by Aristotle


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ISBN-13: 9780486813516
Publisher: Dover Publications
Publication date: 06/21/2017
Series: Dover Thrift Editions
Edition description: Reprint
Pages: 272
Product dimensions: 5.00(w) x 8.00(h) x (d)

About the Author

Student of Plato and teacher of Alexander the Great, Aristotle (384–322 BCE) is a giant of Greek philosophy. He made significant contributions to a remarkable range of areas, including logic, metaphysics, mathematics, physics, biology, botany, ethics, politics, agriculture, medicine, dance, and theater. The founder of formal logic and a pioneer in zoology, Aristotle influenced every subsequent scientist and philosopher through his development of the scientific method.

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By Aristotle

Dover Publications, Inc.

Copyright © 2017 Dover Publications, Inc.
All rights reserved.
ISBN: 978-0-486-82229-7


1 When the objects of an inquiry, in any department, have principles, conditions, or elements, it is through acquaintance with these that knowledge, that is to say scientific knowledge, is attained. For we do not think that we know a thing until we are acquainted with its primary conditions or first principles, and have carried our analysis as far as its simplest elements. Plainly therefore in the science of Nature, as in other branches of study, our first task will be to try to determine what relates to its principles.

The natural way of doing this is to start from the things which are more knowable and obvious to us and proceed towards those which are clearer and more knowable by nature; for the same things are not 'knowable relatively to us' and 'knowable' without qualification. So in the present inquiry we must follow this method and advance from what is more obscure by nature, but clearer to us, towards what is more clear and more knowable by nature.

Now what is to us plain and obvious at first is rather confused masses, the elements and principles of which become known to us later by analysis. Thus we must advance from generalities to particulars; for it is a whole that is best known to sense-perception, and a generality is a kind of whole, comprehending many things within it, like parts. Much the same thing happens in the relation of the name to the formula. A name, e.g., 'round,' means vaguely a sort of whole: its definition analyses this into its particular senses. Similarly a child begins by calling all men 'father,' and all women 'mother,' but later on distinguishes each of them.

2 The principles in question must be either (a) one or (b) more than one.

If (a) one, it must be either (i) motionless, as Parmenides and Melissus assert, or (ii) in motion, as the physicists hold, some declaring air to be the first principle, others water.

If (b) more than one, then either (i) a finite or (ii) an infinite plurality. If (i) finite (but more than one), then either two or three or four or some other number. If (ii) infinite, then either as Democritus believed one in kind, but differing in shape or form; or different in kind and even contrary.

A similar inquiry is made by those who inquire into the number of existents: for they inquire whether the ultimate constituents of existing things are one or many, and if many, whether a finite or an infinite plurality. So they too are inquiring whether the principle or element is one or many.

Now to investigate whether Being is one and motionless is not a contribution to the science of Nature. For just as the geometer has nothing more to say to one who denies the principles of his science — this being a question for a different science or for one common to all — so a man investigating principles cannot argue with one who denies their existence. For if Being is just one, and one in the way mentioned, there is a principle no longer, since a principle must be the principle of some thing or things.

To inquire therefore whether Being is one in this sense would be like arguing against any other position maintained for the sake of argument (such as the Heraclitean thesis, or such a thesis as that Being is one man) or like refuting a merely contentious argument — a description which applies to the arguments both of Melissus and of Parmenides: their premisses are false and their conclusions do not follow. Or rather the argument of Melissus is gross and palpable and offers no difficulty at all: accept one ridiculous proposition and the rest follows — a simple enough proceeding.

We physicists, on the other hand, must take for granted that the things that exist by nature are, either all or some of them, in motion — which is indeed made plain by induction. Moreover, no man of science is bound to solve every kind of difficulty that may be raised, but only as many as are drawn falsely from the principles of the science: it is not our business to refute those that do not arise in this way: just as it is the duty of the geometer to refute the squaring of the circle by means of segments, but it is not his duty to refute Antiphon's proof. At the same time the holders of the theory of which we are speaking do incidentally raise physical questions, though Nature is not their subject: so it will perhaps be as well to spend a few words on them, especially as the inquiry is not without scientific interest.

The most pertinent question with which to begin will be this: In what sense is it asserted that all things are one? For 'is' is used in many senses. Do they mean that all things 'are' substance or quantities or qualities? And, further, are all things one substance — one man, one horse, or one soul — or quality and that one and the same — white or hot or something of the kind? These are all very different doctrines and all impossible to maintain.

