Heavens

Chapter 1-1 Natural science primarily concerns bodies, magnitudes, their properties, and movements, along with their principles. Some natural entities are bodies and magnitudes, while others possess these qualities or are principles thereof. A continuum is divisible into infinitely many parts, while a body is divisible in three dimensions. Three dimensions define all magnitudes. The number three is significant in nature, representing completeness and totality. Hence, a body, defined by three dimensions, is considered complete. This completeness signifies being in every respect. Bodies composed of complete magnitudes are themselves complete, ensuring that the whole remains complete.

Chapter 1-2 The nature of the universe, whether finite or infinite, is a significant question. Natural bodies, by nature, can move, and their motion is either straight or circular. Circular motion involves rotation about a center, while straight motion moves toward or away from a center. Bodies can be simple (like fire and earth) or composite. Simple bodies possess natural motion. Circular motion suggests the existence of a body naturally moving this way. This primary body moves circularly, separate from fire, air, earth, and water. Circular motion's perfection implies it belongs to this divine, simple body.

Chapter 1-3 Not every body possesses lightness or heaviness. 'Heavy' means moving towards the center, and 'light' means moving away. The heaviest sinks to the bottom, the lightest rises to the top. A body moving circularly cannot be heavy or light. Its motion is neither toward nor away from the center, making it impossible for the body to move unnaturally in straight lines. Circular motion is primary and perfect. This primary body, different from the four known elements, is ungenerated, indestructible, unalterable, and without contrary movement. Its divinity and eternal nature are evidenced by its continuous, unchanging motion.

Chapter 1-4 No motion contrary to circular motion exists. Circular motion's simplicity and perfection mean no straight-line motion can oppose it. Straight motions (up and down) are contrary due to their opposite directions. Circular motion's uniqueness lies in its continuous nature. Circular motion isn't opposed by straight-line motion because circular paths are infinite, unlike straight paths. Circular motion involves moving towards the same point repeatedly, unlike straight-line motion, which moves from one point to another. Circular motion's continuous, repetitive nature prevents it from having a contrary. This perfection reflects the divine nature of the body performing it.

Chapter 1-5 An infinite body is impossible. If a body is infinite, its radii and the space between them are also infinite, making circular motion impossible. Circular motion is observed in the heavens, so the universe cannot be infinite. Infinite bodies cannot move circularly or linearly in finite time. If an infinite body moved, it would require infinite time, which contradicts observable celestial motion. The heavens revolve in a finite time, proving their finiteness. Infinite bodies are unfeasible as their movements would be contradictory, demonstrating that the universe and celestial bodies are finite, thus aligning with observable reality.

Chapter 1-6 Bodies moving towards or away from the center must be finite because their contrary movements define a finite space. The center's determinacy implies the upper and lower places are also finite, making the intermediate space determinate. Therefore, bodies within this space are finite. Infinite bodies cannot exist because they would require infinite weight, leading to absurdities in motion. Infinite weight cannot traverse any distance in finite time, making motion impossible. The universe, celestial bodies, and their movements are finite, confirming that neither infinite weight nor lightness is feasible. This aligns with observable celestial phenomena.

Chapter 1-7 Every body must be either finite or infinite, with similar or dissimilar parts. Infinite kinds are impossible, given finite primary movements. Infinite weight or lightness cannot exist. Bodies in dispersion, each infinite, must be extended infinitely in all directions. Infinite bodies can't move circularly or linearly due to lack of infinite space. Infinite bodies can't be acted upon or act upon finite ones. Infinite time renders infinite interaction impossible. Perceptible bodies can't be infinite. Thus, there is no infinite body beyond the universe, and no place, void, or time exists outside the universe.

