Aristotle quotes - page 11
It is necessary that every thing which is harmonized, should be generated from that which is void of harmony, and that which is void of harmony from that which is harmonized. ...But there is no difference, whether this is asserted of harmony, or of order, or composition... the same reason will apply to all of these.
Aristotle
Plato... introduces two infinities, because both in increase and diminution there appears to be transcendency, and a progression to infinity. Though... he did not use them: for neither is there infinity in numbers by diminution or division; since unity is a minimum: nor by increase; for he extends number as far as to the decad.
Aristotle
After these matters we ought perhaps next to discuss pleasure. For it is thought to be most intimately connected with our human nature, which is the reason why in educating the young we steer them by the rudders of pleasure and pain; it is thought, too, that to enjoy the things we ought and to hate the things we ought has the greatest bearing on virtue of character. For these things extend right through life, with a weight and power of their own in respect both to virtue and to the happy life, since men choose what is pleasant and avoid what is painful; and such things, it will be thought, we should least of all omit to discuss, especially since they admit of much dispute.
Aristotle
But it is better to assume principles less in number and finite, as Empedocles makes them to be. All philosophers... make principles to be contraries... (for Parmenides makes principles to be hot and cold, and these he demominates fire and earth) as those who introduce as principles the rare and the dense. But Democritus makes the principles to be the solid and the void; of which the former, he says, has the relation of being, and the latter of non-being. ...it is necessary that principles should be neither produced from each other, nor from other things; and that from these all things should be generated. But these requisites are inherent in the first contraries: for, because they are first, they are not from other things; and because they are contraries, they are not from each other.
Aristotle
Since the science of nature is conversant with magnitudes, motion, and time, each of which must necessarily be either infinite or finite...[we] should speculate the infinite, and consider whether it is or not; and if it is what it is. ...[A]ll those who appear to have touched on a philosophy of this kind... consider it as a certain principle of beings. Some, indeed, as the Pythagoreans and Plato, consider it, per se, not as being an accident to any thing else, but as having an essential subsistence... the Pythagoreans... consider the infinite as subsisting in sensibles; for they do not make number to be separate; and they assert that what is beyond the heavens is infinite; but Plato says that beyond the heavens there is not any body, nor ideas, because these are no where: he affirms, however, that the infinite is both in sensibles, and in ideas. ...Plato establishes two infinities, viz. the great and the small.
Aristotle
[I]t's gravity is the cause; and that which is heavy abides in the middle, and the earth is in the middle: in like manner also, the infinite will abide in itself, through some other cause... and will itself support itself. ...[T]he places of the whole and the part are of the same species; as of the whole earth and a clod, the place is downward; and of the whole of fire, and a spark, the place is upward. So that if the place of the infinite is in itself, there will be the same place also of a part of the infinite.
Aristotle
If, then, in the sphere of action there is some one end which we desire for its own sake, and for the sake of which we desire every thing else; and if we do not choose every thing for the sake of something else, for this would go on without limit, and our desire would be idle and futile, it is clear that this must be the supreme good, and the best thing of all.
Aristotle
But it is clear there is a difference in the ends proposed: for in some cases they are activities, and in others results beyond the mere activities, and where there are certain ends beyond and beside the actions, the results are naturally superior to the activities. Now, as there are numerous kinds of actions and numerous arts and sciences, it follows that the ends are also various. Thus the end of the healing art is health, of ship-building ships, of strategy victory, of economy wealth.
Aristotle
The natural way of doing this [seeking scientific knowledge or explanation of fact] 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 became known to us by later analysis...
Aristotle
The premisses of demonstrative knowledge must be true, primary, immediate, more knowable than and prior to the conclusion, which is further related to them as effect to cause... The premisses must be the cause of the conclusion, more knowable than it, and prior to it; its causes, since we posses scientific knowledge of a thing only when we know its cause; prior, in order to be causes; antecedently known, this antecedent knowledge being not our mere understanding of the meaning, but knowledge of the fact as well. Now 'prior' and 'more knowable' are ambiguous terms, for there is a difference between what is prior and more knowable in the order of being and what is prior and knowable to man. I mean that objects nearer to sense are prior and more knowable to man; objects without qualification prior and more knowable are those further from sense. Now the most universal causes are furthest from sense and particular causes are nearest to sense, and they are thus exactly opposed to each other.
Aristotle
[T]he ancient philosophers... all of them assert that the elements, and those things which are called by them principles, are contraries, though they establish them without reason, as if they were compelled to assert this by truth itself. They differ, however... that some of them assume prior, and others posterior principles; and some of them things more known according to reason, but others such as are more known according to sense: for some establish the hot and the cold, others the moist and the dry, others the odd and the even, and others strife and friendship, as the causes of generation. ...in a certain respect they assert the same things, and speak differently from each other. They assert different things... but the same things, so far as they speak analogously. For they assume principles from the same co-ordination; since, of contraries, some contain, and others are contained.
Aristotle
Since... nature is a principle of motion and mutation... it is necessary that we should not be ignorant of what motion is... But motion appears to belong to things continuous; and the infinite first presents itself to the view in that which is continuous. ...[F]requently ...those who define the continuous, employ the nature or the infinite, as if that which is divisible to infinity is continuous.
Aristotle
[B]ecause that which is finite is always bounded with reference to something... it is necessary that there should be no end... [N]umber also appears to be infinite, and mathematical magnitudes, and that which is beyond the heavens. And since that which is beyond is infinite, body also appears to be infinite, and it would seem that there are infinite worlds; for why is there rather void here than there? ...If also there is a vacuum, and an infinite place, it is necessary that there should be an infinite body: for in things which have a perpetual subsistence, capacity differs nothing from being. The speculation of the infinite is, however, attended with doubt: for many impossibilities happen both to those who do not admit that it has a subsistence, and to those who do. ...It is ...especially the province of a natural philosopher to consider if there be a sensible infinite magnitude.
Aristotle
[H]ow will one part of the infinite be above, and another below? Or how will it have extremes or a middle? Further still, every sensible body is in place; but the species and differences of place are upward and downward, before and behind, to the right hand and to the left: and these things not only thus subsist with relation to us, and by position, but have a definite subsistence in the universe itself. But it is impossible that these things should be in the infinite: and... that there should be an infinite place. But every body is in place; and therefore it is also impossible that there should be an infinite body. ...[T]herefore ...there is not an infinite body in energy.
Aristotle
[T]he infinite is in capacity. That, however, which is infinite in capacity is not to be assumed as that which is infinite in energy. ...[I]t has its being in capacity, and in division and diminution. ...[I]t is always possible to assume something beyond it. It does not, however, on this account surpass every definite magnitude; as in division it surpasses every definite magnitude, and will be less.
Aristotle