For how do we know that the thoughts which occur in dreaming are false rather than those others which we experience when awake, since the former are often not less vivid and distinct than the latter?

I should consider that I know nothing about physics if I were able to explain only how things might be, and were unable to demonstrate that they could not be otherwise.

It must not be thought that it is ever possible to reach the interior earth by any perseverance in mining: both because the exterior earth is too thick, in comparison with human strength; and especially because of the intermediate waters, which would gush forth with greater impetus, the deeper the place in which their veins were first opened; and which would drown all miners.

With me, everything turns into mathematics.

This result could have been achieved either by his [God] endowing my intellect with a clear and distinct perception of everything about which I would ever deliberate, or simply by impressing the following rule so firmly upon my memory that I could never forget it: I should never judge anything that I do not clearly and distinctly understand.

How can you be certain that your whole life is not a dream?

Although my knowledge grows more and more, nevertheless I do not for that reason believe that it can ever be actually infinite, since it can never reach a point so high that it will be unable to attain any greater increase.