For if both substance and quantity and quality are, then, whether these exist independently of each other or not, Being will be many.

If on the other hand it is asserted that all things are quality or quantity, then, whether substance exists or not, an absurdity results, if indeed the impossible can properly be called absurd. For none of the others can exist independently: substance alone is independent: for everything is predicated of substance as subject. Now Melissus says that Being is infinite. It is then a quantity. For the infinite is in the category of quantity, whereas substance or quality or affection cannot be infinite except through a concomitant attribute, that is, if at the same time they are also quantities. For to define the infinite you must use quantity in your formula, but not substance or quality. If then Being is both substance and quantity, it is two, not one: if only substance, it is not infinite and has no magnitude; for to have that it will have to be a quantity.

Again, 'one' itself, no less than 'being,' is used in many senses, so we must consider in what sense the word is used when it is said that the All is one.

Now we say that (a) the continuous is one or that (b) the indivisible is one, or (c) things are said to be 'one,' when their essence is one and the same, as 'liquor' and 'drink.'

If (a) their One is one in the sense of continuous, it is many, for the continuous is divisible ad infinitum.

15 There is, indeed, a difficulty about part and whole, perhaps not relevant to the present argument, yet deserving consideration on its own account — namely, whether the part and the whole are one or more than one, and how they can be one or many, and, if they are more than one, in what sense they are more than one. (Similarly with the parts of wholes which are not continuous.) Further, if each of the two parts is indivisibly one with the whole, the difficulty arises that they will be indivisibly one with each other also.

But to proceed: If (b) their One is one as indivisible, nothing will have quantity or quality, and so the one will not be infinite, as Melissus says — nor, indeed, limited, as Parmenides says, for though the limit is indivisible, the limited is not.

But if (c) all things are one in the sense of having the same definition, like 'raiment' and 'dress,' then it turns out that they are maintaining the Heraclitean doctrine, for it will be the same thing 'to be good' and 'to be bad,' and 'to be good' and 'to be not good,' and so the same thing will be 'good' and 'not good,' and man and horse; in fact, their view will be, not that all things are one, but that they are nothing; and that 'to be of such-and-such a quality' is the same as 'to be of such-and-such a size.'

Even the more recent of the ancient thinkers were in a pother lest the same thing should turn out in their hands both one and many. So some, like Lycophron, were led to omit 'is,' others to change the mode of expression and say 'the man has been whitened' instead of 'is white,' and 'walks' instead of 'is walking,' for fear that if they added the word 'is' they should be making the one to be many — as if 'one' and 'being' were always used in one and the same sense. What 'is' may be many either in definition (for example 'to be white' is one thing, 'to be musical' another, yet the same thing may be both, so the one is many) or by division, as the whole and its parts. On this point, indeed, they were already getting into difficulties and admitted that the one was many — as if there was any difficulty about the same thing being both one and many, provided that these are not opposites; for 'one' may mean either 'potentially one' or 'actually one.'

3 If, then, we approach the thesis in this way it seems impossible for all things to be one. Further, the arguments they use to prove their position are not difficult to expose. For both of them reason contentiously — I mean both Melissus and Parmenides. [Their premisses are false and their conclusions do not follow. Or rather the argument of Melissus is gross and palpable and offers no difficulty at all: admit one ridiculous proposition and the rest follows — a simple enough proceeding.]

The fallacy of Melissus is obvious. For he supposes that the assumption 'what has come into being always has a beginning' justifies the assumption 'what has not come into being has no beginning.' Then this also is absurd, that in every case there should be a beginning of the thing — not of the time and not only in the case of coming to be in the full sense but also in the case of coming to have a quality — as if change never took place suddenly. Again, does it follow that Being, if one, is motionless? Why should it not move, the whole of it within itself, as parts of it do which are unities, e.g., this water? Again, why is qualitative change impossible? But, further, Being cannot be one in form, though it may be in what it is made of. (Even some of the physicists hold it to be one in the latter way, though not in the former.) Man obviously differs from horse in form, and contraries from each other.

The same kind of argument holds good against Parmenides also, besides any that may apply specially to his view: the answer to him being that 'this is not true' and 'that does not follow.' His assumption that one is used in a single sense only is false, because it is used in several. His conclusion does not follow, because if we take only white things, and if 'white' has a single meaning, none the less what is white will be many and not one. For what is white will not be one either in the sense that it is continuous or in the sense that it must be defined in only one way. 'Whiteness' will be different from 'what has whiteness.' Nor does this mean that there is anything that can exist separately, over and above what is white. For 'whiteness' and 'that which 30 is white' differ in definition, not in the sense that they are things which can exist apart from each other. But Parmenides had not come in sight of this distinction.