Chapter 1-8 We must explain why there can't be more than one heaven. Natural bodies rest or move by constraint or naturally. Similar worlds composed of the same elements would have the same movements. Earth and fire move naturally to specific places, showing finite movement. Bodies can't move infinitely fast; constrained movement slows. Bodies must reach their proper place. The universe must be one; fire and earth occupy specific places, confirming finite movement. Bodily elements' places are fixed, confirming only one universe. The universe includes all physical matter, confirming it is one, complete, and without void, place, or time outside.

Chapter 1-9 The heaven must be one, ungenerated, and indestructible. While some say the world was generated and is eternal, others believe in periodic creation and destruction. Generated things are destructible. The world can't be eternal and generated. Some believe in the world's eternal existence post-generation, like Plato in the Timaeus. A generated world can't be eternal; generation implies possible destruction. If the world was generated from changeable elements, it must eventually disperse. Theories of alternating world creation and destruction are plausible. However, arguments show the world is unique and eternal, opposing these alternating generation theories.

Chapter 1-10 We must examine whether the heaven is generated or eternal. Reviewing other theories helps clarify our argument. Some claim the world was generated but is eternal; others say it is destructible. Alternation theories, like those of Empedocles and Heraclitus, propose periodic creation and destruction. Generated things are destructible. Claiming the world is generated but eternal is contradictory. Demonstrating generation involves temporal change, opposing eternal existence. The universe's continuous change would only affect dispositions, not its fundamental existence. Infinite worlds aren't feasible. Arguments for heaven's eternality and uniqueness show it cannot be generated or destructible.

Chapter 1-11 'Generated' and 'ungenerated,' 'destructible' and 'indestructible' have multiple meanings. 'Ungenerated' can mean something existing without becoming, capable of being without existing, or absolutely incapable of being. 'Generated' refers to something that now exists but didn't before, capable of existing, or undergoing a process of becoming. 'Destructible' and 'indestructible' follow similar definitions. The truly possible has a maximum limit. Anything capable of always existing and not existing must exist and not exist at the same time, which is impossible. Therefore, what always exists is indestructible and ungenerated. These concepts prove the heaven is eternal.

Chapter 1-12 If things can exist or not exist, there must be a maximum time for each state. If existence or non-existence isn't time-bound, something could exist and not exist infinitely, which is impossible. False and impossible aren't synonymous; some things are hypothetically possible but not in reality. A thing existing infinitely cannot be destructible. What always is cannot be generated or destroyed. If ungenerated and indestructible coincide, they both imply eternality. Generated and destructible things are intermediate between always existing and never existing. Therefore, generated and destructible coincide, and ungenerated and indestructible coincide, affirming the heaven's eternality.

Chapter 1-1 Natural science studies bodies, magnitudes, their properties, movements, and principles.

Chapter 1-2 Simple and compound bodies have either circular or straight movements.

Chapter 1-3 Circular motion is unique, ungenerated, indestructible, and without heaviness.

Chapter 1-4 Circular motion has no contrary; it involves unique continuous movement.

Chapter 1-5 Infinite body is impossible due to unfeasible circular or straight movement.

Chapter 1-6 Bodies moving towards or away from the center are finite.

Chapter 1-7 Bodies must be finite or infinite; infinite bodies can't exist.

Chapter 1-8 No more than one heaven exists; the universe is unique.

Chapter 1-9 Heaven is ungenerated, indestructible, and eternal, opposing alternating creation theories.

Chapter 1-10 Heaven is eternal, not generated or destructible, despite other theories.

Chapter 1-11 What always exists is indestructible and ungenerated, proving heaven's eternality.

Chapter 1-12 Generated and destructible coincide; ungenerated and indestructible imply heaven's eternality.

Chapter 2-1 Heaven is eternal, neither generated nor destructible, encompassing infinite time. This view is supported by arguments against the impossibility of its generation. The universe's immortality and eternity are further affirmed by ancient theories suggesting a divine and limitless movement. This movement, being perfect, contains all other movements with limits and goals, itself having no beginning or end. The ancients believed the heavens were divine and indestructible, requiring no external force to maintain their path. Therefore, the heaven is an ungenerated, indestructible entity, moving eternally without effort or necessity.

