The whole problem with the world is that fools and fanatics are always so certain of themselves, and wiser people so full of doubts.
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 not 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.
The demand for certainty is one which is natural to man, but is nevertheless an intellectual vice. So long as men are not trained to withhold judgment in the absence of evidence, they will be led astray by cocksure prophets, and it is likely that their leaders will be either ignorant fanatics or dishonest charlatans. To endure uncertainty is difficult, but so are most of the other virtues.
In all affairs it's a healthy thing now and then to hang a question mark on the things you have long taken for granted.
One of the painful things about our time is that those who feel certainty are stupid, and those with any imagination and understanding are filled with doubt and indecision.
Some care is needed in using Descartes' argument. "I think, therefore I am" says rather more than is strictly certain. It might seem as though we are quite sure of being the same person to-day as we were yesterday, and this is no doubt true in some sense. But the real Self is as hard to arrive at as the real table, and does not seem to have that absolute, convincing certainty that belongs to particular experiences.
To teach how to live without certainty and yet without being paralysed by hesitation is perhaps the chief thing that philosophy, in our age, can do for those who study it.
Dogmatism and skepticism are both, in a sense, absolute philosophies; one is certain of knowing, the other of not knowing. What philosophy should dissipate is certainty, whether of knowledge or ignorance.
Fools and fanatics are always so certain of themselves.
A habit of basing convictions upon evidence, and of giving to them only that degree or certainty which the evidence warrants, would, if it became general, cure most of the ills from which the world suffers.
The demand for certainty is one which is natural to man, but is nevertheless an intellectual vice.
Philosophy, though unable to tell us with certainty what is the true answer to the doubts which it raises, is able to suggest many possiblities which enlarge our thoughts and free them from the tyranny of custom. Thus, while diminishing our feeling of certainty as to what things are, it greatly increases our knowledge as to what the may be; it removes the somewhat arrogant dogmatism of those who have never travelled into the region of liberating doubt, and it keeps alive our sense of wonder by showing familar things in an unfamilar aspect
What men really want is not knowledge but certainty.
While the dogmatist is harmful, the sceptic is useless ...; one is certain of knowing, the other of not knowing. What philosophy should dissipate is certainty, whether of knowledge or of ignorance. Knowledge is not so precise a concept as is commonly thought. Instead of saying 'I know this', we ought to say 'I more or less know something more or less like this'. ... Knowledge in practical affairs has not the certainty or the precision of arithmetic.
The demand for certainty is one which is natural to man, but is nevertheless an intellectual vice. If you take your children for a picnic on a doubtful day, they will demand a dogmatic answer as to whether it will be fine or wet, and be disappointed in you when you cannot be sure.
All that passes for knowledge can be arranged in a hierarchy of degrees of certainty, with arithmetic and the facts of perception at the top.
I have throughout been curious about how much we can be said to know and with what degree of certainty or doubtfulness.
When one admits that nothing is certain one must, I think, also admit that some things are much more nearly certain than others. It is much more nearly certain that we are assembled here tonight than it is that this or that political party is in the right. Certainly there are degrees of certainty, and one should be very careful to emphasize that fact, because otherwise one is landed in an utter skepticism, and complete skepticism would, of course, be totally barren and completely useless.
Belief in a Divine mission is one of the many forms of certainty that have afflicted the human race.
Philosophy, though unable to tell us with certainty what is the true answer to the doubts which it raises, is able to suggest many possibilities which enlarge our thoughts and free them from the tyranny of custom.
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