The theory of probabilities is basically only common sense reduced to a calculus. It makes one estimate accurately what right-minded people feel by a sort of instinct, often without being able to give a reason for it.

Such is the advantage of a well constructed language that its simplified notation often becomes the source of profound theories.

The weight of evidence for an extraordinary claim must be proportioned to its strangeness.

The mind has its illusions as the sense of sight; and in the same manner that the sense of feeling corrects the latter, reflection and calculation correct the former.

The most important questions of life are indeed, for the most part, really only problems of probability.

I have lived long enough to know what I did not at one time believe--that no society can be upheld in happiness and honor without the sentiment of religion.

The word 'chance' then expresses only our ignorance of the causes of the phenomena that we observe to occur and to succeed one another in no apparent order. Probability is relative in part to this ignorance, and in part to our knowledge.