Halley's Comet and the Metaphysics of Science

Should the metaphysical understandings of Isaac Newton and Immanuel Kant be taken to be the most universal understanding of astronomical phenomena, then their philosophies also become the conduits for what becomes known as contemporary knowledge. More specifically, Newton and Kant's dynamic interpretations regarding matter, motion, space and time are all applicable to Halley's comet in terms of its existence in space and time and its motion through the solar system. This essay will outline the essential metaphysical outlines of Newton and Kant, particularly in reference to the above mentioned phenomena. Moreover, the paper will discuss these metaphysical beliefs of Newton and Kant in terms of Halley's comet. Following this, the metaphysics of both Newton and Kant will be discussed for estimation of accuracy, validity, and strength in terms of their respective scientific arguments, specifically in reference to the metaphysical underpinnings.

SECTION I-ISAAC NEWTON-METAPHYSICS OF PHYSICS AND HALLEY'S COMET:

It is understood that Halley's comet is an object of matter and presumably mass that moves through space at a predictable velocity and pattern. The questions thus become, what is this matter? what exactly is the time and space that this matter moves through? and why does move the way it does? Isaac Newton offered much explanation to these questions and they are briefly summarized as follows. Moreover, it is important to note that the notions of matter, space, time and motion that follow are all primarily founded on mathematical principles of universality and/or probability, thereby making Newtonian science/principles of nature a mathematical metaphysics of science.

Newton understood matter to be most importantly a mathematical relation involving gravity. In other words, Newton was more concerned with the notion of mass than that of corpuscular content as a fundamental feature of matter. That is to say, Newton did believe in the existence of atoms as constitutional matter as well as geometrical shape of matter. However, Newton was more concerned with the idea of an object as something with mass i.e. containing a certain amount of force, specifically inertial motion and its relation to other masses. (Burtt, P.241) Hence, matter for Newton was most significantly a mathematical contrivance, specifically something with mass.

Second, is Newton's understanding of space and time. Both space and time are often considered to be either 'absolute' or 'relative'. Moreover, time that is absolute for Newton is a time that "flows equibly, without regard to anything external, and by another name is called duration." (Burtt p.245) However, this interpretation of Newton's 'time' is ambiguous and is enhanced by further exegesis. Moreover, absolute time for Newton was that which exists beyond any form of limited measurement and is consequently enduring of its own volition and hence, 'of duration without regard to anything external'. Still, in other words, absolute time is infinite in nature and exists infinitely in an 'equible' manner. By 'equible' one can only assume the property of consistency as inequitable would be of differing characteristics in different parts of time. Thus, absolute time for Newton is constantly infinite.

This notion of equity is also apparent in Newton's understanding of relative time which is inequitable. Moreover, time in its relative form is measured in reference to something that is not of complete duration. For example, the rotation of the Earth around the Sun takes approximately 365 'days' --where a day is equal to one earth rotation, where a complete circle is circumscribed by the rotation of a point on Earth such as a city-- Moreover, the Earth performs approximately 364 of these rotations in its rotation around the Sun. This can be considered a specific amount of time with which measurement of time can be made. However, this measurement of time is crude in the sense that it does not take into account the duration of absolute time, but rather a small period within absolute time, that is itself approximate because one Earth rotation itself is not always equal to the next i.e.each day does not always consist of exactly 24 'hours'. (Burtt, p.246)

Also relevant to the later application to Halley's comet is the Newtonian notion of space. Like time, space can also be absolute or relative in Newton's metaphysics. Absolute space, like absolute time, is "always similar and immovable".(Burtt, P.245) Moreover, absolute space is also constant and equable in the sense that it is not subject to inequity. For example, the amount of matter or time within a given space may vary depending on reference point, velocity, cosmic phenomena such as black holes etc. Absolute space is not affected by these events or concepts because it is simply beyond them in terms of itself. Furthermore, absolute space is constant whereas space within absolute space can be moveable and subject to change. This latter type of space is relative space. To illustrate, if absolute space is represented by a rug or plane of interwoven fibers that extends infinitely in all directions, any change that occurs to the fiber in terms of length, density, width etc. is relative to the complete wholeness of the total rug or plane because the total rug always includes the same amount of relative rug. Moreover, absolute time and space can be conceived of as the bottom of a pool that is made of concrete and painted three different colors, red, white and blue. Each of the colors forms an equal stripe or one-third of the concrete base of the pool. If the base itself is considered absolute and constant, then any compression, alteration or change in the space that is represented by colors will be relative only. Moreover, if somehow, only the red painted concrete freezes, it will contract, whereas the white and blue concrete remain in the same state of space. The resulting red painted section of the pool will be smaller, yet the complete amount of concrete will be the same thus making it absolute or constant (relatively speaking.) Both absolute space and time were justified by Newton through induction in reference to absolute motion. Furthermore, by establishing absolute motion, Newton believed that absolute space and time must also exist. However, as we shall see again later, absolute space and time is ultimately a property of God who is the divine sensorium and eternal past and future. (Notes) Thus, a theological element is also attributed to absoluteness by Newton.

