Galileo Galilei

I do not feel obliged to believe that same God, who has endowed us with sense, reason, and intellect has intended us to forgo their use. — — — God does not intend to forgo the use of sense, reason, and intellect that he has gifted us, but not to use in a wrong direction and the evil way. God has also enriched the knowledge of the devil that uses in a wrong way.

I see that you have hitherto been one of that herd who, in order to learn how matters such as this take place, and in order to acquire a knowledge of natural effects, do not exhaust themselves in waking and studying, and mortify themselves with experiments and observations, but retire into their studies and glance through an index and a table of contents to see whether Aristotle has said any thing about them; and, being assured of the true sense of his text, consider that nothing else can be known.

If I shall have sufficient strength to improve and amplify what was written and published by me up to now about motion by adding some little speculations, and in particular those relating to the force of percussion, in the investigation of which I have consumed hundreds and thousands of hours, and finally reduced this to very easy explanation, so that people can understand it in less than half an hour of time.

I think that in the discussion of natural problems we ought to begin not with the Scriptures, but with experiments and demonstrations.

I do not feel obliged to believe that the same God who has endowed us with senses, reason, and intellect has intended us to forgo their use and by some other means to give us knowledge which we can attain by them.

All inconveniences will be removed as you propound them. Up to this point, only the first and most general reasons have been mentioned which render it not entirely improbable that the daily rotation belongs to the earth rather than to the rest of the universe.

About ten months ago a report reached my ears that a certain Fleming had constructed a spyglass by means of which visible objects, though very distant from the eye of the observer, were distinctly seen as if nearby. Of the truly remarkable effect several experiences were related, to which some persons gave credence while others denied them. A few days later a report was confirmed to me in a letter from a noble Frenchman in Paris, Jacques Badovere, which caused me to apply myself wholeheartedly to inquire into means by which I might arrive at the invention of a similar instrument. This I did shortly afterwards, my basis being the theory of refraction. First I prepared a tube of lead, at the ends I fitted two glass lenses, both plane on one side while on the other side one was spherically convex and the other concave. Then placing my eye near the concave lens I perceived objects satisfactorily large and near, for they appeared three times closer and nine times larger than when seen with the naked eye alone. Next I constructed another one, more accurate, which represented objects as enlarged more than sixty times. Finally, sparing neither labor nor expense, I succeeded in constructing for myself so excellent an instrument that objects seen by means of it appeared nearly one thousand times larger and over thirty times closer than when regarded with our natural vision.

Names and attributes must be accommodated to the essence of things, and not the essence to the names, since things come first and names afterwards.

Nature first made things in
her own way, and then made human reason skillful enough to be able to understand, but
only by hard work, some part of her secrets.

My dear Kepler, I wish that we might laugh at the stupidity of the human herd. What do you have to say about the principal philosophers of this academy who are filled with the stubbornness of an asp and do not want to look at either the planets, the moon or the telescope, even though I have freely and deliberately offered them the opportunity a thousand times? Truly, just as the asp stops its ears, so do these philosophers shut their eyes to the light of truth.

Philosophy is written in that great book which ever lies before our eyes — I mean the universe — but we cannot understand it if we do not first learn the language and grasp the symbols, in which it is written. This book is written in the mathematical language, and the symbols are triangles, circles and other geometrical figures, without whose help it is impossible to comprehend a single word of it; without which one wanders in vain through a dark labyrinth.

It always seems to me extreme rashness on the part of some when they want to make human abilities the measure of what nature can do. On the contrary, there is not a single effect in nature, even the least that exists, such that the most ingenious theorists can arrive at a complete understanding of it. This vain presumption of understanding everything can have no other basis than never understanding anything. For anyone who had experienced just once the perfect understanding of one single thing, and had truly tasted how knowledge is accomplished, would recognize that of the infinity of other truths he understands nothing.

I entertain no doubts as to the truth of the transfinites, which I have recognized with God's help.

Of such are the mathematical sciences alone; that is, geometry and arithmetic, in which the Divine intellect indeed knows infinitely more propositions, since it knows all. But with regard to those few which the human intellect does understand, I believe its knowledge equals the Divine in objective certainty, for here it succeeds in understanding necessity, beyond which there can be no greater sureness.

Well, since paradoxes are at hand, let us see how it might be demonstrated that in a finite continuous extension it is not impossible for infinitely many voids to be found.