical reasoning, nor the practical accordance with phenomena, great and important as they are, which gives the highest value and the deepest truth to the dynamical theory of gravitation.  Do you think that we see the attraction of the Planets? We scarcely see their orbits...


"I [will] touch on...the existence of a scientific faculty analogous to poetical imagination, and the analogies of other kinds between the scientific and the poetical spirit...  


"As to the imagination, it results, I think, from the analysis which I have offered of the design and   nature of physical science, that into such science generally, and eminently into astronomy,  imagination enters as an essential element…to the faculty which constructs dynamical and other physical theories, by seeking for analogies in the laws of outward phenomena to our own inward laws and forms of thought. Be not startled at this, as if in truth there were no beauty, and in beauty no truth; as if these two great poles of love and contemplation were separated by a diametral space, impassible to the mind of man, and no connecting influences could radiate from their common centre. Be not surprised that there should exist an analogy, and that not faint nor distant, between the workings of the poetical and of the scientific imagination..."


Thus, a hypothesized causal principle does indeed “shape”, or determine, the rational ordering (the space and time) of events in our experience and in our hypothesized physical world (that is the very definition of a causal principle). But we shouldn’t leave out that, in another sense, the causal principle we conceive of is also “shaped” by the rational orderings of experience and calculation. (Else, what could the causal principle have as its subject?)


But this is not the whole story with Kepler.


A Distinction


It should be noted that not all hypothetical causal principles -or associative concepts which we utilize for the purpose of putting distinct elements of our universe into knowable relation to each other- are of the same order. Beyond the merely descriptive rational orderings which we might attribute to the world, there seem to be two different qualities of principle which we conceive of in order to provide the reason as to why such rational orderings are exhibited.(Fn.32)


First: Rational/Causal concepts which serve the purpose of “efficient cause”. These concepts, or factors, are utilized in a logical sense- they are utilized to demonstrate why certain rational orderings are necessary outcomes of the action of such factors. The concept of “force” is such a concept. For example: We come to the conclusion concerning the rational ordering of the planets- they move around the sun in certain shapes with certain mathematical regularities. The concept of a causal force is introduced in order to provide the basis upon which the aforementioned rational ordering is logically necessary given the conditions of the system and the presence of the physical factor. These kinds of causal concepts, despite the fact that they exemplify the kind of concepts which Hamilton was describing in the quote above, (despite the fact that they are intuitive concepts existing in a separate cognitive domain than mere descriptive relation), these concepts are, in fact, deductive in nature, or quasi mathematical. Even while they are intuitive, they are only justified through logical -that is, deductive- procedure, because they are hypothesized for the sole purpose of establishing why certain rational orderings are necessary in certain situations. These kinds of causal concepts are thus limited in a certain way- limited in their character to the specific class of phenomena they try to explain (or, alternatively, the effective power they are considered to have). This is the level of thinking which Cusa would call the rational which approaches the intellectual.


Second: Metaphorical/Intellectual concepts. These associative concepts play the most fundamental role in human knowledge. They are not logically or rationally verifiable however, because, by their very nature, they do not relate to their subject in a logically or mechanically direct way. The relationship is metaphorical, or intentional, as opposed to merely rational or even causative (in the sense of efficient cause). Cusa called this the intellectual level of conception.


Kepler’s Harmony


Kepler used this second quality of concept in his hypothesis of “The Solar System” found in his Harmonies of the World(Fn.33): A higher principle which established the Solar System as a unity, a one, as opposed to a group of bodies which just so happen to wind up in positions which allow them to be affected by the same mechanical influence emanating from the sun. The “Solar System” is governed by an intention.


Incredibly, the physical characteristics of the solar system which were not explained by the physical/causal theory of Kepler (or Newton), namely, the relative distances between the planets, were shown to be necessary for the fulfillment of that intention: the establishment of a tempered harmonic ordering of the system.


Again we see that the higher principle determines the rational ordering of the process. There are underlying principles of action, or intention, which necessitate certain forms of rational/perceptible expression based on the contingencies within the world of actuality.


A Concluding Word


Music, art, drama; all the perceptible/rational orderings in these (when competent) submit to the higher principle in their presentation. Compare this to Aristotle who said that the drama should be in “real time”- no manipulation of the rational ordering (space or time) is permitted.


The idea that causative principles -which share a common identity with our own forms of thought- are the things which determine the characteristics of our experience and the hypothesized world of rational constructions, is something to be kept in mind. We seek out new principles which necessarily result in the rational orderings of the quantum domain; will we need to resort to metaphorical or CO concepts to find such principles (based on the mutually exclusive rational interpretations of quantum phenomena)? Or, will such a resolution be made through utilization of some strange new rational orderings such as multiple dimensions or other orderings in other hypothesized domains? Knowledge of the deductively consistent rational ordering of nature is never permanent- it is never completely true. Therefore we ask, what kinds of changes -possibly radical changes- to our notions of the rational ordering of nature await us upon our discovery of fundamentally new principles? What kinds of notions respecting the rational ordering of nature should we dispense with now such that our thinking will be led to discover such new principles? Whatever they may be, it is very likely that the new concepts of our rational picture of the universe will differ radically from our currently held -largely sense-perception based- understanding. Strange as they may be, we trust that the underlying causal principles will be familiar (in a certain sense), or, rather, welcoming- being, as they are, “The projections of ourselves”.