The idea of motion, specifically gravitational attraction, absolute, relative and true motion, are of prime importance to Newton's metaphysics of science, and are described as follows. Newton believed relative motion to be that motion which remains unchanged within a change in the motion of surrounding matter. Moreover, relative motion is motion that is not effected by an external force acting upon it. Newton uses the example of a filled spinning water container to illustrate. If the container is attached to a rope and twisted so that the rope holding it also twists, then the sudden force of facilitating motion in the opposite direction to that which the container and rope has been twisted will yield a significant rotation in that opposite direction. Moreover, at first the water in the container remains at rest while the container spins, but later begins to match the motion of the external container. It is the motion of the water at rest within the spinning container that Newton terms 'relative' and the later matching motion that Newton terms 'true motion'. According to Newton, the same relationship holds true for water on the Earth which spins in space. That is to say, even though the Earth spins, the seas and lakes do not necessarily spin in the same way. This relationship is important in defining motion because if motion were defined in terms of the external body i.e. container or Earth, the apparent motion of the water would be undefined; thus, motion is defined in terms of the relative within the absolute or from effect to cause. (Burtt p.252) But what is true motion? true motion for Newton is that motion which is affected by external force, namely the water after it begins to move in the direction of the container. Moreover, Newton believes the Earth moves in relative motion within space as otherwise relative motion would have to follow the same pattern of forces within space and beyond. Moreover, these relative motions are only defined by effect. Thus, consequently, an absolute motion of immovability is implied because if it were not, all things within it would eventually assume the same pattern of motion as the universe using the container example to illustrate. Moreover, if absolute space were in motion, then it would eventually, if not presently be impossible to spin water in the opposite direction due to the eventual conformity of relative motion to true motion. This would be empirically demonstrable through a gradual quickening of the time it takes water to assume true motion in spinning container experiments. Furthermore, relative motion implies an absolute time and space in which things can exist relatively and not always truly, whether they exist in terms of absolute motion, space or time. (Burtt P.251) That is to say, true motion can only be relative to other bodies within an absolute motion, space and time because of the findings described through relative motion herein. This is of particular importance and further illustrated by Halley's comet.

Halley's comet, as noted earlier moves in the opposite direction as the planets orbit around the sun. So, if Newton's theory of absolute motion i.e. a state of immobility is correct, then Halley's comet can travel in such a way. However, if the space which Halley's comet traveled through were not absolute, or in motion, then Halley's comet would eventually slow down, stop and begin its orbit around the solar system in synchronicity with the rest of the universe. Therefore, absolute immovable motion must exist according to Newton. Moreover, it is again this absolute motion that implies absolute space and time.

Still another aspect of motion that Newton discusses is Gravity. Gravity is that 'invisible and innate' force that exists between two masses thereby creating action at a distance. (Burtt p.266) Furthermore, Newton justifies this force through necessity. That is to say, without gravity, inertia would be impossible and motion would not be conserved.

"The vis inertiae is a passive principle by which bodies persist in their motion or rest, receive
motion in proportion to the force impressing it, and resist as much as they are resisted. By this
principle alone there never could have been any motion in the world. Some other principle is
necessary for putting bodies into motion' and now they are in motion, some other principle is
necessary for conserving motion."(Burtt p.267)

Newton extends this necessity to comets and planets and consequently applies to the motion of Halley's comet. "Seeing therefore the variety of motion which we find in the world is always decreasing, there is a necessity of conserving and recruiting it by active principles, such as are the cause of gravity, by which planets and comets keep their motions in their orbits, and bodies acquire motion in their falling..." (Burtt p.268) Thus, Halley's comet continues its motion around the planets and sun out of a necessary force, namely gravity. Moreover, this force is evident through the continuation of inertia and the lack of loss of force that would naturally occur if two equal forces came into contact with each other. That is to say, gravity is also implied by the notion that force is not lost but rather transferred when to objects with force collide. (Ibid)

SECTION II-IMMANUEL KANT-METAPHYSICS OF PHYSICS AND HALLEY'S COMET

Immanuel Kant endorsed much of Newton's mathematical 'explanation' of the universe and attempted to provide the underlying philosophy which Newton denied to exist as 'hypotheses' within experimental science. This underlying philosophy took the form of metaphysical conditions for knowledge of external reality, specifically that found within Kant's Philosophy of Material Nature. The primary theme of such 'conditions' of knowledge is that of intuitive knowledge and the knowledge of sense faculties as a-priori, or pre-existent in the mind. (Notes) Furthermore, these inherent ideas themselves allow concepts to be formed and demonstrated, most proficiently within mathematical and geometrical principles.

