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Philosopher Quotes - page 13 - Quotesdtb.com
Philosopher Quotes - page 13
Mathematics have a triple aim. They must furnish an instrument for the study of nature. But that is not all: they have a philosophic aim and, I dare maintain, an esthetic aim. They must aid the philosopher to fathom the notions of number, of space, of time. And above all, their adepts find therein delights analogous to those given by painting and music. They admire the delicate harmony of numbers and forms; they marvel when a new discovery opens to them an unexpected perspective; and has not the joy they thus feel the esthetic character, even though the senses take no part therein? Only a privileged few are called to enjoy it fully, it is true, but is not this the case for all the noblest arts?
This is why I do not hesitate to say that mathematics deserve to be cultivated for their own sake, and the theories inapplicable to physics as well as the others. Even if the physical aim and the esthetic aim were not united, we ought not to sacrifice either.
Henri Poincaré
[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
You want to have proven to you that the soul is imperishable and immortal, and you think that the philosopher who is confident in death has but a vain and foolish confidence, if he thinks that he will fare better than one who has led another sort of life, in the world below, unless he can prove this; and you say that the strength and divinity of the soul, and of her existence prior to our becoming men, does not necessarily imply her immortality. ...For any man, who is not devoid of natural feeling, has reason to fear, if he has no knowledge or proof of the soul's immortality. That is what I suppose you to say, Cebes, which I designedly repeat, in order that nothing may escape us...
Socrates