1.) “So in one of this very major works called {The New Astronomy}, Kepler used Cusa's technique of the "coincidence of opposites" in a specific way, to lead to a higher truth, to force people consider, and he then demonstrated, his physical concept. He did this through what's called the "vicarious hypothesis."  In this Kepler asked one question, and he got multiple, different answers; he got contradictory answers.” - Webcast 1/31/15 Also, the LPAC video production “Metaphor: An Intermezzo” (transcript available here : ) The section on the vicareous hypothesis, I dissagree with the opening and the closing paragraphs of that section, which serve, I think, to obfuscate the actual significance of Kepler’s procedure.

2.) For his own words, see the quote a few pages below.

3.) Here is a good link to a discussion of Aristotle’s theory of knowlege (it begins around 25 min)

4.) The limitations of deduction’s validity will not be treated here in depth. I do not pretend to have a full conception which would enable a precise identification of  those limits, but I believe Cusa’s discussion in De Conjecturis is a starting point, and I elaborated my thoughts on it in more depth in a paper posted on LNET a few months ago titled “Thoughts on  the Scientific Import of Metaphor”.  (a paper stimulated in it’s birth by a discussion on the very issue which we are taking up here now).  I think the question is one of the most profound in all science and philosophy.

5.) This is equivalent to saying that the assumed magnitude of A implies a different magnitude for B than we had originally assumed, and visa versa.

6.) Any theorem, contradictory or not, is only a restatement of the original axiom- nothing more. Thus by eliminating the original statement, you eliminate all possible reformulations of that statement, contradictory or not.

7.) In my paper “Thoughts on the Scientific…” I provide more examples like this one, and discuss the concept further, especially as it flows from Cusa’s work.

8.) Also line 8, but we will only examine 7 because the principle of CO is clearer there.

9.) Of course, someone could try to interpret “where” as being in the same room, or something like that, which would make the statement logically consistent, but this is absolutely not what Shakespeare intended- he intended an interpretation containing logical contradiction.

10.) Aristotle implicitly rejected the CO  though his adherence to the idea that the POL were the standards to which all propositions must conform.

11.)In my paper previously mentioned, I demonstrated (in what I think to be a clear way) why the CO per se is a special case of the more encompassing notion of metaphor- although, admittedly, perhaps the most striking and illustrative special case of metaphor.

12.) See my paper on Metaphor where I elaborate a slightly different point- that is, that deductive reasoning is a sort of  limited case of metaphorical reasoning.

13.) It should be noted also that Kepler’s hypothetical forces do not in any way influence the consistency of his new theory with observation. The correspondence of the new theory with observation is completely dependant on it’s mathematical axioms (the ellipse and area-time law)- these were the only features of the new theory which served to establish consistency with observations after the discovery of the inconsistencies of the vicarious theory. The addition of forces into the theory serves to satisfy our desire to move into the direction of causal concepts which are intuitively comprehensible to us- to move beyond merely descriptive hypotheses. But, again, they were not relevant to the consistency of Kepler’s new theory with observation.

14.) Quoted from Kepler

15.) Although, of course, Kepler’s theory contained many elements which Aristotle never used in his theories. But this is irrelevant to the distinction between the CO and POL approaches to addressing contradictions.

16.) At least, not in any way more than any other valid theoretical modification in the history of science.See my other paper for more discussion on this point.

17.) Did Kepler ever use CO/Metaphor in his scientific elaboration of the universe? Yes. The Harmonies of the world provides us with the best example. I treat this in my paper “Thoughts on the Scientific Import of Metaphor”. Also, Megan Beets’ discussion on the New Paradigm Show of 2/25/15 I found to be incredibly helpful. Also Jason Ross’ “Metaphor: An Intermezzo” in the section on the harmonies.

18.) Briefly, Kepler didn’t actually prove that equants and circles couldn't be used in creating a consistent theory of the planets, just that the equant couldn't lie on a “unique point on the line of apsides at a fixed and constant distance from the center of the eccentric”. (And even this I am not certain was proved in the precise sense of logic.) Thus, hypothetically  there could still be another arrangement of circles and equants which provides a consistent theory. Kepler did demonstrated, however, that such a theory was extremely implausible.

19.) Obviously, Kepler’s entire investigation was informed by his physical theory- the area time law comes from it directly for example. But, still, the distinctions being made here are valid.

20.) If my memory serves me correctly, Kepler never attempted to provide a physical explanation as to why this force had these mathematical characteristics on the basis of physical theory, as he had done with his sun based force (although I don't think he settled on a final answer there either)

21.) I do not intend to say that Kepler only postulated deductively bound causal concepts. In his work. In his “Harmonies of the World” he demonstrated that there must be other principles by which physical processes relate to each other which go beyond deductive interpretation.