Chapter 2-2 Right and left, above and below, are principles applicable to animate bodies. In animals, distinctions like above-below and right-left are clear, but plants only have above-below. The heaven, being animate and possessing a principle of movement, must exhibit these distinctions. In the universe, the poles (above-below) are distinguished by immobility. The visible pole is below, the invisible is above. The right is where stars rise, and the left is where they set. Thus, the invisible pole is above, contrary to the Pythagoreans' view. Differences in function and shape determine these positions.

Chapter 2-3 The reason for the heaven's movement direction is not chance but divine purpose. The heaven's movement is eternal, reflecting the divine nature. This movement is circular because the heaven is a divine body, and circular movement is the most perfect. The presence of fire and earth necessitates other elements, leading to generation. The necessity of earth requires another circular motion. The reason for multiple circular motions lies in the necessity of generation and the presence of contraries. Therefore, the heaven's movement direction and the existence of multiple circular motions are due to the nature of the divine.

Chapter 2-4 Heaven is spherical, the most appropriate shape for its substance. The sphere is primary among solids, just as the circle is among planes. Every plane figure is either rectilinear or curvilinear, with the circle being the simplest and most complete. Similarly, the sphere, bounded by a single surface, is the primary solid figure. Bodies within the heaven, being continuous with spheres, are spherical. The sphere's rotation and the absence of void or place outside the heaven confirm its spherical shape. The universe's spherical shape reflects its eternal, perfect movement and the finer matter of the enveloping body.

Chapter 2-5 Heaven's movement direction follows nature's best course, not chance. Nature always follows the best possible course, and front-back is superior to left-right. The heaven's movement is eternal and natural, reflecting divine perfection. The distinction of prior and posterior in front-back provides a reason for the movement direction. This principle of movement ensures the heaven's eternal, unceasing motion. Therefore, the heaven moves in the superior direction, following the best course possible. The eternal, natural movement of the heaven reflects the divine order and perfection, ensuring its unceasing motion in the best possible direction.

Chapter 2-6 Heaven's movement is regular, without acceleration or retardation. Irregular motion would show acceleration, maximum speed, and retardation, but circular movement has no beginning, end, or middle. The mover and the moved in the heaven are unchanging, preventing irregularity. The primary, simple, and ungenerated nature of the mover and the moved ensures a regular, unchanging movement. Irregularity would imply change, but the heaven's movement remains consistent. Therefore, the heaven's movement is eternally regular, reflecting its primary, simple, and unchanging nature, free from any irregularity or change.

Chapter 2-7 Stars are composed of the same substance as their paths, reflecting the circular motion. The warmth and light from stars are caused by friction in the air due to their motion. Movement creates fire in materials like wood and iron, and similarly affects the air. Missiles heated by motion in the air illustrate this effect. The upper bodies, carried by a moving sphere, heat the air beneath. This explains the warmth from the sun. Stars, neither fiery nor moving in fire, cause warmth and light through their motion, affecting the surrounding air.

Chapter 2-8 Changes in the position of stars and the heaven indicate three possibilities: both at rest, both in motion, or one at rest and the other in motion. Both being at rest is impossible; the earth's motion must be constrained. If stars alone move, outer stars would be swifter, contradicting natural movement. The reasonable alternative is that circles move while stars remain at rest. Spherical stars have two movements: rolling and spinning, neither observed. Nature would not overlook movement organs for stars. The heavens move in one place, stars are immobile, fitting their spherical shape.

Chapter 2-9 The theory that the stars' movement produces a harmonious sound is untrue. Bodies in motion producing noise is understandable, but the stars' sound is supposedly undetectable because it's constant. Yet, no physical effects are observed from this sound. Moving bodies within a larger moving system, like a ship, create no noise. Similarly, stars fixed in moving spheres wouldn't create noise. If heavenly bodies moved in a mass of air or fire, their noise would shatter us. The stars are spherical, not self-moved, and their silent movement aligns with nature's design.

