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...
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Opus Majus, bk. 1, ch. 4. Translated by Robert B. Burke, in: Edward Grant (1974) Source Book in Medieval Science. Harvard University Press. p.93Roger Bacon
It is almost as difficult to make a man unlearn his errors as his knowledge. Mal-information is more hopeless than non-information; for error is always more busy than ignorance. Ignorance is a blank sheet, on which we may write; but error is a scribbled one, on which we must first erase. Ignorance is contented to stand still with her back to the truth; but error is more presumptuous, and proceeds in the same direction. Ignorance has no light, but error follows a false one. The consequence is, that error, when she retraces her footsteps, has further to go, before she can arrive at the truth, than ignorance.
Charles Caleb Colton
I wanted certainty in the kind of way in which people want religious faith. I thought that certainty is more likely to be found in mathematics than elsewhere. But I discovered that many mathematical demonstrations, which my teachers expected me to accept, were full of fallacies, and that, if certainty were indeed discoverable in mathematics, it would be in a new field of mathematics, with more solid foundations than those that had hitherto been thought secure. But as the work proceeded, I was continually reminded of the fable about the elephant and the tortoise. having constructed an elephant upon which the mathematical world could rest, I found the elephant tottering, and proceeded to construct a tortoise to keep the elephant from falling. But the tortoise was no more secure than the elephant, and after some twenty years of very arduous toil, I came to the conclusion that there was nothing more that I could do in the way of making mathematical knowledge indubitable.
Bertrand Russell
The philosophical tradition that goes from Descartes to Husserl, and indeed a large part of the philosophical tradition that goes back to Plato, involves a search for foundations: metaphysically certain foundations of knowledge, foundations of language and meaning, foundations of mathematics, foundations of morality, etc. […] Now, in the twentieth century, mostly under the influence of Wittgenstein and Heidegger, we have come to believe that this general search for these sorts of foundations is misguided.
Martin Heidegger
The philosophical tradition that goes from Descartes to Husserl, and indeed a large part of the philosophical tradition that goes back to Plato, involves a search for foundations: metaphysically certain foundations of knowledge, foundations of language and meaning, foundations of mathematics, foundations of morality, etc. […] Now, in the twentieth century, mostly under the influence of Wittgenstein and Heidegger, we have come to believe that this general search for these sorts of foundations is misguided.
Ludwig Wittgenstein
There is no certainty in sciences where one of the mathematical sciences cannot be applied, or which are not in relation with these mathematics.
Leonardo da Vinci
Bacon, Roger
Badawi, Abdullah Ahmad
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