It is necessary for him, then, to assume not only that 'being' has the same meaning, of whatever it is predicated, but further that it means (1) what just is and (2) what is just one.

It must be so, for (1) an attribute is predicated of some subject, so that the subject to which 'being' is attributed 35 will not be, as it is something different from 'being.' Something, therefore, which is not will be. Hence 'substance' will not be a predicate of anything else. For the subject cannot be a being, unless 'being' means several things, in such a way that each is something. But ex hypothesi 'being' means only one thing.

If, then, 'substance' is not attributed to anything, but other things are attributed to it, how does 'substance' 5 mean what is rather than what is not? For suppose that 'substance' is also 'white.' Since the definition of the latter is different (for being cannot even be attributed to white, as nothing is which is not 'substance'), it follows that 'white' is not-being — and that not in the sense of a particular not-being, but in the sense that it is not at all. Hence 'substance' is not; for it is true to say that it is white, which we found to mean not-being. If to avoid this we say that even 'white' means substance, it follows that 'being' has more than one meaning.

In particular, then, Being will not have magnitude, if it is substance. For each of the two parts must be in a different sense.

(2) Substance is plainly divisible into other substances, if we consider the mere nature of a definition. For instance, if 'man' is a substance, 'animal' and 'biped' must also be substances. For if not substances, they must be attributes — and if attributes, attributes either of (a) man or of (b) some other subject. But neither is possible.

(a) An attribute is either that which may or may not belong to the subject or that in whose definition the subject of which it is an attribute is involved. Thus 'sitting' is an example of a separable attribute, while 'snubness' contains the definition of 'nose,' to which we attribute snubness. Further, the definition of the whole is not contained in the definitions of the contents or elements of the definitory formula; that of 'man' for instance in 'biped,' or that of 'white man' in 'white.' If then this is so, and if 'biped' is supposed to be an attribute of 'man,' it must be either separable, so that 'man' might possibly not be 'biped,' or the definition of 'man' must come into the definition of 'biped' — which is impossible, as the converse is the case.

(b) If, on the other hand, we suppose that 'biped' and 'animal' are attributes not of man but of something else, and are not each of them a substance, then 'man' too will be an attribute of something else. But we must assume that substance is not the attribute of anything, and that the subject of which both 'biped' and 'animal' and each separately are predicated is the subject also of the complex 'biped animal.'

Are we then to say that the AH is composed of indivisible substances? Some thinkers did, in point of fact, give way to both arguments. To the argument that all things are one if being means one thing, they conceded that not-being is; to that from bisection, they yielded by positing atomic magnitudes. But obviously it is not true that if being means one thing, and cannot at the same time mean the contradictory of this, there will be nothing which is not, for even if what is not cannot be without qualification, there is no reason why it should not be a particular not-being. To say that all things will be one, if there is nothing besides Being itself, is absurd. For who understands 'being itself' to be anything but a particular substance? But if this is so, there is nothing to prevent there being many beings, as has been said.

It is, then, clearly impossible for Being to be one in this sense.

4 The physicists on the other hand have two modes of explanation.

The first set make the underlying body one — either one of the three or something else which is denser than fire and rarer than air — then generate everything else from this, and obtain multiplicity by condensation and rarefaction. Now these are contraries, which may be generalized into 'excess and defect.' (Compare Plato's 'Great and Small' — except that he makes these his matter, the one his form, while the others treat the one which underlies as matter and the contraries as differentiae, i.e., forms).

The second set assert that the contrarieties are contained in the one and emerge from it by segregation, for example Anaximander and also all those who assert that 'what is' is one and many, like Empedocles and Anaxagoras; for they too produce other things from their mixture by segregation. These differ, however, from each other in that the former imagines a cycle of such changes, the latter a single series. Anaxagoras again made both his 'homrœmerous' substances and his contraries infinite in multitude, whereas Empedocles posits only the so-called elements.


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Table of Contents


1. The scope and method of this book.
2. The problem: the number and character of the first principles of nature.
185a 20. Reality is not one in the way that Parmenides and Melissus supposed.
3. Refutation of their arguments.
4. Statement and examination of the opinions of the natural philosophers.
5. The principles are contraries.
6. The principles are two, or three, in number.
7. The number and nature of the principles.
8. The true opinion removes the difficulty felt by the early philosophers.
9. Further reflections on the first principles of nature.