Beginning with Kant's metaphysics of matter, one finds that matter unlike the belief of atomists, is a continuous whole. (Kant, I. p.viii) Moreover, Kant believes that this is so because the 'infinite divisibility' of atoms does not necessarily imply that the matter itself is not whole. That is to say, if matter does indeed comprise forces in motion, then, the whole of matter could in fact be a 'continuous' whole that simply appears to be infinitely divisible. Furthermore, matter for Kant is just that, forces in motion. These forces are understood by Kant, to be attractive or repulsive in nature and not only one or the other. That is, if matter were only attractive force, it would ultimately compress into itself, leaving only an infinitely small point; and if matter were only repulsive force, it would ultimately expand leaving only infinitely sparse extended matter. Hence, matter is a combination of attractive and repulsive forces. It is from this premise of an existent matter, that Kant becomes able to extend his argument to an understanding to absolute space and time.

According to Kant, absolute space is "the largest space which includes all smaller spaces." (Kant, I. p.xv) That is to say, absolute space is the largest of space which would have to be infinite to include all smaller dimensions of space. Moreover, this space, when considered in terms of Kant's a-priori conditions for understanding, is empirically verified through principles of mathematics and geometry. Consequently, absolute space as well as other items of knowledge, are most prominently aspects of human knowledge and not 'things in themselves' or true to an external reality. (Martin, G. p.38) That is, even Kantian knowledge in its a-priori state, is only a-priori to the mind as necessary for further concept formation and not necessarily true of the external reality itself.

"The terms space and time refer us only to concepts of 'forms' whose designates have empirical status solely in so far as they 'make it possible' that the sensory manifold should be intuited as 'appearance'; and they are the manner (apatio-temporal) in which intuition occurs." (Buchdahl, G. P.591)

Therefore, if actual space exists beyond knowledge, then the possibility of it existing of its own volitions and in different ways to that understood by knowledge, it at all, is itself a possibility. In other words, knowledge is limited to that which it knows a-priori only; the dimension of absolute space is knowledge insofar as it is an idea posed by the a-priori formation of lesser concepts such as relative space. However, the notion that these concepts are used to mathematically represent space, does not imply that space exists in exactly the same way, as space is a separate entity that can itself carry its own volitions just as human knowledge does. Moreover, this is so simply by possibility of its own virtue; consequently, absolute space itself is not entirely predictable or representable by a-priori knowledge of the mind, and thus, undefined. Still in further explanation, absolute space is not perceivable by the senses, but only intuited as a concept of a possible reality, that is itself infinite and therefore never wholly knowable by human knowledge.

Relative space on the other hand, is more knowable to Kant. This is so because relative space includes the smaller spaces within the absolute space and are thus, not infinite but finite. Furthermore, relative space is the space in which notions themselves are perceived. (Kant, I. p.19) That is to say, similar to absolute space, relative space is an idea. However, relative space differs from absolute space in that it is necessary for any concepts such as circle, square or triangle to be know, therefore it is definable and perceivable in terms of those structures. However, absolute space is not necessary to form these same geometrical structures, and consequently not defined through geometrical verification.

Similar notions apply to Kant's understanding of absolute and relative time. Moreover, absolute time is an idea that represent an unperceived possibility and not a mathematically verified actuality. However, relative time, like relative space is necessary for the formation of mathematical and geometrical concepts and therefore a-priori. That is, a cause and effect relationship is necessary for mathematical principles to be actualized, and such a relationship requires time.

Another important aspect of Kant's metaphysics is gravity, which is also related to the notion of relativity. Kant explains that for matter to be understood as being in motion, it can only be know in terms of other objects within an absolute space and time, and not the absolute space and time itself. Moreover, since absolute space and time are unknowable for Kant, who is to say that an object in motion is not actually at rest in terms of the possible motion of absolute space and time. (Kant, I. P.126) i.e. in synchronicity with absolute time and space in much the same way as a drink in an airplane does not spill when the plane slows. Thus, matter can only be understood in reference to other matter. Furthermore, since matter consists of forces in motion whether it be attractive force, repulsive force or both, it is the interaction of such forces that gives the impression of 'gravity'.

