Aristotle examines whether place could be identified with either the matter or the form of a thing. Sometimes “place” (81) refers to the general location containing all bodies and sometimes to the immediate location surrounding a particular body. Since a place seems to contain a body, one might think it corresponds either to the body’s form (which defines its boundary) or to its matter (which underlies its extension). Aristotle rejects both possibilities. Form and matter are inseparable from the object whose form and matter they are, whereas place can remain while different bodies replace one another within it. A place therefore exists independently of the particular body occupying it, much like a vessel that holds different contents.

He also notes that if place were form or matter, movement to a place would be impossible—place itself would require another place. Aristotle concludes that place cannot be identified with either matter or form, though its nature still requires clarification.

Aristotle examines the different senses in which one thing can be said to be “in” (83) another. The expression may refer to a part within a whole, a whole consisting of its parts, a species within a genus, a genus within a definition, a form within matter, something under the control of an agent, something directed toward an end, or—most fundamentally—a body contained in a vessel or place.

Aristotle considers whether anything can be in itself. In a derivative sense, this may seem possible when container and contained are parts of a larger whole, as with wine in a jar forming a jar of wine. Aristotle argues, however, that nothing can be in itself in “the primary sense” (84). Container and contained must remain distinct and their definitions differ. This analysis resolves the difficulty, Aristotle believes, that place might require another place. Since “in” can have meanings other than spatial containment, the regress does not arise. Aristotle says that place cannot be matter or form, but “must be something else” (85).

Aristotle seeks to determine “what actually is place” (85) by identifying the properties that belong to it. Place appears to be the immediate container of a body, not a part of it, and equal in size to the body it contains. It can remain when a body leaves it, and natural bodies move toward their proper places, such as upward or downward.

He examines several possibilities for what place might be: The form of the body, its matter, an empty extension between boundaries, or the boundary itself. Aristotle rejects the first three. Form and matter are “not separable from the object” (87), whereas place is separable. The idea of an independent extension would imply multiple overlapping places. Aristotle suggests that place is the inner boundary of the containing body where it touches what it contains. In this sense, place resembles an unmoving vessel that defines where a body is located.

Aristotle argues that a body is in place only if it is contained by another body. If nothing surrounds it, it cannot properly be said to be in a place. For this reason, the universe as a whole is not in a place, since nothing exists outside it to contain it and “the heavens are not in anything else” (89). Individual bodies within the universe do occupy places because each is contained by another body, forming a sequence: Earth in water, water in air, air in fire, and fire in the heavens.

Aristotle distinguishes between things potentially in place and things actually in place. Bodies capable of movement or growth are in place in their own right, while other things may be in place only coincidentally. This account resolves earlier difficulties. Place does not expand with bodies, two bodies do not occupy the same place, and place does not require another place. Aristotle says that place exists as the boundary of a containing body that touches the body it contains.

Aristotle examines the arguments for and against the existence of “void” (91). Some thinkers claim that void is a kind of empty place capable of containing bodies, distinguishing between a plenum (which is filled) and a void (which is empty). Others deny the existence of void, though Aristotle notes that some of their arguments only show that air is something rather than proving that empty space cannot exist.

Supporters of void offer several arguments. They claim that movement and growth would be impossible without empty space, because a completely full universe could not receive additional bodies. They also argue that compression and contraction—such as in containers or bodies—imply the presence of void within them. Growth likewise seems to require space for additional matter. The Pythagoreans, Aristotle notes, also propose that void exists and enters the world from the infinite, separating and distinguishing things. Aristotle summarizes these competing arguments before proceeding to evaluate them.

Aristotle begins by clarifying “what the term ‘void’ means” (92). Most take void to be a place containing nothing, because they assume that everything that exists is body and that every body must be in a place. In this view, void is simply a place where no body is present. Since bodies are tangible and possess weight or lightness, void would therefore be a place in which nothing heavy or light exists.

Aristotle notes that this definition leads to difficulties, such as implying that a point would count as a void. Properly speaking, he says, void must refer to a place capable of containing an extended body but currently lacking one. Some thinkers also describe void as a place lacking any specific substance or body, sometimes even identifying it with the matter of bodies. Aristotle rejects this, since matter cannot exist separately from objects, while void is supposed to exist independently.

He then refutes the arguments for void. Even if place exists, it does not follow that an empty extension separate from bodies exists. Movement and change do not require void, because bodies can move by displacing one another within a continuous plenum. Compression and growth can also be explained without void, either by the expulsion or transformation of matter. Aristotle claims that the arguments offered for the existence of void fail to demonstrate that such a thing exists.

Aristotle argues that there is “no separated void” (94). If natural bodies such as fire and earth each have their own natural motions, these motions must arise from the nature of the bodies themselves, not from void. A void, lacking any distinctions such as above or below, could not determine different directions of motion. Without such distinctions, natural motion would be impossible. He also argues that motion in a void would lead to contradictions. In ordinary movement, bodies travel faster or slower depending on the resistance of the medium and the weight or lightness of the moving object. In a void, however, there would be no resistance. As a result, motion would occur at equal speeds regardless of weight, which contradicts observed differences in motion.

