The beliefs which we have ...

The beliefs which we have most warrant for have no safeguard to rest on but a standing invitation to the whole world to prove them unfounded. If the challenge is not accepted, or is accepted and the attempt fails, we are far enough from certainty still; but we have done the best that the existing state of human reason admits of; we have neglected nothing that could give the truth a chance of reaching us.
The beliefs which we have most warrant for have no safeguard to rest on but a standing invitation to the whole world to prove them unfounded. If the challenge is not accepted, or is accepted and the attempt fails, we are far enough from certainty still; but we have done the best that the existing state of human reason admits of; we have neglected nothing that could give the truth a chance of reaching us.
 John Stuart Mill

Quotes from the same author

Accordingly, France Had Voltaire, and his school of negative thinkers, and England (or rather Scotland) had the profoundest negative thinker on record, David Hume: a man, the peculiarities of whose mind qualified him to detect failure of proof, and want of logical consistency, at a depth which French skeptics, with their comparatively feeble powers of analysis and abstractions stop far short of, and which German subtlety alone could thoroughly appreciate, or hope to rival.
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 John Stuart Mill
What citizens of a free country would listen to any offers of good and skillful administration in return for the abdication of freedom?
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 John Stuart Mill
Men and governments must act to the best of their ability. There is no such thing as absolute certainty but there is assurance sufficient for the purposes of human life.
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 John Stuart Mill
When one's ideas are not challenged, one's ability to defend them weakens.
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 John Stuart Mill
One person with a belief is equal to ninety-nine who have only interests.
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 John Stuart Mill