outubro 24, 2007

«So too, in order to explain the features of nature, we are permitted to assume any hypothesis we please, provided we deduce from it by mathematical inference all the phenomena of nature. And a more important point to note is this, that there is hardly any assumption we can make from which the same effects cannot be deduced — although perhaps with more trouble — from the laws of nature explained previously. For because, by the operation of those laws, matter assumes successively all the forms of which it is capable, if we consider those forms in due order, we shall finally be able to arrive at the form that is the form og this world. So one need fear no error from a false hypothesis.»

Spinoza, Principles of Cartesian Philosophy, Part 3

outubro 22, 2007

«Next, we say that the principles we seek are such that we may demonstrate that from them the stars, the earth, etc., could have arisen. [ ] Now to discover these causes, the following are the requirements of a good hypothesis.

1. Considered only in itself, it must not imply any contradiction.
2. It must be the simplest that can be.
3. Following from (2), it must be very easy to know.
4. Everything that is observed in the whole of nature must be able to be deduced from it.»

Spinoza, Principles of Cartesian Philosophy, Part 3

outubro 18, 2007

«Then again, because the best way to understand the nature of Plants or Man is to consider in what way they gradually come into existence and are generated from their seeds, we must devise such principles as are the simplest and easiest to know, from which we may demonstrate that the stars, the earth, in short, everything we observe in this visible world, could have arisen as from certain seeds — although we may well know that they never did thus arise. For in this way we shall explain their nature far better than if we were to describe them only as they are now.
I say that we seek principles that are simple and easy to know; for unless they are such, we shall not be in need of them. The only reason why we assign seeds to things is to get to know their nature more easily and, like mathematicians, to ascend from the clearest to the more obscure and from the simplest to the more complex.»

Spinoza, Principles of Cartesian Philosophy, Part 3

outubro 16, 2007

Propostion 32. - «If a body B is surrounded on all sides by particles in motion, which at the same time are impelling it with equal force in all directions, as long as no other cause occurs it will remain unmoved in the same place.»

Proof. - «This proposition is self-evident. For if it were to move in any direction through the impulse of particles coming from one direction, the particles that move it would be impelling it with greater force than other particles that at the same time are impelling it in the opposite direction, with no effect [ ]. This would be contrary to the hypothesis.»

Spinoza, Principles of Cartesian Philosophy

outubro 11, 2007

«Everybody that moves in a circle
endeavours to move away from the center
of the circle that it describes.»

Spinoza, Principles of Cartesian Philosophy, Part II, Prop. 17

outubro 01, 2007

«Each single thing,
insofar as it is simple and undivided
and is considered only in itself,
always preserves in the same state,
as far as in it lies.»

Spinoza, Principles of Cartesian Philosophy, Part II, Prop. 14