Metaphysics

It is the mark of an educated mind to be able to entertain a thought without accepting it.

If things do not turn out as we wish, we should wish for them as they turn out.

Those who assert that the mathematical sciences say nothing of the beautiful or the good are in error. For these sciences say and prove a great deal about them; if they do not expressly mention them, but prove attributes which are their results or definitions, it is not true that they tell us nothing about them. The chief forms of beauty are order and symmetry and definiteness, which the mathematical sciences demonstrate in a special degree.

The investigation of the truth is in one way hard, in another easy. An indication of this is found in the fact that no one is able to attain the truth adequately, while, on the other hand, no one fails entirely, but everyone says something true about the nature of all things, and while individually they contribute little or nothing to the truth, by the union of all a considerable amount is amassed.

[I]t is rather the case that we desire something because we believe it to be good than that we believe a thing to be good because we desire it. It is the thought that starts things off.

But with regard to incomposites, what is being or not being, and truth or falsity? A thing of this sort is not composite, so as to 'be' when it is compounded, and not to 'be' if it is separated, like 'that the wood is white' or 'that the diagonal is incommensurable'; nor will truth and falsity be still present in the same way as in the previous cases. In fact, as truth is not the same in these cases, so also being is not the same; but (a) truth or falsity is as follows--contact and assertion are truth (assertion not being the same as affirmation), and ignorance is non-contact. For it is not possible to be in error regarding the question what a thing is, save in an accidental sense; and the same holds good regarding non-composite substances (for it is not possible to be in error about them). And they all exist actually, not potentially; for otherwise they would have come to be and ceased to be; but, as it is, being itself does not come to be (nor cease to be); for if it had done so it would have had to come out of something. About the things, then, which are essences and actualities, it is not possible to be in error, but only to know them or not to know them. But we do inquire what they are, viz. whether they are of such and such a nature or not.

It is impossible that there should be demonstration of absolutely everything; [for then] there would be an infinite regress, so that there would still be no demonstration.

For it is owing to their wonder that men both now begin and at first began to philosophize.

[986a] [1] they assumed the elements of numbers to be the elements of everything, and the whole universe to be a proportion1 or number. Whatever analogues to the processes and parts of the heavens and to the whole order of the universe they could exhibit in numbers and proportions, these they collected and correlated;and if there was any deficiency anywhere, they made haste to supply it, in order to make their system a connected whole. For example, since the decad is considered to be a complete thing and to comprise the whole essential nature of the numerical system, they assert that the bodies which revolve in the heavens are ten; and there being only nine2 that are visible, they make the "antichthon"3 the tenth.We have treated this subject in greater detail elsewhere4; but the object of our present review is to discover from these thinkers too what causes they assume and how these coincide with our list of causes.Well, it is obvious that these thinkers too consider number to be a first principle, both as the material5 of things and as constituting their properties and states.6 The elements of number, according to them, are the Even and the Odd. Of these the former is limited and the latter unlimited; Unity consists of both [20] (since it is both odd and even)7; number is derived from Unity; and numbers, as we have said, compose the whole sensible universe.Others8 of this same school hold that there are ten principles, which they enunciate in a series of corresponding pairs: (1.) Limit and the Unlimited; (2.) Odd and Even; (3.) Unity and Plurality; (4.) Right and Left; (5.) Male and Female; (6.) Rest and Motion; (7.) Straight and Crooked; (8.) Light and Darkness; (9.) Good and Evil; (10.) Square and Oblong.

So while a thing in a finite time cannot come in contact with things quantitatively infinite, it can come in contact with things infinite in respect of divisibility: for in this sense the time itself is also infinite

For nothing is moved at haphazard, but in every case there must be some reason present [1071b]

El filósofo no pretende aparecer si no tal cual es, busca la verdad con el solo fin de conocer sin mira alguna de interés personal; su vida es un sacrificio perpetuo en honor a la ciencia.