The question still remains however, how do these Kantian principles relate to Halley's comet's orbit in relation to Earth. The apparent constancy of the comet's motion can be explained in terms of a fixed amount of matter within the solar system and consequently a fixed relation of attractive and repulsive forces between the comet, space, the planets and the sun (not including action reaction forces imposed by stray asteroids). Moreover, the motion of Halley's comet is relative from Earth and satellite telescopes that orbit Earth. That is to say, the motion occurs as a difference in the pattern of attraction and repulsion of the two objects (comet and Earth) within the solar system which for convenience can be considered to be in absolute rest. For this to occur, a separate space that is relative to each object must be conceived. This relative space is also affiliated with a relative time i.e. a period of approximately 75 years for an orbit measured in terms of the (relative) motion of Earth around the sun.

PART III-NEWTON AND KANT CONTRASTED

Kant's understanding, and conditions for understanding offer much for the metaphysical verification and/or expansion of Newton's principles. To illustrate this point, Newtons principles, such as the laws of motion must be discussed in terms of Kant's conditions for understanding. Moreover, it must also be shown that Kant was actually referring to Newton when contriving such an understanding.

Despite this possible relationship however, both Newton and Kant clearly differ in regard to general focus. Where Newton gave much attention to scientific experimentation through empirical mathematical verification of external phenomena, Kant attempted to explain the underlying metaphysics of such a science. Moreover, 'the Foundations of Dynamics' offers what Newton would place in the realm of natural science, theology and metaphysics simply because of the lack of experimentation involved in verifying the 'dynamics'. However, Kant would disagree with this by stating that the two are connected by a-priori possibility; specifically where mathematics and geometry are concerned. Moreover, the mathematics used by Newton become empirical as soon as they are applied to external reality given Kant's metaphysics of knowledge. Newton would find this preposterous because his experimental science "claimed no hypotheses". Nevertheless, in Kant, we find the fallacy of the later positivistic notion that reality can be verified through a-priori logical means. Still in other words, it is again important to note that Kant's a-priori knowledge is limited to the presuppositions or initial conditions of the senses, and consequently does little to verify anything other than 'appearance' to the senses. Moreover, an appearance is understandable by the mind according to the principles of the mind, but not necessarily the principles of the external world which is still an independent and separate entity in its own right, regardless of its relations to the mind.

"To say that space and time are conditions of things, that they are basic, individual, infinite, does not seem to clinch the matter. Nor does the contention that space and time universally belong to all appearance, and that this can be known antecedently to all experience, in contrast with sensory qualifications. And for Kant, crucial argument that they are the basis for geometry, regarded as a synthetic a priori body of knowledge, might likewise be said to beg the question." (Buchdahl, G. p.589)

Hence, based on these counter claims, both Newton's laws and Kant's knowledge are somewhat restricted to say the least. However, Kant does not beg the question as his argument logically follows from an antecedent through premises to a conclusion. That is, Kant does not justify his conclusion by restating the initial premise. Moreover, Kant claims that time and space are at least empirically real and possibly absolutely real in the mind because they are embedded within systems of knowing. Thus, the argument is as follows.

P1-Kant experiences relative space when he conceives of a circle.
P2-The circles spacing can be demonstrated through geometry
C1-The space necessitated by conception of the circle is an a-priori experience to the senses.
C2-The space is empirically demonstrated in geometry.

Thus, a-priori experience is validated through necessary outcomes that follow out of such an experience. "So Kant's main point comes down to saying that space and time are 'empirically real', i.e. that 'we can speak of space and time at the phenomenal level precisely because these entities have no logical place outside this linguistic situation; that they are empirically real simply because we have an empirical linguistic location for them, that the phenomenal level is indeed absolutely required." (Buchdal, G. P.591) Moreover, knowledge of anything follows from the ability to have knowledge in much the same way as knowledge of the a-priori follows from the ability to know the a-priori from its own volition to be known.

So again, Kant does successfully account for Newton's empirical claims at a deeper metaphysical level; but, Kant nevertheless does not negate the notion that empirical claims of external reality are indeed empirical and not absolutely certain. Therefore, complete certainty of knowledge is impossible for both Newton and Kant.

Last, it is important to note that what Newton considered to be in the realm of natural science also included the notion of God, whereas Kant rejected to use God as an explanation for that knowledge which he later found to be a-priori. (Notes) Hence, a rejection or lack of inclusion of theology is more attributable to Kant's understanding than to that of Newton. Furthermore, what Newton assumed to be a-priori could also be assumed to be a product of God, whereas for Kant, what was assumed to be a-priori was explained through a union of epistemology and metaphysics. (Notes) This is further illustrated in Newton's Theology where God is attributed three essential principles which include knowledge of absolute space and time. (Notes) Again here, what Newton attributed to God, Kant did not by simply accounting for absolute space and time as undefined or not completely knowable by the senses.