Furthermore, Aristotle maintains that if a void existed, bodies placed within it would have no reason to stop moving at one place rather than another, leading to continuous motion without explanation. He also notes that if void were an empty extension, bodies could coincide with the space they occupy, producing the absurd result that multiple bodies might occupy the same place. From these arguments, Aristotle concludes that “a separated void” (99) cannot exist.

Aristotle examines the argument that “rarity and density” (99) prove the existence of void. Some thinkers claim that compression and expansion require empty spaces within bodies; otherwise, change would be impossible, the universe would swell outward, or every transformation would require an equal exchange of matter. In this view, rare bodies contain void spaces between their parts. Aristotle rejects this interpretation. If rarity meant that bodies contained separate voids, he says, this would contradict his earlier arguments that no void exists independently of bodies. Even if void were thought to exist only within rare bodies, it would still fail to explain motion, since void itself cannot move or determine direction.

Instead, Aristotle explains compression and expansion through changes in the same underlying matter. Matter that is potentially hot or cold, dense or rare, becomes actually one or the other without anything being added or removed. When water becomes air, or air becomes water, the same matter persists but changes in actuality, producing differences in size or density. Thus, rarity and density result from the potential of matter rather than from empty spaces within bodies. He concludes that there is neither a separate void nor a void contained within bodies, and that natural change can be explained without it.

Aristotle begins his investigation of time by presenting the difficulties involved in understanding it. A major problem is whether time “is a real entity” (102) as well as the true nature of time. The past no longer exists and the future does not yet exist, he reasons, yet together they make up the whole of time. This raises the question of how something composed of non-existent parts could itself exist. Another difficulty concerns the present moment, or the “now” (103). Time appears divisible into past and future, with the now marking the boundary between them.

Aristotle, however, notes problems with both possibilities: If each now is different from the previous one, it becomes difficult to explain how earlier nows cease to exist; if the now remains the same, then events separated by long periods would occur simultaneously. Thus, the nature of the now is unclear.

Aristotle also reviews earlier theories about time. Some thinkers claim that time is the motion of the universe or the heavenly sphere, while others associate it with change in general. Aristotle rejects these views. Change occurs only in particular things, while time is present everywhere. Moreover, speed and slowness are defined by time, so time itself cannot simply be change.

Aristotle argues that although time is not identical with change, it cannot exist “without change” (104). When no change is perceived, time seems not to pass, as in cases where a person sleeps without noticing any events. When change is noticed, however, people immediately judge that time has passed. This shows that time is connected with change, though it is not itself change.

Aristotle therefore examines what aspect of change time might be. Since change occurs along a continuous magnitude and has a sequence of before and after, time follows this structure as well. We recognize time when we distinguish earlier and later moments within a process of change. When the mind marks two different “nows” (106) and recognizes something between them, it judges that time has elapsed.

From this Aristotle concludes that time is the number of change with respect to before and after. Time measures change by counting the sequence of earlier and later stages. The now functions like a boundary or unit that divides time, similar to how a point divides a line. In this way, time is continuous yet also divisible. Aristotle therefore defines time as the “number of change in respect of before and after” (108).

Aristotle clarifies further features of time based on his definition of time as the number of change with respect to before and after. Like other numbers, time can be considered in two ways. In terms of plurality, a smallest unit can be identified. In terms of magnitude, there is no smallest time because time (like a line) is continuously divisible. Time is described as long or short and as much or little, but not as fast or slow. Speed belongs to change, not to time itself. Time remains the same everywhere at a given moment, but past and future times differ because the sequence of nows that mark change is continually different.

Aristotle explains that time measures change and is also measured by it. Just as we count objects by number, we recognize time through changes that occur. Something is said to be “in time” (110) when its existence is measured by time. Thus events, changes, and states are contained within time in the same way that things in number are contained by number or things in place by place. Since time measures change, it also measures rest. However, things that are eternal are not in time, since their existence is not measured by time and they are unaffected by it.

Aristotle clarifies common temporal expressions such as recently, long ago, and suddenly. He reiterates that time itself tends toward destruction rather than generation because it accompanies change. The now, he says, is “what holds time together” (112).

Aristotle concludes that every change and every changing object occurs “in time” (114). The concepts of faster and slower apply to all change, and these distinctions depend on the notions of before and after. Since before and after are defined in relation to the present moment, or now, and the now belongs to time, every change must therefore occur within time.

He explains that time seems to be everywhere because it is closely tied to change. Since things on earth, in the sea, and in the heavens all undergo change, time accompanies them all. Aristotle also considers whether time could exist without mind. Since time is a number of change—and numbering requires a mind to count—time in its full sense requires a mind. However, the underlying sequence of before and after in change could still exist even without a mind to count it.

Time is not the number of one specific type of change but of continuous change in general. Different changes may occur simultaneously, yet they share the same time if their limits coincide. Aristotle also notes that circular motion, especially the motion of the heavens, serves as the primary measure of time because it is uniform and regular. This connection between time and the circular motion of the heavens explains why people often think of time and natural processes as cyclical. He concludes that time itself has now been fully explained along with its related concepts.