Chapter 2-10 Astronomy deals with the order and position of stars. The outermost heaven moves fastest with a simple motion, while other bodies move slower with composite motions. Bodies closer to the primary movement take longer to complete their circles. The outermost revolution is the swiftest, influencing the speed of inner bodies. The nearer a body is to the primary revolution, the more it is affected, while distant bodies are less influenced. Thus, the order and movement of stars depend on their distance from the primary celestial motion.

Chapter 2-11 The stars are spherical, the most suitable shape for immobile bodies. A sphere, lacking movement instruments, is ideal for stationary entities. Observations confirm the moon's spherical shape, visible in its phases and eclipses. Astronomical evidence supports this, as only spherical shapes account for observed crescent shapes. Since one heavenly body is spherical, others must be too. The spherical shape ensures they remain stationary, fitting their nature and the lack of movement instruments.

Chapter 2-12 Two difficulties arise: why intermediate bodies have more movements and why primary motion includes many stars while others are separate. Stars should be seen as animate, having life and action. The best-conditioned have fewer movements. Lower stars act like animals and plants, with varying actions. Earth, moving least, is farthest from divine principle. Primary motion moves many stars, each single motion moves one. Nature balances many bodies in one motion and one body in many motions. Thus, the celestial order reflects varying levels of movement, with primary motion affecting many stars.

Chapter 2-13 The earth's position and movement are debated. Most believe it lies at the center, but Pythagoreans place fire there. The earth's position as center is supported by its natural movement to the center, similar to fire's upward motion. Some argue the earth floats on water or is flat. These views are flawed, as heavy objects move towards the center. The earth's immobility is due to its natural centripetal movement, and its shape is spherical, confirmed by observations and eclipses.

Chapter 2-14 The earth is at the center, immobile. Its movement, whether at the center or away, must be constrained. Every part moves straight to the center, indicating constrained motion cannot be eternal. The earth’s natural movement is centripetal, ensuring immobility. Mathematical observations support the earth’s central position. Its spherical shape results from all parts moving towards the center, confirmed by lunar eclipses and star observations. The earth’s immobility and central position align with natural laws, making the universe's order stable and eternal.

Chapter 2-1 Heaven is eternal, not generated or destructible, containing infinite time.

Chapter 2-2 Right and left, above and below, apply to animate bodies.

Chapter 2-3 Heaven's movement is eternal, natural, and best explained by divine purpose.

Chapter 2-4 Heaven is spherical, perfect, and primary among solid shapes.

Chapter 2-5 Heaven's motion direction is not random, following nature's best course.

Chapter 2-6 Heaven's movement is regular, without acceleration or retardation, due to its simplicity.

Chapter 2-7 Stars are composed of heavenly substance, causing warmth and light through friction.

Chapter 2-8 Circles move; stars are stationary; stars lack movement organs.

Chapter 2-9 Star movements produce no sound; stars are spherical and stationary.

Chapter 2-10 Outer heavens move fastest; inner bodies move slower with composites.

Chapter 2-11 Stars are spherical, best shape for stationary, immobile entities.

Chapter 2-12 Intermediate stars move more; primary motion affects many stars.

Chapter 2-13 Earth is spherical, centered, and immobile, moving centripetally.

Chapter 2-14 Earth's center, immobility explained by centripetal movement, supporting observations.

Chapter 3-1 We have discussed the first heaven, moving stars, their matter, and their eternal nature. Natural things are either substances or functions and attributes of substances. Substances include simple bodies like fire and earth, and things composed of them, such as the heaven, animals, and plants. Attributes and functions include their movements, alterations, and transformations. Natural substances are bodies or require bodies to exist. The inquiry into nature mainly concerns bodies. We must now consider whether generation is a fact. Some argue that nothing is generated or destroyed, while others believe everything is subject to generation except one indestructible substance.