A FINAL CONSIDERATION OF HALLEY'S COMET

Using what we know of Newton and Kant, Halley's comet is something that can only exist empirically in external reality. However, the comet can also be represented in a more absolute way through a-priori principles of the senses. Keeping this in mind, Halley's comet is also a body of matter that exists as both a collection of atoms --according to Newton-- and as a specific unity of forces in motion within a greater system of forces --according to Kant--. Furthermore, Halley's comet travels through space the way it does because it is bound to a trajectory largely determined by the gravitational forces imposed on it by the masses/planets and star which it orbits. These gravitational forces act in unison, possibly with other forces such as inertia of the comet to allow a fairly predictable patter of motion for the comet. This motion is further verified metaphysically by Kant's notions of 'dynamics' and 'mechanics' i.e. the relation of forces in motion as matter. Also, the Newtonian idea that force is directly proportional to speed, specifically in regard to Halley's comet, is verified by the Kantian condition that the notion that space is inherent to knowledge. This is explained in regard to the defining of a line segment where extension of a point to another point necessitates space. (Notes) Furthermore, all these concepts of gravity, matter, motion and knowledge of them are indicative of a cause and effect relationship within knowledge for both Kant and Newton. This cause-effect pattern is again extrapolated more extensively by Kant, and more assumed as a necessary relationship for Newton.

Thus, we have a brief survey of the metaphysics and science of Isaac Newton and Immanuel Kant, and the application of their knowledge to Halley's comet. It is evident that the most consistent feature within the ideas of both these philosophers is the use of geometry and mathematics as fundamental methods of explanation. For Newton this system is assumed to be magnificent as evident in the ability for its extension to universal laws in his methodology (which was also considered the end of science). (Notes) However, for Kant, Newton's methodology did not thoroughly account for the verification of necessity which was pointed out by Hume. Thus, the Newtonian methodology that expanded conceptual pictures form isolated 'domains of events', was further analyzed by Kant's 'Transcendental deduction of categories' i.e. a study of what a-priori knowledge actually is and how its necessity could be validated. Moreover, for Newton, and Kant, the natural world is embedded in a metaphysical system of constructed concepts that most consistently represents that external world. Consequently, Halley's comet is best described by such geometrical and mathematical systems. Nevertheless, the existence of a mathematical system does not imply that an enhanced system that transcends mathematics cannot also exist assuming the same standards of probability within an even greater and more expansive system of knowledge.

APPENDIX:

HALLEY'S COMET

FIRST DISCOVERED: 239 BCE Possibly 1140 BCE (Tattersfield, D. P.6)

IDENTITY: Named after Edmond Halley (1656-1742) who although did not observe it first, did predict its elliptical flight path and approximate flight time using Newton's principles of gravity.(Tattersfield, P.6)

CONSTITUTION: Compounds of atoms and isotopes (atoms charged negatively, neutral or positively) (Tattersefield P.102)

FLIGHT PATH: "Elongated orbit round the solar system as far as Pluto and the Sun at either end of its travel forming a closed loop." (Tattersfield P.102)

FLIGHT DIRECTION: Flight Path opposite to the direction of planetary orbits around the sun. (Flaste, Nobel, Sullivan and Wilford, p.viii)

FLIGHT TIME: 74-79 Years

VELOCITY: In kilometers velocity = 0.00198 * (150 * 10 ) * v (2/r -1/17.94) (Tattersfield, p.110)

See Tattersfield p.110 for calculations.

MAGNITUDE: See Tattersfield p.102.

SOURCES CITED:

Buchdal, Gerd. Metaphysics And the Philosophy of Science: The Classical Origins: Descartes to Kant.
Cambridge, Massachusetts: The MIT Press, 1969.

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International Inc., 1996.

Hall, Rupert. A. 'From Galileo To Newton'. New York: Dover Publications, Inc. 1981.

Kant, Immanuel. 'Philosophy of Material Nature.' Indianapolis, Indiana: Hackett Publishing Company, Inc.,
1985.

Richard Flaste, Holcomb Noble, Walter Sullivan and John N.Wilford. 'The New York Times Guide To The
Return Of Halley's Comet.' New York: Times Books, 1985.

Martin, Gottfried. ' Kant's Metaphysics and Theory of Science'. Westport, Connecticut: Greenwood Press,
Publishers, 1974.

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Tattersfield, Donald. 'Halley's Comet'. New York: Basil Blackwell Inc., 1985.