philosopher, physicist, theologian, musicologist, music theorist, astrologer, alchemist, translator, inventor, mathematician, writer
🔗 Read on Wikipedia1219 – 1291
Argument is conclusive... but... it does not remove doubt, so that the mind may never rest in the sure knowledge of the truth, unless it finds it by the method of experiment. For if any man who never saw fire proved by satisfactory arguments that fire burns, his hearer's mind would never be satisfied, nor would he avoid the fire until he put his hand in it that he might learn by experiment what argument taught.
There are in fact four very significant stumbling blocks in the way of grasping the truth, which hinder every man however learned, and scarcely allow anyone to win a clear title to wisdom, namely, the example of weak and unworthy authority, longstanding custom, the feeling of the ignorant crowd, and the hiding of our own ignorance while making a display of our apparent knowledge.
Many secrets of art and nature are thought by the unlearned to be magical.
Reasoning draws a conclusion and makes us grant the conclusion, but does not make the conclusion certain, nor does it remove doubt so that the mind may rest on the intuition of truth, unless the mind discovers it by the path of experience.
If in other sciences we should arrive at certainty without doubt and truth without error, it behooves us to place the foundations of knowledge in mathematics...
Argument is conclusive, but it does not remove doubt, so that the mind may rest in the sure knowledge of the truth, unless it finds it by the method of experiment.
I shall draw... a figure (which all these matters are made clear as far as possible on a surface, but the full demonstration would require a body like the eye... The eye of a cow, pig, and other animals can be used for illustration, if anyone wishes to experiment.
Mathematics is the gate and key of the sciences. ... Neglect of mathematics works injury to all knowledge, since he who is ignorant of it cannot know the other sciences or the things of this world. And what is worse, men who are thus Ignorant are unable to perceive their own ignorance and so do not seek a remedy.
All science requires mathematics. The knowledge of mathematical things is almost innate in us. This is the easiest of sciences, a fact which is obvious in that no one's brain rejects it; for laymen and people who are utterly illiterate know how to count and reckon.
For the things of this world cannot be made known without a knowledge of mathematics.
Reasoning draws a conclusion, but does not make the conclusion certain, unless the mind discovers it by the path of experience.