Chapter 3-2 Every simple body has a natural movement. Bodies move, and if they have no natural movement, their movement is constrained, which presupposes a natural movement it opposes. Rest is either constrained or natural. A body at rest at the center rests naturally, implying natural movement towards that place. If constrained, what hinders its movement? An infinite regress or a natural rest must follow. Leucippus and Democritus, proposing perpetual movement in a void, must explain the natural movement of primary bodies. Bodies must have definite weight or lightness, and natural movement is either helped or hindered by air.

Chapter 3-3 To understand the generation of bodies, we must identify which bodies are elements. An element is a body into which other bodies can be analyzed and is not divisible into different forms. Fire and earth are elements because they are present in other bodies and can exude from them. However, elements cannot be indivisible points, as this contradicts observations and mathematical principles. Bodies have attributes divisible into kinds and per accidens. Indivisible elements cannot explain weight or other attributes. Elements must be generated from one another, not from an indivisible or incorporeal source.

Chapter 3-4 The elements cannot be infinite in number. Anaxagoras' view that all homoeomerous bodies are elements is flawed because even mixed bodies are often divisible into homoeomerous parts. Elements should be finite, as shown by mathematicians who limit principles to a finite number. Leucippus and Democritus proposed infinite atomic bodies, but this conflicts with the finite number of simple movements and the observable finite differences in bodies. Atomic theory also contradicts mathematical sciences and observable data. Elements are finite, and their differences are not infinite, thus limiting their number and ensuring they have distinct natural movements.

Chapter 3-5 Elements cannot be single; natural bodies possess unique movements. If all bodies are one, they share one movement, contradicting observable differences. Fire, water, air, and earth exhibit different natural movements. Empedocles and others who propose one element, like fire, fail because a single body cannot account for diverse movements. Bodies must have varying movements, and the single-element theory cannot explain this. If elements were single, they would have one natural movement, which is false. Bodies of different kinds must have distinct elements, ensuring multiple natural movements. Elements must be several, not infinite or singular.

Chapter 3-6 Elements are not eternal. Observations show fire, water, and other simple bodies undergoing analysis, leading to generation and destruction. Infinite analysis implies infinite time, conflicting with the finite nature of bodies. Elements must be generated from other bodies, not from incorporeal sources or bodies without weight or lightness. An extra-corporeal void is impossible, and elements cannot arise from an incorporeal source. Elements are generated from one another. Fire, water, air, and earth transform into each other, undergoing generation and destruction, disproving their eternal existence. Bodies must be finite and subject to these processes.

Chapter 3-7 Elements transform into one another through change, not excretion. Excretion theory implies finite bodies contain infinite parts, which is impossible. Elements must change shapes or resolve into planes. Shape-change implies atomic bodies, contradicting divisibility. Resolution into planes suggests not all elements transform, contradicting observations. Principles should match observations, not predetermined views. Elements must transform into each other, not via excretion or plane resolution. Differences in properties, powers, and functions define elements. Natural bodies exhibit unique functions and transformations. Elements must be perceptible, transforming naturally, ensuring the consistency of observable phenomena.

Chapter 3-8 Elements' shapes don't define them; functions and properties do. Shapes can't fill space entirely. Elements like water and air change shapes based on their containers. Nature shows elements as formless materials for composites. Elements' distinctive qualities are changeable. Fire, earth, water, and air perform specific functions. Functions, not shapes, distinguish elements. Fire combines and separates substances, showing multiple functions. Hot and cold elements lack clear shape-based distinction. Shape theory fails to account for natural properties and observable behaviors. Elements are better understood by their natural roles and functions.

Chapter 3-1 Natural things are substances or attributes; generation occurs within elements.

Chapter 3-2 Simple bodies have natural movements; constrained movements prove natural rest.