22.) Assuming, of course, that the definition of “Universal Gravitation” is the one in this (footnoted) sentence. I do not exclude, however,  the possibility that when Lyn has referenced “Universal Gravitation” he had in mind a concept other that this one. A concept deeper than the notion of mechanical relationships, something very profound residing in the depths of the universe, perhaps revealed, at least in part, by Kepler’s discovery of the Harmonies of the World. My own thoughts on this have been elaborated to some degree in my previously mentioned paper “Thoughts the Scientific Import of Metaphor” Now, despite this distinction, it is very likely that many people, including in our organization, interpret this term, in statements concerning Kepler’s discovery, as meaning what is popularly known as “universal gravitation”. Hence, the legitimacy of this objection. If something other than this common notion of “universal gravitation” is meant when this term arises in our discussions, then that should be made as clear as possible.

23.) An idea which seems to be at odds with Aristotle’s insistence that all motion arises through material contact. Perhaps he admitted that souls could move objects too and that the elements had souls?

24.) (Granted that we admit into our concept of physics “immaterial species” in the universe which diffuse themselves through space in a way similar to light or matter.)

25.)It is safe to say that Kepler would have sided with Leibniz had he been alive in the late 17th century. Kepler would have recognized the fatal irrationality introduced by the absolutist view pointed out by Leibniz; something which was completely at odds with his convictions respecting God’s creation- this despite the fact that both options seem to be identical for the purposes of theoretical constructions. Besides Kepler’s use of the physical nexus of his planetary system as a reference point, it would be useful to find quotes from Kepler reaffirming this more explicitly; I would love to see them. For now though, it seems to me that Kepler was actually unaware of this issue, at least for the most part.

26.) It should be noted that, even in Einstein's theory relativity, the idea of curved space-time is not said to be the necessary result of any physical/hypothetical concept or factor. Thus, when I sometimes hear it said that in Einstein’s theory “space is curved by gravitation” I am confused. For, in Einstein’s theory “gravitation” is the word ascribed to the phenomena of mutual attraction between matter/mass, and this phenomena is said to be an effect of the curvature of space-time. As far as I can tell, Einstein never provided a physical/causal reason as to why space-time should be curved. Thus to say that “space is curved by gravitation” would be to change the meaning of the word “gravitation” from the mutual attraction between bodies, to the principle which necessitated that space-time be ordered in such and such a way. It is interesting to note also that, in this sense, Einstein’s theory of gravitation is less casual, and more rationally descriptive than the gravitation theories of Kepler or Newton for instance. Einstein’s concept of space also seems to blend the “relationalist” and “absolutist” ideas of space in a certain way. Clearly, his concept of space is purely relational, since, no spatial ordering can be considered without reference to a body/mass. But, at the same time, he seems theory seems to suggest thinking about space as if it did exist around bodies, as a thing in itself with it’s own metrical relations- sort of as a “field of potential relations”, and within which all processes unfold according to these metrical relations.

27.) Traditionally, one constraint imposed on the selection of possible rational orderings in the hypothetical world has been the correspondence of observation with the processes implied by such a selection of rational ordering. Obviously, many different orderings might imply that which we met with in observation.

28.)The debate between what might be called the “relationist” and “spatialist” school (as exemplified by the Leibniz-Clarke debate) will not be addressed here since, as far as I can tell, both viewpoints render the same results with respect to our discussion at this point.  This question is separate from the question as to what rational ordering characterizes the relations between bodies or the relations of space. For example, to say that Euclidean geometry characterizes the rational orderings of objects and their relations is descriptively equivalent (but not ontologically equivalent) to saying that Euclidean geometry characterizes the absolute space in which objects exist and relate to each other. (Absolute space can be non-Euclidean.)

29.) Admittedly, Kepler did not adhere to this idea of inertia. He seemed to think that a body would only move if under the influence of a force- which  is why his circular force theory might seem a little strange to people today. In the following examples we illustrate our point using cases in which theoretical alterations of the rational ordering of space is changed to accommodate phenomena. I do this despite that it seems to me that Kepler -to accommodate phenomena- would have needed to modify time, i he had wanted to treat the planetary motions in this way (due to his concept of inertia).

30.) Actually this is already done in the first option: admit a certain space and the forces in it. But in this third case, we would (for whatever reason) modify space, but not to the extent that it accounts for the motion, and then add a force (or some other strange rules or elements)  to complete the construction.

31.) Cusa likens this relationship to water descending unto the clouds into the streams and henceforth into the oceans- but then also in the reverse order. He also uses the analogy of the growth of a tree: From the tree the branch is made, from the branch a seed, and then from the seed a branch then into a tree. Such are his analogies which describe the flow of cognition from the Divine, through the intellect, reason and to sense, and thence unto the reason, intellect, and the Divine. No one who has seriously studies LaRouche’s notion of economic anti-entropy could help but be absolutely struck by the way in which Cusa elaborates precisely the same principle.

32.) In Kepler’s New Astronomy the investigation is primarily focused on determining the rational ordering of the planets and on finding the first kind of hypothetical factor described in what follows. In Kepler’s Harmony of the World the investigation is primarily dedicated to uncovering the Second kind of principle described in what follows.  

33.) For a wonderfull presentation and discussion on this principle, see


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