1. Nature and the natural.
2. Distinction of the natural philosopher from the mathematician and the metaphysician.
C. The conditions of change.
3. The essential conditions.
4. The opinions of others about chance and spontaneity.
5. Do chance and spontaneity exist? What is chance and what are its characteristics?
6. Distinction between chance and spontaneity, and between both and the essential conditions of change.
D. Proof in natural philosophy.
7. The physicist demonstrates by means of the four conditions of change.
8. Does nature act for an end?
9. The sense in which necessity is present in natural things.


A. Motion.
1, 2. The nature of motion.
3. The mover and the moved.
B. The infinite.
4. Opinions of the early philosophers.
203b 15. Main arguments for belief in the infinite.
5. Criticism of the Pythagorean and Platonic belief in a separately existing infinite.
204a 34. There is no infinite sensible body.
6. That the infinite exists and how it exists.
206b 33. What the infinite is.
7. The various kinds of infinite.
207b 34. Which of the four conditions of change the infinite is to be referred to.
8. Refutation of the arguments for an actual infinite.


A. Place.
1. Does place exist?
209a 2. Doubts about the nature of place.
2. Is place matter or form?
3. Can a thing be in itself or a place be in a place?
4. What place is.
5. Corollaries.
B. The void.
6. The views of others about the void.
7. What ‘void’ means.
214a 16. Refutation of the arguments for belief in the void.
8. There is no void separate from bodies.
216a 26. There is no void occupied by any body.
9. There is no void in bodies.
C. Time.
10. Doubts about the existence of time.
218a 31. Various opinions about the nature of time.
11. What time is.
219b 9. The ‘now.’
12. Various attributes of time.
220b 32. The things that are in time.
13. Definitions of temporal terms.
14. Further reflections about time.


1. Classification of movements and changes.
224b 35. Classification of changes per se.
2. Classification of movements per se.
226b 10. The unmovable.
3. The meaning of ‘together,’ ‘apart,’ ‘touch,’ ‘intermediate,’ ‘successive,’ ‘contiguous,’ ‘continuous.’
4. The unity and diversity of movements.
5. Contrariety of movement.
6. Contrariety of movement and rest.
230a 18. Contrariety of natural and unnatural movement or rest.


1, 2. Every continuum consists of continuous and divisible parts.
3. A moment is indivisible and nothing is moved, or rests, in a moment.
4. Whatever is moved is divisible.
234b 21. Classification of movement.
235a 13. The time, the movement, the being-in-motion, the moving body, and the sphere of
movement, are all similarly divided.
5. Whatever has changed is, as soon as it has changed, in that to which it has changed.
235b 32. That in which (directly) it has changed is indivisible.
236a 7. In change there is a last but no first element.
6. In whatever time a thing changes (directly), it changes in any part of that time.
236b 32. Whatever changes has changed before, and whatever has changed, before was changing.
7. The finitude or infinity of movement, of extension, and of the moved.
8. Of coming to rest, and of rest.
239a 23. A thing that is moved in any time directly is in no part of that time in a part of the space
through which it moves.
9. Refutation of the arguments against the possibility of movement.
10. That which has not parts cannot move.
241a 26. Can change be infinite?


1. Whatever is moved is moved by something.
242a 19. There is a first movent which is not moved by anything else.
2. The movent and the moved are together.
3. All alteration pertains to sensible qualities.
4. Comparison of movements.
5. Proportion of movements.


1. There always has been and always will be movement.
2. Refutation of objections to the eternity of movement.
3. There are things that are sometimes in movement, sometimes at rest.
4. Whatever is in movement is moved by something else.
5. The first movent is not moved by anything outside itself.
257a 31. The first movent is immovable.
6. The immovable first movent is eternal and one.
259a 20. The first movent is not moved even incidentally.
259b 32. The primum mobile is eternal.
7. Locomotion is the primary kind of movement.
261a 28. No movement or change is continuous except locomotion.
8. Only circular movement can be continuous and infinite.
9. Circular movement is the primary kind of locomotion.
265a 27. Confirmation of the above doctrines.
10. The first movent has no parts nor magnitude, and is at the circumference of the world.

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Physics 3.4 out of 5 based on 0 ratings. 9 reviews.
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