Chapter 3-3 Elements exist, derived from primary bodies; potential bodies become actual.

Chapter 3-4 Elements are finite; mixed bodies cannot be elements.

Chapter 3-5 Elements can't be single; all bodies move differently.

Chapter 3-6 Elements undergo generation and destruction, disproving eternal existence.

Chapter 3-7 Elements transform into each other; generation involves change.

Chapter 3-8 Shape doesn't define elements; functions, properties differentiate them.

Chapter 4-1 We must consider 'heavy' and 'light', what these terms mean for bodies, and why they possess these properties. This inquiry is part of the theory of movement, as these terms denote a natural power of movement. Previous thinkers have mainly focused on relative heaviness and lightness but have not addressed absolute heaviness or lightness. We observe some bodies naturally moving upward (light) and others downward (heavy). Absolute lightness means moving upward, while absolute heaviness means moving downward. Relative lightness and heaviness are determined by comparing the speed of natural movement in equally sized bodies.

Chapter 4-2 Previous philosophers have primarily considered relative heaviness and lightness. In the Timaeus, it is suggested that the body with more identical parts is heavier. However, this does not explain absolute heaviness and lightness. Fire always moves upward (light), and earthy things move downward (heavy). Fire's upward movement should be slower if it depends on the number of triangles, yet larger quantities of fire rise faster. Air and water, composed of the same triangles, should show differences in relative heaviness, but this contradicts observable facts. Some suggest void within bodies affects their weight, but this theory also fails to explain observed behaviors.

Chapter 4-3 We must address why some bodies move upward, others downward, and some both ways. Each body's local movement to its place resembles other forms of change, proceeding from a contrary or intermediate state. The body moving upward or downward changes towards its form. Fire moves upward and earth downward because their elements differ. The source of movement appears inherent due to matter's nature. Elements attain their natural place, reaching actuality from potentiality. This explains why fire and earth move to their places without external force, driven by their inherent properties and the original creative force.

Chapter 4-4 We distinguish the absolutely heavy (sinks to the bottom) from the absolutely light (rises to the surface). Fire moves upward, and earth downward, unaffected by quantity. Air and water exhibit both lightness and heaviness, depending on their surroundings. Heavier in air, lighter in water. Heaviness and lightness result from elementary properties, not void presence. Earth and fire are absolutely heavy and light, respectively. Fire has no weight, rising to the extremity, while earth sinks to the center. Spatial duality (center and extremity) explains this duality. Thus, elements have distinct places and properties, determining their natural movements.

Chapter 4-5 A thing with one kind of matter is light, moving upward; with the opposite matter, it is heavy, moving downward. Air and water possess both weight and lightness, sinking below some bodies and rising above others. Earth and fire are absolutely heavy and light, respectively. There must be as many distinct species of matter as there are elements (fire, air, water, earth). Each element moves according to its nature: earth to the center, fire to the extremity. If composed of one matter, all things would move the same way, contradicting observations. Elements' movements depend on their specific matter.

Chapter 4-6 Bodies' shapes affect their speed of movement, not the direction. A flat piece of iron floats, but smaller, round objects sink. Democritus' explanation that warm bodies lift broad objects fails, especially in air. Bodies that are easily divided or disrupted move differently. Broader objects cover more surface area, resisting division and floating, while narrow objects sink. Air, being more easily divided than water, affects movement. The force applied by a heavy object versus the continuum's resistance determines movement speed. Our examination of heavy and light phenomena is now complete.

Chapter 4-1 Heavy and light bodies move naturally due to their properties.

Chapter 4-2 Previous theories inadequately address absolute heaviness and lightness properties.

Chapter 4-3 Bodies move to natural places, influenced by inherent properties.

Chapter 4-4 Elements have distinct places and properties determining natural movements.

Chapter 4-5 Elements' movements depend on their specific matter and nature.

Chapter 4-6 Shape affects speed of movement, not direction or heaviness.